{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 10), (38, 21), (25, 28), (25, 33), (41, 16), (8, 13), (20, 40), (28, 40), (23, 12), (18, 5), (6, 7), (31, 1), (5, 32), (36, 13), (10, 2), (20, 1), (37, 6), (43, 14), (24, 33), (40, 10), (5, 6), (16, 16), (6, 36), (13, 21), (36, 15), (18, 35), (28, 43), (2, 2), (13, 27), (16, 30), (5, 0), (27, 6), (41, 41), (14, 35), (2, 14), (27, 35), (25, 34), (34, 6), (38, 23), (2, 25), (22, 42), (19, 33), (19, 40), (5, 8), (15, 41), (20, 38), (12, 15), (9, 5), (2, 27), (29, 16), (2, 46), (12, 3), (5, 7), (19, 35), (7, 15), (24, 43), (31, 11), (14, 0), (25, 19), (42, 35), (39, 22), (19, 43), (27, 24), (20, 10), (34, 42), (11, 39), (22, 38), (7, 7), (44, 29), (33, 45), (33, 30), (44, 5), (2, 26), (14, 18), (32, 39), (8, 10), (8, 1), (39, 35), (17, 23), (8, 5), (28, 28), (7, 2), (44, 0), (11, 23), (40, 41), (21, 0), (12, 7), (15, 22), (15, 12), (17, 0), (16, 42), (7, 26), (39, 14), (32, 20), (41, 46), (14, 24), (18, 24), (35, 18), (36, 37), (9, 19), (15, 32), (12, 9), (5, 37), (37, 44), (5, 18), (42, 33), (0, 1), (40, 9), (20, 14), (17, 14), (32, 43), (21, 35), (21, 8), (0, 15), (25, 13), (24, 39), (5, 25), (6, 38), (13, 23), (8, 32), (33, 14), (36, 44), (5, 39), (43, 12), (33, 37), (29, 0), (28, 10), (44, 14), (25, 37), (31, 18), (10, 15), (9, 12), (5, 16), (33, 24), (17, 2), (13, 18), (15, 40), (15, 23), (14, 21), (14, 4), (33, 0), (36, 4), (10, 44), (44, 38), (25, 31), (35, 14), (15, 28), (9, 45), (6, 26), (7, 10), (32, 38), (21, 15), (12, 37), (38, 45), (37, 0), (34, 8), (1, 17), (40, 14), (6, 5), (37, 17), (39, 12), (24, 17), (5, 14), (4, 6), (20, 30), (36, 30), (6, 37), (20, 33), (9, 14), (40, 39), (7, 27), (11, 20), (42, 6), (6, 10), (17, 43), (14, 44), (32, 7), (29, 8), (7, 29), (1, 23), (26, 4), (38, 4), (4, 7), (12, 40), (23, 43), (19, 17), (5, 5), (42, 30), (33, 29), (12, 36), (26, 10), (31, 24), (0, 39), (6, 30), (7, 8), (21, 39), (43, 19), (2, 33), (29, 3), (44, 1), (27, 21), (30, 32), (0, 28), (32, 27), (41, 25), (42, 29), (3, 11), (42, 19), (10, 11), (2, 34), (1, 43), (2, 19), (43, 4), (23, 35), (1, 5), (22, 15), (24, 41), (6, 39), (21, 36), (4, 15), (16, 20), (18, 38), (4, 45), (8, 18), (4, 37), (5, 44), (7, 16), (24, 0), (27, 37), (8, 16), (20, 37), (19, 30), (42, 10), (33, 21), (32, 28), (23, 25), (1, 14), (33, 1), (23, 7), (27, 25), (3, 37), (31, 6), (4, 11), (10, 25), (12, 1), (10, 18), (11, 43), (3, 16), (30, 17), (14, 2), (43, 13), (20, 15), (15, 43), (20, 45), (29, 40), (13, 33), (17, 17), (11, 0), (38, 36), (16, 36), (17, 11), (21, 28), (13, 16), (26, 28), (34, 28), (44, 33), (42, 28), (19, 13), (42, 23), (22, 25), (19, 32), (0, 25), (12, 22), (32, 13), (42, 27), (44, 26), (12, 41), (34, 12), (39, 26), (16, 9), (24, 31), (26, 44), (14, 43), (29, 29), (2, 37), (31, 30), (22, 13), (35, 8), (30, 7), (9, 36), (10, 32), (24, 21), (26, 45), (2, 1), (31, 15), (8, 37), (36, 5), (8, 8), (13, 45), (44, 4), (29, 33), (43, 22), (39, 7), (24, 15), (16, 3), (8, 33), (4, 16), (41, 30), (37, 25), (43, 18), (14, 37), (11, 19), (30, 45), (26, 26), (10, 26), (30, 20), (28, 3), (37, 37), (13, 14), (3, 35), (5, 28), (21, 16), (15, 26), (22, 27), (40, 17), (42, 36), (38, 35), (8, 41), (9, 38), (2, 42), (9, 44), (13, 41), (27, 14), (32, 6), (14, 27), (13, 42), (2, 8), (4, 44), (35, 11), (15, 21), (22, 24), (32, 0), (44, 45), (8, 30), (0, 44), (42, 5), (24, 7), (37, 33), (0, 5), (8, 4), (1, 12), (5, 33), (39, 43), (9, 29), (27, 5), (29, 43), (17, 24), (4, 12), (6, 41), (24, 46), (37, 7), (26, 13), (14, 20), (7, 28), (27, 13), (37, 18), (43, 25), (7, 23), (23, 2), (38, 42), (16, 12), (18, 0), (41, 38), (5, 11), (8, 26), (0, 16), (26, 22), (44, 36), (41, 43), (16, 46), (41, 2), (22, 43), (15, 10), (18, 42), (5, 1), (20, 7), (10, 37), (33, 26), (13, 32), (29, 28), (13, 19), (32, 36), (8, 28), (17, 46), (35, 38), (33, 4), (20, 17), (20, 27), (1, 34), (6, 31), (24, 36), (36, 11), (42, 15), (38, 25), (4, 26), (4, 19), (19, 31), (5, 35), (43, 30), (23, 41), (31, 46), (39, 15), (7, 1), (32, 31), (30, 43), (32, 25), (37, 40), (21, 11), (6, 44), (23, 11), (25, 16), (35, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 49x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 17), (15, 11), (16, 25), (6, 16), (23, 15), (48, 34), (19, 13), (14, 28), (42, 19), (40, 45), (32, 3), (30, 10), (24, 31), (46, 29), (40, 7), (40, 37), (31, 23), (32, 25), (38, 18), (34, 7), (26, 42), (19, 22), (4, 23), (8, 13), (10, 7), (39, 37), (42, 20), (3, 34), (34, 37), (15, 14), (12, 9), (25, 6), (30, 44), (17, 38), (6, 41), (23, 0), (35, 28), (12, 5), (34, 8), (41, 3), (1, 4), (35, 8), (16, 35), (47, 34), (19, 21), (18, 35), (21, 28), (0, 34), (36, 4), (27, 21), (36, 30), (32, 43), (17, 33), (14, 41), (43, 29), (24, 16), (8, 2), (16, 28), (12, 25), (29, 20), (20, 40), (27, 20), (7, 5), (17, 19), (23, 21), (44, 37), (3, 35), (43, 40), (9, 12), (7, 36), (23, 44), (31, 8), (18, 1), (13, 4), (30, 13), (39, 26), (22, 24), (14, 43), (32, 41), (29, 19), (42, 17), (29, 26), (24, 14), (5, 18), (4, 41), (17, 2), (0, 14), (46, 24), (34, 45), (44, 5), (32, 21), (7, 12), (41, 10), (12, 17), (15, 20), (23, 1), (6, 3), (37, 42), (36, 18), (32, 39), (23, 12), (30, 0), (47, 31), (11, 21), (27, 32), (19, 30), (25, 7), (33, 0), (6, 29), (26, 29), (13, 23), (15, 18), (33, 45), (26, 25), (10, 5), (27, 34), (9, 20), (1, 46), (14, 7), (35, 44), (24, 23), (1, 27), (45, 25), (39, 41), (40, 30), (26, 16), (21, 45), (25, 28), (9, 26), (10, 42), (33, 1), (4, 42), (2, 1), (30, 17), (17, 10), (30, 42), (25, 43), (6, 17), (30, 35), (26, 4), (43, 21), (30, 1), (26, 40), (43, 42), (33, 42), (37, 10), (2, 39), (48, 31), (18, 22), (37, 28), (25, 2), (45, 31), (22, 22), (25, 46), (33, 41), (12, 23), (47, 8), (47, 21), (14, 39), (17, 20), (19, 36), (40, 0), (21, 44), (46, 40), (25, 39), (48, 21), (6, 25), (30, 30), (25, 21), (35, 18), (29, 36), (20, 8), (41, 46), (39, 10), (23, 8), (35, 25), (12, 26), (13, 5), (43, 30), (8, 0), (8, 43), (42, 11), (32, 32), (9, 36), (46, 13), (47, 35), (28, 16), (45, 38), (13, 25), (22, 28), (45, 2), (47, 11), (33, 7), (43, 0), (17, 9), (47, 14), (15, 41), (29, 7), (20, 36), (5, 32), (38, 14), (48, 2), (7, 32), (14, 6), (9, 25), (4, 37), (22, 6), (2, 11), (35, 32), (3, 32), (37, 26), (21, 46), (45, 29), (42, 12), (15, 8), (41, 43), (34, 43), (5, 3), (2, 37), (26, 33), (5, 0), (19, 26), (4, 26), (30, 45), (29, 35), (27, 31), (4, 10), (5, 44), (5, 24), (46, 3), (43, 12), (15, 33), (24, 36), (31, 7), (19, 3), (32, 27), (31, 1), (22, 26), (43, 15), (38, 36), (18, 38), (6, 14), (32, 19), (36, 20), (18, 33), (20, 43), (18, 2), (38, 17), (31, 31), (16, 9), (40, 33), (44, 38), (28, 25), (45, 10), (45, 0), (33, 39), (24, 19), (28, 23), (16, 5), (1, 42), (0, 2), (46, 4), (34, 17), (24, 30), (32, 16), (37, 13), (0, 18), (14, 38), (41, 7), (37, 0), (28, 29), (35, 1), (30, 19), (37, 31), (40, 41), (15, 28), (6, 8), (6, 31), (41, 24), (12, 21), (10, 15), (48, 11), (44, 39), (19, 43), (15, 16), (21, 23), (45, 19), (14, 26), (21, 2), (44, 46), (29, 2), (16, 0), (36, 8), (9, 28), (12, 35), (13, 41), (40, 22), (45, 7), (38, 35), (46, 11), (36, 13), (39, 46), (32, 29), (34, 25), (27, 41), (14, 27), (20, 12), (2, 24), (0, 25), (18, 25), (2, 16), (35, 5), (14, 42), (36, 23), (1, 9), (42, 29), (42, 34), (4, 11), (33, 44), (24, 15), (30, 46), (47, 10), (10, 37), (22, 23), (7, 7), (31, 45), (28, 33), (20, 5), (17, 17), (20, 38), (5, 27), (40, 43), (30, 3), (32, 14), (4, 29), (11, 16), (38, 0), (19, 16), (35, 43), (9, 15), (2, 15), (28, 6), (27, 22), (27, 6), (2, 41), (0, 40), (43, 31), (6, 24), (46, 30), (6, 21), (18, 37), (37, 6), (34, 5), (8, 44), (45, 24), (34, 22), (29, 0), (10, 0), (46, 12), (34, 6), (24, 10), (38, 16), (13, 3), (10, 20), (39, 40), (46, 27), (4, 2), (11, 5), (0, 37), (37, 35), (7, 45), (21, 36), (25, 9), (29, 8), (30, 8), (35, 33), (44, 9), (13, 30), (18, 32), (28, 12), (8, 18), (30, 29), (37, 33), (23, 3), (21, 41), (47, 3), (15, 46), (26, 39), (29, 4), (42, 6), (31, 42), (0, 35), (29, 41), (10, 34), (5, 9), (16, 22), (7, 20), (19, 44), (17, 28), (1, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 44), (29, 44), (23, 39), (8, 2), (33, 3), (2, 48), (28, 29), (18, 31), (45, 1), (41, 2), (43, 29), (33, 36), (17, 19), (26, 28), (10, 25), (20, 16), (41, 8), (22, 3), (19, 21), (23, 19), (46, 4), (8, 39), (41, 40), (8, 14), (26, 21), (19, 33), (16, 20), (37, 34), (5, 39), (19, 35), (24, 41), (32, 26), (41, 47), (36, 2), (31, 6), (33, 20), (4, 42), (16, 40), (17, 24), (10, 6), (1, 15), (2, 21), (10, 20), (31, 16), (43, 13), (32, 39), (27, 14), (6, 35), (42, 10), (27, 10), (43, 27), (17, 42), (21, 43), (38, 34), (43, 32), (13, 5), (23, 15), (24, 24), (28, 40), (17, 28), (27, 16), (34, 19), (13, 27), (42, 19), (30, 25), (9, 20), (12, 30), (4, 5), (43, 12), (33, 31), (4, 3), (40, 28), (18, 35), (21, 31), (27, 45), (38, 38), (30, 1), (22, 32), (27, 29), (34, 36), (21, 38), (43, 28), (4, 33), (23, 32), (33, 41), (42, 16), (30, 35), (33, 18), (44, 22), (8, 6), (11, 1), (16, 45), (9, 40), (20, 15), (26, 1), (34, 16), (32, 14), (31, 42), (15, 12), (15, 20), (26, 40), (4, 40), (36, 30), (24, 4), (45, 40), (33, 11), (42, 35), (2, 35), (21, 17), (40, 30), (8, 20), (16, 12), (8, 29), (34, 17), (2, 4), (13, 34), (5, 38), (44, 40), (33, 12), (37, 25), (36, 42), (45, 31), (15, 48), (20, 4), (0, 10), (19, 32), (19, 25), (1, 16), (24, 5), (43, 4), (27, 30), (11, 12), (10, 19), (21, 23), (33, 29), (13, 21), (44, 2), (1, 23), (41, 1), (43, 35), (11, 7), (34, 18), (6, 9), (24, 3), (34, 10), (24, 47), (23, 34), (23, 43), (3, 12), (41, 35), (18, 34), (2, 25), (46, 16), (17, 23), (14, 47), (25, 18), (28, 20), (18, 14), (25, 24), (22, 35), (21, 6), (28, 43), (11, 29), (18, 41), (9, 41), (36, 41), (11, 6), (28, 21), (16, 19), (8, 46), (42, 26), (31, 17), (16, 11), (1, 32), (34, 30), (40, 36), (29, 41), (32, 16), (24, 0), (42, 30), (21, 28), (39, 33), (6, 14), (21, 32), (38, 19), (0, 11), (38, 28), (34, 0), (13, 8), (39, 7), (21, 47), (9, 25), (28, 25), (17, 30), (14, 25), (44, 38), (10, 46), (37, 18), (27, 43), (24, 23), (34, 47), (8, 30), (34, 33), (25, 7), (36, 15), (14, 24), (23, 38), (24, 48), (31, 37), (46, 10), (36, 25), (24, 46), (40, 22), (46, 27), (43, 44), (40, 12), (46, 32), (42, 21), (44, 5), (16, 35), (20, 21), (44, 35), (44, 16), (17, 39), (11, 14), (32, 2), (25, 16), (41, 29), (45, 29), (22, 29), (16, 39), (16, 26), (13, 47), (1, 21), (4, 2), (18, 6), (4, 39), (9, 9), (11, 35), (5, 16), (33, 33), (35, 34), (45, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 36), (23, 20), (8, 29), (3, 33), (25, 41), (24, 47), (16, 44), (20, 22), (0, 29), (30, 30), (37, 38), (43, 18), (23, 14), (3, 37), (6, 40), (12, 4), (41, 42), (30, 6), (27, 29), (29, 28), (23, 5), (18, 46), (24, 37), (30, 40), (14, 21), (0, 47), (37, 1), (2, 42), (19, 32), (16, 27), (19, 7), (39, 40), (21, 24), (5, 39), (8, 23), (20, 32), (25, 15), (24, 31), (40, 41), (13, 19), (13, 5), (7, 48), (7, 24), (20, 25), (39, 27), (38, 9), (38, 16), (40, 46), (17, 15), (24, 8), (12, 48), (3, 9), (36, 0), (32, 36), (3, 20), (2, 11), (23, 7), (9, 44), (40, 27), (8, 0), (17, 12), (13, 41), (13, 1), (23, 47), (41, 27), (13, 17), (43, 46), (41, 0), (2, 40), (12, 33), (7, 12), (40, 13), (16, 10), (15, 41), (40, 15), (42, 29), (27, 27), (17, 40), (3, 42), (15, 5), (40, 28), (12, 36), (38, 34), (7, 23), (33, 6), (44, 12), (19, 9), (18, 4), (23, 6), (11, 32), (21, 9), (17, 21), (1, 17), (17, 14), (17, 5), (4, 26), (14, 14), (25, 10), (13, 43), (27, 20), (17, 6), (29, 4), (33, 26), (25, 17), (5, 29), (12, 7), (22, 21), (12, 45), (26, 46), (19, 43), (21, 22), (16, 48), (0, 32), (22, 48), (14, 28), (25, 2), (22, 41), (25, 21), (33, 25), (26, 36), (34, 35), (9, 18), (44, 29), (24, 20), (26, 38), (29, 14), (29, 10), (28, 45), (13, 22), (31, 40), (37, 11), (25, 18), (34, 44), (15, 30), (1, 31), (29, 34), (30, 9), (40, 10), (38, 47), (8, 46), (24, 21), (41, 11), (34, 12), (13, 42), (2, 6), (36, 30), (32, 9), (32, 33), (25, 30), (0, 33), (12, 15), (20, 0), (32, 25), (37, 24), (16, 40), (11, 38), (11, 34), (14, 24), (35, 21), (8, 7), (9, 34), (9, 16), (39, 16), (36, 14), (32, 12), (44, 43), (22, 39), (30, 46), (35, 4), (28, 43), (31, 44), (7, 42), (16, 22), (9, 23), (1, 35), (44, 11), (43, 24), (42, 6), (35, 42), (6, 0), (14, 18), (10, 13), (18, 24), (26, 42), (18, 34), (14, 19), (4, 37), (8, 12), (37, 47), (13, 31), (20, 37), (40, 31), (14, 46), (19, 11), (18, 8), (8, 8), (17, 10), (34, 36), (24, 26), (6, 48), (6, 28), (35, 2), (29, 29), (3, 17), (27, 16), (5, 47), (35, 23), (41, 44), (29, 48), (10, 22), (28, 8), (9, 36), (17, 18), (1, 42), (44, 7), (10, 31), (5, 11), (11, 25), (22, 12), (39, 32), (37, 41), (0, 8), (2, 13), (1, 13), (37, 6), (4, 5), (35, 7), (25, 42), (27, 46), (10, 7), (14, 48), (18, 2), (5, 8), (32, 43), (38, 42), (4, 17), (14, 9), (12, 39), (19, 33), (43, 9), (8, 47), (36, 4), (33, 9), (16, 3), (31, 13), (20, 12), (0, 9), (8, 17), (15, 48), (13, 38), (14, 33), (6, 11), (3, 32), (29, 42), (44, 32), (11, 21), (29, 5), (17, 35), (4, 7), (2, 39), (6, 4), (26, 21), (26, 18), (32, 31), (16, 12), (22, 38), (41, 5), (0, 37), (0, 17), (40, 45), (36, 5), (25, 48), (8, 31), (20, 34), (18, 7), (15, 4), (41, 31), (27, 43), (23, 25), (3, 48), (37, 39), (29, 11), (23, 22), (18, 13), (18, 15), (9, 39), (19, 24), (1, 6), (4, 2), (30, 42), (21, 14), (15, 33), (4, 32), (1, 14), (5, 38), (1, 29), (7, 35), (3, 5), (33, 28), (18, 44), (16, 17), (11, 2), (40, 21), (2, 32), (32, 5), (34, 7), (41, 6), (1, 41), (40, 43), (11, 7), (21, 32), (28, 27), (26, 24), (1, 5), (44, 41), (31, 43), (10, 28), (35, 12), (7, 20), (13, 39), (16, 36), (31, 47), (13, 26), (26, 4), (15, 31), (7, 37), (35, 40), (1, 12), (19, 46), (37, 46), (19, 25), (39, 11), (43, 1), (16, 46), (39, 25), (31, 23), (16, 4), (2, 3), (36, 2), (32, 23), (5, 23), (14, 6), (25, 22), (19, 27), (9, 4), (32, 46), (26, 23), (40, 12), (17, 7), (43, 34), (43, 47), (7, 13), (29, 16), (2, 1), (36, 15), (34, 48), (16, 19), (36, 36), (33, 15), (16, 34), (13, 20), (9, 20), (13, 12), (10, 8), (29, 8), (36, 33), (27, 4), (41, 10), (20, 10), (7, 3), (36, 39), (40, 29), (29, 41), (33, 2), (4, 42), (20, 21), (31, 21), (42, 18), (23, 43), (26, 17), (41, 23), (0, 46), (42, 28), (39, 28), (31, 10), (31, 1), (20, 26), (13, 27), (7, 6), (18, 9), (35, 44), (4, 35), (26, 20), (44, 1), (37, 23), (44, 46), (2, 8), (28, 21), (9, 11), (20, 29), (12, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 14), (15, 13), (15, 0), (0, 38), (11, 34), (9, 21), (43, 3), (12, 9), (29, 18), (4, 41), (24, 33), (2, 5), (35, 40), (6, 11), (39, 25), (42, 11), (11, 15), (39, 28), (30, 27), (32, 4), (3, 36), (44, 15), (14, 18), (44, 26), (32, 3), (41, 41), (15, 18), (21, 22), (9, 7), (6, 30), (34, 14), (36, 7), (18, 14), (33, 14), (29, 37), (17, 20), (5, 37), (16, 9), (16, 14), (4, 16), (17, 9), (21, 4), (6, 21), (24, 26), (39, 37), (26, 23), (2, 40), (43, 16), (43, 32), (13, 6), (33, 33), (39, 12), (14, 37), (29, 9), (27, 38), (40, 12), (13, 35), (30, 5), (16, 13), (38, 1), (35, 32), (42, 42), (14, 25), (4, 23), (3, 8), (30, 2), (16, 36), (9, 37), (29, 25), (41, 17), (7, 28), (17, 42), (43, 10), (31, 27), (33, 41), (13, 34), (6, 0), (8, 19), (41, 29), (20, 3), (2, 39), (25, 4), (33, 38), (15, 3), (1, 31), (13, 38), (8, 0), (5, 26), (1, 28), (7, 1), (0, 28), (37, 31), (5, 4), (28, 9), (35, 21), (1, 23), (20, 26), (0, 7), (8, 42), (36, 17), (6, 29), (18, 35), (16, 26), (35, 20), (5, 39), (10, 25), (11, 32), (42, 24), (16, 39), (43, 26), (10, 31), (34, 9), (5, 17), (42, 36), (20, 39), (37, 7), (0, 1), (19, 9), (7, 18), (1, 12), (20, 42), (30, 33), (10, 37), (19, 23), (40, 4), (29, 14), (30, 13), (14, 23), (35, 6), (5, 5), (38, 33), (3, 33), (39, 39), (37, 30), (11, 18), (30, 22), (27, 9), (42, 34), (28, 4), (0, 40), (6, 38), (39, 27), (16, 8), (19, 42), (28, 5), (28, 0), (17, 23), (11, 12), (9, 36), (24, 6), (24, 5), (34, 28), (38, 12), (9, 42), (27, 33), (23, 10), (13, 23), (6, 34), (10, 27), (24, 35), (16, 1), (20, 30), (27, 35), (15, 10), (7, 38), (14, 24), (9, 19), (13, 33), (26, 5), (5, 15), (26, 14), (19, 8), (28, 24), (3, 16), (24, 7), (24, 34), (19, 26), (17, 40), (28, 12), (32, 30), (38, 23), (3, 42), (28, 8), (3, 10), (13, 12), (9, 24), (32, 6), (44, 24), (2, 29), (20, 14), (39, 30), (9, 20), (10, 21), (14, 0), (6, 42), (0, 12), (31, 20), (40, 15), (12, 25), (26, 6), (41, 8), (29, 40), (8, 1), (1, 8), (34, 4), (42, 13), (25, 8), (23, 8), (33, 7), (29, 36), (33, 6), (35, 18), (15, 36), (26, 8), (28, 29), (43, 12), (4, 9), (35, 12), (15, 29), (14, 9), (18, 5), (31, 29), (34, 8), (24, 0), (4, 34), (1, 17), (32, 2), (10, 10), (34, 34), (5, 36), (34, 41), (41, 31), (3, 23), (19, 10), (44, 10), (40, 8), (1, 11), (13, 13), (44, 16), (17, 30), (30, 8), (15, 41), (44, 37), (0, 13), (36, 10), (4, 1), (1, 24), (21, 32), (13, 32), (38, 37), (21, 30), (25, 5), (32, 34), (41, 26), (18, 6), (41, 15), (19, 30), (1, 5), (6, 32), (23, 35), (35, 31), (16, 23), (36, 21), (26, 25), (32, 32), (13, 31), (17, 19), (35, 5), (15, 33), (14, 27), (3, 6), (11, 7), (30, 42), (22, 27), (7, 37), (33, 16), (36, 33), (17, 31), (14, 19), (41, 28), (13, 29), (34, 19), (37, 41), (31, 8), (42, 21), (26, 10), (21, 37), (8, 23), (38, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 35), (9, 33), (16, 10), (33, 15), (25, 15), (21, 8), (39, 0), (37, 34), (33, 38), (8, 22), (2, 28), (24, 34), (14, 18), (35, 11), (15, 42), (25, 3), (41, 21), (17, 20), (28, 35), (16, 20), (24, 32), (1, 34), (18, 17), (41, 2), (38, 41), (14, 36), (41, 16), (40, 24), (4, 15), (38, 31), (22, 42), (37, 28), (14, 0), (17, 14), (14, 20), (0, 42), (9, 43), (40, 37), (24, 4), (3, 20), (18, 28), (19, 33), (18, 1), (0, 44), (24, 9), (34, 18), (14, 30), (32, 25), (31, 9), (43, 16), (23, 26), (31, 17), (32, 17), (38, 24), (39, 32), (34, 38), (26, 26), (1, 5), (20, 6), (20, 2), (16, 27), (3, 8), (44, 42), (2, 31), (27, 33), (25, 9), (44, 28), (33, 39), (34, 39), (20, 32), (33, 12), (36, 23), (4, 35), (20, 42), (25, 23), (12, 25), (12, 24), (25, 11), (8, 44), (37, 26), (12, 16), (21, 32), (43, 3), (24, 7), (44, 14), (29, 21), (18, 37), (33, 3), (34, 36), (27, 5), (15, 17), (34, 32), (27, 14), (16, 19), (27, 18), (16, 22), (37, 39), (12, 0), (30, 31), (20, 35), (19, 40), (19, 5), (7, 41), (32, 9), (0, 13), (8, 43), (18, 30), (2, 30), (31, 37), (13, 35), (24, 15), (7, 15), (15, 34), (11, 5), (29, 9), (5, 16), (4, 4), (10, 39), (37, 13), (10, 13), (7, 5), (18, 21), (11, 7), (32, 2), (39, 22), (3, 23), (11, 20), (21, 34), (28, 24), (36, 39), (22, 36), (44, 12), (3, 39), (15, 38), (21, 33), (4, 3), (30, 25), (32, 3), (35, 25), (40, 20), (23, 22), (5, 24), (3, 38), (13, 37), (43, 7), (10, 16), (38, 10), (31, 38), (15, 40), (30, 13), (6, 5), (17, 25), (42, 40), (21, 18), (0, 26), (35, 0), (41, 4), (18, 36), (1, 14), (16, 34), (16, 1), (22, 44), (18, 11), (8, 29), (22, 33), (8, 4), (29, 42), (43, 26), (17, 28), (12, 41), (5, 21), (41, 0), (3, 22), (28, 44), (33, 34), (19, 34), (2, 41), (43, 25), (14, 3), (5, 10), (25, 25), (20, 33), (24, 37), (23, 33), (32, 15), (38, 43), (8, 25), (12, 1), (32, 7), (26, 31), (37, 30), (19, 30), (22, 0), (27, 36), (26, 13), (11, 35), (19, 16), (40, 32), (13, 24), (16, 29), (10, 21), (9, 41), (24, 27), (5, 26), (38, 18), (39, 9), (33, 11), (1, 21), (40, 19), (11, 29), (20, 44), (19, 23), (8, 34), (40, 26), (15, 18), (7, 2), (26, 32), (1, 1), (39, 34), (38, 39), (34, 10), (5, 30), (12, 8), (22, 40), (3, 37), (35, 3), (11, 33), (36, 27), (21, 27), (8, 36), (13, 34), (28, 30), (36, 8), (12, 40), (23, 39), (5, 1), (44, 43), (43, 28), (1, 4), (29, 29), (40, 34), (6, 29), (6, 39), (27, 37), (35, 31), (42, 26), (36, 2), (44, 2), (5, 35), (39, 30), (9, 13), (15, 36), (19, 19), (16, 44), (13, 44), (21, 9), (39, 12), (28, 38), (13, 16), (25, 41), (8, 23), (0, 2), (42, 22), (17, 8), (8, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 21), (37, 7), (27, 18), (9, 18), (20, 34), (23, 20), (24, 24), (8, 17), (7, 2), (40, 21), (24, 31), (8, 26), (28, 38), (19, 38), (22, 14), (40, 4), (18, 38), (25, 29), (33, 5), (10, 14), (34, 39), (19, 26), (21, 22), (2, 0), (39, 1), (23, 36), (16, 0), (16, 41), (13, 3), (24, 5), (23, 23), (41, 22), (35, 39), (32, 12), (39, 2), (31, 25), (27, 15), (14, 19), (1, 32), (8, 27), (4, 0), (10, 27), (7, 13), (12, 33), (18, 10), (36, 17), (32, 11), (15, 34), (29, 1), (33, 35), (6, 25), (3, 2), (26, 21), (33, 19), (10, 24), (30, 2), (24, 32), (31, 17), (42, 22), (10, 12), (12, 13), (40, 24), (35, 10), (13, 28), (3, 24), (15, 38), (12, 14), (37, 39), (16, 22), (26, 18), (25, 35), (1, 7), (12, 8), (13, 4), (5, 20), (26, 26), (36, 29), (23, 40), (30, 39), (6, 13), (20, 28), (38, 19), (5, 19), (5, 33), (21, 17), (13, 19), (22, 41), (20, 3), (14, 27), (12, 18), (10, 16), (40, 10), (18, 7), (3, 33), (41, 39), (25, 7), (24, 39), (8, 7), (19, 28), (41, 13), (7, 22), (5, 18), (18, 27), (3, 35), (29, 40), (28, 41), (18, 3), (15, 29), (11, 22), (1, 18), (2, 31), (28, 25), (20, 14), (29, 30), (30, 41), (28, 8), (3, 9), (0, 21), (7, 6), (7, 7), (6, 15), (38, 25), (12, 12), (40, 2), (41, 2), (29, 38), (32, 36), (1, 36), (28, 1), (22, 6), (32, 10), (22, 29), (34, 15), (39, 15), (2, 11), (36, 4), (19, 1), (33, 34), (31, 19), (25, 40), (37, 12), (26, 41), (17, 32), (38, 8), (36, 31), (26, 19), (11, 19), (13, 8), (3, 17), (38, 26), (29, 23), (35, 34), (15, 18), (12, 7), (26, 8), (22, 21), (5, 25), (33, 4), (14, 34), (23, 17), (16, 33), (1, 41), (18, 40), (21, 11), (19, 19), (31, 29), (20, 31), (19, 41), (26, 10), (13, 5), (0, 33), (26, 34), (31, 16), (37, 34), (32, 18), (13, 6), (26, 32), (27, 29), (11, 32), (0, 36), (35, 3), (3, 36), (5, 10), (6, 41), (11, 12), (20, 32), (41, 17), (13, 11), (37, 40), (16, 27), (34, 29), (20, 37), (0, 12), (8, 20), (0, 28), (42, 7), (29, 12), (16, 9), (10, 21), (25, 20), (4, 14), (25, 6), (15, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 19), (3, 9), (47, 11), (15, 16), (5, 9), (4, 38), (31, 11), (44, 1), (20, 15), (13, 21), (4, 36), (2, 38), (15, 42), (8, 5), (1, 15), (31, 44), (31, 20), (16, 14), (36, 20), (14, 22), (20, 2), (29, 25), (32, 10), (32, 24), (19, 41), (13, 27), (5, 32), (2, 9), (13, 41), (5, 1), (4, 21), (31, 24), (41, 41), (30, 43), (14, 38), (8, 40), (3, 38), (15, 36), (28, 34), (23, 40), (24, 34), (30, 42), (35, 38), (20, 19), (5, 25), (40, 5), (20, 39), (6, 2), (7, 33), (1, 42), (17, 33), (5, 24), (18, 13), (7, 5), (35, 28), (46, 14), (36, 8), (3, 34), (9, 25), (35, 10), (11, 19), (24, 4), (27, 24), (14, 3), (43, 11), (26, 42), (28, 35), (16, 0), (38, 40), (36, 37), (40, 2), (48, 32), (32, 37), (27, 40), (13, 6), (8, 2), (34, 29), (33, 34), (39, 43), (26, 22), (1, 24), (19, 31), (23, 44), (33, 6), (23, 39), (3, 5), (26, 32), (34, 9), (7, 20), (24, 28), (31, 17), (47, 25), (14, 20), (39, 8), (6, 17), (32, 25), (2, 31), (15, 4), (22, 25), (31, 22), (9, 35), (35, 22), (37, 34), (15, 28), (43, 6), (16, 24), (1, 37), (46, 25), (42, 6), (47, 27), (4, 26), (18, 10), (2, 44), (3, 21), (17, 41), (12, 0), (41, 36), (47, 18), (14, 41), (33, 10), (27, 25), (36, 44), (22, 11), (10, 4), (7, 44), (8, 29), (7, 27), (15, 11), (26, 28), (15, 14), (6, 7), (7, 12), (37, 0), (23, 11), (43, 5), (10, 32), (10, 43), (17, 14), (31, 6), (48, 2), (3, 42), (2, 33), (7, 23), (12, 25), (46, 2), (46, 26), (17, 38), (19, 18), (39, 12), (25, 12), (3, 13), (41, 31), (5, 37), (26, 10), (12, 42), (14, 23), (8, 10), (9, 44), (21, 20), (45, 33), (15, 3), (25, 14), (28, 19), (11, 15), (34, 6), (38, 11), (3, 2), (32, 12), (40, 36), (32, 13), (19, 35), (20, 22), (31, 30), (26, 21), (44, 41), (44, 24), (28, 39), (45, 39), (3, 33), (45, 17), (8, 4), (11, 9), (24, 38), (32, 23), (21, 31), (16, 26), (13, 8), (12, 33), (3, 30), (8, 1), (38, 29), (24, 16), (46, 4), (38, 15), (32, 16), (35, 16), (18, 12), (13, 42), (16, 16), (3, 22), (6, 5), (37, 1), (27, 12), (31, 7), (3, 31), (36, 39), (32, 32), (1, 11), (10, 31), (22, 26), (41, 10), (33, 43), (43, 43), (6, 20), (47, 38), (18, 2), (22, 36), (33, 30), (20, 23), (44, 13), (39, 24), (25, 35), (35, 12), (17, 12), (11, 24), (30, 41), (6, 23), (27, 11), (24, 7), (48, 28), (23, 9), (13, 25), (45, 15), (9, 10), (17, 5), (37, 7), (19, 37), (30, 39), (16, 21), (34, 2), (28, 33), (19, 32), (0, 16), (9, 5), (10, 16), (41, 19), (7, 34), (16, 4), (31, 12), (31, 2), (6, 33), (39, 2), (21, 9), (8, 25), (18, 4), (23, 30), (27, 0), (11, 40), (0, 31), (34, 35), (0, 23), (12, 14), (2, 6), (9, 8), (30, 4), (9, 42), (29, 1), (41, 32), (14, 35), (26, 41), (35, 37), (28, 28), (15, 7), (35, 43), (4, 12), (7, 31), (14, 43), (21, 36), (16, 28), (1, 27), (8, 15), (48, 17), (15, 12), (16, 25), (19, 12), (22, 7), (42, 8), (37, 6), (25, 1), (10, 12), (28, 38), (5, 20), (17, 35), (21, 41), (35, 35), (34, 13), (27, 36), (33, 16), (12, 10), (3, 39), (10, 26), (23, 18), (22, 17), (24, 29), (2, 40), (11, 27), (36, 11), (30, 18), (3, 19), (25, 9), (28, 1), (11, 30), (10, 7), (26, 24), (41, 17), (29, 30), (14, 15), (42, 42), (10, 3), (33, 40), (28, 31), (26, 35), (32, 4), (24, 20), (33, 5), (28, 9), (41, 44), (4, 14), (41, 30), (19, 0), (0, 43), (32, 34), (17, 30), (19, 23), (35, 9), (21, 34), (3, 35), (40, 44), (9, 24), (21, 13), (18, 11), (7, 35), (17, 42), (21, 11), (37, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 32), (36, 16), (18, 16), (29, 14), (28, 8), (10, 13), (28, 5), (36, 22), (24, 31), (7, 28), (40, 19), (28, 15), (17, 42), (23, 31), (18, 42), (13, 7), (27, 5), (22, 6), (39, 2), (28, 36), (42, 16), (11, 22), (2, 29), (31, 22), (30, 0), (38, 17), (3, 42), (19, 12), (21, 40), (6, 36), (31, 33), (30, 24), (0, 7), (29, 7), (19, 5), (40, 31), (35, 30), (32, 9), (35, 5), (28, 20), (38, 19), (7, 22), (20, 8), (1, 30), (22, 37), (26, 10), (35, 7), (1, 12), (34, 4), (0, 42), (28, 30), (34, 16), (22, 9), (20, 21), (13, 30), (34, 7), (8, 41), (36, 7), (36, 17), (28, 6), (21, 25), (42, 25), (30, 26), (25, 41), (7, 12), (29, 0), (26, 5), (5, 26), (6, 1), (10, 29), (39, 9), (17, 18), (25, 9), (17, 10), (30, 37), (10, 11), (15, 13), (42, 13), (8, 2), (24, 15), (13, 29), (32, 10), (13, 35), (4, 34), (26, 24), (16, 9), (7, 6), (14, 20), (7, 3), (25, 22), (29, 24), (18, 18), (2, 40), (10, 39), (32, 23), (38, 15), (15, 18), (0, 35), (23, 20), (41, 41), (21, 36), (26, 30), (21, 20), (6, 39), (14, 7), (16, 10), (16, 31), (29, 37), (5, 30), (5, 10), (11, 17), (28, 41), (41, 42), (32, 20), (34, 0), (0, 31), (15, 41), (31, 1), (43, 26), (14, 39), (17, 28), (3, 41), (15, 29), (14, 0), (27, 4), (23, 17), (34, 14), (5, 41), (12, 4), (16, 19), (28, 42), (42, 9), (17, 30), (28, 22), (19, 8), (19, 42), (22, 42), (24, 33), (36, 29), (11, 35), (30, 32), (24, 39), (28, 14), (13, 37), (22, 24), (37, 10), (42, 36), (0, 29), (23, 21), (6, 7), (21, 13), (38, 9), (36, 3), (9, 42), (10, 34), (27, 27), (24, 10), (28, 38), (10, 7), (40, 5), (32, 0), (22, 3), (43, 17), (27, 26), (15, 23), (13, 40), (43, 15), (21, 22), (28, 10), (38, 13), (21, 39), (0, 12), (42, 1), (24, 3), (15, 31), (42, 15), (4, 23), (18, 1), (11, 13), (43, 36), (22, 0), (0, 21), (3, 9), (34, 9), (13, 21), (40, 32), (18, 2), (25, 37), (42, 31), (35, 21), (19, 34), (4, 25), (39, 15), (18, 6), (32, 6), (12, 27), (38, 33), (43, 37), (16, 20), (8, 25), (19, 32), (26, 36), (41, 16), (0, 41), (1, 3), (40, 12), (17, 39), (12, 12), (11, 6), (23, 15), (15, 21), (21, 15), (1, 0), (11, 8), (18, 25), (16, 18), (15, 42), (26, 15), (29, 12), (16, 38), (40, 9), (25, 17), (13, 10), (14, 10), (32, 32), (2, 41), (27, 38), (39, 20), (6, 20), (29, 17), (25, 12), (40, 10), (17, 34), (40, 25), (35, 22), (2, 33), (26, 16), (6, 0), (34, 23), (15, 6), (2, 34), (16, 0), (37, 34), (1, 14), (19, 4), (0, 25), (13, 36), (37, 39), (17, 20), (40, 4), (32, 31), (39, 31), (2, 19), (35, 6), (7, 39), (29, 8), (9, 25), (30, 21), (12, 15), (31, 18), (17, 16), (37, 36), (40, 20), (12, 16), (15, 7), (1, 1), (18, 38), (38, 0), (42, 21), (21, 7), (4, 5), (27, 18), (38, 6), (27, 35), (41, 12), (32, 13), (9, 23), (21, 17), (8, 42), (9, 37), (6, 28), (4, 35), (43, 19), (43, 35), (22, 7), (22, 2), (36, 25), (15, 0), (28, 24), (2, 6), (33, 26), (35, 41), (43, 13), (24, 6), (23, 37), (1, 23), (10, 28), (13, 33), (31, 11), (43, 0), (34, 40), (31, 17), (29, 34), (30, 13), (17, 38), (25, 36), (35, 40), (28, 34), (11, 1), (18, 23), (39, 24), (39, 11), (18, 31), (12, 32), (14, 35), (37, 6), (7, 25), (1, 22), (18, 3), (8, 0), (36, 21), (13, 17), (37, 4), (25, 29), (20, 34), (26, 13), (11, 32), (6, 18), (17, 31), (40, 23), (10, 33), (27, 39), (18, 0), (26, 8), (28, 27), (32, 7), (8, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 22), (34, 2), (1, 9), (42, 15), (47, 8), (30, 34), (4, 0), (10, 15), (47, 22), (9, 40), (34, 8), (4, 19), (17, 14), (28, 3), (12, 29), (11, 25), (14, 10), (31, 25), (24, 4), (8, 32), (14, 32), (40, 26), (43, 25), (19, 36), (8, 11), (9, 22), (1, 19), (15, 6), (45, 7), (15, 0), (6, 1), (32, 35), (37, 40), (20, 5), (5, 20), (43, 35), (43, 26), (15, 35), (30, 17), (33, 7), (0, 35), (28, 32), (26, 40), (18, 31), (27, 14), (41, 20), (1, 24), (39, 7), (41, 8), (39, 27), (42, 24), (28, 36), (29, 17), (23, 25), (6, 32), (36, 20), (0, 36), (14, 33), (9, 5), (2, 4), (40, 21), (40, 27), (26, 1), (36, 6), (34, 34), (47, 5), (26, 25), (42, 8), (29, 8), (32, 12), (33, 30), (37, 39), (7, 15), (31, 33), (47, 18), (25, 33), (32, 19), (22, 28), (37, 37), (3, 0), (34, 36), (3, 29), (21, 28), (29, 6), (39, 37), (45, 36), (40, 12), (36, 9), (30, 19), (6, 39), (6, 12), (11, 17), (2, 16), (17, 37), (12, 12), (10, 7), (15, 22), (7, 35), (9, 19), (35, 21), (43, 10), (28, 34), (29, 18), (18, 36), (47, 4), (27, 36), (18, 25), (22, 35), (7, 11), (39, 40), (32, 20), (34, 28), (5, 19), (8, 13), (7, 1), (14, 8), (10, 27), (36, 40), (12, 21), (7, 14), (10, 10), (21, 27), (14, 18), (41, 24), (6, 11), (5, 8), (20, 23), (37, 5), (27, 3), (17, 30), (20, 24), (46, 35), (8, 36), (17, 1), (4, 32), (34, 9), (34, 33), (44, 22), (35, 0), (2, 11), (43, 7), (25, 15), (6, 4), (0, 21), (23, 4), (47, 17), (17, 4), (19, 32), (25, 7), (15, 40), (25, 1), (21, 35), (18, 33), (1, 22), (44, 16), (46, 0), (27, 21), (21, 5), (21, 21), (45, 6), (16, 14), (1, 28), (20, 21), (27, 13), (17, 19), (2, 39), (31, 39), (37, 32), (32, 27), (46, 32), (35, 17), (29, 23), (43, 31), (18, 20), (30, 23), (45, 34), (14, 9), (11, 24), (44, 34), (16, 19), (12, 2), (0, 15), (31, 9), (34, 29), (21, 38), (32, 5), (45, 22), (14, 40), (13, 25), (35, 24), (3, 10), (18, 29), (27, 24), (11, 10), (5, 10), (6, 27), (11, 1), (2, 21), (29, 1), (42, 34), (22, 25), (21, 14), (46, 38), (43, 1), (25, 10), (29, 19), (40, 7), (15, 2), (9, 24), (0, 9), (20, 16), (35, 15), (9, 32), (45, 21), (4, 38), (26, 21), (11, 26), (40, 20), (39, 19), (35, 37), (45, 4), (37, 8), (24, 23), (0, 28), (33, 0), (31, 5), (13, 13), (38, 15), (44, 12), (7, 5), (21, 16), (28, 10), (14, 22), (3, 4), (4, 11), (9, 36), (15, 10), (46, 11), (7, 40), (13, 27), (28, 5), (19, 17), (4, 40), (2, 10), (24, 32), (16, 25), (45, 33), (4, 34), (38, 2), (7, 37), (44, 30), (7, 21), (39, 25), (9, 10), (44, 31), (13, 8), (44, 25), (16, 35), (36, 34), (7, 4), (33, 31), (13, 34), (29, 10), (27, 34), (43, 24), (34, 3), (0, 5), (29, 26), (5, 0), (44, 11), (20, 7), (33, 38), (24, 10), (37, 35), (33, 22), (42, 7), (36, 32), (41, 28), (45, 11), (40, 29), (12, 16), (14, 0), (13, 23), (47, 11), (0, 6), (10, 5), (41, 14), (34, 16), (22, 36), (7, 22), (3, 28), (30, 21), (37, 34), (12, 15), (46, 15), (15, 15), (21, 24), (46, 1), (40, 23), (34, 31), (36, 38), (36, 31), (1, 29), (39, 8), (29, 14), (42, 38), (13, 38), (37, 16), (16, 13), (33, 19), (31, 28), (7, 2), (25, 34), (2, 18), (34, 15), (1, 37), (41, 35), (5, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 37), (41, 12), (1, 9), (30, 38), (5, 11), (17, 20), (10, 31), (6, 6), (40, 15), (34, 17), (35, 8), (31, 0), (1, 17), (19, 29), (16, 28), (35, 11), (32, 0), (47, 10), (21, 31), (7, 17), (29, 29), (38, 8), (48, 26), (45, 18), (39, 6), (29, 37), (18, 16), (39, 37), (15, 11), (25, 1), (26, 31), (42, 0), (23, 0), (6, 8), (14, 7), (21, 8), (11, 21), (4, 10), (32, 2), (27, 40), (8, 8), (2, 6), (36, 27), (30, 28), (1, 2), (7, 14), (26, 19), (26, 27), (16, 21), (20, 33), (23, 19), (34, 8), (24, 31), (7, 2), (30, 10), (44, 8), (39, 21), (38, 14), (29, 3), (28, 17), (11, 30), (35, 2), (22, 31), (13, 6), (28, 5), (0, 10), (2, 26), (37, 8), (31, 4), (33, 37), (37, 26), (22, 35), (27, 25), (12, 9), (19, 26), (0, 26), (47, 29), (34, 13), (48, 21), (14, 36), (40, 1), (42, 9), (23, 11), (30, 23), (23, 17), (47, 0), (20, 13), (10, 30), (46, 10), (25, 20), (48, 14), (4, 21), (8, 36), (45, 37), (7, 5), (37, 21), (48, 11), (21, 11), (24, 9), (44, 30), (1, 7), (41, 1), (45, 23), (30, 16), (36, 2), (39, 30), (4, 25), (37, 12), (46, 12), (40, 32), (43, 31), (21, 40), (8, 24), (34, 16), (47, 1), (41, 3), (4, 23), (28, 19), (36, 20), (40, 33), (22, 15), (44, 37), (43, 5), (16, 3), (30, 17), (1, 33), (23, 30), (40, 0), (27, 11), (44, 35), (4, 3), (12, 33), (6, 38), (33, 33), (24, 8), (1, 10), (39, 1), (24, 37), (10, 29), (21, 1), (1, 22), (10, 2), (14, 8), (17, 15), (24, 20), (28, 1), (0, 14), (26, 26), (23, 37), (19, 14), (29, 0), (19, 40), (21, 19), (18, 4), (8, 33), (7, 23), (40, 18), (1, 5), (4, 29), (32, 16), (48, 28), (8, 38), (43, 20), (38, 23), (14, 21), (16, 27), (28, 24), (18, 25), (5, 12), (41, 30), (12, 25), (37, 28), (5, 35), (38, 39), (15, 21), (4, 14), (33, 23), (6, 1), (10, 20), (38, 36), (0, 22), (12, 34), (26, 0), (11, 26), (12, 20), (39, 26), (12, 39), (35, 17), (47, 21), (4, 0), (40, 30), (36, 13), (2, 15), (37, 19), (6, 16), (41, 23), (11, 19), (12, 12), (48, 2), (19, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 19), (41, 43), (30, 16), (6, 13), (19, 8), (27, 19), (22, 20), (15, 32), (39, 20), (12, 6), (8, 12), (31, 15), (40, 11), (3, 18), (9, 13), (30, 10), (37, 15), (19, 44), (35, 5), (32, 0), (35, 46), (34, 37), (39, 9), (33, 29), (1, 32), (6, 38), (25, 20), (23, 16), (20, 36), (19, 4), (33, 21), (18, 29), (20, 26), (9, 2), (11, 44), (39, 26), (8, 36), (43, 22), (9, 35), (43, 38), (38, 36), (3, 13), (44, 13), (1, 43), (8, 18), (6, 25), (45, 8), (1, 36), (3, 33), (34, 25), (11, 13), (43, 1), (10, 36), (5, 44), (18, 8), (39, 10), (37, 6), (3, 42), (10, 7), (21, 24), (34, 21), (45, 41), (9, 29), (2, 46), (32, 28), (41, 37), (26, 35), (9, 9), (28, 10), (19, 18), (33, 43), (27, 44), (20, 13), (37, 17), (14, 0), (37, 11), (32, 33), (24, 24), (25, 12), (18, 21), (24, 13), (1, 15), (4, 7), (2, 12), (13, 24), (7, 26), (37, 36), (40, 2), (24, 29), (38, 39), (20, 42), (2, 8), (44, 19), (23, 35), (17, 34), (41, 7), (36, 31), (9, 12), (7, 20), (5, 23), (5, 22), (3, 45), (2, 13), (17, 11), (0, 15), (40, 7), (44, 46), (29, 30), (9, 3), (13, 28), (36, 45), (17, 37), (6, 22), (31, 4), (1, 31), (11, 17), (5, 18), (15, 3), (32, 45), (37, 21), (39, 35), (18, 39), (34, 22), (28, 2), (30, 15), (25, 5), (8, 4), (20, 7), (38, 41), (40, 1), (3, 44), (23, 12), (20, 28), (31, 39), (29, 19), (0, 45), (20, 40), (15, 31), (13, 12), (45, 16), (7, 27), (3, 1), (5, 43), (6, 18), (42, 46), (22, 29), (9, 28), (26, 21), (42, 0), (5, 24), (2, 19), (17, 14), (35, 6), (30, 29), (34, 7), (11, 5), (45, 7), (11, 24), (27, 6), (10, 4), (45, 42), (25, 24), (10, 19), (1, 46), (36, 23), (26, 18), (17, 16), (22, 4), (19, 46), (36, 33), (19, 7), (13, 20), (43, 26), (25, 18), (31, 9), (16, 15), (37, 32), (35, 27), (28, 37), (5, 6), (27, 38), (32, 12), (4, 9), (22, 6), (34, 17), (19, 29), (45, 18), (3, 23), (24, 18), (2, 36), (26, 27), (5, 9), (44, 7), (12, 2), (42, 30), (31, 37), (30, 35), (18, 24), (38, 10), (1, 20), (34, 11), (5, 11), (0, 36), (7, 32), (43, 43), (5, 21), (17, 42), (41, 29), (36, 42), (25, 14), (27, 36), (16, 39), (33, 6), (13, 25), (42, 1), (4, 10), (15, 11), (38, 33), (40, 17), (37, 44), (24, 8), (4, 35), (37, 9), (23, 34), (1, 7), (16, 20), (39, 36), (29, 34), (32, 3), (19, 43), (39, 43), (41, 3), (41, 38), (27, 9), (8, 32), (39, 1), (44, 21), (37, 37), (4, 8), (14, 39), (12, 39), (18, 0), (34, 34), (36, 17), (33, 9), (30, 13), (44, 23), (40, 13), (38, 32), (0, 41), (38, 29), (3, 12), (13, 46), (44, 33), (1, 34), (23, 0), (21, 4), (31, 12), (30, 26), (40, 26), (29, 38), (22, 21), (32, 6), (12, 19), (34, 41), (10, 13), (41, 4), (44, 39), (9, 38), (24, 35), (41, 45), (36, 35), (1, 22), (35, 13), (35, 26), (10, 37), (44, 25), (22, 13), (13, 15), (28, 21), (41, 15), (15, 40), (8, 21), (39, 31), (40, 38), (17, 3), (28, 31), (14, 45), (32, 20), (14, 30), (34, 44), (42, 35), (36, 3), (7, 34), (15, 21), (23, 14), (27, 4), (2, 34), (31, 35), (12, 27), (37, 35), (42, 31), (1, 21), (10, 45), (28, 32), (6, 37), (3, 7), (3, 25), (44, 37), (36, 18), (7, 45), (35, 44), (10, 9), (21, 35), (22, 14), (17, 22), (39, 29), (32, 2), (10, 31), (6, 9), (39, 2), (43, 18), (10, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 7), (6, 13), (44, 10), (17, 42), (21, 41), (27, 5), (12, 16), (44, 33), (0, 22), (22, 36), (19, 8), (12, 29), (33, 13), (43, 28), (21, 28), (35, 10), (6, 0), (36, 10), (3, 42), (33, 33), (29, 29), (40, 32), (2, 33), (31, 8), (37, 6), (19, 3), (22, 23), (35, 41), (19, 20), (6, 5), (8, 34), (38, 21), (41, 9), (34, 3), (41, 2), (14, 16), (12, 36), (37, 11), (32, 44), (42, 17), (19, 10), (31, 35), (27, 20), (10, 44), (14, 35), (10, 34), (33, 39), (26, 21), (27, 15), (23, 46), (11, 33), (22, 5), (11, 9), (41, 27), (39, 17), (1, 3), (4, 45), (34, 21), (18, 21), (11, 10), (44, 29), (32, 20), (0, 43), (44, 15), (1, 41), (41, 19), (16, 28), (39, 2), (16, 19), (18, 4), (1, 8), (15, 21), (1, 45), (10, 15), (27, 12), (29, 3), (0, 20), (28, 20), (25, 31), (27, 21), (39, 14), (35, 26), (9, 42), (28, 37), (1, 13), (4, 15), (8, 3), (3, 30), (19, 15), (3, 44), (0, 17), (43, 15), (25, 5), (4, 6), (43, 46), (18, 5), (4, 27), (19, 32), (19, 14), (8, 38), (24, 12), (24, 34), (39, 26), (15, 31), (7, 2), (33, 38), (3, 15), (32, 32), (5, 17), (26, 26), (36, 17), (5, 3), (12, 20), (35, 2), (42, 36), (11, 45), (9, 25), (9, 27), (31, 37), (21, 8), (15, 42), (42, 5), (13, 28), (5, 13), (31, 19), (36, 11), (30, 29), (31, 43), (19, 35), (13, 18), (3, 39), (40, 16), (32, 5), (4, 21), (42, 13), (32, 9), (39, 9), (8, 46), (8, 1), (34, 46), (35, 29), (30, 19), (26, 27), (8, 33), (26, 38), (32, 2), (17, 7), (38, 27), (9, 7), (16, 36), (0, 29), (34, 2), (1, 25), (17, 19), (32, 10), (27, 26), (36, 42), (32, 7), (5, 35), (33, 20), (26, 9), (11, 31), (41, 43), (29, 38), (7, 28), (22, 32), (27, 4), (35, 15), (38, 36), (17, 37), (25, 9), (0, 26), (10, 16), (5, 30), (37, 31), (34, 18), (17, 10), (7, 44), (31, 14), (25, 3), (25, 36), (14, 22), (43, 25), (28, 2), (27, 39), (17, 8), (36, 28), (9, 29), (38, 31), (36, 46), (24, 11), (43, 6), (10, 13), (42, 46), (34, 1), (36, 36), (7, 31), (25, 41), (2, 4), (37, 21), (5, 45), (31, 30), (34, 19), (30, 45), (6, 19), (27, 37), (13, 6), (26, 15), (32, 33), (41, 17), (37, 20), (26, 29), (38, 9), (44, 36), (34, 31), (26, 23), (24, 16), (13, 39), (28, 0), (29, 25), (7, 24), (11, 38), (39, 7), (34, 15), (12, 1), (9, 35), (12, 13), (0, 21), (42, 26), (38, 10), (42, 3), (31, 4), (41, 30), (17, 33), (29, 34), (10, 41), (16, 29), (22, 45), (29, 35), (36, 1), (33, 10), (4, 38), (28, 33), (7, 8), (18, 40), (8, 39), (31, 25), (43, 9), (35, 21), (38, 19), (11, 35), (8, 5), (40, 19), (1, 12), (3, 3), (32, 22), (7, 32), (3, 34), (4, 5), (13, 19), (0, 15), (21, 44), (3, 7), (16, 5), (30, 4), (31, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 35), (29, 31), (23, 15), (20, 5), (4, 45), (29, 3), (0, 30), (10, 44), (23, 19), (17, 36), (7, 8), (28, 41), (23, 14), (38, 11), (11, 19), (2, 11), (28, 9), (0, 33), (37, 16), (44, 16), (38, 34), (22, 30), (40, 15), (24, 29), (7, 19), (32, 0), (18, 17), (15, 18), (18, 3), (10, 23), (25, 6), (12, 8), (13, 37), (30, 40), (14, 7), (4, 4), (8, 43), (38, 38), (24, 24), (24, 40), (18, 36), (7, 33), (4, 44), (34, 41), (7, 24), (43, 19), (6, 42), (5, 27), (11, 11), (11, 17), (27, 24), (12, 17), (43, 17), (22, 37), (20, 30), (27, 32), (39, 37), (41, 39), (16, 42), (39, 23), (25, 19), (35, 8), (26, 37), (46, 23), (26, 38), (2, 34), (17, 12), (40, 19), (40, 22), (3, 23), (22, 24), (26, 3), (20, 32), (17, 33), (15, 43), (4, 17), (12, 39), (31, 24), (30, 42), (2, 0), (44, 17), (44, 44), (4, 21), (35, 11), (25, 2), (41, 17), (42, 2), (21, 24), (0, 4), (20, 33), (3, 5), (19, 17), (45, 27), (5, 37), (31, 8), (33, 5), (15, 38), (42, 28), (35, 12), (42, 35), (41, 11), (0, 3), (24, 17), (24, 5), (33, 20), (43, 39), (17, 29), (12, 32), (0, 28), (27, 22), (34, 37), (24, 15), (18, 29), (41, 18), (1, 17), (3, 4), (5, 16), (44, 35), (5, 3), (1, 16), (27, 18), (19, 44), (22, 6), (33, 12), (21, 3), (36, 12), (37, 42), (34, 35), (9, 23), (1, 43), (46, 42), (16, 14), (22, 3), (3, 39), (36, 1), (25, 37), (21, 39), (6, 37), (27, 20), (46, 10), (31, 35), (26, 45), (36, 2), (5, 36), (20, 40), (28, 39), (4, 31), (30, 2), (32, 11), (8, 12), (1, 9), (34, 11), (33, 4), (5, 42), (8, 2), (37, 13), (22, 1), (36, 9), (41, 8), (1, 6), (32, 37), (34, 40), (38, 12), (36, 42), (19, 16), (38, 2), (29, 8), (26, 25), (4, 27), (24, 37), (42, 12), (35, 25), (45, 41), (0, 21), (1, 44), (1, 15), (14, 0), (12, 13), (8, 39), (38, 40), (41, 41), (31, 13), (4, 19), (28, 34), (4, 35), (12, 22), (13, 13), (11, 32), (16, 35), (36, 19), (15, 17), (28, 31), (0, 2), (32, 22), (12, 3), (35, 9), (44, 20), (16, 10), (8, 14), (31, 23), (32, 25), (43, 11), (41, 2), (16, 6), (28, 32), (14, 36), (3, 14), (32, 5), (0, 29), (17, 32), (10, 41), (23, 6), (4, 16), (3, 18), (26, 11), (26, 7), (3, 11), (10, 26), (7, 42), (0, 42), (8, 18), (29, 34), (35, 37), (19, 15), (14, 12), (42, 39), (17, 39), (8, 28), (23, 0), (45, 15), (17, 9), (5, 10), (10, 40), (21, 32), (21, 38), (13, 14), (34, 8), (0, 25), (31, 30), (31, 19), (37, 36), (3, 24), (14, 15), (5, 6), (46, 27), (21, 21), (23, 1), (3, 36), (36, 11), (5, 1), (23, 35), (21, 0), (9, 14), (20, 34), (41, 1), (28, 43), (24, 11), (1, 2), (32, 20), (39, 5), (19, 20), (22, 32), (18, 43), (45, 8), (23, 38), (13, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 34), (26, 17), (43, 41), (17, 17), (16, 35), (23, 3), (7, 21), (12, 9), (28, 23), (5, 35), (18, 2), (24, 35), (15, 40), (34, 41), (35, 4), (19, 34), (25, 17), (16, 9), (4, 14), (22, 20), (31, 20), (24, 39), (0, 9), (22, 30), (8, 13), (11, 21), (20, 17), (12, 38), (9, 38), (16, 19), (16, 20), (18, 22), (23, 22), (2, 35), (44, 37), (17, 28), (26, 11), (26, 3), (15, 31), (13, 2), (23, 12), (8, 5), (20, 13), (17, 26), (27, 29), (9, 19), (19, 35), (30, 3), (36, 8), (1, 10), (9, 28), (5, 13), (31, 18), (35, 35), (21, 31), (42, 40), (30, 35), (41, 36), (3, 11), (3, 29), (6, 26), (30, 28), (11, 32), (10, 5), (16, 8), (15, 9), (2, 17), (2, 23), (38, 6), (8, 36), (33, 12), (3, 10), (32, 17), (42, 31), (39, 35), (11, 3), (30, 23), (14, 23), (37, 0), (35, 29), (13, 23), (25, 5), (36, 9), (34, 24), (11, 29), (18, 38), (14, 10), (34, 5), (41, 21), (29, 9), (9, 36), (36, 41), (21, 40), (5, 27), (28, 38), (26, 32), (26, 27), (27, 8), (44, 18), (19, 39), (38, 7), (18, 1), (21, 18), (43, 4), (16, 30), (44, 27), (13, 27), (17, 25), (1, 7), (13, 14), (27, 30), (37, 29), (35, 33), (22, 3), (7, 38), (5, 9), (5, 21), (19, 32), (39, 29), (23, 9), (6, 20), (44, 0), (31, 38), (4, 37), (19, 28), (23, 18), (39, 28), (42, 9), (12, 13), (17, 6), (43, 28), (12, 34), (35, 18), (39, 8), (39, 41), (27, 10), (37, 17), (33, 41), (27, 5), (14, 24), (43, 40), (2, 34), (19, 33), (36, 40), (33, 13), (25, 1), (25, 15), (27, 41), (37, 3), (40, 16), (12, 16), (7, 13), (30, 17), (42, 29), (32, 10), (10, 6), (26, 7), (35, 41), (12, 4), (6, 16), (7, 22), (44, 4), (24, 4), (31, 39), (33, 20), (26, 20), (27, 24), (34, 15), (22, 32), (3, 13), (23, 34), (5, 34), (43, 25), (16, 10), (14, 36), (8, 33), (27, 22), (6, 24), (13, 17), (33, 29), (39, 36), (44, 36), (28, 35), (12, 12), (4, 8), (2, 21), (32, 23), (37, 35), (30, 12), (2, 22), (26, 9), (26, 2), (21, 7), (15, 2), (2, 9), (35, 21), (27, 27), (42, 20), (1, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 19), (5, 9), (16, 17), (30, 19), (4, 19), (15, 2), (14, 35), (1, 12), (2, 33), (30, 2), (30, 10), (6, 20), (9, 40), (13, 4), (4, 35), (37, 7), (42, 36), (2, 27), (31, 40), (22, 34), (3, 29), (15, 33), (26, 42), (5, 39), (12, 15), (32, 19), (17, 35), (28, 41), (0, 40), (6, 14), (21, 8), (39, 42), (24, 26), (22, 27), (42, 8), (8, 36), (3, 42), (30, 14), (10, 29), (26, 19), (10, 33), (4, 16), (26, 41), (4, 33), (21, 7), (2, 31), (22, 9), (18, 3), (4, 21), (27, 11), (40, 8), (10, 13), (32, 30), (5, 42), (21, 11), (33, 30), (10, 31), (4, 27), (13, 36), (25, 13), (16, 30), (1, 38), (28, 36), (34, 27), (1, 10), (32, 18), (9, 13), (31, 20), (28, 20), (12, 31), (2, 14), (41, 29), (6, 3), (8, 5), (19, 1), (24, 2), (35, 2), (42, 1), (9, 28), (4, 8), (24, 30), (13, 1), (0, 22), (31, 27), (38, 14), (14, 24), (21, 39), (21, 24), (25, 7), (0, 33), (5, 1), (30, 24), (21, 20), (5, 41), (40, 2), (23, 17), (24, 42), (26, 33), (36, 4), (17, 15), (1, 9), (23, 0), (7, 15), (16, 29), (3, 12), (9, 16), (17, 3), (22, 42), (20, 24), (28, 14), (7, 35), (40, 28), (23, 16), (19, 26), (21, 9), (13, 14), (33, 28), (41, 5), (1, 2), (18, 21), (5, 22), (11, 28), (22, 6), (42, 13), (6, 34), (29, 33), (11, 24), (19, 35), (15, 11), (29, 24), (18, 24), (34, 21), (12, 22), (29, 31), (22, 24), (38, 27), (13, 29), (17, 36), (7, 32), (13, 23), (3, 31), (38, 18), (20, 3), (18, 34), (3, 10), (29, 29), (4, 24), (42, 41), (28, 15), (31, 41), (39, 2), (27, 5), (2, 20), (42, 11), (42, 31), (31, 31), (20, 37), (26, 23), (17, 17), (34, 42), (22, 40), (10, 36), (25, 11), (24, 7), (3, 17), (34, 30), (10, 20), (5, 26), (41, 34), (40, 11), (6, 38), (34, 24), (33, 15), (29, 19), (30, 32), (25, 26), (5, 27), (2, 2), (27, 12), (20, 12), (19, 8), (22, 1), (7, 42), (4, 25), (25, 18), (0, 14), (38, 13), (33, 37), (34, 8), (30, 21), (6, 4), (16, 40), (14, 16), (7, 33), (32, 28), (12, 40), (32, 9), (10, 16), (5, 18), (27, 39), (24, 12), (6, 25), (38, 26), (10, 26), (36, 23), (27, 17), (7, 22), (12, 36), (25, 12), (36, 39), (39, 1), (32, 3), (1, 0), (40, 24), (18, 29), (7, 26), (8, 21), (33, 35), (39, 0), (41, 26), (11, 12), (34, 40), (5, 10), (22, 10), (4, 34), (0, 39), (19, 32), (31, 17), (19, 34), (13, 10), (11, 10), (38, 17), (34, 35), (33, 22), (26, 26), (24, 22), (12, 27), (19, 40), (34, 31), (10, 2), (2, 8), (22, 35), (9, 1), (34, 22), (24, 18), (40, 32), (30, 18), (12, 12), (9, 42), (27, 22), (14, 1), (37, 5), (7, 12), (22, 5), (25, 33), (33, 16), (21, 21), (40, 4), (2, 26), (13, 9), (24, 19), (35, 33), (15, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 37), (11, 27), (35, 6), (32, 10), (20, 30), (19, 33), (32, 0), (36, 38), (29, 32), (38, 17), (13, 14), (32, 40), (9, 38), (34, 25), (9, 29), (15, 14), (16, 26), (32, 21), (0, 33), (10, 38), (30, 39), (3, 14), (3, 7), (1, 18), (25, 13), (22, 9), (24, 27), (1, 14), (24, 24), (13, 23), (39, 18), (34, 13), (16, 22), (12, 40), (24, 14), (11, 31), (24, 2), (39, 1), (35, 27), (1, 32), (40, 36), (29, 12), (24, 19), (29, 23), (40, 20), (12, 14), (3, 37), (17, 1), (7, 3), (14, 18), (14, 29), (10, 35), (18, 13), (35, 5), (2, 2), (30, 33), (16, 10), (7, 12), (12, 18), (21, 33), (9, 27), (6, 19), (35, 21), (30, 8), (5, 25), (10, 26), (16, 1), (22, 2), (8, 28), (6, 18), (28, 30), (5, 24), (16, 35), (39, 17), (16, 38), (34, 17), (38, 35), (14, 19), (40, 25), (38, 3), (29, 4), (0, 14), (39, 6), (31, 35), (25, 39), (32, 5), (2, 7), (26, 15), (25, 21), (8, 4), (24, 22), (18, 33), (18, 34), (14, 33), (25, 1), (17, 5), (25, 38), (32, 15), (21, 27), (14, 34), (23, 5), (30, 9), (7, 15), (14, 5), (7, 24), (7, 34), (6, 5), (1, 19), (22, 30), (17, 15), (30, 1), (1, 0), (13, 13), (1, 35), (36, 17), (18, 30), (37, 34), (33, 29), (36, 23), (10, 34), (9, 11), (3, 26), (24, 33), (17, 17), (13, 2), (13, 27), (27, 34), (10, 13), (8, 21), (6, 21), (32, 17), (9, 1), (20, 36), (11, 20), (39, 22), (7, 14), (23, 18), (18, 36), (16, 0), (39, 2), (35, 9), (19, 11), (2, 15), (24, 10), (24, 36), (30, 30), (6, 36), (25, 35), (29, 14), (34, 16), (22, 16), (13, 22), (32, 7), (8, 15), (15, 31), (32, 37), (40, 34), (31, 10), (28, 39), (18, 10), (28, 21), (2, 8), (26, 22), (22, 26), (16, 9), (0, 17), (16, 3), (7, 25), (20, 34), (21, 26), (24, 20), (38, 12), (1, 4), (38, 10), (6, 29), (14, 23), (23, 22), (9, 3), (2, 38), (40, 11), (38, 27), (27, 21), (21, 31), (30, 11), (22, 35), (25, 16), (40, 31), (9, 19), (36, 12), (20, 6), (12, 20), (30, 37), (39, 32), (6, 26), (37, 25), (38, 30), (27, 31), (39, 3), (31, 26), (15, 24), (37, 24), (26, 18), (22, 31), (36, 2), (5, 6), (16, 29), (7, 2), (40, 15), (33, 8), (38, 40), (14, 16), (35, 19), (11, 9), (11, 29), (17, 12), (5, 36), (32, 28), (31, 0), (0, 26), (34, 31), (13, 17), (17, 34), (30, 22), (23, 40), (9, 17), (31, 31), (5, 26), (19, 30), (39, 35), (0, 19), (3, 18), (0, 10), (33, 0), (24, 5), (11, 23), (27, 23), (6, 38), (3, 30), (36, 21), (16, 36), (8, 39), (5, 0), (20, 8), (37, 5), (22, 20), (27, 17), (23, 13), (18, 21), (12, 2), (5, 32), (31, 18), (31, 29), (23, 39), (34, 39), (10, 14), (0, 37), (14, 12), (23, 12), (4, 31), (37, 8), (26, 12), (12, 7), (38, 38), (0, 28), (27, 29), (18, 28), (22, 28), (5, 13), (2, 20), (8, 0), (30, 18), (36, 15), (11, 1), (30, 6), (38, 34), (22, 8), (20, 25), (15, 15), (14, 38), (27, 9), (5, 38), (17, 36), (37, 22), (36, 29), (40, 12), (30, 3), (38, 37), (17, 21), (40, 14), (5, 30), (33, 40), (17, 37), (31, 9), (23, 29), (37, 17), (34, 6), (33, 24), (4, 20), (12, 0), (39, 39), (19, 34), (6, 31), (15, 2), (21, 13), (11, 39), (39, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 13), (37, 4), (22, 37), (47, 30), (46, 17), (25, 28), (13, 21), (19, 12), (7, 1), (44, 16), (15, 29), (13, 22), (17, 27), (10, 7), (17, 14), (32, 7), (19, 24), (0, 4), (38, 14), (16, 35), (8, 35), (24, 21), (26, 15), (7, 18), (43, 40), (0, 3), (15, 19), (12, 28), (19, 25), (7, 3), (30, 8), (35, 15), (25, 4), (42, 39), (37, 7), (20, 35), (44, 2), (13, 23), (8, 12), (36, 30), (44, 6), (32, 33), (46, 38), (15, 6), (40, 28), (16, 31), (11, 39), (23, 17), (40, 10), (45, 15), (45, 22), (25, 3), (11, 27), (38, 34), (22, 34), (6, 38), (14, 32), (15, 18), (31, 40), (26, 4), (19, 20), (36, 35), (11, 6), (47, 29), (11, 24), (31, 9), (2, 13), (45, 4), (37, 24), (11, 0), (22, 6), (22, 26), (9, 23), (0, 29), (37, 10), (25, 17), (38, 3), (27, 4), (24, 23), (34, 11), (47, 37), (34, 3), (0, 8), (25, 11), (5, 35), (1, 25), (18, 14), (21, 37), (18, 13), (1, 16), (6, 13), (22, 9), (32, 41), (29, 4), (15, 28), (14, 15), (0, 22), (39, 28), (40, 34), (43, 26), (18, 18), (5, 27), (38, 27), (35, 25), (8, 15), (47, 36), (25, 20), (44, 10), (31, 32), (2, 29), (30, 11), (15, 22), (0, 19), (25, 32), (16, 40), (33, 35), (19, 35), (0, 2), (25, 39), (34, 12), (34, 22), (41, 28), (11, 4), (46, 4), (16, 39), (46, 39), (7, 9), (9, 41), (24, 9), (29, 39), (19, 30), (31, 6), (31, 27), (6, 2), (26, 9), (43, 0), (34, 29), (38, 0), (36, 9), (6, 5), (26, 6), (17, 36), (36, 15), (9, 39), (11, 14), (29, 37), (12, 27), (11, 41), (20, 40), (17, 16), (19, 9), (27, 3), (14, 24), (26, 22), (21, 16), (29, 32), (21, 3), (37, 16), (32, 29), (12, 39), (14, 3), (13, 7), (41, 26), (10, 23), (3, 2), (14, 29), (9, 16), (24, 31), (2, 38), (14, 30), (10, 20), (11, 9), (0, 37), (8, 25), (5, 6), (22, 10), (18, 7), (21, 2), (21, 31), (23, 41), (30, 10), (32, 24), (8, 3), (12, 11), (36, 6), (3, 31), (34, 15), (45, 40), (23, 24), (47, 18), (35, 22), (25, 13), (8, 18), (29, 14), (5, 29), (37, 26), (10, 13), (18, 2), (7, 29), (26, 28), (39, 19), (20, 4), (28, 24), (31, 7), (18, 24), (19, 31), (32, 12), (37, 3), (40, 16), (11, 40), (25, 35), (17, 7), (13, 13), (39, 11), (37, 41), (45, 3), (4, 18), (41, 2), (5, 24), (33, 5), (31, 20), (23, 13), (47, 11), (1, 14), (6, 1), (23, 29), (28, 0), (33, 21), (36, 40), (34, 14), (12, 31), (0, 15), (11, 21), (39, 20), (7, 17), (39, 35), (40, 4), (20, 12), (29, 26), (10, 28), (10, 21), (25, 24), (9, 1), (30, 3), (23, 37), (36, 37), (40, 35), (8, 38), (27, 16), (29, 2), (15, 40), (2, 28), (9, 25), (2, 14), (29, 27), (19, 36), (15, 33), (30, 20), (27, 22), (2, 34), (16, 26), (28, 36), (31, 12), (10, 3), (45, 21), (43, 23), (7, 12), (6, 39), (30, 2), (5, 38), (6, 33), (24, 16), (13, 19), (18, 15), (22, 41), (36, 3), (40, 2), (6, 19), (28, 35), (27, 32), (5, 20), (17, 11), (32, 15), (26, 33), (10, 11), (0, 1), (0, 28), (38, 23), (8, 24), (14, 27), (36, 34), (8, 22), (20, 27), (44, 26), (9, 35), (43, 39), (26, 29), (35, 39), (23, 22), (43, 9), (46, 0), (34, 8), (39, 12), (27, 26), (34, 20), (45, 9), (18, 41), (26, 17), (5, 16), (44, 1), (7, 11), (20, 33), (24, 35), (10, 35), (1, 12), (42, 29), (15, 39), (4, 24), (25, 21), (21, 19), (41, 11), (4, 40), (18, 17), (19, 37), (21, 29), (14, 38), (42, 7), (36, 23), (18, 26), (1, 39), (32, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 32), (30, 12), (11, 14), (6, 16), (21, 4), (1, 37), (26, 35), (1, 43), (22, 11), (46, 18), (10, 1), (12, 1), (4, 2), (5, 6), (1, 20), (0, 21), (34, 23), (12, 31), (33, 20), (30, 33), (26, 14), (14, 1), (20, 12), (30, 0), (6, 17), (8, 30), (10, 6), (39, 42), (29, 36), (12, 7), (45, 33), (15, 30), (7, 19), (9, 29), (34, 19), (12, 11), (38, 6), (35, 32), (23, 1), (22, 4), (37, 43), (35, 25), (15, 20), (37, 40), (37, 26), (26, 18), (25, 7), (29, 22), (24, 35), (37, 17), (12, 16), (14, 13), (37, 19), (31, 21), (43, 3), (26, 27), (47, 33), (9, 41), (28, 20), (9, 34), (30, 21), (38, 18), (4, 14), (7, 41), (25, 15), (4, 39), (22, 5), (35, 24), (22, 21), (7, 22), (6, 24), (14, 36), (33, 34), (34, 35), (1, 21), (33, 10), (39, 8), (24, 37), (23, 2), (26, 20), (46, 34), (24, 19), (23, 33), (33, 27), (25, 36), (19, 25), (17, 24), (6, 4), (42, 35), (33, 9), (21, 36), (34, 30), (33, 32), (10, 28), (27, 42), (46, 15), (5, 24), (43, 12), (8, 22), (25, 32), (41, 30), (2, 15), (44, 42), (39, 0), (30, 17), (27, 2), (42, 9), (2, 25), (26, 9), (4, 10), (1, 6), (10, 25), (24, 0), (6, 28), (45, 23), (17, 36), (25, 11), (20, 6), (11, 31), (33, 23), (42, 5), (25, 9), (25, 28), (28, 42), (40, 41), (18, 6), (46, 6), (39, 39), (14, 23), (34, 3), (21, 27), (46, 24), (4, 6), (15, 12), (10, 17), (14, 18), (41, 15), (42, 13), (13, 3), (32, 19), (7, 38), (47, 5), (11, 5), (35, 21), (33, 24), (13, 41), (14, 39), (26, 0), (23, 4), (38, 19), (38, 14), (27, 5), (45, 25), (9, 9), (44, 34), (18, 36), (26, 5), (4, 13), (15, 42), (37, 13), (40, 3), (16, 6), (6, 19), (13, 20), (43, 17), (31, 37), (18, 23), (44, 23), (44, 26), (17, 9), (28, 15), (5, 8), (33, 15), (36, 12), (29, 15), (14, 32), (15, 13), (12, 42), (11, 36), (27, 40), (29, 10), (27, 34), (24, 16), (40, 26), (14, 22), (38, 28), (29, 11), (27, 12), (36, 26), (8, 42), (10, 30), (34, 5), (47, 42), (47, 34), (11, 16), (17, 4), (5, 35), (11, 39), (14, 38), (46, 37), (1, 29), (12, 5), (23, 3), (8, 14), (13, 6), (37, 10), (22, 33), (44, 8), (5, 0), (8, 34), (9, 37), (40, 24), (35, 42), (45, 35), (13, 43), (16, 17), (5, 14), (13, 0), (30, 13), (35, 40), (30, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 8), (5, 19), (15, 37), (12, 46), (19, 44), (35, 43), (0, 6), (29, 34), (1, 10), (40, 16), (41, 32), (34, 15), (32, 14), (32, 20), (27, 36), (24, 14), (22, 16), (22, 42), (27, 21), (4, 7), (13, 7), (43, 23), (35, 2), (6, 20), (23, 0), (39, 40), (38, 45), (37, 1), (37, 10), (22, 31), (38, 42), (24, 11), (31, 30), (11, 41), (34, 23), (14, 23), (26, 15), (1, 23), (23, 24), (26, 7), (0, 10), (5, 16), (12, 39), (12, 28), (42, 25), (15, 39), (12, 19), (28, 23), (18, 34), (18, 44), (0, 11), (26, 36), (25, 5), (8, 5), (35, 26), (3, 26), (1, 34), (16, 39), (20, 46), (35, 46), (37, 3), (17, 32), (2, 24), (6, 9), (35, 30), (18, 24), (5, 33), (0, 13), (17, 15), (23, 39), (2, 14), (17, 20), (16, 38), (3, 15), (11, 12), (25, 46), (27, 27), (22, 27), (38, 30), (28, 32), (19, 18), (38, 11), (32, 12), (28, 0), (28, 38), (8, 37), (14, 35), (29, 7), (11, 32), (28, 21), (32, 28), (41, 8), (38, 28), (29, 22), (25, 4), (29, 46), (37, 28), (27, 22), (27, 30), (24, 22), (5, 24), (0, 29), (38, 17), (38, 4), (3, 27), (30, 19), (29, 37), (14, 4), (16, 46), (7, 39), (8, 7), (39, 45), (40, 36), (10, 36), (27, 13), (36, 43), (6, 25), (43, 4), (24, 4), (29, 5), (16, 22), (10, 13), (17, 43), (29, 1), (9, 29), (18, 14), (11, 35), (12, 0), (9, 44), (16, 24), (0, 28), (39, 15), (39, 41), (17, 37), (37, 7), (28, 41), (39, 43), (42, 46), (6, 38), (2, 18), (1, 17), (30, 12), (29, 24), (37, 41), (33, 4), (6, 34), (15, 19), (24, 3), (30, 8), (25, 21), (2, 43), (23, 8), (25, 30), (9, 25), (1, 8), (30, 41), (33, 8), (25, 12), (3, 31), (4, 37), (40, 44), (1, 6), (5, 30), (27, 33), (27, 37), (36, 32), (10, 14), (31, 24), (42, 23), (6, 10), (4, 8), (7, 4), (43, 3), (17, 45), (7, 12), (31, 36), (41, 18), (40, 40), (9, 38), (4, 24), (27, 42), (5, 1), (5, 37), (11, 18), (32, 8), (8, 30), (24, 39), (28, 11), (23, 27), (20, 14), (7, 38), (12, 31), (25, 20), (8, 42), (8, 3), (41, 37), (28, 25), (33, 14), (5, 38), (16, 31), (14, 18), (41, 31), (36, 11), (27, 28), (14, 22), (1, 18), (39, 29), (39, 24), (25, 31), (28, 18), (33, 29), (2, 0), (16, 18), (41, 4), (4, 34), (34, 16), (28, 7), (15, 5), (34, 29), (7, 5), (0, 24), (41, 0), (24, 32), (16, 32), (26, 4), (20, 27), (20, 39), (24, 27), (10, 23), (42, 22), (4, 18), (36, 33), (15, 31), (14, 25), (36, 7), (13, 1), (38, 13), (14, 7), (40, 46), (36, 12), (32, 21), (16, 12), (10, 11), (2, 21), (40, 34), (39, 25), (38, 29), (27, 32), (38, 36), (20, 23), (11, 3), (4, 40), (13, 0), (24, 7), (12, 44), (44, 11), (6, 22), (8, 0), (40, 22), (12, 6), (36, 4), (14, 45), (9, 15), (21, 4), (13, 38), (19, 42), (0, 35), (19, 20), (13, 15), (18, 29), (19, 4), (20, 4), (25, 16), (42, 5), (35, 31), (39, 23), (16, 5), (40, 5), (5, 34), (8, 36), (4, 33), (37, 16), (13, 9), (32, 18), (24, 36), (22, 20), (32, 9), (21, 35), (15, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 41x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 43), (4, 44), (28, 12), (37, 26), (20, 41), (20, 25), (13, 19), (23, 19), (39, 28), (40, 6), (10, 12), (18, 3), (39, 8), (16, 29), (27, 8), (15, 19), (10, 5), (35, 1), (22, 18), (30, 4), (8, 5), (13, 34), (24, 4), (17, 43), (28, 27), (33, 23), (32, 44), (27, 9), (23, 16), (4, 6), (20, 15), (5, 36), (6, 0), (7, 41), (4, 15), (32, 1), (19, 36), (34, 13), (38, 26), (30, 17), (32, 10), (3, 44), (23, 30), (39, 22), (8, 24), (38, 15), (36, 13), (29, 13), (2, 41), (30, 14), (0, 30), (35, 40), (1, 9), (17, 27), (3, 35), (14, 21), (20, 13), (25, 35), (34, 11), (16, 3), (17, 41), (16, 42), (13, 39), (22, 9), (13, 15), (25, 26), (19, 24), (28, 7), (22, 7), (22, 4), (12, 24), (13, 17), (31, 5), (33, 34), (10, 8), (3, 43), (36, 29), (19, 2), (28, 33), (16, 37), (4, 20), (27, 42), (9, 14), (32, 31), (37, 28), (6, 32), (23, 5), (15, 35), (6, 35), (30, 26), (33, 33), (27, 34), (7, 25), (38, 38), (0, 16), (17, 28), (23, 8), (30, 31), (8, 35), (10, 29), (25, 41), (40, 20), (8, 44), (3, 10), (12, 2), (7, 19), (5, 17), (16, 34), (30, 25), (13, 7), (27, 22), (20, 24), (39, 5), (21, 26), (14, 33), (20, 1), (32, 36), (25, 28), (6, 36), (36, 26), (3, 36), (0, 37), (15, 3), (21, 44), (19, 5), (11, 27), (0, 8), (10, 11), (33, 16), (7, 16), (25, 43), (1, 2), (15, 30), (26, 32), (2, 38), (2, 37), (36, 21), (15, 23), (11, 28), (9, 2), (23, 12), (21, 42), (37, 20), (32, 7), (25, 2), (32, 8), (6, 39), (11, 38), (20, 30), (4, 14), (29, 38), (33, 35), (12, 3), (3, 11), (15, 8), (32, 22), (38, 13), (33, 24), (10, 14), (17, 7), (17, 35), (23, 17), (22, 8), (2, 16), (2, 18), (7, 20), (30, 7), (2, 32), (16, 20), (27, 7), (31, 43), (22, 27), (38, 30), (7, 36), (13, 36), (19, 26), (29, 4), (23, 27), (25, 32), (12, 12), (15, 11), (2, 19), (34, 44), (16, 39), (17, 18), (28, 35), (5, 31), (12, 18), (9, 28), (3, 5), (20, 33), (32, 25), (29, 40), (20, 40), (39, 44), (3, 4), (11, 31), (22, 35), (0, 40), (24, 10), (33, 30), (9, 39), (39, 31), (0, 25), (27, 10), (5, 24), (25, 11), (8, 8), (8, 26), (20, 8), (18, 18), (23, 25), (33, 22), (39, 21), (10, 40), (13, 42), (27, 44), (5, 7), (37, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 28), (17, 4), (15, 17), (23, 15), (39, 9), (38, 16), (23, 12), (21, 15), (16, 10), (29, 34), (16, 24), (7, 20), (18, 19), (21, 16), (38, 28), (12, 5), (20, 11), (1, 33), (9, 35), (17, 3), (28, 16), (31, 23), (8, 12), (11, 3), (24, 22), (1, 20), (38, 35), (38, 14), (8, 32), (15, 31), (19, 22), (20, 24), (16, 25), (9, 28), (27, 29), (6, 8), (37, 17), (27, 3), (25, 22), (20, 10), (4, 32), (17, 9), (18, 1), (26, 0), (3, 25), (38, 24), (21, 20), (32, 24), (37, 37), (14, 17), (20, 21), (26, 39), (23, 30), (25, 18), (15, 1), (8, 33), (0, 4), (34, 6), (4, 30), (35, 16), (25, 20), (8, 35), (16, 16), (2, 28), (28, 20), (35, 18), (18, 33), (25, 28), (39, 28), (18, 25), (33, 38), (28, 22), (9, 11), (35, 9), (38, 23), (12, 12), (33, 32), (16, 21), (33, 5), (19, 31), (24, 16), (13, 31), (11, 18), (15, 19), (38, 7), (21, 25), (24, 13), (29, 2), (16, 6), (34, 34), (25, 23), (18, 15), (34, 33), (17, 10), (26, 32), (19, 18), (11, 17), (14, 22), (6, 30), (33, 28), (9, 9), (25, 0), (1, 4), (37, 1), (35, 15), (1, 28), (14, 13), (33, 1), (12, 30), (22, 6), (18, 14), (14, 28), (17, 7), (15, 0), (20, 9), (30, 12), (2, 11), (0, 30), (26, 9), (13, 34), (37, 35), (13, 25), (19, 30), (30, 11), (2, 8), (14, 23), (27, 25), (6, 25), (20, 36), (27, 37), (12, 26), (22, 37), (39, 25), (1, 29), (24, 28), (19, 34), (30, 16), (32, 34), (1, 35), (19, 13), (23, 32), (7, 21), (31, 33), (36, 11), (32, 39), (31, 21), (18, 12), (15, 27), (15, 24), (2, 14), (37, 27), (24, 34), (36, 23), (33, 9), (34, 17), (35, 33), (20, 31), (16, 29), (13, 30), (0, 13), (21, 18), (27, 0), (16, 0), (18, 26), (39, 14), (17, 29), (19, 20), (6, 4), (24, 15), (1, 10), (21, 10), (18, 39), (3, 13), (6, 2), (3, 3), (16, 27), (8, 23), (18, 6), (5, 10), (23, 3), (28, 39), (0, 16), (9, 37), (12, 18), (24, 8), (6, 24), (7, 33), (23, 4), (39, 36), (30, 0), (32, 7), (29, 31), (15, 2), (16, 4), (17, 12), (27, 7), (30, 19), (1, 6), (37, 29), (4, 11), (32, 12), (5, 21), (3, 21), (21, 36), (36, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 49x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (48, 37), (14, 5), (33, 6), (17, 12), (30, 34), (12, 36), (19, 0), (7, 1), (41, 1), (10, 19), (8, 11), (21, 38), (31, 35), (33, 37), (26, 14), (5, 19), (4, 35), (14, 15), (16, 19), (27, 21), (13, 31), (39, 25), (47, 31), (21, 27), (18, 14), (48, 9), (0, 7), (11, 20), (40, 7), (0, 23), (18, 33), (35, 25), (7, 7), (32, 28), (46, 24), (17, 36), (22, 36), (3, 37), (38, 26), (21, 37), (24, 6), (32, 26), (44, 8), (30, 0), (17, 31), (2, 3), (41, 27), (5, 5), (20, 19), (42, 30), (7, 10), (4, 27), (45, 1), (18, 13), (32, 37), (28, 18), (7, 38), (21, 9), (30, 25), (13, 18), (48, 17), (36, 13), (44, 17), (40, 39), (45, 37), (15, 12), (29, 22), (29, 27), (48, 12), (21, 39), (39, 12), (37, 34), (45, 30), (34, 3), (46, 13), (25, 34), (29, 17), (22, 23), (27, 28), (3, 36), (13, 25), (16, 17), (34, 13), (19, 4), (5, 18), (48, 7), (28, 7), (15, 33), (36, 32), (5, 27), (4, 4), (5, 34), (43, 7), (16, 23), (48, 11), (17, 17), (9, 31), (30, 36), (22, 35), (1, 18), (23, 2), (42, 31), (7, 2), (10, 36), (23, 21), (6, 37), (37, 21), (47, 36), (24, 15), (4, 38), (13, 14), (13, 22), (28, 15), (29, 21), (36, 0), (31, 13), (7, 8), (17, 29), (21, 6), (0, 12), (38, 35), (39, 30), (1, 12), (44, 11), (45, 4), (1, 35), (41, 36), (19, 38), (5, 39), (17, 35), (32, 3), (11, 14), (41, 0), (7, 17), (46, 25), (39, 10), (46, 16), (44, 18), (31, 12), (27, 12), (25, 19), (3, 15), (26, 16), (46, 12), (2, 22), (15, 8), (33, 10), (3, 18), (27, 17), (34, 22), (45, 6), (36, 23), (4, 15), (27, 5), (28, 21), (41, 34), (16, 21), (1, 23), (29, 33), (29, 10), (20, 25), (32, 34), (35, 14), (25, 4), (38, 39), (22, 11), (46, 14), (37, 37), (0, 36), (21, 7), (32, 20), (20, 14), (6, 30), (13, 30), (36, 39), (1, 2), (34, 11), (39, 18), (35, 34), (13, 32), (10, 9), (48, 21), (9, 9), (8, 37), (18, 31), (43, 16), (20, 38), (9, 35), (2, 32), (2, 27), (43, 17), (45, 22), (17, 5), (16, 5), (39, 1), (28, 8), (42, 19), (23, 10), (28, 31), (26, 34), (36, 25), (47, 25), (39, 0), (2, 30), (2, 36), (8, 1), (20, 16), (10, 29), (26, 27), (0, 24), (34, 18), (4, 24), (6, 2), (34, 19), (24, 19), (34, 16), (24, 30), (37, 2), (28, 4), (46, 3), (20, 35), (42, 7), (38, 4), (14, 1), (34, 37), (5, 1), (46, 4), (17, 10), (36, 37), (25, 12), (9, 7), (34, 9), (3, 24), (4, 28), (31, 7), (41, 8), (47, 4), (6, 15), (6, 22), (20, 29), (16, 25), (44, 15), (17, 9), (34, 8), (9, 36), (14, 10), (42, 27), (31, 22), (3, 7), (22, 22), (29, 4), (42, 8), (4, 26), (46, 5), (1, 30), (37, 25), (13, 1), (26, 9), (35, 16), (6, 21), (8, 28), (22, 3), (8, 23), (15, 13), (9, 6), (6, 14), (48, 23), (7, 34), (30, 11), (45, 19), (33, 14), (23, 1), (8, 24), (9, 38), (29, 13), (12, 31), (35, 21), (15, 31), (25, 13), (32, 31), (2, 18), (11, 17), (48, 30), (33, 30), (25, 31), (24, 1), (41, 33), (15, 10), (47, 27), (48, 36), (43, 21), (29, 11), (21, 28), (21, 25), (26, 30), (33, 2), (43, 38), (44, 32), (39, 7), (13, 26), (24, 3), (5, 20), (16, 37), (33, 5), (6, 20), (11, 30), (12, 8), (46, 22), (15, 15), (7, 20), (44, 5), (13, 39), (25, 27), (36, 6), (42, 32), (16, 8), (30, 9), (22, 29), (0, 4), (30, 8), (20, 24), (6, 0), (11, 22), (5, 23), (18, 27), (7, 33), (18, 20), (20, 27), (5, 29), (20, 33), (3, 27), (27, 29), (37, 19), (14, 37), (25, 8), (21, 19), (37, 11), (4, 18), (27, 27), (40, 12), (28, 14), (37, 16), (42, 18), (23, 20), (16, 35), (47, 17), (15, 11), (18, 4), (11, 12), (36, 29), (47, 32), (29, 5), (30, 39), (42, 26), (27, 31), (43, 31), (31, 16), (10, 5), (33, 0), (13, 17), (17, 4), (20, 0), (27, 26), (21, 22), (22, 4), (0, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 38), (9, 2), (9, 30), (9, 29), (13, 29), (24, 27), (3, 16), (17, 37), (10, 6), (9, 16), (18, 42), (2, 17), (24, 16), (14, 23), (38, 18), (35, 39), (19, 41), (39, 33), (19, 44), (19, 30), (36, 25), (22, 0), (31, 42), (6, 25), (34, 10), (35, 25), (0, 30), (4, 11), (6, 26), (23, 13), (13, 4), (14, 4), (21, 0), (0, 16), (11, 21), (7, 22), (12, 37), (36, 35), (38, 43), (38, 34), (15, 32), (7, 42), (19, 32), (39, 13), (5, 44), (2, 8), (6, 43), (7, 25), (5, 11), (20, 12), (39, 19), (14, 21), (2, 44), (20, 7), (11, 24), (16, 12), (11, 45), (23, 4), (37, 16), (37, 12), (33, 9), (11, 0), (26, 11), (19, 22), (27, 29), (4, 16), (6, 45), (11, 32), (8, 32), (25, 19), (19, 17), (27, 12), (24, 17), (28, 31), (1, 28), (39, 31), (27, 39), (9, 35), (32, 27), (9, 20), (20, 6), (37, 6), (0, 14), (3, 12), (14, 31), (2, 3), (23, 23), (34, 11), (15, 22), (35, 36), (22, 19), (7, 41), (29, 12), (12, 25), (16, 0), (17, 26), (8, 39), (7, 9), (39, 44), (2, 16), (28, 30), (6, 3), (35, 40), (7, 20), (23, 3), (9, 5), (0, 20), (0, 22), (22, 8), (16, 21), (6, 11), (26, 27), (28, 13), (29, 42), (19, 5), (11, 9), (7, 28), (7, 40), (34, 30), (26, 19), (14, 38), (34, 0), (16, 9), (6, 28), (3, 44), (10, 3), (25, 22), (29, 44), (30, 34), (5, 34), (6, 33), (14, 17), (27, 38), (24, 21), (1, 45), (8, 27), (25, 35), (4, 26), (37, 41), (15, 14), (21, 28), (4, 42), (8, 37), (39, 12), (25, 12), (15, 31), (28, 36), (19, 39), (5, 22), (11, 16), (26, 7), (3, 38), (27, 30), (22, 31), (1, 19), (26, 9), (35, 44), (4, 8), (1, 15), (35, 0), (28, 7), (16, 23), (19, 10), (1, 1), (38, 19), (1, 20), (35, 43), (3, 20), (24, 25), (35, 21), (2, 23), (0, 18), (29, 14), (3, 22), (10, 44), (33, 3), (20, 0), (20, 34), (35, 18), (1, 38), (25, 41), (7, 0), (21, 10), (30, 35), (16, 30), (13, 5), (9, 28), (22, 29), (16, 20), (30, 43), (16, 17), (23, 7), (16, 29), (37, 1), (13, 45), (25, 27), (2, 20), (18, 28), (31, 40), (29, 27), (12, 21), (7, 1), (0, 32), (10, 25), (36, 42), (7, 12), (12, 43), (28, 37), (38, 12), (29, 13), (37, 29), (31, 41), (20, 28), (38, 42), (36, 21), (27, 31), (26, 15), (8, 45), (1, 30), (9, 31), (9, 3), (16, 44), (38, 22), (33, 0), (21, 45), (9, 9), (21, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 8), (11, 25), (20, 0), (36, 26), (23, 28), (18, 22), (26, 45), (5, 34), (6, 31), (10, 2), (15, 36), (35, 26), (1, 14), (16, 0), (10, 41), (11, 14), (13, 35), (32, 2), (23, 1), (6, 20), (10, 0), (9, 19), (39, 9), (30, 25), (36, 38), (34, 33), (33, 28), (38, 4), (12, 47), (11, 21), (31, 42), (36, 27), (40, 45), (13, 18), (32, 43), (22, 36), (4, 46), (28, 21), (19, 17), (19, 35), (0, 43), (15, 31), (20, 20), (3, 16), (13, 4), (30, 39), (2, 23), (12, 26), (1, 29), (38, 13), (42, 43), (21, 38), (36, 23), (31, 20), (25, 8), (34, 10), (23, 6), (32, 10), (22, 37), (41, 21), (16, 23), (40, 6), (28, 44), (29, 21), (12, 31), (1, 19), (15, 29), (25, 31), (6, 41), (16, 7), (36, 17), (22, 29), (5, 21), (0, 18), (29, 5), (34, 34), (15, 8), (20, 45), (2, 17), (26, 8), (18, 9), (18, 36), (33, 32), (21, 26), (38, 34), (18, 33), (31, 45), (26, 39), (22, 6), (6, 0), (22, 10), (40, 8), (32, 44), (11, 30), (17, 32), (32, 23), (42, 44), (6, 6), (13, 25), (19, 15), (9, 42), (10, 30), (15, 37), (21, 37), (41, 17), (32, 4), (21, 41), (6, 2), (39, 2), (15, 5), (31, 47), (21, 35), (3, 46), (24, 2), (23, 37), (2, 38), (21, 4), (16, 15), (16, 32), (42, 22), (18, 5), (14, 37), (3, 6), (19, 37), (30, 41), (22, 44), (2, 20), (14, 8), (17, 41), (42, 38), (41, 16), (34, 20), (40, 37), (25, 5), (39, 27), (40, 43), (28, 41), (9, 29), (42, 18), (4, 12), (26, 46), (10, 14), (1, 40), (38, 30), (24, 16), (4, 34), (30, 36), (8, 38), (25, 1), (38, 5), (28, 14), (31, 39), (39, 18), (35, 24), (33, 17), (16, 35), (18, 47), (22, 38), (9, 13), (27, 30), (0, 17), (5, 3), (32, 35), (19, 18), (0, 13), (31, 3), (11, 36), (38, 20), (36, 36), (17, 13), (39, 14), (18, 4), (29, 1), (14, 16), (20, 44), (16, 42), (34, 32), (11, 44), (1, 34), (36, 15), (5, 11), (26, 4), (32, 17), (35, 40), (13, 13), (9, 17), (20, 22), (32, 11), (34, 46), (27, 38), (32, 14), (22, 9), (19, 6), (19, 9), (10, 19), (36, 30), (27, 31), (16, 29), (39, 16), (4, 11), (23, 14), (23, 44), (36, 41), (6, 1), (16, 4), (4, 20), (13, 40), (2, 2), (29, 4), (42, 30), (27, 35), (33, 18), (39, 28), (26, 15), (28, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 39), (28, 30), (13, 28), (7, 20), (0, 33), (9, 20), (14, 17), (28, 38), (7, 13), (34, 23), (43, 8), (14, 28), (38, 0), (39, 14), (11, 8), (17, 0), (43, 22), (2, 37), (24, 29), (25, 3), (29, 0), (15, 37), (12, 40), (21, 40), (26, 2), (36, 15), (23, 18), (22, 32), (27, 2), (7, 11), (16, 22), (41, 19), (7, 17), (24, 15), (29, 34), (1, 6), (8, 36), (6, 40), (16, 34), (26, 4), (6, 15), (39, 9), (0, 27), (32, 38), (42, 36), (34, 35), (13, 41), (29, 40), (23, 25), (36, 6), (12, 15), (24, 4), (24, 10), (0, 36), (7, 2), (43, 13), (2, 13), (21, 7), (16, 27), (30, 34), (8, 23), (40, 15), (15, 9), (20, 33), (18, 22), (4, 4), (0, 10), (19, 0), (40, 26), (31, 22), (38, 1), (47, 4), (43, 17), (20, 30), (26, 28), (10, 15), (30, 27), (36, 5), (34, 5), (9, 25), (24, 9), (45, 30), (47, 31), (30, 6), (39, 1), (26, 11), (0, 35), (15, 8), (36, 1), (38, 28), (47, 9), (8, 22), (7, 36), (38, 36), (32, 6), (12, 39), (12, 30), (26, 25), (36, 16), (38, 3), (1, 12), (19, 1), (44, 12), (33, 39), (2, 6), (7, 37), (33, 33), (40, 36), (18, 23), (37, 3), (25, 34), (11, 14), (24, 13), (37, 7), (5, 34), (15, 22), (37, 31), (26, 8), (16, 11), (30, 14), (36, 39), (41, 3), (20, 19), (1, 23), (16, 28), (25, 19), (3, 36), (38, 30), (28, 20), (43, 12), (2, 9), (25, 28), (10, 24), (28, 13), (8, 14), (33, 9), (18, 8), (37, 32), (3, 10), (8, 28), (12, 27), (6, 35), (7, 25), (40, 17), (32, 5), (13, 36), (22, 25), (35, 23), (4, 6), (4, 33), (26, 14), (7, 9), (31, 23), (13, 24), (21, 13), (36, 34), (4, 0), (47, 6), (19, 32), (7, 34), (35, 1), (10, 37), (7, 41), (3, 19), (33, 7), (7, 3), (26, 20), (5, 23), (33, 12), (46, 31), (43, 0), (1, 37), (21, 16), (15, 31), (20, 11), (8, 5), (22, 23), (43, 19), (36, 4), (23, 29), (24, 33), (7, 6), (23, 21), (17, 19), (6, 30), (17, 40), (44, 40), (23, 30), (27, 5), (19, 15), (21, 37), (11, 36), (28, 15), (18, 3), (42, 12), (30, 28), (27, 20), (46, 11), (44, 13), (39, 21), (5, 25), (47, 13), (12, 8), (24, 3), (34, 2), (37, 17), (27, 40), (24, 16), (13, 4), (34, 10), (25, 36), (37, 15), (45, 2), (12, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 38), (31, 4), (18, 30), (24, 9), (1, 35), (27, 3), (30, 11), (14, 1), (39, 11), (16, 32), (25, 7), (4, 6), (13, 25), (0, 26), (30, 28), (34, 3), (15, 21), (32, 37), (20, 34), (15, 5), (33, 14), (35, 0), (43, 2), (44, 0), (33, 3), (16, 11), (41, 14), (18, 20), (25, 17), (1, 36), (2, 13), (31, 7), (28, 28), (40, 25), (21, 16), (16, 16), (34, 16), (35, 21), (5, 22), (21, 6), (43, 36), (13, 27), (4, 38), (18, 12), (21, 35), (11, 13), (33, 12), (10, 10), (17, 35), (32, 35), (10, 37), (35, 24), (9, 2), (34, 10), (18, 0), (25, 8), (26, 34), (38, 38), (25, 25), (16, 18), (29, 12), (21, 10), (26, 12), (4, 35), (6, 5), (29, 22), (23, 30), (32, 14), (37, 5), (5, 12), (20, 30), (8, 11), (34, 28), (35, 27), (3, 35), (18, 34), (20, 23), (12, 7), (43, 11), (37, 26), (14, 10), (4, 8), (36, 29), (25, 18), (3, 26), (42, 38), (7, 34), (23, 29), (16, 38), (43, 5), (22, 28), (40, 38), (1, 33), (26, 7), (19, 34), (42, 29), (43, 12), (9, 23), (13, 2), (26, 26), (19, 3), (30, 14), (38, 4), (40, 10), (39, 26), (8, 12), (40, 9), (39, 29), (35, 15), (10, 0), (34, 1), (12, 2), (22, 11), (5, 37), (18, 10), (21, 19), (43, 4), (4, 28), (41, 33), (17, 20), (27, 32), (26, 29), (18, 35), (1, 21), (7, 3), (39, 24), (34, 26), (33, 20), (0, 15), (12, 3), (24, 4), (33, 8), (1, 12), (24, 2), (34, 6), (37, 20), (3, 5), (32, 17), (9, 39), (32, 15), (31, 30), (37, 14), (31, 21), (8, 18), (32, 25), (45, 4), (2, 27), (4, 21), (11, 17), (44, 22), (37, 4), (8, 8), (44, 34), (28, 16), (8, 20), (41, 28), (14, 2), (36, 28), (22, 22), (8, 21), (31, 8), (38, 3), (44, 1), (22, 36), (28, 3), (2, 12), (26, 33), (5, 7), (8, 33), (23, 34), (9, 33), (5, 15), (0, 31), (14, 13), (17, 29), (6, 39), (44, 15), (15, 15), (17, 11), (0, 19), (44, 29), (37, 2), (12, 20), (15, 18), (6, 8), (2, 26), (16, 20), (18, 27), (43, 23), (15, 36), (22, 6), (17, 0), (3, 22), (29, 17), (31, 24), (9, 13), (44, 26), (13, 11), (23, 18), (39, 31), (30, 15), (1, 32), (37, 25), (24, 19), (31, 34), (33, 11), (12, 23), (29, 6), (0, 6), (20, 11), (3, 4), (18, 14), (40, 28), (21, 7), (44, 20), (22, 38), (35, 16), (6, 24), (41, 22), (38, 32), (16, 35), (42, 21), (14, 32), (38, 8), (29, 4), (16, 13), (7, 6), (5, 27), (7, 0), (4, 37), (8, 5), (16, 2), (32, 2), (45, 21), (12, 35), (6, 11), (14, 21), (15, 2), (13, 28), (12, 34), (4, 13), (21, 12), (18, 2), (2, 2), (28, 13), (11, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 34), (38, 24), (16, 0), (16, 5), (1, 19), (9, 13), (11, 0), (35, 11), (35, 20), (43, 39), (16, 35), (18, 37), (15, 13), (1, 36), (41, 1), (18, 34), (27, 36), (14, 33), (0, 34), (12, 6), (42, 41), (42, 38), (14, 22), (6, 39), (44, 23), (32, 13), (14, 40), (30, 22), (7, 2), (28, 21), (36, 6), (7, 26), (35, 40), (7, 1), (40, 36), (9, 19), (22, 39), (13, 40), (8, 10), (26, 32), (2, 12), (36, 23), (28, 5), (30, 5), (9, 21), (29, 38), (20, 0), (35, 5), (26, 21), (40, 11), (31, 0), (23, 7), (9, 8), (36, 24), (3, 7), (31, 28), (13, 18), (31, 37), (1, 26), (34, 29), (28, 38), (8, 0), (17, 39), (0, 8), (7, 30), (18, 39), (15, 6), (9, 25), (25, 23), (30, 40), (4, 3), (16, 12), (24, 36), (3, 16), (21, 6), (12, 9), (23, 35), (19, 4), (2, 3), (42, 12), (27, 11), (26, 20), (12, 16), (34, 41), (42, 35), (40, 22), (38, 30), (8, 31), (35, 15), (33, 23), (8, 24), (33, 33), (7, 10), (34, 17), (2, 18), (24, 9), (13, 36), (35, 25), (44, 12), (41, 37), (16, 15), (35, 39), (42, 4), (1, 10), (8, 39), (0, 39), (26, 38), (33, 37), (35, 12), (35, 32), (31, 25), (41, 36), (9, 3), (22, 35), (5, 4), (38, 37), (6, 40), (10, 35), (20, 16), (23, 25), (5, 7), (10, 10), (6, 15), (12, 0), (28, 14), (44, 8), (28, 22), (39, 15), (41, 30), (22, 19), (40, 27), (20, 29), (33, 0), (39, 13), (29, 17), (40, 41), (19, 6), (10, 36), (33, 22), (34, 25), (0, 6), (9, 38), (36, 3), (34, 14), (28, 3), (21, 3), (34, 7), (41, 33), (31, 13), (19, 35), (0, 10), (37, 41), (11, 12), (14, 11), (12, 31), (10, 17), (42, 28), (32, 24), (16, 6), (30, 7), (25, 0), (1, 20), (6, 14), (17, 5), (37, 27), (44, 5), (24, 41), (25, 19), (22, 32), (28, 25), (27, 35), (0, 35), (12, 35), (21, 8), (32, 39), (15, 23), (28, 19), (4, 28), (4, 16), (35, 21), (11, 26), (0, 2), (37, 13), (29, 0), (18, 21), (0, 29), (30, 31), (27, 38), (3, 17), (12, 28), (44, 7), (41, 25), (13, 17), (6, 32), (25, 1), (11, 8), (4, 15), (14, 7), (12, 22), (32, 6), (11, 6), (42, 2), (27, 6), (8, 15), (43, 12), (7, 8), (41, 22), (4, 27), (32, 11), (19, 36), (12, 14), (18, 0), (28, 13), (40, 8), (7, 39), (35, 31), (34, 3), (39, 3), (36, 33), (34, 16), (8, 36), (38, 34), (40, 0), (37, 37), (6, 28), (29, 11), (15, 22), (31, 35), (15, 12), (37, 15), (22, 18), (8, 21), (15, 25), (0, 16), (29, 5), (43, 35), (34, 36), (37, 17), (23, 38), (38, 0), (20, 10), (36, 15), (8, 18), (32, 17), (34, 0), (25, 32), (27, 1), (4, 26), (31, 9), (8, 5), (4, 20), (32, 25), (2, 26), (6, 2), (38, 10), (10, 6), (36, 39), (7, 35), (28, 20), (30, 27), (10, 23), (18, 33), (43, 8), (39, 41), (39, 30), (11, 7), (29, 20), (21, 30), (31, 40), (25, 4), (42, 33), (3, 35), (30, 38), (21, 28), (38, 16), (4, 0), (19, 20), (0, 32), (15, 16), (22, 12), (21, 19), (31, 18), (15, 26), (36, 14), (5, 38), (36, 10), (18, 31), (6, 16), (32, 36), (11, 22), (5, 36), (25, 21), (7, 29), (18, 15), (31, 22), (2, 35), (29, 3), (24, 17), (10, 34), (20, 24), (33, 17), (0, 18), (6, 10), (8, 25), (26, 22), (1, 32), (44, 15), (30, 9), (39, 36), (30, 0), (28, 9), (31, 12), (42, 27), (3, 25), (38, 15), (0, 27), (32, 16), (3, 37), (37, 6), (35, 36), (1, 12), (39, 18), (34, 9), (4, 1), (19, 23), (16, 24), (33, 36), (28, 30), (19, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 14), (21, 39), (19, 9), (33, 13), (39, 25), (24, 39), (29, 23), (32, 14), (8, 35), (21, 12), (26, 19), (31, 31), (1, 29), (42, 4), (36, 15), (16, 28), (39, 0), (5, 24), (31, 21), (34, 39), (4, 2), (11, 13), (29, 31), (19, 23), (29, 6), (28, 36), (32, 30), (43, 37), (40, 10), (42, 14), (25, 35), (33, 6), (35, 11), (41, 27), (11, 0), (5, 32), (39, 35), (35, 37), (3, 17), (38, 13), (37, 25), (9, 7), (27, 26), (19, 4), (23, 30), (38, 6), (30, 28), (5, 14), (33, 33), (4, 37), (19, 3), (29, 24), (32, 5), (35, 35), (33, 25), (25, 1), (23, 31), (21, 7), (30, 2), (15, 4), (33, 28), (26, 30), (42, 16), (21, 28), (15, 33), (26, 1), (40, 13), (23, 16), (30, 5), (33, 20), (18, 26), (39, 8), (6, 29), (5, 35), (1, 21), (31, 17), (10, 12), (27, 8), (25, 27), (10, 29), (43, 0), (20, 8), (2, 39), (27, 2), (24, 30), (9, 21), (9, 23), (43, 19), (40, 22), (22, 22), (5, 16), (27, 9), (2, 24), (24, 20), (8, 7), (31, 7), (20, 4), (13, 36), (36, 2), (5, 8), (37, 37), (37, 18), (36, 32), (33, 29), (10, 10), (10, 6), (27, 39), (13, 1), (39, 30), (0, 6), (11, 19), (14, 2), (40, 15), (38, 0), (7, 0), (18, 22), (39, 15), (12, 29), (4, 10), (38, 20), (29, 0), (24, 3), (4, 4), (14, 34), (1, 25), (41, 32), (20, 30), (1, 23), (2, 32), (11, 26), (0, 7), (29, 39), (15, 1), (17, 33), (11, 31), (17, 28), (12, 3), (32, 25), (16, 1), (16, 19), (14, 6), (0, 17), (0, 23), (22, 8), (28, 9), (24, 25), (6, 33), (34, 20), (25, 11), (25, 16), (34, 4), (36, 16), (41, 5), (41, 7), (5, 25), (25, 23), (33, 39), (21, 22), (37, 29), (31, 36), (2, 27), (10, 28), (32, 13), (16, 31), (25, 12), (13, 25), (39, 27), (9, 1), (4, 11), (38, 29), (32, 38), (10, 15), (6, 34), (14, 7), (8, 1), (18, 9), (19, 12), (33, 1), (14, 32), (10, 11), (7, 4), (3, 12), (27, 4), (6, 31), (38, 7), (35, 28), (36, 14), (32, 4), (16, 39), (25, 7), (7, 1), (20, 29), (32, 39), (21, 27), (20, 37), (21, 1), (32, 3), (27, 11), (33, 14), (28, 28), (6, 17), (12, 21), (5, 23), (29, 34), (30, 25), (3, 5), (21, 30), (23, 27), (30, 33), (33, 26), (34, 12), (3, 27), (34, 30), (30, 20), (40, 4), (29, 27), (13, 24), (12, 23), (11, 30), (36, 20), (21, 25), (28, 4), (20, 33), (8, 34), (34, 11), (2, 15), (29, 9), (43, 9), (30, 32), (43, 8), (23, 12), (25, 28), (33, 4), (7, 22), (0, 20), (42, 33), (10, 16), (2, 25), (25, 30), (42, 6), (27, 33), (6, 39), (22, 23), (26, 39), (24, 18), (15, 27), (29, 38), (34, 6), (19, 38), (8, 9), (34, 7), (35, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 26), (11, 34), (30, 27), (8, 10), (5, 13), (34, 37), (13, 40), (11, 0), (0, 30), (34, 33), (34, 2), (6, 18), (3, 29), (2, 15), (25, 9), (22, 9), (19, 39), (10, 44), (16, 11), (43, 28), (0, 3), (17, 20), (26, 38), (12, 42), (36, 30), (0, 44), (12, 40), (39, 24), (7, 42), (36, 33), (5, 14), (37, 6), (4, 35), (0, 24), (6, 5), (29, 30), (46, 22), (39, 2), (37, 24), (35, 23), (21, 24), (13, 33), (13, 24), (38, 29), (47, 20), (13, 38), (38, 31), (3, 26), (25, 34), (16, 39), (4, 42), (45, 11), (17, 35), (3, 23), (2, 13), (14, 14), (33, 37), (24, 3), (24, 9), (30, 38), (44, 5), (45, 0), (21, 23), (17, 22), (41, 38), (24, 20), (6, 34), (2, 43), (40, 32), (26, 28), (25, 41), (45, 43), (13, 44), (33, 10), (18, 13), (45, 5), (28, 9), (43, 30), (32, 22), (28, 8), (45, 1), (28, 34), (26, 39), (37, 22), (46, 41), (34, 28), (10, 34), (38, 6), (29, 43), (14, 20), (18, 8), (7, 16), (15, 10), (24, 31), (31, 0), (10, 13), (40, 23), (42, 34), (47, 10), (36, 25), (10, 18), (17, 43), (6, 35), (39, 44), (12, 1), (16, 40), (11, 20), (11, 12), (42, 14), (40, 6), (29, 6), (26, 16), (33, 30), (26, 1), (12, 24), (19, 37), (18, 25), (0, 9), (25, 35), (34, 40), (26, 19), (44, 44), (3, 38), (39, 0), (47, 12), (29, 32), (35, 44), (28, 37), (20, 26), (13, 16), (13, 39), (0, 17), (25, 27), (17, 7), (40, 25), (24, 29), (22, 44), (16, 35), (44, 29), (8, 6), (9, 42), (37, 19), (41, 16), (35, 28), (11, 8), (1, 15), (17, 15), (3, 36), (5, 8), (40, 39), (47, 27), (17, 44), (21, 34), (30, 19), (29, 34), (0, 26), (1, 18), (33, 0), (41, 14), (7, 6), (0, 32), (39, 19), (29, 28), (42, 38), (30, 35), (31, 1), (22, 42), (7, 17), (15, 11), (12, 10), (1, 8), (7, 39), (16, 1), (15, 31), (4, 17), (43, 16), (15, 16), (46, 36), (45, 21), (6, 24), (32, 43), (32, 27), (28, 40), (0, 37), (46, 39), (41, 43), (29, 20), (28, 1), (21, 12), (15, 41), (16, 21), (23, 33), (25, 20), (28, 30), (3, 6), (41, 4), (26, 34), (22, 17), (25, 40), (8, 7), (31, 11), (32, 24), (13, 10), (41, 32), (38, 14), (11, 31), (7, 43), (47, 37), (35, 14), (46, 9), (4, 44), (22, 43), (13, 31), (38, 0), (2, 25), (16, 42), (39, 9), (0, 13), (19, 21), (9, 7), (4, 20), (46, 6), (44, 41), (33, 31), (15, 24), (16, 25), (19, 20), (41, 22), (15, 37), (30, 40), (4, 39), (43, 1), (40, 38), (5, 36), (42, 44), (6, 33), (39, 14), (14, 19), (6, 14), (38, 25), (6, 15), (29, 10), (1, 29), (15, 27), (7, 23), (42, 4), (13, 14), (1, 3), (5, 39), (15, 18), (45, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 15), (14, 4), (25, 7), (33, 15), (22, 35), (5, 26), (41, 22), (29, 22), (27, 27), (0, 34), (21, 20), (41, 33), (28, 39), (41, 9), (10, 26), (4, 16), (31, 10), (10, 32), (41, 32), (1, 21), (21, 3), (38, 12), (17, 23), (9, 9), (22, 9), (8, 32), (1, 1), (34, 11), (10, 14), (20, 35), (12, 27), (11, 12), (18, 1), (23, 38), (32, 33), (6, 9), (0, 13), (30, 30), (38, 13), (27, 13), (17, 22), (10, 35), (17, 17), (2, 17), (27, 29), (30, 13), (39, 28), (18, 36), (9, 3), (19, 32), (18, 3), (27, 3), (15, 16), (21, 22), (35, 7), (25, 6), (21, 4), (31, 37), (20, 26), (18, 20), (11, 28), (6, 35), (21, 39), (32, 11), (2, 4), (38, 19), (17, 38), (21, 29), (7, 17), (11, 26), (25, 26), (3, 28), (0, 35), (33, 34), (19, 7), (17, 39), (11, 17), (10, 34), (19, 35), (24, 14), (30, 4), (17, 20), (19, 20), (37, 5), (30, 0), (35, 4), (5, 6), (16, 20), (8, 16), (6, 37), (38, 36), (19, 19), (19, 8), (35, 25), (22, 21), (14, 38), (1, 4), (26, 1), (11, 8), (33, 17), (29, 21), (6, 14), (35, 28), (14, 28), (20, 6), (30, 2), (41, 12), (29, 9), (19, 22), (24, 22), (10, 28), (14, 0), (18, 4), (8, 26), (38, 11), (3, 34), (16, 15), (40, 12), (25, 3), (38, 0), (31, 38), (29, 7), (13, 21), (7, 19), (23, 35), (23, 6), (16, 19), (4, 26), (0, 10), (29, 10), (1, 38), (18, 21), (28, 27), (33, 39), (5, 39), (3, 21), (0, 6), (26, 18), (1, 28), (9, 19), (38, 1), (9, 22), (21, 7), (14, 14), (30, 39), (13, 11), (36, 6), (27, 16), (10, 21), (41, 19), (40, 8), (15, 3), (25, 11), (31, 4), (10, 17), (30, 38), (24, 16), (21, 35), (5, 21), (39, 6), (39, 14), (10, 16), (14, 16), (19, 39), (27, 35), (24, 21), (36, 24), (30, 20), (14, 15), (10, 38), (5, 31), (1, 30), (9, 32), (34, 39), (36, 34), (13, 34), (13, 0), (17, 32), (28, 34), (20, 0), (37, 31), (3, 33), (33, 12), (34, 5), (11, 1), (1, 15), (29, 8), (5, 30), (28, 4), (32, 16), (24, 33), (6, 25), (3, 23), (32, 31), (40, 20), (27, 8), (40, 3), (33, 10), (19, 24), (23, 22), (25, 37), (37, 8), (26, 24), (38, 28), (12, 36), (25, 35), (34, 36), (5, 12), (8, 27), (40, 7), (17, 37), (32, 9), (9, 29), (7, 13), (23, 1), (17, 35), (34, 3), (1, 33), (40, 18), (22, 0), (26, 35), (28, 17), (17, 9), (36, 38), (7, 5), (0, 21), (35, 23), (24, 18), (25, 5), (6, 24), (28, 10), (12, 0), (39, 29), (15, 0), (37, 33), (34, 25), (14, 33), (3, 36), (40, 21), (19, 0), (6, 11), (4, 3), (10, 39), (19, 29), (6, 21), (29, 32), (32, 10), (13, 32), (21, 37), (35, 13), (13, 35), (25, 23), (24, 27), (22, 15), (28, 23), (40, 4), (1, 24), (11, 38), (26, 20), (8, 25), (32, 34), (34, 1), (37, 20), (11, 19), (30, 31), (1, 6), (29, 4), (4, 10), (24, 19), (14, 24), (0, 14), (10, 12), (24, 4), (5, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 10), (6, 23), (22, 18), (17, 24), (45, 20), (31, 24), (5, 22), (45, 5), (29, 25), (17, 36), (39, 15), (23, 2), (16, 18), (46, 7), (37, 38), (39, 36), (23, 8), (5, 33), (30, 35), (9, 9), (9, 28), (8, 15), (30, 29), (29, 5), (37, 28), (10, 4), (16, 39), (28, 33), (16, 19), (47, 11), (16, 25), (21, 9), (3, 22), (34, 21), (6, 14), (19, 25), (6, 31), (17, 26), (1, 23), (47, 25), (32, 20), (5, 24), (0, 8), (36, 0), (39, 29), (0, 6), (8, 0), (4, 30), (25, 39), (5, 37), (10, 0), (24, 13), (27, 19), (36, 33), (15, 25), (24, 0), (36, 39), (44, 1), (47, 16), (8, 17), (18, 26), (3, 32), (46, 8), (9, 14), (28, 24), (45, 39), (30, 31), (42, 6), (48, 23), (26, 28), (33, 30), (32, 17), (18, 27), (40, 30), (8, 7), (7, 27), (15, 20), (0, 29), (31, 12), (25, 27), (36, 15), (16, 31), (45, 7), (8, 11), (33, 18), (0, 12), (17, 37), (13, 22), (19, 34), (48, 14), (34, 15), (16, 12), (13, 19), (2, 36), (30, 2), (32, 39), (1, 36), (37, 35), (34, 13), (46, 17), (47, 28), (11, 17), (23, 3), (4, 16), (16, 3), (44, 0), (22, 19), (34, 16), (39, 32), (38, 33), (30, 34), (30, 38), (26, 30), (5, 10), (18, 11), (44, 30), (19, 20), (26, 16), (15, 30), (29, 14), (31, 22), (24, 4), (12, 21), (22, 9), (43, 16), (28, 7), (40, 38), (36, 5), (42, 19), (36, 36), (1, 1), (2, 30), (12, 23), (0, 10), (6, 20), (15, 6), (25, 21), (8, 23), (16, 23), (36, 8), (45, 14), (14, 4), (43, 31), (3, 11), (40, 17), (1, 27), (39, 24), (6, 11), (26, 3), (12, 17), (1, 0), (12, 24), (37, 16), (5, 25), (14, 34), (28, 1), (48, 33), (11, 21), (32, 29), (35, 38), (23, 20), (35, 29), (44, 8), (12, 0), (2, 11), (5, 31), (12, 13), (9, 12), (43, 21), (3, 3), (22, 16), (38, 2), (19, 36), (17, 15), (4, 11), (28, 30), (16, 22), (45, 9), (35, 20), (11, 28), (40, 39), (26, 21), (21, 12), (31, 20), (2, 2), (47, 19), (37, 17), (18, 39), (25, 4), (31, 31), (17, 9), (2, 32), (24, 25), (5, 1), (5, 13), (28, 0), (34, 32), (13, 16), (0, 20), (21, 36), (14, 10), (40, 19), (21, 10), (17, 23), (1, 16), (4, 32), (23, 30), (16, 9), (22, 14), (11, 14), (27, 15), (23, 0), (10, 14), (21, 4), (19, 23), (48, 28), (27, 22), (4, 25), (46, 32), (25, 31), (29, 8), (7, 9), (7, 5), (0, 35), (48, 11), (15, 27), (17, 4), (11, 34), (39, 1), (36, 19), (46, 29), (5, 36), (19, 11), (10, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 22), (7, 1), (26, 33), (38, 32), (21, 39), (39, 3), (14, 27), (0, 36), (19, 17), (34, 10), (24, 24), (3, 30), (2, 31), (15, 21), (2, 9), (19, 6), (14, 12), (3, 3), (2, 12), (0, 31), (21, 8), (2, 26), (22, 23), (2, 19), (26, 38), (25, 5), (9, 21), (29, 0), (17, 40), (32, 10), (32, 30), (12, 2), (35, 13), (10, 21), (7, 30), (16, 5), (34, 7), (11, 15), (26, 25), (7, 36), (20, 24), (2, 10), (35, 5), (35, 10), (9, 29), (16, 32), (8, 36), (22, 0), (22, 17), (5, 31), (14, 18), (36, 35), (1, 38), (23, 14), (2, 15), (28, 6), (8, 20), (19, 19), (7, 26), (11, 31), (38, 10), (21, 19), (12, 22), (20, 28), (23, 20), (5, 6), (22, 10), (35, 29), (12, 17), (29, 11), (30, 10), (27, 41), (9, 39), (40, 16), (12, 28), (27, 22), (28, 15), (3, 2), (13, 1), (27, 26), (38, 40), (32, 35), (37, 23), (9, 5), (20, 41), (12, 3), (1, 28), (38, 22), (26, 5), (14, 36), (10, 6), (34, 20), (38, 23), (12, 27), (28, 37), (3, 17), (24, 19), (17, 14), (20, 22), (17, 16), (18, 0), (36, 14), (17, 30), (16, 16), (31, 21), (31, 15), (17, 3), (28, 18), (10, 2), (31, 9), (17, 31), (26, 20), (24, 25), (4, 21), (39, 5), (27, 7), (27, 10), (26, 36), (32, 32), (32, 2), (11, 11), (35, 12), (27, 5), (33, 22), (12, 4), (36, 17), (25, 4), (9, 25), (38, 16), (28, 14), (40, 40), (38, 37), (27, 31), (26, 11), (22, 24), (33, 28), (39, 29), (2, 13), (29, 9), (15, 32), (11, 9), (3, 11), (25, 6), (23, 1), (14, 28), (13, 41), (1, 15), (19, 2), (17, 6), (12, 29), (34, 4), (28, 11), (30, 33), (5, 3), (3, 8), (31, 28), (9, 11), (17, 15), (1, 7), (30, 16), (11, 38), (3, 12), (20, 19), (7, 27), (39, 31), (3, 39), (1, 19), (36, 23), (36, 2), (25, 27), (8, 14), (7, 37), (7, 10), (0, 16), (38, 4), (12, 8), (11, 13), (13, 27), (10, 17), (40, 14), (17, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 3), (21, 40), (4, 39), (6, 14), (9, 23), (33, 21), (36, 24), (26, 4), (17, 21), (37, 39), (24, 41), (30, 17), (25, 3), (23, 4), (22, 20), (14, 6), (39, 24), (12, 16), (4, 19), (36, 12), (33, 44), (2, 48), (36, 11), (15, 24), (11, 35), (32, 1), (38, 6), (7, 39), (16, 0), (2, 23), (19, 34), (3, 36), (26, 39), (33, 39), (21, 48), (25, 46), (20, 29), (10, 46), (5, 35), (39, 16), (26, 10), (33, 19), (28, 12), (24, 44), (3, 27), (28, 33), (9, 7), (17, 29), (5, 30), (2, 21), (35, 25), (28, 13), (12, 11), (5, 24), (9, 32), (4, 11), (29, 7), (9, 22), (32, 5), (16, 24), (10, 32), (31, 12), (13, 43), (27, 39), (21, 35), (9, 8), (32, 14), (12, 36), (9, 42), (21, 20), (29, 43), (34, 34), (14, 5), (29, 4), (8, 41), (30, 39), (2, 41), (40, 39), (21, 43), (4, 4), (11, 32), (16, 12), (17, 7), (38, 44), (23, 40), (40, 15), (25, 23), (5, 1), (4, 41), (12, 46), (25, 35), (14, 29), (13, 35), (23, 22), (33, 10), (21, 27), (5, 13), (20, 15), (3, 33), (0, 9), (24, 11), (4, 5), (16, 14), (15, 15), (25, 44), (37, 37), (26, 22), (13, 37), (18, 25), (25, 41), (19, 21), (10, 45), (24, 25), (16, 3), (17, 3), (34, 11), (32, 16), (12, 14), (34, 8), (2, 0), (13, 19), (35, 27), (10, 20), (24, 15), (37, 6), (34, 31), (10, 17), (9, 9), (1, 0), (34, 32), (18, 47), (26, 12), (39, 27), (20, 25), (2, 1), (20, 12), (6, 32), (22, 45), (36, 22), (25, 15), (39, 5), (8, 0), (21, 21), (26, 27), (36, 26), (29, 44), (5, 9), (24, 12), (10, 1), (4, 17), (20, 39), (3, 34), (13, 47), (19, 0), (23, 6), (1, 7), (5, 25), (18, 6), (31, 27), (32, 4), (16, 27), (14, 13), (29, 48), (30, 28), (32, 15), (24, 31), (6, 7), (4, 31), (29, 33), (10, 13), (32, 11), (18, 27), (27, 42), (39, 38), (0, 43), (35, 31), (31, 38), (28, 47), (40, 31), (1, 9), (33, 41), (1, 36), (7, 12), (18, 36), (32, 44), (16, 39), (17, 36), (31, 22), (1, 24), (7, 8), (29, 10), (31, 17), (19, 33), (35, 22), (34, 15), (6, 34), (35, 48), (4, 10), (3, 37), (19, 19), (5, 15), (27, 14), (4, 38), (26, 23), (22, 12), (31, 18), (11, 30), (4, 15), (13, 31), (15, 27), (5, 7), (2, 30), (32, 3), (5, 22), (36, 21), (40, 34), (1, 45), (34, 44), (2, 9), (34, 3), (17, 32), (7, 24), (4, 34), (0, 32), (0, 31), (40, 0), (38, 23), (11, 17), (2, 12), (37, 16), (16, 44), (20, 26), (19, 35), (13, 29), (25, 25), (4, 26), (25, 43), (33, 20), (7, 4), (27, 25), (37, 48), (12, 6), (40, 9), (24, 0), (19, 1), (30, 29), (28, 4), (27, 0), (33, 37), (7, 35), (37, 28), (13, 14), (18, 1), (21, 30), (10, 14), (27, 3), (30, 22), (25, 11), (34, 2), (14, 20), (27, 1), (34, 27), (7, 21), (1, 1), (3, 24), (8, 15), (3, 29), (23, 26), (5, 41), (31, 13), (29, 29), (29, 27), (7, 37), (14, 17), (16, 16), (21, 12), (13, 7), (25, 16), (26, 41), (19, 42), (24, 30), (28, 31), (33, 8), (40, 8), (17, 42), (8, 13), (29, 32), (9, 40), (13, 5), (30, 40), (10, 3), (6, 8), (36, 37), (8, 18), (21, 41), (13, 12), (6, 24), (40, 22), (30, 31), (40, 12), (33, 11), (26, 19), (19, 11), (16, 8), (10, 47), (23, 35), (31, 43), (13, 27), (18, 37), (7, 38), (1, 32), (3, 43), (10, 33), (40, 14), (24, 33), (23, 42), (32, 27), (26, 43), (18, 10), (8, 33), (18, 24), (8, 37), (16, 32), (0, 10), (22, 25), (14, 32), (36, 16), (21, 42), (21, 9), (2, 6), (12, 33), (17, 28), (19, 8), (38, 37), (22, 36), (37, 24), (16, 46), (0, 5), (11, 47), (23, 32), (14, 8), (28, 30), (38, 12), (16, 30), (5, 40), (38, 7), (17, 34), (25, 38), (34, 13), (30, 2), (15, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 27), (34, 39), (7, 44), (32, 6), (3, 10), (11, 18), (19, 7), (45, 10), (29, 24), (3, 33), (14, 39), (30, 29), (40, 3), (12, 32), (21, 24), (41, 22), (37, 12), (39, 43), (25, 33), (27, 42), (41, 13), (33, 12), (19, 15), (40, 8), (47, 25), (24, 36), (7, 17), (44, 7), (31, 27), (40, 30), (29, 39), (39, 18), (42, 35), (32, 12), (1, 19), (18, 45), (25, 46), (37, 39), (2, 21), (44, 23), (40, 11), (9, 25), (2, 16), (20, 22), (33, 0), (33, 46), (7, 29), (7, 43), (0, 40), (22, 9), (10, 35), (39, 21), (36, 20), (36, 29), (7, 42), (17, 46), (26, 48), (27, 45), (38, 1), (24, 43), (27, 10), (35, 45), (6, 28), (35, 46), (42, 8), (14, 11), (7, 18), (17, 33), (13, 8), (9, 15), (25, 26), (19, 21), (31, 1), (34, 21), (24, 4), (5, 15), (46, 5), (32, 0), (8, 14), (36, 30), (2, 43), (44, 37), (2, 18), (5, 38), (11, 14), (20, 47), (12, 34), (20, 32), (1, 0), (30, 9), (5, 3), (24, 15), (34, 47), (43, 4), (13, 30), (9, 13), (22, 48), (28, 8), (28, 13), (11, 25), (26, 4), (32, 37), (37, 4), (38, 16), (3, 27), (2, 41), (13, 33), (23, 34), (17, 20), (36, 38), (11, 46), (22, 33), (34, 15), (12, 42), (44, 30), (19, 26), (17, 39), (5, 5), (29, 3), (22, 22), (12, 13), (1, 46), (23, 45), (32, 38), (18, 36), (30, 28), (36, 19), (3, 42), (42, 32), (37, 40), (20, 7), (16, 46), (37, 43), (16, 47), (46, 23), (0, 29), (47, 39), (28, 39), (14, 0), (36, 3), (24, 16), (22, 44), (28, 16), (0, 37), (14, 25), (44, 34), (40, 32), (3, 36), (24, 2), (18, 9), (5, 4), (19, 14), (13, 36), (21, 9), (21, 36), (2, 12), (26, 3), (20, 33), (8, 46), (32, 10), (14, 37), (1, 42), (3, 14), (30, 27), (15, 39), (35, 12), (9, 45), (8, 4), (25, 15), (30, 45), (26, 28), (25, 19), (35, 24), (21, 16), (23, 47), (6, 46), (43, 26), (32, 9), (21, 6), (41, 24), (36, 39), (12, 39), (24, 48), (41, 37), (32, 41), (23, 8), (11, 40), (14, 13), (9, 16), (0, 16), (46, 10), (19, 25), (13, 1), (4, 45), (26, 13), (13, 35), (7, 35), (45, 5), (35, 3), (40, 26), (41, 15), (1, 34), (41, 35), (41, 41), (43, 20), (34, 12), (19, 45), (3, 35), (23, 32), (30, 38), (37, 29), (37, 38), (39, 39), (11, 15), (41, 4), (28, 24), (39, 25), (43, 48), (38, 34), (6, 34), (5, 45), (16, 19), (7, 5), (47, 33), (22, 43), (39, 46), (35, 37), (12, 35), (3, 32), (18, 31), (16, 26), (42, 46), (6, 3), (32, 7), (39, 44), (34, 29), (33, 14), (29, 31), (29, 42), (22, 27), (39, 34), (14, 19), (14, 24), (5, 35), (41, 48), (44, 17), (39, 22), (19, 27), (29, 18), (24, 9), (24, 45), (27, 7), (9, 39), (43, 47), (35, 20), (29, 47), (4, 19), (2, 15), (39, 20), (34, 16), (42, 1), (44, 15), (46, 46), (24, 42), (7, 46), (29, 21), (21, 37), (0, 28), (34, 28), (13, 10), (37, 45), (40, 45), (2, 28), (23, 35), (46, 25), (32, 29), (3, 11), (24, 10), (18, 29), (9, 18), (8, 21), (47, 21), (2, 13), (14, 29), (46, 38), (23, 27), (19, 8), (16, 39), (11, 24), (46, 4), (21, 27), (30, 43), (40, 29), (27, 9), (3, 47), (47, 32), (36, 37), (42, 36), (35, 1), (2, 0), (3, 21), (43, 14), (46, 42), (45, 1), (8, 38), (10, 27), (17, 22), (16, 3), (35, 38), (6, 37), (2, 36), (43, 13), (17, 9), (23, 20), (40, 35), (11, 4), (17, 21), (1, 45), (11, 22), (36, 35), (3, 43), (13, 32), (41, 23), (22, 39), (42, 45), (9, 14), (42, 5), (14, 27), (32, 26), (10, 41), (35, 11), (25, 40), (25, 38), (17, 26), (34, 38), (24, 26), (1, 13), (21, 39), (27, 13), (26, 24), (21, 2), (4, 25), (0, 19), (11, 3), (44, 18), (22, 42), (47, 2), (9, 0), (38, 24), (6, 19), (14, 30), (47, 10), (25, 14), (10, 48), (8, 39), (8, 23), (43, 3), (3, 0), (27, 11), (8, 30), (20, 41), (44, 10), (11, 17), (12, 37), (44, 43), (29, 45), (37, 33), (18, 13), (15, 32), (35, 8), (33, 38), (2, 40), (31, 35), (16, 14), (22, 46), (22, 38), (11, 9), (31, 45), (35, 34), (26, 38), (43, 18), (5, 47), (31, 30), (5, 8), (0, 44), (42, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 26), (44, 27), (37, 27), (46, 18), (5, 37), (17, 13), (15, 17), (15, 0), (47, 1), (3, 26), (28, 37), (13, 15), (24, 27), (47, 8), (25, 42), (40, 36), (26, 28), (41, 3), (47, 42), (27, 22), (21, 17), (14, 17), (19, 23), (3, 7), (18, 35), (26, 41), (3, 25), (20, 14), (23, 34), (4, 1), (29, 43), (3, 4), (7, 21), (0, 2), (40, 15), (21, 2), (34, 21), (0, 4), (46, 27), (44, 16), (5, 35), (35, 20), (20, 26), (39, 4), (34, 26), (37, 41), (28, 20), (5, 14), (42, 42), (28, 0), (5, 8), (17, 44), (2, 33), (31, 11), (12, 31), (21, 28), (19, 38), (34, 10), (34, 35), (31, 26), (4, 22), (2, 13), (46, 7), (43, 31), (32, 43), (29, 39), (8, 9), (19, 16), (39, 2), (37, 35), (10, 30), (34, 4), (7, 42), (15, 26), (40, 42), (15, 36), (4, 6), (30, 13), (37, 11), (13, 5), (37, 13), (17, 12), (3, 41), (41, 38), (15, 16), (15, 1), (22, 7), (38, 23), (24, 24), (35, 24), (46, 41), (28, 5), (26, 24), (38, 26), (3, 2), (19, 42), (33, 20), (11, 10), (20, 18), (7, 12), (40, 23), (7, 28), (25, 9), (44, 14), (17, 30), (9, 24), (18, 32), (41, 43), (4, 23), (32, 1), (13, 17), (6, 42), (32, 19), (16, 17), (19, 35), (21, 5), (41, 26), (47, 21), (46, 25), (33, 22), (15, 39), (0, 20), (42, 32), (39, 32), (28, 11), (21, 0), (24, 18), (25, 34), (15, 32), (28, 2), (10, 25), (25, 33), (10, 7), (15, 27), (23, 20), (22, 36), (44, 22), (25, 7), (40, 39), (14, 1), (33, 17), (36, 12), (26, 34), (45, 23), (22, 15), (16, 32), (9, 9), (26, 30), (10, 35), (13, 14), (30, 1), (9, 16), (36, 26), (28, 32), (33, 10), (41, 12), (11, 40), (42, 37), (37, 22), (2, 37), (28, 35), (9, 0), (15, 19), (18, 26), (12, 17), (22, 30), (29, 20), (1, 6), (38, 16), (12, 27), (39, 11), (1, 38), (19, 8), (21, 3), (15, 30), (25, 28), (10, 36), (45, 19), (12, 34), (46, 15), (11, 32), (10, 10), (18, 41), (17, 22), (26, 4), (47, 5), (35, 7), (31, 36), (45, 35), (13, 23), (34, 29), (3, 40), (20, 4), (31, 29), (43, 38), (7, 0), (12, 12), (26, 12), (46, 24), (14, 11), (3, 3), (10, 3), (28, 18), (44, 21), (45, 17), (35, 29), (45, 31), (16, 13), (3, 23), (26, 0), (15, 40), (32, 31), (24, 12), (9, 5), (23, 43), (5, 28), (16, 18), (10, 34), (3, 31), (29, 5), (41, 30), (38, 33), (24, 16), (22, 0), (17, 41), (39, 17), (39, 5), (45, 0), (30, 19), (25, 22), (47, 9), (18, 10), (39, 6), (14, 20), (9, 36), (9, 42), (18, 30), (17, 40), (46, 20), (15, 20), (12, 25), (25, 8), (30, 37), (4, 12), (40, 30), (33, 32), (38, 17), (18, 18), (31, 33), (47, 17), (39, 22), (14, 34), (30, 24), (26, 38), (35, 40), (4, 19), (2, 34), (12, 19), (20, 28), (44, 5), (25, 12), (23, 41), (46, 37), (46, 23), (19, 18), (5, 38), (43, 21), (38, 0), (42, 4), (37, 39), (23, 17), (28, 1), (18, 6), (31, 34), (18, 39), (7, 19), (39, 19), (38, 31), (13, 8), (3, 42), (9, 26), (0, 34), (41, 40), (12, 6), (40, 16), (45, 9), (40, 0), (44, 11), (27, 7), (10, 18), (4, 20), (17, 39), (38, 19), (6, 44), (42, 24), (29, 23), (3, 29), (20, 31), (5, 3), (21, 34), (36, 17), (21, 7), (21, 26), (37, 32), (22, 12), (18, 25), (11, 13), (1, 10), (9, 21), (40, 13), (15, 28), (4, 26), (33, 6), (20, 44), (36, 4), (14, 26), (13, 31), (35, 11), (19, 27), (2, 3), (19, 6), (27, 33), (45, 18), (39, 16), (12, 14), (47, 38), (1, 12), (26, 3), (8, 35), (6, 32), (21, 37), (47, 43), (31, 31), (4, 2), (27, 0), (1, 32), (36, 44), (23, 27), (11, 29), (23, 16), (29, 6), (10, 20), (5, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 31), (15, 15), (12, 17), (32, 2), (23, 0), (19, 28), (9, 21), (33, 21), (9, 18), (0, 39), (14, 12), (23, 36), (9, 34), (3, 18), (21, 31), (28, 15), (6, 37), (37, 10), (38, 9), (35, 9), (6, 40), (3, 6), (11, 15), (20, 39), (39, 4), (39, 43), (34, 6), (11, 13), (24, 15), (24, 33), (31, 16), (18, 13), (15, 8), (5, 38), (10, 10), (8, 4), (34, 19), (10, 12), (2, 34), (23, 13), (15, 2), (32, 10), (3, 15), (28, 24), (23, 37), (21, 5), (16, 43), (12, 5), (12, 14), (18, 39), (0, 17), (3, 23), (31, 6), (3, 31), (15, 35), (14, 31), (40, 30), (4, 41), (19, 14), (24, 20), (1, 16), (32, 6), (0, 15), (40, 6), (38, 33), (14, 40), (24, 37), (36, 18), (23, 19), (22, 35), (1, 24), (13, 1), (23, 10), (40, 35), (36, 16), (7, 22), (6, 29), (11, 43), (27, 12), (2, 27), (26, 31), (3, 34), (12, 35), (11, 34), (2, 26), (7, 16), (32, 30), (15, 22), (23, 31), (24, 35), (38, 28), (24, 8), (15, 30), (13, 2), (36, 3), (38, 25), (14, 5), (12, 39), (18, 26), (4, 23), (9, 32), (40, 5), (1, 21), (4, 3), (25, 31), (25, 42), (31, 1), (12, 20), (8, 36), (19, 26), (26, 8), (21, 19), (3, 29), (0, 28), (34, 35), (29, 36), (20, 32), (11, 19), (13, 26), (16, 25), (34, 13), (24, 18), (10, 34), (39, 6), (23, 4), (28, 35), (31, 15), (35, 14), (23, 29), (7, 32), (7, 30), (16, 38), (16, 34), (20, 12), (2, 13), (17, 17), (23, 23), (26, 35), (19, 17), (11, 10), (33, 28), (33, 32), (36, 40), (19, 11), (12, 36), (3, 10), (35, 31), (21, 27), (21, 40), (0, 43), (9, 12), (31, 38), (4, 34), (34, 22), (22, 16), (34, 37), (32, 17), (29, 3), (23, 38), (13, 36), (2, 20), (4, 22), (6, 4), (4, 10), (7, 36), (2, 21), (10, 26), (37, 39), (5, 27), (25, 5), (32, 40), (15, 14), (26, 20), (23, 34), (4, 21), (30, 15), (1, 20), (21, 20), (8, 23), (9, 29), (22, 13), (21, 17), (10, 40), (34, 36), (37, 18), (39, 31), (1, 1), (39, 5), (11, 33), (38, 36), (4, 24), (13, 40), (20, 7), (31, 22), (19, 31), (36, 5), (37, 22), (36, 24), (6, 33), (5, 39), (25, 27), (24, 36), (22, 42), (18, 18), (17, 41), (32, 20), (14, 14), (18, 1), (40, 36), (11, 11), (5, 16), (10, 23), (19, 25), (33, 15), (14, 28), (13, 6), (22, 11), (34, 27), (17, 11), (35, 22), (3, 16), (2, 6), (19, 8), (30, 8), (23, 26), (22, 23), (29, 14), (7, 11), (25, 8), (37, 41), (25, 2), (8, 5), (31, 37), (35, 30), (36, 32), (23, 43), (36, 1), (34, 4), (31, 34), (0, 36), (3, 33), (16, 2), (27, 8), (8, 21), (6, 21), (17, 9), (18, 2), (35, 26), (11, 39), (37, 36), (2, 32), (26, 6), (0, 4), (21, 29), (29, 20), (37, 11), (19, 38), (1, 15), (25, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 39), (1, 3), (36, 7), (27, 36), (25, 23), (41, 2), (27, 40), (39, 36), (19, 42), (25, 37), (30, 18), (38, 6), (1, 36), (22, 3), (31, 7), (25, 38), (8, 11), (6, 24), (10, 41), (40, 37), (7, 6), (2, 20), (20, 0), (24, 18), (33, 8), (0, 15), (23, 8), (16, 10), (40, 15), (35, 10), (18, 40), (42, 30), (13, 14), (25, 8), (34, 36), (27, 12), (9, 28), (5, 23), (2, 4), (36, 38), (0, 23), (34, 29), (13, 4), (23, 29), (22, 31), (32, 21), (0, 42), (7, 7), (2, 39), (23, 22), (35, 11), (33, 30), (14, 1), (18, 17), (39, 3), (31, 20), (12, 22), (7, 15), (9, 36), (30, 11), (37, 34), (7, 5), (1, 41), (1, 30), (8, 5), (8, 10), (8, 39), (16, 8), (40, 41), (4, 27), (19, 24), (1, 14), (15, 25), (26, 11), (18, 23), (30, 26), (11, 36), (28, 2), (39, 39), (4, 20), (33, 9), (18, 3), (6, 29), (3, 16), (20, 2), (42, 9), (15, 41), (14, 10), (14, 8), (23, 40), (21, 38), (30, 38), (35, 38), (34, 30), (5, 5), (24, 3), (8, 19), (18, 6), (40, 4), (5, 17), (6, 39), (37, 15), (5, 38), (24, 23), (28, 8), (13, 1), (34, 19), (10, 42), (2, 9), (24, 9), (12, 21), (42, 2), (12, 35), (41, 39), (7, 35), (11, 32), (4, 41), (29, 30), (12, 26), (20, 27), (34, 24), (42, 13), (37, 39), (41, 0), (5, 40), (23, 2), (14, 18), (2, 3), (41, 5), (34, 42), (22, 34), (4, 23), (24, 29), (33, 24), (12, 18), (16, 21), (31, 17), (10, 32), (37, 6), (2, 7), (33, 1), (1, 19), (28, 42), (20, 10), (29, 17), (6, 4), (15, 17), (18, 20), (40, 19), (28, 3), (32, 8), (25, 33), (16, 15), (19, 40), (4, 7), (14, 9), (39, 1), (33, 0), (3, 24), (36, 37), (35, 21), (25, 24), (26, 13), (19, 32), (32, 16), (18, 5), (30, 27), (22, 10), (33, 14), (34, 37), (16, 29), (24, 24), (11, 14), (11, 8), (40, 13), (34, 3), (41, 30), (12, 25), (0, 18), (21, 12), (26, 36), (35, 12), (37, 21), (10, 33), (9, 31), (16, 41), (12, 31), (8, 33), (33, 31), (26, 31), (7, 1), (11, 21), (3, 42), (27, 10), (12, 38), (32, 33), (34, 8), (16, 28), (25, 28), (31, 13), (6, 20), (10, 31), (10, 17), (25, 34), (22, 38), (15, 4), (37, 7), (16, 19), (36, 18), (2, 25), (10, 4), (15, 34), (2, 32), (20, 33), (3, 19), (13, 5), (20, 25), (36, 6), (26, 7), (7, 9), (26, 40), (35, 24), (3, 22), (23, 27), (31, 29), (34, 35), (36, 14), (12, 27), (16, 24), (4, 26), (30, 2), (29, 22), (33, 15), (17, 28), (10, 16), (19, 20), (14, 7), (15, 32), (20, 32), (42, 24), (17, 9), (18, 15), (31, 14), (41, 38), (41, 16), (36, 24), (38, 26), (30, 35), (27, 17), (28, 14), (16, 42), (9, 15), (27, 42), (42, 33), (11, 22), (16, 2), (28, 31), (36, 16), (12, 9), (36, 28), (10, 40), (4, 39), (29, 8), (11, 16), (31, 38), (7, 34), (6, 12), (26, 8), (3, 7), (7, 22), (35, 22), (10, 19), (39, 10), (39, 29), (2, 36), (42, 5), (11, 3), (13, 29), (34, 16), (9, 12), (3, 10), (1, 42), (4, 30), (3, 18), (4, 24), (18, 11), (26, 28), (22, 40), (14, 6), (42, 35), (10, 14), (38, 3), (17, 4), (11, 4), (13, 36), (21, 27), (18, 10), (31, 25), (31, 39), (21, 1), (29, 10), (39, 37), (5, 1), (29, 15), (39, 14), (7, 33), (16, 31), (31, 10), (22, 22), (28, 6), (14, 39), (20, 9), (3, 27), (35, 17), (27, 24), (13, 15), (35, 33), (38, 28), (17, 14), (26, 2), (40, 12), (18, 36), (28, 41), (1, 11), (14, 36), (27, 35), (6, 25), (25, 14), (17, 15), (20, 35), (41, 15), (32, 19), (32, 9), (5, 14), (11, 13), (36, 12), (5, 10), (19, 41), (17, 1), (15, 40), (12, 15), (40, 5), (25, 30), (26, 29), (31, 18), (38, 17), (8, 23), (13, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 17), (0, 14), (42, 26), (10, 4), (37, 9), (34, 41), (10, 30), (37, 14), (16, 13), (14, 45), (12, 12), (6, 47), (16, 1), (35, 37), (25, 5), (41, 24), (36, 10), (16, 34), (17, 29), (16, 11), (5, 27), (24, 46), (7, 32), (13, 34), (6, 5), (5, 4), (18, 17), (25, 0), (23, 42), (11, 24), (26, 31), (22, 7), (21, 35), (3, 11), (21, 24), (13, 44), (39, 29), (28, 3), (7, 45), (22, 23), (41, 41), (26, 29), (27, 35), (1, 12), (38, 32), (0, 5), (9, 23), (20, 11), (41, 33), (22, 6), (33, 32), (18, 6), (24, 41), (11, 29), (24, 45), (28, 5), (5, 11), (9, 28), (22, 4), (2, 3), (28, 15), (23, 24), (42, 7), (15, 3), (42, 1), (33, 3), (1, 27), (15, 41), (14, 40), (16, 15), (2, 15), (14, 22), (13, 17), (11, 31), (13, 16), (21, 20), (18, 35), (38, 10), (16, 47), (2, 16), (20, 38), (36, 22), (10, 6), (27, 30), (33, 10), (9, 32), (30, 28), (40, 14), (23, 40), (27, 41), (17, 23), (29, 13), (23, 3), (22, 45), (27, 7), (16, 2), (31, 13), (5, 25), (30, 9), (31, 39), (35, 20), (9, 16), (20, 7), (40, 13), (27, 17), (42, 16), (35, 27), (27, 19), (20, 21), (30, 31), (0, 12), (0, 41), (19, 47), (6, 17), (25, 39), (16, 24), (4, 28), (40, 43), (7, 12), (33, 43), (5, 23), (22, 38), (41, 25), (8, 41), (12, 20), (36, 30), (1, 6), (15, 38), (35, 2), (0, 1), (26, 47), (0, 23), (25, 46), (3, 25), (37, 16), (19, 20), (23, 23), (4, 20), (37, 8), (40, 27), (17, 4), (25, 27), (18, 28), (13, 12), (19, 35), (42, 12), (39, 13), (11, 16), (14, 27), (31, 5), (23, 22), (17, 38), (28, 7), (1, 31), (30, 45), (6, 6), (24, 3), (40, 12), (24, 36), (5, 41), (34, 19), (29, 26), (40, 16), (40, 2), (19, 12), (19, 7), (12, 4), (8, 25), (5, 17), (25, 38), (23, 33), (29, 23), (29, 6), (41, 2), (11, 17), (6, 20), (21, 26), (36, 46), (6, 11), (21, 37), (26, 8), (1, 39), (38, 4), (34, 36), (15, 43), (5, 33), (30, 22), (12, 9), (2, 21), (32, 36), (35, 31), (12, 2), (22, 27), (25, 12), (15, 22), (3, 26), (13, 22), (6, 15), (41, 44), (33, 24), (22, 16), (26, 18), (42, 42), (24, 20), (12, 11), (1, 41), (1, 20), (20, 3), (0, 26), (33, 19), (24, 2), (30, 13), (38, 18), (14, 29), (15, 20), (31, 43), (11, 23), (28, 2), (2, 13), (42, 25), (12, 47), (4, 25), (32, 43), (24, 17), (42, 15), (18, 46), (10, 13), (7, 35), (25, 41), (33, 2), (22, 40), (30, 41), (18, 31), (20, 47), (3, 20), (42, 43), (42, 10), (10, 39), (0, 46), (5, 19), (25, 32), (32, 11), (35, 5), (28, 13), (3, 22), (28, 23), (7, 20), (13, 19), (8, 46), (3, 38), (21, 5), (33, 26), (9, 27), (13, 32), (4, 46), (11, 8), (29, 0), (28, 20), (20, 42), (29, 37), (12, 37), (1, 8), (18, 5), (14, 30), (4, 5), (18, 24), (17, 17), (38, 31), (4, 36), (25, 2), (31, 36), (13, 46), (7, 15), (41, 7), (19, 8), (22, 43), (9, 13), (37, 22), (36, 23), (37, 34), (24, 9), (12, 17), (2, 11), (30, 23), (17, 39), (31, 11), (9, 18), (3, 16), (31, 21), (7, 40), (7, 47), (31, 15), (36, 43), (31, 4), (36, 12), (40, 42), (30, 3), (11, 9), (32, 28), (39, 16), (25, 18), (12, 39), (9, 6), (32, 17), (31, 37), (18, 40), (42, 19), (37, 24), (23, 44), (26, 40), (30, 6), (30, 12), (39, 35), (34, 18), (34, 35), (15, 46), (15, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 29), (37, 2), (37, 20), (33, 14), (31, 8), (43, 8), (1, 22), (31, 10), (16, 10), (33, 9), (41, 30), (5, 2), (11, 10), (7, 9), (6, 38), (40, 21), (15, 13), (28, 7), (27, 11), (14, 26), (15, 30), (0, 28), (14, 18), (0, 39), (41, 36), (15, 38), (7, 27), (36, 4), (7, 16), (3, 28), (22, 25), (2, 28), (5, 5), (40, 31), (5, 38), (33, 8), (26, 31), (41, 26), (34, 10), (30, 21), (26, 27), (14, 15), (39, 14), (12, 19), (24, 18), (39, 40), (32, 34), (20, 11), (36, 16), (8, 24), (27, 1), (14, 31), (42, 3), (6, 30), (26, 30), (19, 22), (32, 28), (18, 2), (38, 14), (29, 5), (12, 13), (0, 34), (23, 31), (7, 30), (2, 31), (16, 39), (33, 40), (25, 21), (27, 35), (30, 39), (0, 27), (6, 6), (16, 22), (31, 14), (0, 29), (44, 36), (29, 13), (11, 7), (37, 4), (26, 6), (16, 19), (25, 17), (36, 14), (33, 4), (9, 14), (19, 9), (36, 3), (36, 26), (5, 27), (10, 10), (23, 25), (4, 3), (11, 31), (26, 4), (33, 22), (10, 28), (17, 16), (31, 27), (23, 13), (1, 5), (36, 32), (0, 4), (3, 39), (20, 24), (37, 0), (5, 20), (16, 3), (8, 15), (33, 2), (37, 35), (3, 40), (40, 3), (1, 25), (19, 34), (7, 8), (40, 2), (9, 25), (1, 29), (13, 23), (22, 2), (15, 1), (25, 22), (18, 40), (30, 19), (21, 13), (38, 27), (35, 29), (24, 30), (25, 26), (43, 4), (34, 24), (16, 34), (8, 7), (44, 26), (10, 17), (13, 0), (20, 27), (9, 38), (26, 37), (43, 13), (35, 4), (44, 5), (39, 32), (35, 16), (10, 39), (33, 27), (2, 19), (6, 20), (16, 24), (22, 15), (24, 31), (9, 29), (8, 9), (44, 25), (25, 40), (17, 29), (11, 0), (4, 29), (31, 35), (5, 25), (36, 10), (27, 13), (7, 1), (20, 12), (35, 28), (41, 25), (39, 10), (25, 34), (12, 37), (10, 11), (3, 10), (18, 16), (36, 39), (36, 38), (40, 24), (25, 6), (9, 23), (29, 6), (43, 39), (3, 34), (43, 5), (13, 22), (27, 33), (22, 22), (43, 16), (28, 36), (13, 5), (42, 9), (17, 27), (44, 6), (32, 32), (4, 7), (4, 9), (36, 7), (27, 10), (27, 4), (23, 10), (24, 33), (35, 21), (9, 28), (38, 31), (23, 40), (28, 4), (6, 36), (15, 10), (16, 8), (10, 30), (0, 18), (33, 7), (10, 6), (10, 27), (27, 18), (39, 18), (22, 8), (14, 2), (37, 12), (14, 5), (25, 14), (33, 13), (37, 7), (43, 25), (43, 31), (33, 12), (5, 15), (35, 34), (38, 21), (41, 7), (4, 21), (16, 40), (23, 17), (39, 39), (25, 25), (3, 33), (9, 3), (19, 21), (8, 35), (5, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 13), (18, 15), (46, 28), (1, 36), (48, 6), (12, 12), (1, 21), (32, 16), (2, 6), (2, 1), (28, 11), (42, 8), (37, 15), (20, 20), (37, 2), (25, 24), (35, 28), (35, 23), (41, 14), (48, 2), (3, 38), (43, 25), (6, 22), (24, 2), (12, 19), (2, 11), (10, 16), (33, 39), (33, 0), (1, 23), (5, 12), (48, 34), (33, 27), (0, 3), (30, 35), (14, 3), (30, 21), (3, 20), (33, 28), (32, 37), (23, 35), (7, 28), (38, 39), (44, 3), (15, 21), (41, 37), (37, 29), (8, 9), (0, 35), (31, 37), (44, 6), (1, 30), (12, 16), (38, 37), (39, 39), (27, 9), (7, 29), (37, 1), (14, 10), (5, 17), (48, 9), (48, 31), (23, 39), (28, 28), (46, 29), (31, 32), (33, 1), (2, 17), (46, 17), (3, 15), (20, 4), (24, 14), (19, 38), (11, 24), (12, 21), (40, 24), (1, 27), (39, 4), (19, 34), (18, 20), (39, 30), (14, 16), (16, 38), (23, 10), (40, 19), (8, 39), (6, 31), (34, 21), (9, 39), (13, 22), (41, 24), (0, 28), (34, 34), (29, 23), (23, 37), (35, 7), (18, 8), (30, 13), (41, 33), (25, 21), (16, 5), (27, 23), (30, 4), (31, 25), (31, 6), (23, 17), (18, 32), (41, 27), (36, 18), (34, 16), (32, 35), (6, 15), (48, 27), (45, 15), (15, 12), (21, 13), (1, 1), (33, 20), (37, 24), (33, 24), (43, 13), (48, 3), (29, 14), (5, 3), (5, 15), (25, 30), (31, 11), (1, 25), (20, 18), (41, 10), (2, 31), (27, 5), (23, 6), (13, 0), (45, 29), (27, 36), (26, 19), (41, 38), (14, 36), (29, 22), (2, 0), (12, 1), (12, 10), (15, 24), (44, 25), (10, 19), (0, 30), (9, 3), (38, 13), (23, 0), (40, 38), (30, 17), (25, 38), (30, 14), (1, 8), (25, 15), (29, 27), (27, 16), (29, 15), (36, 28), (32, 21), (13, 13), (20, 9), (39, 33), (3, 23), (45, 38), (6, 28), (1, 12), (21, 23), (32, 24), (35, 27), (17, 3), (23, 15), (18, 3), (31, 17), (37, 20), (48, 24), (16, 33), (31, 12), (38, 21), (19, 5), (15, 37), (18, 6), (47, 4), (10, 31), (3, 0), (18, 2), (40, 26), (40, 37), (43, 15), (30, 9), (9, 2), (19, 13), (40, 23), (10, 11), (38, 29), (47, 33), (32, 12), (34, 12), (22, 7), (37, 36), (2, 39), (16, 1), (10, 9), (3, 2), (22, 6), (8, 7), (24, 23), (35, 34), (34, 19), (36, 22), (19, 14), (34, 5), (2, 5), (25, 32), (4, 11), (25, 33), (18, 21), (12, 14), (36, 19), (39, 24), (14, 9), (23, 24), (7, 15), (10, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 33), (25, 45), (2, 32), (30, 39), (4, 5), (1, 3), (26, 2), (19, 29), (26, 43), (23, 29), (24, 6), (35, 31), (26, 19), (31, 35), (11, 24), (28, 26), (16, 46), (19, 37), (20, 29), (32, 8), (12, 41), (17, 5), (16, 22), (38, 40), (21, 29), (12, 14), (11, 15), (9, 25), (12, 2), (24, 18), (21, 45), (25, 28), (32, 26), (24, 40), (8, 26), (29, 17), (38, 27), (13, 7), (11, 31), (38, 3), (25, 15), (2, 18), (39, 1), (28, 46), (6, 32), (23, 4), (31, 16), (21, 21), (11, 34), (3, 0), (33, 25), (28, 42), (37, 32), (28, 22), (10, 3), (33, 5), (19, 10), (24, 26), (6, 37), (14, 31), (13, 21), (33, 12), (34, 31), (38, 11), (18, 13), (30, 36), (2, 35), (3, 18), (23, 12), (15, 27), (35, 23), (37, 44), (0, 16), (26, 4), (13, 15), (17, 30), (22, 39), (12, 22), (9, 27), (20, 4), (16, 33), (23, 15), (6, 10), (12, 19), (3, 43), (13, 6), (8, 42), (9, 35), (29, 7), (23, 0), (24, 21), (0, 25), (32, 23), (20, 6), (23, 46), (22, 13), (33, 38), (31, 21), (10, 45), (7, 33), (17, 11), (3, 41), (18, 2), (10, 20), (26, 23), (5, 0), (5, 33), (12, 29), (16, 17), (24, 35), (19, 34), (11, 11), (4, 26), (18, 41), (4, 40), (39, 23), (29, 41), (7, 1), (15, 15), (14, 21), (8, 27), (8, 14), (4, 39), (19, 19), (22, 28), (32, 29), (1, 42), (8, 36), (38, 35), (9, 33), (19, 3), (9, 32), (13, 45), (11, 6), (29, 18), (28, 27), (32, 10), (9, 34), (27, 16), (34, 45), (16, 0), (3, 38), (37, 20), (27, 36), (38, 6), (8, 20), (2, 46), (22, 18), (29, 35), (10, 11), (14, 27), (35, 32), (12, 40), (10, 17), (30, 13), (17, 7), (36, 18), (27, 4), (7, 21), (39, 36), (37, 23), (5, 18), (11, 42), (37, 18), (18, 17), (30, 8), (1, 10), (4, 12), (18, 18), (24, 36), (5, 21), (10, 8), (18, 30), (39, 24), (37, 19), (37, 30), (9, 44), (15, 40), (17, 44), (25, 39), (31, 6), (6, 29), (38, 34), (6, 35), (10, 19), (2, 21), (6, 2), (22, 34), (31, 43), (26, 14), (13, 10), (6, 21), (18, 33), (37, 33), (38, 31), (2, 2), (6, 39), (22, 6), (26, 24), (3, 30), (25, 10), (9, 39), (30, 29), (11, 45), (36, 3), (24, 16), (36, 7), (23, 6), (9, 2), (7, 6), (39, 38), (23, 35), (10, 27), (35, 28), (34, 8), (25, 6), (2, 20), (34, 35), (1, 7), (18, 28), (11, 39), (3, 31), (5, 10), (10, 38), (19, 36), (32, 38), (27, 28), (25, 40), (29, 10), (38, 16), (4, 43), (0, 7), (33, 10), (38, 2), (12, 1), (17, 3), (6, 33), (24, 17), (16, 28), (10, 13), (12, 33), (1, 13), (24, 22), (21, 5), (26, 32), (17, 42), (16, 16), (20, 22), (1, 46), (26, 21), (15, 7), (16, 31), (18, 32), (18, 12), (37, 7), (23, 44), (19, 17), (31, 22), (4, 44), (1, 11), (20, 36), (6, 41), (31, 23), (1, 26), (26, 11), (12, 6), (16, 27), (11, 19), (19, 44), (4, 32), (0, 33), (33, 2), (20, 34), (3, 17), (29, 42), (26, 20), (11, 17), (30, 46), (25, 16), (9, 23), (16, 25), (28, 23), (30, 32), (22, 2), (12, 7), (23, 18), (12, 0), (2, 24), (3, 21), (20, 26), (12, 34), (39, 25), (39, 27), (5, 45), (7, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 15), (38, 30), (30, 39), (5, 31), (32, 10), (1, 24), (9, 12), (25, 12), (12, 32), (27, 2), (3, 45), (30, 23), (41, 16), (22, 23), (3, 14), (4, 19), (22, 44), (17, 28), (43, 36), (6, 25), (10, 3), (13, 19), (7, 24), (4, 8), (4, 1), (22, 10), (25, 21), (8, 20), (12, 23), (21, 22), (5, 27), (9, 24), (31, 40), (0, 1), (36, 11), (13, 4), (23, 2), (11, 4), (22, 45), (12, 1), (15, 13), (18, 30), (7, 2), (43, 13), (27, 10), (6, 34), (30, 28), (28, 18), (14, 45), (19, 6), (12, 17), (9, 39), (0, 8), (40, 29), (9, 5), (2, 44), (26, 6), (34, 12), (22, 0), (5, 43), (24, 47), (31, 30), (8, 23), (4, 23), (15, 33), (4, 36), (12, 34), (5, 2), (2, 40), (2, 17), (6, 15), (14, 2), (22, 21), (17, 17), (21, 37), (19, 42), (10, 23), (18, 20), (35, 17), (8, 18), (33, 14), (9, 31), (40, 7), (27, 18), (28, 43), (1, 19), (36, 21), (5, 4), (28, 20), (39, 12), (23, 31), (43, 23), (12, 33), (28, 46), (33, 40), (39, 43), (29, 17), (24, 24), (25, 45), (3, 13), (33, 11), (35, 42), (15, 38), (43, 17), (34, 37), (41, 5), (34, 36), (20, 9), (11, 45), (31, 4), (41, 11), (40, 6), (7, 18), (12, 28), (11, 39), (26, 40), (8, 34), (12, 6), (13, 3), (39, 9), (39, 25), (31, 17), (36, 15), (32, 30), (0, 21), (39, 35), (33, 4), (42, 40), (28, 25), (30, 18), (30, 15), (16, 32), (4, 10), (35, 0), (1, 3), (19, 22), (33, 10), (12, 7), (15, 46), (16, 40), (5, 32), (15, 5), (20, 32), (27, 19), (42, 16), (40, 34), (17, 11), (30, 22), (16, 37), (19, 12), (12, 31), (22, 46), (38, 6), (29, 44), (4, 44), (11, 11), (41, 20), (1, 32), (15, 7), (41, 40), (2, 47), (29, 36), (11, 33), (8, 5), (14, 22), (17, 24), (41, 41), (27, 12), (36, 7), (30, 43), (20, 13), (18, 40), (11, 7), (30, 11), (16, 36), (43, 34), (8, 43), (23, 14), (0, 12), (19, 25), (10, 0), (4, 16), (32, 25), (28, 4), (9, 8), (5, 7), (32, 40), (9, 19), (26, 32), (31, 26), (19, 47), (7, 7), (4, 20), (27, 32), (14, 6), (36, 5), (39, 30), (35, 25), (33, 2), (32, 16), (5, 44), (5, 25), (32, 21), (26, 36), (15, 1), (8, 46), (11, 22), (11, 20), (23, 44), (27, 11), (40, 37), (2, 34), (24, 37), (2, 11), (41, 36), (8, 27), (3, 23), (10, 28), (32, 20), (30, 42), (26, 47), (9, 32), (24, 5), (42, 4), (7, 5), (35, 20), (31, 47), (37, 36), (11, 27), (42, 27), (40, 13), (27, 31), (17, 16), (19, 18), (15, 21), (27, 4), (12, 8), (21, 44), (43, 30), (13, 2), (35, 32), (28, 40), (5, 36), (38, 14), (36, 20), (30, 31), (8, 45), (28, 36), (12, 26), (4, 28), (18, 29), (6, 46), (38, 22), (26, 15), (29, 33), (41, 30), (32, 47), (37, 14), (25, 46), (8, 42), (15, 9), (17, 6), (0, 24), (4, 22), (21, 3), (23, 4), (19, 37), (43, 0), (24, 18), (17, 3), (8, 40), (7, 11), (32, 3), (1, 38), (43, 24), (11, 40), (16, 29), (1, 42), (39, 45), (38, 11), (34, 38), (27, 3), (18, 31), (26, 31), (27, 41), (8, 6), (6, 20), (14, 0), (30, 19), (38, 17), (23, 28), (15, 17), (12, 0), (9, 30), (35, 27), (19, 45), (33, 38), (28, 30), (15, 45), (35, 28), (28, 34), (38, 27), (19, 21), (20, 12), (38, 41), (13, 23), (33, 15), (35, 21), (37, 12), (23, 24), (26, 21), (0, 27), (9, 28), (29, 14), (41, 46), (15, 27), (3, 27), (11, 15), (5, 10), (27, 0), (11, 8), (7, 32), (36, 9), (39, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 27), (12, 6), (8, 6), (12, 34), (9, 37), (33, 16), (42, 19), (17, 27), (26, 22), (20, 17), (8, 19), (3, 19), (33, 37), (7, 34), (31, 2), (11, 25), (12, 3), (9, 9), (31, 5), (10, 3), (1, 1), (18, 34), (24, 40), (5, 18), (28, 39), (36, 2), (6, 8), (35, 4), (38, 35), (16, 3), (12, 23), (9, 38), (10, 11), (9, 21), (4, 17), (21, 6), (25, 40), (4, 42), (12, 26), (27, 12), (14, 14), (22, 13), (1, 10), (38, 7), (14, 10), (30, 13), (20, 10), (4, 26), (41, 16), (12, 1), (11, 14), (25, 41), (24, 30), (30, 18), (39, 27), (19, 10), (11, 22), (25, 32), (41, 38), (11, 6), (38, 40), (42, 26), (38, 37), (2, 22), (24, 29), (20, 4), (26, 17), (18, 7), (17, 15), (5, 32), (38, 8), (37, 23), (23, 10), (19, 18), (31, 14), (37, 5), (1, 2), (5, 29), (3, 31), (5, 23), (8, 14), (2, 18), (31, 36), (5, 21), (13, 10), (7, 18), (6, 42), (12, 18), (7, 17), (20, 25), (28, 30), (42, 5), (17, 6), (17, 30), (13, 13), (0, 12), (22, 32), (14, 29), (0, 1), (13, 21), (22, 39), (31, 33), (20, 2), (4, 27), (26, 41), (1, 42), (34, 8), (20, 33), (31, 39), (12, 33), (4, 20), (32, 21), (37, 19), (7, 5), (24, 16), (6, 22), (35, 2), (28, 40), (12, 30), (42, 15), (35, 30), (40, 42), (41, 12), (39, 5), (13, 19), (9, 1), (1, 15), (19, 32), (40, 24), (41, 7), (13, 22), (14, 11), (40, 15), (1, 5), (24, 33), (7, 0), (40, 8), (23, 27), (19, 20), (22, 40), (2, 34), (11, 15), (11, 32), (4, 7), (17, 38), (22, 38), (25, 27), (40, 23), (2, 3), (36, 29), (31, 41), (22, 29), (18, 41), (19, 11), (21, 30), (30, 31), (39, 41), (41, 30), (33, 6), (36, 34), (22, 11), (29, 7), (4, 23), (20, 39), (28, 23), (13, 31), (16, 13), (18, 16), (15, 21), (33, 35), (25, 4), (41, 41), (42, 28), (40, 41), (7, 30), (38, 34), (10, 18), (0, 20), (39, 42), (31, 32), (10, 37), (13, 9), (15, 17), (22, 9), (10, 28), (25, 1), (10, 12), (12, 2), (3, 42), (11, 37), (1, 11), (18, 36), (24, 28), (34, 4), (37, 27), (38, 19), (29, 15), (5, 14), (39, 6), (8, 25), (14, 33), (7, 16), (13, 5), (41, 0), (2, 17), (32, 31), (9, 33), (19, 14), (0, 42), (7, 2), (7, 10), (23, 1), (1, 37), (18, 9), (4, 6), (3, 22), (2, 1), (14, 18), (32, 41), (4, 36), (12, 36), (39, 39), (42, 3), (15, 26), (24, 36), (27, 30), (17, 11), (37, 9), (23, 19), (41, 21), (28, 7), (29, 38), (15, 35), (6, 4), (39, 18), (4, 1), (6, 35), (36, 27), (40, 37), (20, 34), (9, 2), (15, 4), (41, 3), (33, 11), (23, 23), (28, 17), (6, 31), (14, 6), (40, 32), (40, 16), (29, 29), (9, 32), (2, 11), (2, 19), (42, 13), (23, 17), (24, 23), (3, 17), (8, 23), (28, 41), (34, 17), (35, 41), (16, 9), (36, 16), (33, 0), (39, 24), (28, 18), (14, 21), (4, 18), (38, 28), (35, 27), (3, 5), (40, 5), (6, 38), (2, 36), (11, 8), (27, 0), (28, 15), (41, 13), (37, 12), (25, 39), (17, 17), (41, 17), (27, 32), (15, 23), (26, 9), (18, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 28), (7, 45), (41, 12), (10, 25), (21, 16), (20, 0), (16, 32), (33, 35), (14, 23), (25, 20), (17, 29), (0, 27), (34, 29), (44, 14), (24, 38), (3, 31), (5, 36), (33, 39), (38, 26), (46, 14), (33, 36), (14, 39), (2, 27), (42, 30), (14, 25), (23, 28), (31, 27), (17, 10), (43, 8), (17, 11), (6, 38), (46, 33), (42, 27), (36, 32), (1, 24), (4, 25), (37, 15), (0, 43), (22, 38), (17, 3), (33, 14), (6, 20), (40, 43), (38, 23), (27, 10), (25, 21), (18, 45), (45, 39), (15, 7), (33, 13), (1, 47), (0, 21), (20, 1), (26, 3), (32, 19), (14, 3), (7, 37), (28, 41), (28, 2), (4, 15), (46, 41), (22, 36), (23, 18), (5, 16), (2, 21), (8, 13), (7, 40), (42, 6), (25, 15), (36, 17), (2, 44), (46, 11), (7, 4), (35, 46), (9, 47), (13, 14), (35, 15), (30, 18), (35, 28), (29, 30), (34, 12), (21, 0), (19, 30), (30, 36), (13, 34), (43, 30), (10, 20), (12, 13), (33, 23), (8, 3), (28, 37), (46, 46), (45, 46), (16, 5), (42, 10), (26, 4), (8, 8), (32, 41), (4, 28), (9, 31), (17, 0), (32, 11), (21, 35), (5, 44), (12, 20), (11, 21), (14, 37), (20, 19), (34, 30), (7, 1), (26, 25), (13, 36), (37, 45), (9, 23), (14, 38), (19, 11), (19, 9), (9, 1), (22, 30), (17, 12), (41, 29), (7, 46), (41, 30), (20, 13), (3, 12), (16, 45), (10, 10), (5, 35), (38, 27), (41, 37), (44, 40), (4, 29), (37, 23), (8, 24), (18, 39), (11, 35), (44, 8), (7, 14), (25, 23), (37, 41), (0, 25), (5, 11), (3, 10), (27, 28), (35, 33), (34, 26), (42, 1), (14, 41), (31, 17), (28, 16), (8, 27), (45, 30), (13, 13), (41, 9), (21, 12), (45, 45), (22, 12), (9, 39), (7, 18), (29, 19), (38, 21), (33, 16), (19, 36), (2, 12), (22, 46), (43, 3), (44, 27), (29, 29), (1, 32), (35, 34), (26, 27), (29, 16), (8, 22), (6, 30), (42, 11), (30, 9), (18, 25), (45, 7), (40, 44), (14, 33), (0, 10), (13, 11), (1, 39), (16, 4), (15, 24), (42, 25), (29, 42), (45, 31), (33, 31), (23, 27), (22, 32), (43, 1), (20, 47), (21, 10), (41, 46), (5, 22), (45, 18), (22, 41), (16, 34), (24, 16), (27, 37), (46, 30), (2, 30), (41, 32), (31, 4), (19, 5), (15, 45), (0, 24), (37, 28), (29, 14), (39, 31), (4, 39), (25, 3), (42, 43), (25, 30), (2, 29), (27, 31), (6, 1), (14, 28), (40, 19), (15, 13), (0, 44), (4, 1), (13, 31), (28, 9), (23, 20), (23, 34), (0, 4), (29, 47), (25, 16), (40, 35), (34, 23), (25, 1), (21, 13), (29, 9), (30, 21), (6, 16), (18, 32), (39, 10), (20, 6), (40, 11), (0, 2), (10, 38), (1, 9), (27, 0), (38, 32), (29, 12), (15, 4), (39, 13), (29, 28), (25, 28), (29, 34), (36, 4), (32, 16), (35, 44), (35, 16), (45, 15), (34, 32), (23, 3), (13, 16), (45, 25), (46, 15), (41, 10), (46, 12), (29, 8), (36, 36), (1, 8), (29, 22), (0, 29), (23, 13), (2, 11), (22, 13), (20, 4), (41, 25), (22, 33), (32, 23), (35, 4), (10, 14), (2, 47), (20, 7), (38, 33), (43, 36), (25, 31), (23, 45), (23, 12), (36, 6), (46, 43), (31, 32), (31, 9), (6, 10), (32, 4), (29, 39), (45, 37), (25, 9), (23, 21), (5, 9), (40, 3), (0, 5), (24, 27), (25, 0), (15, 41), (21, 41), (27, 23), (34, 24), (13, 6), (16, 8), (6, 33), (39, 39), (17, 42), (13, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 7), (19, 28), (19, 21), (34, 15), (29, 27), (35, 27), (23, 25), (36, 36), (20, 6), (44, 4), (3, 5), (44, 18), (42, 8), (10, 2), (20, 1), (2, 42), (10, 15), (7, 41), (15, 29), (15, 31), (4, 1), (25, 11), (13, 4), (40, 22), (11, 37), (7, 35), (7, 14), (10, 41), (14, 15), (13, 2), (1, 4), (34, 9), (42, 43), (14, 32), (2, 19), (35, 36), (19, 32), (44, 24), (33, 12), (29, 12), (12, 6), (27, 20), (13, 25), (3, 36), (3, 7), (10, 23), (23, 32), (31, 34), (12, 16), (42, 6), (3, 25), (23, 26), (16, 18), (20, 23), (37, 36), (11, 2), (15, 8), (10, 14), (18, 12), (3, 2), (1, 20), (14, 25), (42, 21), (36, 8), (43, 25), (3, 1), (28, 18), (4, 7), (3, 13), (32, 0), (4, 41), (31, 3), (8, 27), (19, 3), (33, 17), (6, 40), (8, 9), (41, 23), (34, 40), (34, 3), (34, 28), (25, 23), (41, 1), (37, 26), (32, 16), (4, 9), (9, 14), (26, 33), (18, 36), (32, 27), (17, 32), (42, 18), (28, 4), (20, 43), (6, 17), (42, 9), (13, 32), (6, 41), (43, 29), (17, 14), (42, 42), (26, 5), (24, 4), (33, 35), (27, 17), (25, 10), (30, 14), (35, 0), (15, 7), (23, 43), (42, 31), (27, 39), (38, 32), (16, 27), (12, 0), (0, 4), (27, 32), (33, 28), (5, 15), (10, 1), (29, 41), (20, 32), (44, 0), (16, 21), (9, 27), (42, 19), (4, 29), (16, 28), (14, 8), (39, 13), (4, 19), (15, 13), (0, 30), (16, 22), (44, 36), (36, 24), (27, 23), (7, 22), (31, 37), (23, 31), (13, 33), (32, 7), (36, 25), (37, 33), (1, 6), (30, 28), (40, 3), (35, 33), (16, 16), (18, 17), (2, 25), (16, 14), (26, 30), (38, 37), (18, 15), (7, 2), (34, 26), (28, 32), (2, 39), (26, 1), (3, 38), (31, 40), (10, 34), (19, 25), (0, 9), (21, 34), (7, 32), (2, 13), (5, 3), (2, 41), (30, 26), (42, 36), (10, 8), (14, 36), (27, 34), (37, 1), (37, 25), (1, 39), (15, 34), (19, 34), (4, 22), (27, 41), (7, 36), (29, 39), (6, 14), (4, 39), (16, 37), (20, 28), (5, 8), (19, 5), (13, 21), (34, 38), (4, 21), (19, 4), (9, 15), (3, 18), (5, 31), (13, 29), (42, 11), (19, 26), (9, 32), (10, 24), (32, 10), (24, 2), (41, 21), (30, 3), (27, 36), (32, 33), (37, 24), (30, 2), (3, 27), (13, 38), (16, 8), (12, 13), (29, 10), (7, 11), (4, 11), (31, 13), (36, 12), (16, 25), (10, 21), (20, 11), (22, 38), (16, 15), (38, 8), (15, 21), (28, 43), (5, 1), (19, 13), (0, 3), (3, 43), (41, 35), (39, 34), (28, 11), (34, 4), (27, 9), (23, 14), (19, 30), (42, 27), (6, 22), (26, 0), (16, 26), (38, 40), (27, 8), (21, 1), (13, 27), (17, 0), (30, 33), (22, 31), (28, 31), (8, 34), (32, 20), (20, 12), (9, 17), (42, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 15), (26, 16), (22, 26), (5, 14), (36, 13), (8, 22), (25, 25), (8, 11), (27, 7), (20, 19), (33, 17), (5, 3), (12, 18), (12, 9), (19, 32), (36, 4), (6, 42), (27, 16), (37, 21), (29, 45), (38, 6), (21, 20), (8, 16), (16, 2), (32, 0), (25, 20), (26, 9), (12, 33), (21, 16), (33, 37), (39, 21), (9, 31), (29, 44), (14, 14), (42, 46), (20, 32), (38, 21), (39, 39), (37, 26), (2, 35), (18, 42), (30, 37), (17, 36), (28, 44), (12, 3), (13, 34), (29, 23), (24, 45), (40, 35), (20, 21), (20, 26), (5, 19), (13, 42), (6, 17), (1, 45), (1, 31), (17, 34), (13, 33), (11, 2), (0, 16), (33, 18), (5, 43), (35, 14), (6, 2), (21, 3), (24, 37), (18, 20), (2, 38), (24, 36), (41, 41), (5, 31), (10, 45), (35, 32), (26, 18), (42, 37), (19, 15), (36, 30), (8, 8), (4, 13), (9, 43), (28, 5), (10, 14), (3, 17), (42, 5), (14, 5), (17, 13), (31, 17), (39, 20), (14, 22), (10, 43), (5, 39), (27, 46), (8, 12), (20, 35), (41, 5), (35, 27), (5, 1), (22, 13), (10, 23), (10, 5), (4, 10), (15, 29), (30, 45), (36, 28), (43, 17), (28, 26), (24, 12), (39, 31), (17, 27), (24, 28), (43, 31), (0, 27), (32, 41), (34, 36), (20, 5), (6, 5), (2, 17), (17, 41), (4, 9), (28, 12), (26, 39), (30, 19), (11, 38), (3, 15), (41, 32), (43, 26), (19, 1), (17, 11), (41, 23), (18, 35), (23, 25), (43, 11), (35, 22), (25, 39), (8, 24), (7, 11), (13, 31), (36, 17), (40, 11), (0, 36), (18, 32), (22, 35), (16, 23), (30, 38), (22, 43), (34, 38), (22, 27), (35, 35), (8, 0), (23, 8), (40, 17), (3, 29), (2, 14), (19, 40), (5, 36), (43, 13), (35, 36), (9, 44), (4, 7), (15, 17), (0, 20), (8, 26), (43, 22), (10, 30), (22, 34), (6, 26), (43, 5), (41, 31), (18, 33), (15, 18), (31, 18), (11, 36), (38, 14), (31, 29), (11, 10), (24, 14), (29, 31), (27, 45), (25, 1), (2, 4), (16, 20), (2, 13), (19, 2), (10, 1), (14, 40), (25, 30), (40, 14), (21, 38), (21, 7), (4, 31), (29, 8), (38, 25), (5, 21), (4, 34), (3, 28), (40, 42), (34, 27), (0, 31), (37, 10), (36, 37), (30, 20), (8, 15), (9, 37), (19, 0), (27, 4), (23, 27), (37, 6), (1, 37), (1, 7), (23, 9), (28, 8), (18, 16), (13, 21), (16, 14), (6, 16), (12, 34), (38, 10), (23, 2), (36, 34), (1, 1), (28, 10), (40, 5), (19, 39), (41, 19), (3, 2), (29, 27), (31, 41), (7, 7), (33, 30), (17, 37), (14, 9), (20, 38), (6, 9), (11, 30), (5, 24), (29, 25), (0, 34), (0, 43), (36, 0), (2, 26), (16, 17), (43, 35), (2, 41), (29, 11), (23, 19), (11, 31), (15, 27), (27, 12), (34, 19), (18, 3), (34, 7), (9, 27), (12, 6), (11, 26), (20, 10), (24, 6), (43, 6), (6, 7), (21, 31), (19, 20), (24, 35), (22, 4), (13, 4), (32, 20), (35, 15), (9, 1), (5, 46), (12, 12), (13, 7), (28, 14), (17, 12), (32, 37), (5, 30), (9, 12), (7, 20), (19, 34), (15, 7), (26, 21), (37, 36), (25, 9), (40, 8), (37, 22), (12, 38), (30, 17), (34, 46), (30, 44), (26, 17), (37, 25), (19, 16), (40, 45), (4, 23), (4, 42), (28, 19), (23, 13), (35, 42), (39, 36), (1, 2), (15, 11), (14, 32), (19, 12), (39, 12), (27, 9), (24, 43), (18, 13), (23, 12), (16, 46), (0, 46), (18, 45), (27, 27), (19, 43), (40, 6), (23, 10), (43, 32), (17, 39), (41, 12), (12, 26), (12, 13), (3, 22), (14, 12), (24, 31), (37, 0), (34, 39), (14, 27), (9, 18), (37, 2), (36, 42), (6, 23), (24, 11), (3, 36), (29, 34), (4, 15), (28, 33), (29, 9), (29, 17), (25, 45), (14, 7), (27, 18), (5, 20), (23, 11), (20, 12), (1, 33), (24, 42), (18, 40), (8, 31), (36, 38), (31, 3), (8, 35), (19, 23), (23, 29), (28, 39), (40, 23), (24, 16), (33, 14), (21, 37), (12, 40), (0, 2), (13, 28), (16, 21), (19, 17), (22, 38), (25, 7), (31, 46), (29, 4), (31, 15), (22, 10), (16, 9), (5, 2), (24, 34), (40, 18), (20, 30), (13, 38), (17, 5), (3, 8), (30, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 11), (41, 40), (41, 14), (15, 36), (30, 9), (17, 5), (40, 36), (29, 3), (34, 6), (36, 17), (23, 4), (36, 7), (12, 32), (18, 6), (37, 6), (15, 10), (28, 18), (8, 4), (10, 8), (6, 26), (40, 19), (2, 8), (5, 21), (29, 36), (12, 14), (4, 21), (21, 0), (23, 43), (38, 29), (6, 17), (6, 18), (0, 28), (17, 21), (34, 38), (4, 30), (22, 32), (41, 0), (8, 7), (2, 24), (4, 33), (36, 10), (16, 26), (1, 16), (10, 28), (19, 47), (31, 1), (12, 31), (31, 36), (4, 14), (36, 6), (17, 42), (12, 15), (42, 2), (40, 25), (20, 25), (37, 4), (40, 9), (8, 6), (24, 44), (0, 20), (18, 16), (8, 9), (35, 10), (28, 33), (19, 4), (12, 20), (0, 12), (3, 22), (23, 40), (42, 41), (32, 37), (7, 34), (5, 17), (29, 43), (25, 36), (1, 19), (33, 12), (5, 11), (31, 23), (13, 7), (7, 43), (39, 4), (25, 9), (11, 35), (20, 16), (2, 6), (24, 30), (29, 26), (13, 20), (28, 43), (20, 24), (26, 41), (41, 44), (18, 26), (23, 3), (40, 27), (42, 23), (12, 35), (28, 40), (31, 26), (18, 7), (37, 15), (7, 22), (30, 46), (26, 21), (33, 44), (6, 45), (17, 17), (29, 28), (3, 10), (2, 38), (3, 35), (17, 25), (13, 0), (24, 32), (39, 16), (7, 25), (0, 34), (31, 24), (10, 32), (21, 22), (22, 41), (15, 7), (16, 6), (27, 5), (10, 20), (24, 47), (25, 2), (28, 45), (38, 6), (42, 45), (3, 47), (40, 39), (30, 14), (36, 34), (21, 27), (0, 38), (13, 34), (24, 20), (41, 39), (39, 1), (20, 9), (6, 8), (20, 6), (14, 32), (5, 41), (15, 24), (34, 7), (0, 24), (15, 16), (3, 34), (39, 17), (30, 23), (36, 47), (18, 21), (26, 2), (0, 1), (12, 16), (22, 17), (28, 25), (2, 5), (25, 15), (17, 27), (18, 3), (25, 5), (24, 7), (26, 24), (39, 2), (40, 4), (40, 26), (38, 37), (19, 2), (7, 37), (26, 47), (16, 18), (8, 22), (26, 13), (10, 30), (9, 4), (4, 13), (36, 46), (35, 41), (16, 11), (25, 43), (23, 38), (39, 31), (21, 10), (28, 38), (6, 38), (30, 18), (33, 10), (40, 21), (13, 37), (24, 16), (8, 45), (9, 34), (6, 35), (26, 15), (4, 39), (31, 27), (25, 29), (0, 2), (2, 44), (8, 15), (12, 21), (7, 10), (3, 30), (36, 9), (23, 20), (37, 12), (8, 23), (37, 27), (7, 1), (41, 22), (4, 8), (11, 29), (10, 27), (39, 37), (33, 18), (27, 17), (32, 26), (11, 43), (3, 45), (40, 11), (19, 26), (14, 29), (4, 20), (37, 36), (6, 22), (1, 9), (26, 16), (12, 34), (5, 28), (42, 5), (1, 21), (14, 46), (33, 2), (6, 41), (27, 41), (37, 35), (17, 30), (24, 24), (41, 3), (5, 31), (19, 24), (15, 46), (23, 41), (7, 31), (7, 5), (30, 3), (18, 1), (0, 19), (20, 14), (18, 25), (41, 16), (34, 35), (32, 22), (38, 4), (1, 40), (35, 17), (0, 16), (11, 13), (7, 40), (37, 45), (40, 1), (34, 23), (8, 18), (0, 18), (24, 14), (25, 17), (39, 40), (7, 21), (28, 28), (37, 37), (37, 39), (6, 9), (28, 16), (37, 23), (24, 2), (27, 2), (22, 5), (39, 13), (17, 36), (15, 34), (25, 34), (4, 22), (15, 29), (8, 1), (19, 6), (38, 28), (11, 17), (20, 36), (10, 0), (26, 14), (42, 8), (29, 41), (25, 18), (30, 21), (1, 18), (38, 34), (25, 21), (10, 37), (25, 40), (35, 38), (18, 18), (23, 23), (29, 32), (1, 36), (38, 3), (27, 39), (41, 23), (32, 28), (8, 13), (38, 35), (6, 11), (20, 4), (21, 39), (36, 14), (33, 5), (21, 1), (39, 29), (1, 45), (26, 29), (32, 7), (23, 8), (31, 12), (24, 34), (15, 0), (8, 20), (3, 23), (35, 22), (9, 8), (3, 6), (1, 25), (35, 5), (15, 11), (40, 2), (23, 21), (39, 44), (42, 11), (34, 30), (14, 23), (20, 33), (42, 44), (29, 20), (3, 24), (2, 4), (36, 11), (23, 35), (17, 28), (41, 7), (35, 43), (21, 36), (17, 6), (19, 22), (38, 32), (4, 12), (25, 41), (7, 20), (28, 41), (0, 22), (9, 36), (40, 6), (1, 15), (10, 5), (24, 3), (17, 44), (25, 8), (16, 25), (26, 5), (16, 39), (3, 32), (5, 32), (7, 7), (10, 34), (33, 22), (17, 4), (8, 47), (7, 27), (12, 6), (41, 18), (30, 16), (18, 45), (16, 37), (36, 5), (35, 21), (18, 30), (34, 2), (37, 46), (28, 23), (8, 10), (13, 47), (25, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 15), (26, 0), (15, 37), (7, 11), (7, 2), (0, 20), (30, 26), (17, 0), (31, 25), (38, 20), (5, 33), (18, 6), (37, 18), (19, 1), (8, 23), (9, 8), (21, 6), (12, 17), (11, 8), (38, 13), (14, 27), (13, 15), (8, 36), (40, 36), (7, 9), (30, 20), (21, 31), (1, 42), (26, 31), (4, 12), (38, 29), (17, 20), (39, 32), (9, 38), (30, 36), (40, 27), (5, 4), (22, 33), (17, 16), (6, 36), (34, 23), (41, 30), (6, 31), (20, 38), (24, 13), (39, 23), (27, 6), (37, 26), (10, 21), (13, 2), (10, 18), (34, 1), (23, 39), (14, 38), (14, 5), (1, 40), (28, 32), (40, 33), (15, 25), (13, 40), (7, 29), (29, 11), (18, 27), (7, 7), (40, 3), (31, 39), (31, 41), (6, 17), (14, 20), (5, 17), (22, 35), (23, 31), (27, 38), (26, 26), (6, 40), (2, 18), (20, 29), (20, 9), (21, 36), (35, 12), (25, 16), (35, 39), (14, 41), (32, 37), (4, 27), (25, 0), (2, 2), (23, 34), (36, 21), (23, 18), (36, 3), (25, 38), (32, 31), (20, 41), (16, 5), (2, 42), (3, 13), (36, 8), (7, 30), (22, 3), (16, 31), (2, 0), (32, 2), (31, 40), (9, 25), (11, 34), (33, 28), (5, 36), (4, 4), (11, 33), (11, 21), (34, 30), (35, 25), (26, 36), (32, 20), (28, 6), (21, 4), (25, 15), (24, 26), (6, 21), (29, 5), (39, 35), (10, 8), (21, 16), (22, 15), (11, 30), (28, 7), (24, 28), (37, 0), (36, 36), (41, 4), (3, 7), (20, 31), (30, 4), (37, 28), (39, 31), (37, 32), (29, 37), (22, 26), (39, 40), (5, 10), (3, 22), (29, 40), (28, 5), (4, 11), (40, 40), (0, 13), (27, 36), (23, 6), (18, 21), (22, 30), (6, 3), (5, 37), (37, 16), (36, 32), (0, 31), (18, 8), (31, 20), (23, 36), (27, 41), (18, 12), (23, 19), (33, 39), (21, 14), (27, 31), (27, 1), (2, 15), (19, 35), (24, 2), (27, 4), (15, 4), (7, 0), (15, 16), (11, 7), (15, 26), (10, 11), (29, 17), (22, 11), (21, 20), (35, 10), (4, 19), (24, 39), (1, 27), (10, 29), (8, 9), (37, 17), (9, 13), (0, 16), (5, 9), (17, 40), (12, 32), (12, 34), (41, 12), (25, 3), (18, 38), (7, 8), (29, 1), (0, 33), (36, 11), (1, 17), (1, 36), (34, 29), (13, 31), (13, 17), (19, 25), (39, 0), (27, 23), (24, 8), (0, 2), (27, 20), (5, 14), (6, 7), (39, 3), (1, 0), (20, 35), (13, 30), (0, 25), (30, 19), (3, 6), (29, 2), (31, 22), (12, 39), (5, 23), (41, 17), (26, 15), (21, 15), (6, 20), (14, 4), (36, 19), (28, 14), (11, 36), (34, 41), (29, 35), (26, 8), (14, 19), (25, 23), (31, 4), (38, 7), (8, 15), (17, 5), (14, 13), (16, 11), (9, 32), (5, 40), (21, 42), (2, 12), (29, 25), (38, 22), (14, 32), (36, 16), (10, 22), (38, 26), (10, 12), (20, 34), (32, 18), (24, 36), (18, 2), (35, 18), (26, 33), (18, 7), (13, 38), (23, 3), (32, 34), (21, 28), (0, 39), (40, 31), (2, 40), (19, 33), (28, 38), (14, 8), (33, 36), (8, 40), (41, 24), (37, 29), (25, 8), (2, 31), (34, 35), (18, 1), (1, 28), (40, 18), (17, 15), (31, 31), (19, 27), (26, 4), (40, 20), (7, 20), (34, 34), (32, 4), (24, 31), (5, 7), (22, 28), (0, 7), (15, 36), (36, 1), (16, 9), (18, 26), (38, 41), (34, 11), (19, 23), (6, 26), (34, 33), (6, 15), (11, 4), (3, 1), (23, 40), (19, 36), (24, 16), (37, 5), (40, 4), (9, 30), (13, 9), (37, 3), (10, 38), (30, 31), (26, 9), (16, 23), (8, 32), (0, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 0), (42, 31), (9, 26), (28, 28), (33, 31), (37, 3), (39, 40), (33, 41), (14, 29), (20, 7), (28, 8), (19, 8), (37, 33), (30, 36), (36, 25), (20, 21), (36, 1), (20, 3), (21, 6), (27, 8), (27, 7), (36, 5), (36, 18), (38, 37), (14, 14), (22, 35), (26, 36), (9, 0), (9, 29), (39, 36), (7, 37), (25, 38), (27, 14), (10, 12), (25, 34), (21, 21), (28, 15), (3, 13), (18, 16), (28, 32), (8, 30), (24, 30), (20, 6), (2, 18), (28, 36), (22, 40), (22, 3), (7, 3), (12, 33), (33, 17), (24, 32), (5, 17), (40, 39), (30, 4), (27, 40), (32, 31), (23, 11), (28, 6), (15, 34), (9, 10), (40, 11), (7, 16), (0, 18), (26, 24), (4, 27), (11, 1), (42, 34), (24, 23), (7, 1), (26, 18), (37, 8), (12, 17), (34, 18), (39, 34), (37, 18), (22, 15), (34, 34), (18, 21), (40, 37), (26, 15), (20, 36), (41, 21), (20, 15), (3, 12), (25, 10), (29, 32), (42, 27), (29, 37), (25, 23), (38, 4), (19, 33), (20, 23), (21, 35), (3, 27), (4, 38), (18, 32), (35, 17), (32, 20), (4, 7), (22, 25), (39, 22), (32, 34), (13, 35), (7, 33), (12, 25), (25, 25), (4, 25), (10, 13), (19, 39), (40, 32), (0, 28), (43, 21), (39, 18), (11, 22), (31, 13), (34, 1), (41, 20), (16, 8), (19, 24), (17, 32), (26, 33), (33, 21), (23, 16), (14, 27), (40, 9), (38, 11), (23, 23), (28, 5), (24, 28), (38, 34), (22, 0), (23, 39), (24, 21), (31, 19), (4, 18), (24, 27), (0, 36), (42, 14), (31, 14), (40, 13), (5, 24), (32, 27), (40, 40), (43, 35), (25, 11), (38, 3), (36, 27), (40, 20), (21, 27), (9, 12), (17, 28), (29, 0), (32, 30), (9, 20), (40, 16), (9, 34), (17, 18), (9, 4), (42, 23), (28, 22), (32, 16), (41, 0), (32, 33), (32, 17), (32, 39), (32, 14), (5, 26), (29, 38), (2, 8), (6, 25), (4, 33), (19, 3), (18, 4), (5, 28), (43, 17), (7, 9), (17, 34), (22, 9), (39, 37), (19, 40), (31, 25), (5, 21), (14, 37), (3, 29), (19, 16), (27, 36), (13, 4), (21, 29), (3, 25), (15, 7), (2, 10), (30, 40), (22, 23), (42, 20), (17, 30), (2, 1), (41, 14), (6, 37), (7, 30), (41, 39), (3, 15), (43, 40), (7, 17), (40, 24), (35, 33), (18, 6), (37, 25), (15, 10), (43, 4), (6, 40), (0, 9), (8, 11), (24, 8), (10, 11), (33, 6), (19, 12), (27, 0), (39, 23), (1, 35), (15, 1), (21, 0), (22, 8), (35, 13), (6, 22), (17, 19), (17, 4), (2, 39), (30, 34), (30, 41), (3, 32), (22, 30), (37, 13), (12, 22), (14, 16), (3, 22), (21, 28), (33, 14), (5, 19), (34, 28), (16, 18), (24, 25), (31, 30), (41, 27), (11, 2), (24, 9), (29, 36), (16, 19), (16, 10), (14, 1), (27, 33), (24, 19), (40, 26), (9, 19), (13, 36), (2, 40), (20, 29), (8, 23), (14, 26), (37, 39), (33, 27), (6, 16), (8, 5), (18, 14), (23, 20), (31, 32), (8, 3), (7, 31), (5, 34), (33, 39), (17, 1), (40, 29), (39, 38), (33, 33), (6, 24), (31, 37), (20, 12), (15, 21), (30, 28), (33, 7), (35, 10), (0, 8), (30, 26), (19, 23), (15, 36), (16, 24), (41, 3), (12, 15), (34, 10), (38, 2), (20, 22), (4, 20), (24, 13), (32, 12), (2, 38), (33, 2), (28, 17), (29, 11), (2, 33), (37, 27), (34, 32), (13, 34), (28, 37), (38, 16), (36, 21), (19, 36), (18, 8), (5, 36), (17, 14), (36, 23), (34, 13), (16, 11), (23, 32), (41, 11), (17, 11), (30, 18), (36, 41), (31, 35), (38, 30), (28, 26), (17, 17), (33, 0), (13, 25), (6, 1), (20, 27), (5, 4), (6, 17), (14, 25), (18, 27), (33, 38), (6, 12), (35, 5), (38, 17), (7, 32), (3, 8), (1, 7), (2, 6), (2, 34), (34, 5), (18, 30), (0, 12), (19, 27), (12, 14), (22, 6), (31, 2), (10, 6), (38, 12), (36, 29), (35, 25), (28, 23), (30, 22), (8, 32), (20, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 20), (42, 32), (0, 8), (8, 34), (10, 26), (33, 16), (6, 24), (36, 28), (34, 28), (28, 30), (19, 15), (24, 35), (35, 1), (5, 42), (21, 4), (27, 43), (7, 42), (0, 19), (21, 42), (45, 18), (34, 37), (25, 38), (35, 17), (17, 11), (43, 30), (22, 11), (32, 33), (39, 21), (12, 20), (44, 15), (21, 8), (7, 15), (43, 37), (0, 38), (34, 21), (44, 32), (10, 42), (14, 11), (17, 18), (4, 17), (22, 7), (20, 32), (0, 40), (40, 34), (12, 10), (9, 21), (41, 8), (34, 36), (35, 37), (4, 0), (18, 31), (9, 8), (42, 34), (11, 44), (30, 28), (11, 2), (34, 2), (13, 36), (38, 26), (24, 24), (2, 19), (33, 25), (45, 35), (29, 28), (20, 18), (19, 14), (18, 15), (32, 15), (33, 38), (34, 10), (18, 44), (31, 1), (18, 9), (6, 16), (27, 12), (3, 1), (7, 33), (3, 24), (26, 11), (40, 43), (39, 16), (17, 29), (30, 22), (41, 18), (8, 38), (25, 31), (27, 3), (32, 14), (35, 23), (33, 1), (5, 12), (41, 22), (25, 40), (4, 35), (41, 17), (33, 41), (40, 19), (33, 4), (25, 15), (41, 38), (45, 22), (14, 0), (9, 11), (33, 19), (12, 22), (38, 2), (14, 43), (9, 29), (0, 39), (8, 10), (35, 22), (6, 7), (41, 7), (5, 30), (14, 17), (9, 20), (29, 0), (24, 40), (43, 6), (9, 43), (43, 23), (0, 7), (44, 36), (2, 12), (3, 31), (12, 0), (22, 28), (39, 31), (43, 43), (28, 11), (36, 42), (29, 15), (5, 4), (34, 4), (12, 19), (12, 38), (2, 24), (10, 46), (20, 34), (5, 18), (9, 9), (34, 34), (10, 33), (23, 26), (8, 24), (41, 16), (7, 13), (7, 34), (44, 33), (29, 9), (17, 34), (43, 35), (33, 26), (0, 32), (33, 10), (45, 21), (44, 25), (5, 21), (24, 0), (37, 40), (22, 30), (14, 39), (1, 1), (29, 16), (11, 3), (43, 12), (35, 8), (39, 6), (28, 26), (21, 21), (42, 4), (27, 27), (41, 15), (25, 23), (38, 7), (15, 21), (33, 40), (29, 25), (8, 28), (34, 31), (9, 7), (7, 25), (32, 38), (3, 13), (26, 1), (7, 6), (3, 15), (28, 34), (38, 15), (43, 16), (7, 32), (20, 7), (1, 26), (33, 23), (7, 3), (19, 25), (10, 17), (17, 27), (0, 6), (2, 21), (7, 29), (45, 17), (37, 4), (11, 1), (6, 3), (5, 14), (45, 34), (45, 36), (1, 27), (7, 28), (3, 3), (27, 13), (17, 8), (21, 9), (1, 46), (45, 15), (45, 4), (20, 13), (15, 29), (2, 9), (22, 5), (11, 45), (8, 27), (33, 33), (26, 10), (1, 20), (1, 32), (8, 19), (31, 2), (18, 11), (18, 7), (0, 23), (31, 46), (4, 16), (21, 16), (2, 13), (2, 32), (20, 2), (45, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 13), (3, 8), (17, 7), (1, 31), (31, 0), (37, 6), (27, 29), (20, 16), (14, 13), (29, 4), (27, 11), (22, 35), (2, 38), (6, 16), (29, 27), (24, 17), (24, 25), (15, 27), (25, 22), (35, 7), (31, 18), (19, 28), (4, 0), (36, 5), (23, 3), (24, 14), (30, 25), (7, 32), (27, 18), (17, 11), (11, 9), (12, 0), (10, 2), (19, 27), (21, 5), (5, 18), (1, 10), (31, 11), (27, 5), (27, 40), (25, 24), (10, 20), (24, 8), (30, 18), (29, 10), (38, 3), (7, 14), (32, 3), (12, 30), (1, 21), (26, 2), (36, 31), (4, 39), (7, 11), (28, 2), (32, 15), (35, 35), (4, 27), (19, 16), (2, 28), (8, 24), (23, 34), (30, 29), (21, 12), (5, 35), (18, 0), (10, 8), (29, 8), (23, 19), (6, 24), (16, 38), (34, 29), (24, 1), (12, 12), (10, 10), (17, 12), (24, 33), (16, 13), (37, 27), (18, 34), (4, 24), (8, 14), (2, 30), (35, 26), (8, 36), (0, 9), (10, 32), (26, 20), (22, 14), (8, 34), (12, 17), (7, 9), (8, 31), (10, 11), (6, 37), (3, 35), (13, 20), (25, 4), (19, 18), (22, 13), (27, 27), (7, 15), (5, 22), (4, 6), (36, 10), (6, 34), (0, 21), (4, 23), (31, 33), (29, 31), (15, 22), (12, 31), (4, 10), (33, 3), (23, 17), (4, 40), (5, 33), (12, 24), (19, 6), (24, 40), (3, 32), (33, 35), (3, 4), (24, 28), (25, 37), (13, 14), (38, 9), (18, 9), (18, 8), (2, 36), (26, 13), (21, 23), (2, 14), (39, 21), (19, 24), (31, 35), (36, 18), (5, 26), (22, 8), (2, 12), (31, 22), (28, 30), (1, 17), (23, 10), (15, 10), (1, 6), (21, 10), (16, 11), (9, 4), (2, 11), (10, 27), (34, 11), (2, 5), (23, 33), (30, 21), (0, 17), (29, 20), (34, 32), (16, 27), (29, 1), (26, 22), (16, 9), (32, 25), (5, 30), (14, 29), (33, 12), (4, 36), (17, 39), (4, 31), (28, 14), (17, 30), (22, 24), (36, 39), (14, 27), (21, 19), (24, 36), (23, 18), (6, 22), (10, 3), (22, 26), (32, 17), (32, 10), (18, 32), (9, 22), (20, 23), (39, 10), (5, 31), (21, 29), (17, 13), (8, 38), (10, 36), (2, 21), (6, 0), (0, 24), (37, 11), (6, 14), (13, 19), (30, 16), (35, 25), (12, 20), (15, 30), (12, 11), (19, 33), (15, 35), (6, 1), (26, 30), (19, 3), (26, 5), (1, 28), (20, 7), (14, 3), (36, 22), (6, 23), (24, 2), (29, 40), (19, 23), (39, 1), (17, 15), (6, 33), (26, 24), (38, 11), (35, 14), (38, 39), (15, 2), (16, 26), (32, 27), (30, 23), (11, 26), (14, 33), (37, 38), (20, 33), (36, 12), (12, 10), (7, 38), (6, 28), (15, 28), (14, 7), (27, 4), (38, 30), (20, 13), (32, 28), (13, 6), (34, 40), (21, 27), (9, 19), (24, 30), (14, 22), (39, 11), (16, 19), (18, 3), (16, 1), (25, 5), (0, 29), (3, 6), (14, 9), (16, 7), (28, 10), (27, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 15), (6, 31), (34, 22), (23, 9), (27, 23), (32, 28), (1, 28), (27, 35), (6, 2), (10, 8), (12, 36), (4, 28), (3, 28), (19, 17), (36, 17), (38, 40), (23, 3), (29, 40), (31, 16), (1, 9), (4, 20), (33, 13), (8, 35), (11, 0), (16, 6), (2, 17), (32, 15), (30, 36), (30, 1), (32, 4), (11, 10), (8, 28), (30, 8), (38, 4), (3, 40), (7, 19), (15, 37), (7, 7), (29, 7), (2, 14), (13, 28), (27, 18), (18, 0), (15, 39), (14, 30), (11, 38), (34, 33), (0, 35), (33, 38), (31, 20), (1, 4), (15, 36), (22, 35), (37, 32), (1, 39), (24, 25), (30, 14), (37, 26), (38, 2), (19, 31), (22, 1), (23, 40), (26, 35), (8, 10), (16, 5), (38, 23), (26, 30), (36, 7), (21, 38), (7, 32), (34, 9), (22, 13), (5, 36), (31, 17), (34, 6), (38, 1), (20, 29), (16, 29), (6, 28), (18, 3), (17, 8), (13, 1), (34, 5), (16, 20), (37, 22), (26, 9), (36, 2), (10, 15), (38, 11), (2, 8), (16, 10), (16, 9), (19, 5), (28, 30), (26, 39), (1, 25), (4, 23), (31, 11), (4, 8), (35, 39), (37, 4), (19, 18), (21, 36), (32, 23), (13, 18), (0, 18), (8, 13), (26, 22), (13, 8), (26, 29), (37, 29), (24, 29), (14, 33), (29, 33), (14, 37), (18, 14), (33, 30), (25, 30), (36, 5), (23, 13), (3, 35), (37, 38), (17, 25), (5, 9), (19, 22), (34, 31), (4, 15), (12, 2), (38, 3), (4, 6), (23, 10), (26, 0), (6, 17), (18, 4), (30, 3), (37, 31), (2, 33), (5, 3), (36, 0), (0, 5), (33, 24), (35, 35), (10, 40), (36, 25), (23, 4), (20, 2), (37, 30), (21, 11), (11, 24), (2, 3), (16, 32), (15, 6), (10, 33), (9, 4), (22, 39), (14, 7), (8, 25), (20, 32), (8, 14), (14, 34), (25, 5), (35, 36), (24, 36), (24, 39), (25, 33), (35, 32), (10, 24), (5, 21), (20, 36), (6, 9), (21, 5), (36, 33), (39, 5), (30, 30), (38, 35), (34, 30), (28, 8), (21, 7), (13, 34), (16, 7), (30, 34), (3, 39), (34, 2), (36, 40), (38, 16), (37, 40), (21, 14), (29, 9), (9, 29), (19, 40), (4, 38), (13, 5), (31, 35), (23, 27), (22, 7), (32, 36), (25, 16), (39, 35), (18, 30), (28, 14), (29, 19), (36, 29), (31, 36), (9, 3), (32, 31), (37, 19), (8, 21), (14, 24), (23, 26), (36, 31), (21, 6), (34, 34), (34, 35), (16, 40), (15, 8), (33, 17), (15, 32), (30, 24), (28, 5), (6, 36), (38, 25), (1, 30), (12, 35), (31, 19), (32, 18), (37, 28), (14, 9), (38, 37), (30, 28), (8, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 18), (21, 5), (34, 29), (9, 8), (38, 7), (1, 6), (5, 30), (43, 36), (22, 34), (33, 21), (29, 42), (22, 26), (7, 31), (16, 22), (37, 14), (10, 0), (13, 9), (14, 7), (9, 9), (9, 23), (16, 16), (15, 40), (32, 25), (4, 19), (17, 3), (42, 36), (6, 32), (28, 12), (26, 36), (24, 32), (19, 4), (39, 19), (11, 36), (17, 11), (4, 0), (30, 7), (20, 9), (21, 23), (21, 18), (41, 10), (30, 27), (28, 27), (10, 16), (2, 6), (14, 30), (24, 17), (7, 33), (27, 6), (23, 8), (20, 19), (12, 13), (9, 24), (4, 14), (29, 41), (23, 39), (7, 25), (10, 40), (9, 10), (20, 2), (40, 37), (24, 16), (24, 41), (31, 22), (25, 17), (20, 36), (26, 0), (21, 4), (32, 15), (28, 11), (21, 21), (27, 1), (5, 9), (24, 15), (7, 13), (36, 22), (17, 7), (12, 42), (23, 0), (3, 42), (27, 4), (18, 22), (12, 12), (23, 37), (42, 20), (31, 41), (34, 22), (5, 39), (30, 20), (22, 8), (9, 33), (11, 30), (18, 15), (17, 14), (12, 6), (24, 42), (41, 29), (18, 10), (36, 1), (7, 2), (25, 35), (26, 1), (2, 17), (22, 37), (34, 43), (22, 16), (25, 16), (40, 29), (26, 11), (40, 41), (2, 20), (8, 36), (10, 39), (24, 22), (15, 0), (27, 22), (13, 0), (43, 2), (22, 0), (9, 26), (32, 19), (5, 5), (23, 17), (7, 38), (31, 1), (4, 42), (43, 15), (35, 35), (38, 17), (19, 42), (19, 30), (25, 22), (14, 34), (26, 6), (9, 2), (8, 17), (23, 13), (10, 14), (25, 29), (7, 15), (32, 30), (7, 32), (33, 34), (34, 1), (36, 43), (11, 17), (17, 36), (39, 12), (28, 0), (39, 1), (42, 18), (38, 16), (29, 17), (41, 7), (43, 35), (18, 8), (22, 4), (1, 15), (14, 29), (22, 5), (5, 12), (29, 23), (26, 25), (3, 21), (40, 2), (4, 15), (36, 35), (19, 27), (31, 3), (20, 3), (11, 8), (7, 23), (38, 27), (13, 6), (13, 41), (32, 28), (4, 8), (39, 24), (15, 13), (20, 1), (36, 40), (3, 6), (18, 41), (35, 33), (30, 35), (42, 10), (22, 7), (11, 20), (33, 29), (31, 33), (38, 31), (39, 10), (3, 17), (33, 2), (28, 41), (29, 29), (43, 28), (11, 16), (21, 13), (10, 30), (33, 17), (2, 18), (39, 16), (21, 15), (8, 41), (7, 30), (36, 17), (14, 17), (11, 19), (25, 34), (30, 4), (27, 33), (42, 43), (38, 40), (23, 26), (24, 5), (6, 41), (13, 10), (30, 30), (19, 21), (41, 42), (41, 8), (28, 30), (6, 4), (40, 0), (5, 13), (38, 34), (38, 39), (12, 22), (21, 41), (35, 43), (23, 28), (0, 28), (29, 40), (42, 4), (39, 11), (11, 34), (15, 41), (33, 22), (19, 22), (10, 18), (43, 17), (15, 32), (23, 20), (1, 36), (19, 35), (40, 13), (6, 37), (43, 41), (6, 1), (19, 26), (19, 31), (41, 17), (4, 26), (41, 16), (41, 3), (32, 9), (11, 14), (19, 43), (30, 19), (36, 31), (14, 22), (19, 23), (4, 31), (4, 12), (37, 19), (0, 37), (24, 39), (6, 16), (16, 15), (35, 37), (16, 26), (10, 43), (27, 28), (8, 21), (37, 2), (3, 15), (23, 1), (32, 12), (21, 38), (20, 29), (27, 23), (12, 7), (1, 27), (29, 14), (0, 26), (31, 15), (6, 7), (10, 7), (8, 20), (23, 10), (37, 12), (31, 19), (43, 30), (32, 20), (7, 17), (38, 8), (35, 4), (15, 2), (8, 37), (15, 15), (12, 23), (34, 8), (16, 31), (43, 13), (2, 7), (40, 4), (21, 35), (10, 26), (34, 41), (25, 12), (29, 24), (27, 25), (32, 6), (9, 1), (24, 43), (2, 36), (37, 33), (34, 6), (34, 15), (43, 29), (12, 35), (6, 10), (40, 34), (17, 39), (42, 6), (24, 20), (20, 20), (21, 1), (29, 9), (38, 35), (19, 2), (30, 36), (14, 24), (27, 17), (19, 7), (27, 21), (35, 5), (27, 35), (2, 33), (4, 28), (23, 14), (31, 6), (43, 25), (0, 8), (29, 12), (32, 17), (3, 37), (10, 19), (33, 39), (26, 22), (14, 2), (34, 18), (33, 43), (12, 21), (1, 40), (15, 14), (29, 10), (42, 19), (35, 20), (13, 26), (35, 27), (19, 1), (38, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 30), (35, 0), (2, 5), (37, 33), (22, 20), (33, 7), (14, 27), (23, 27), (11, 15), (27, 42), (14, 44), (5, 19), (27, 9), (15, 8), (22, 42), (27, 44), (30, 19), (33, 33), (5, 1), (13, 24), (17, 2), (4, 44), (35, 34), (38, 31), (8, 19), (5, 20), (24, 2), (5, 26), (3, 42), (27, 37), (33, 35), (25, 20), (40, 41), (29, 19), (12, 2), (40, 28), (13, 27), (4, 9), (35, 14), (8, 41), (12, 35), (19, 9), (18, 30), (1, 9), (28, 23), (21, 5), (1, 12), (10, 40), (34, 30), (5, 47), (23, 31), (11, 44), (31, 24), (3, 36), (4, 34), (17, 3), (4, 17), (13, 6), (34, 35), (16, 25), (22, 12), (14, 35), (6, 43), (36, 43), (13, 9), (16, 6), (14, 6), (37, 39), (4, 43), (34, 0), (29, 34), (14, 42), (3, 14), (25, 28), (21, 34), (14, 17), (16, 0), (37, 43), (9, 16), (9, 32), (2, 37), (28, 36), (17, 26), (29, 20), (29, 36), (5, 4), (11, 20), (30, 8), (1, 31), (34, 41), (15, 13), (28, 42), (21, 41), (39, 3), (13, 22), (38, 0), (35, 36), (34, 17), (38, 28), (18, 5), (28, 8), (25, 6), (36, 18), (12, 28), (17, 23), (3, 39), (17, 9), (33, 12), (10, 19), (13, 29), (32, 44), (31, 21), (3, 40), (28, 43), (30, 6), (22, 18), (30, 45), (22, 27), (38, 16), (31, 6), (32, 19), (0, 33), (12, 47), (8, 21), (22, 0), (13, 45), (9, 29), (13, 4), (10, 32), (2, 22), (26, 31), (14, 3), (40, 16), (15, 6), (2, 40), (20, 23), (2, 1), (28, 9), (37, 37), (34, 15), (7, 36), (3, 15), (22, 41), (19, 36), (24, 31), (22, 10), (25, 21), (1, 45), (0, 27), (37, 28), (40, 1), (1, 37), (21, 20), (34, 29), (19, 11), (27, 1), (12, 21), (39, 45), (11, 36), (5, 18), (9, 18), (32, 9), (22, 44), (40, 30), (13, 0), (9, 28), (38, 24), (31, 39), (22, 29), (7, 35), (37, 17), (24, 14), (17, 30), (24, 25), (4, 18), (31, 17), (17, 18), (36, 47), (23, 8), (36, 45), (27, 8), (25, 37), (17, 6), (37, 27), (40, 5), (8, 38), (24, 12), (2, 20), (10, 30), (39, 33), (2, 9), (37, 42), (1, 33), (2, 27), (27, 27), (19, 23), (25, 8), (19, 22), (28, 14), (6, 41), (15, 20), (1, 46), (29, 29), (26, 33), (7, 28), (15, 46), (24, 0), (9, 13), (5, 38), (10, 47)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 4), (42, 18), (14, 30), (13, 35), (22, 29), (37, 23), (42, 39), (37, 31), (42, 12), (2, 28), (30, 25), (12, 11), (35, 25), (25, 27), (15, 1), (8, 32), (24, 18), (28, 16), (42, 19), (7, 34), (20, 39), (39, 38), (44, 31), (9, 22), (21, 42), (36, 13), (44, 10), (1, 29), (3, 30), (39, 8), (10, 35), (5, 24), (8, 4), (43, 12), (40, 33), (7, 12), (15, 42), (11, 7), (24, 19), (9, 3), (17, 7), (23, 16), (4, 21), (4, 1), (24, 23), (20, 19), (3, 10), (36, 8), (42, 41), (6, 6), (9, 10), (15, 14), (32, 30), (24, 39), (42, 40), (2, 14), (3, 15), (6, 36), (9, 32), (21, 32), (13, 29), (8, 29), (2, 13), (30, 6), (29, 16), (1, 1), (3, 13), (14, 38), (17, 24), (33, 19), (19, 11), (30, 7), (11, 4), (31, 10), (22, 34), (18, 25), (19, 13), (15, 0), (8, 8), (4, 26), (19, 33), (31, 34), (31, 37), (18, 39), (10, 23), (24, 22), (40, 23), (38, 21), (33, 31), (44, 34), (10, 12), (13, 38), (36, 39), (30, 33), (41, 28), (35, 21), (32, 0), (32, 32), (29, 7), (34, 35), (1, 10), (38, 41), (22, 35), (30, 5), (33, 14), (18, 21), (28, 21), (41, 15), (32, 25), (34, 37), (30, 11), (32, 33), (17, 3), (41, 20), (24, 4), (25, 34), (32, 40), (16, 8), (8, 19), (35, 32), (4, 22), (25, 15), (17, 22), (11, 10), (0, 28), (38, 23), (14, 14), (31, 21), (12, 22), (42, 8), (34, 2), (17, 8), (1, 22), (11, 8), (36, 29), (34, 29), (0, 20), (16, 38), (6, 18), (24, 25), (11, 33), (45, 14), (33, 20), (31, 0), (27, 14), (22, 15), (31, 6), (35, 36), (30, 39), (11, 40), (30, 24), (20, 40), (1, 13), (39, 17), (2, 39), (14, 6), (36, 16), (43, 14), (37, 36), (24, 36), (14, 16), (38, 33), (22, 8), (21, 31), (17, 41), (24, 32), (23, 38), (31, 24), (40, 7), (31, 2), (44, 33), (37, 24), (6, 1), (29, 22), (24, 27), (17, 4), (26, 11), (4, 37), (31, 36), (41, 2), (3, 8), (36, 31), (20, 41), (16, 19), (27, 35), (24, 33), (1, 18), (29, 32), (17, 30), (19, 6), (4, 16), (17, 42), (3, 9), (41, 18), (33, 29), (30, 20), (27, 1), (22, 6), (14, 36), (22, 31), (28, 39), (3, 33), (14, 12), (44, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 45), (7, 5), (10, 32), (28, 10), (32, 12), (15, 12), (9, 48), (30, 35), (19, 13), (6, 25), (20, 4), (17, 12), (22, 45), (21, 0), (17, 14), (10, 37), (13, 8), (15, 37), (21, 32), (18, 23), (26, 22), (7, 24), (3, 41), (8, 47), (15, 43), (4, 38), (35, 2), (16, 2), (5, 34), (7, 13), (36, 42), (24, 13), (8, 6), (17, 18), (34, 14), (2, 22), (3, 8), (27, 6), (32, 34), (37, 12), (20, 5), (28, 33), (32, 2), (40, 45), (20, 25), (14, 42), (19, 14), (19, 19), (7, 2), (18, 20), (19, 16), (13, 11), (25, 34), (23, 40), (19, 24), (27, 16), (17, 10), (29, 37), (31, 5), (4, 42), (11, 28), (14, 22), (30, 31), (24, 15), (15, 40), (0, 16), (1, 33), (26, 43), (14, 14), (20, 23), (12, 3), (5, 12), (37, 33), (34, 27), (33, 19), (5, 25), (19, 41), (23, 21), (22, 4), (2, 33), (10, 45), (31, 3), (16, 15), (38, 33), (8, 1), (0, 10), (8, 9), (39, 41), (40, 19), (24, 1), (34, 40), (26, 0), (38, 26), (32, 45), (22, 2), (31, 31), (36, 0), (34, 22), (29, 20), (33, 10), (30, 43), (24, 23), (21, 12), (28, 26), (39, 45), (28, 31), (36, 8), (26, 38), (1, 43), (14, 28), (40, 4), (10, 47), (13, 48), (10, 13), (28, 18), (20, 17), (7, 34), (31, 30), (17, 8), (13, 17), (13, 29), (27, 44), (16, 47), (5, 36), (22, 23), (35, 18), (32, 47), (39, 48), (40, 14), (35, 23), (17, 4), (26, 3), (10, 35), (19, 22), (17, 36), (10, 3), (25, 30), (22, 27), (0, 15), (6, 37), (25, 8), (22, 31), (18, 10), (28, 11), (40, 20), (11, 29), (31, 39), (27, 18), (25, 36), (24, 19), (38, 23), (37, 18), (17, 39), (39, 7), (22, 40), (15, 48), (6, 42), (21, 16), (1, 38), (0, 24), (39, 8), (29, 11), (19, 1), (13, 13), (31, 22), (22, 11), (8, 2), (33, 18), (21, 1), (24, 20), (9, 26), (12, 13), (18, 13), (27, 19), (28, 17), (23, 38), (20, 43), (15, 16), (12, 40), (12, 33), (23, 0), (8, 3), (9, 9), (5, 32), (29, 8), (21, 47), (30, 14), (22, 46), (33, 45), (3, 39), (33, 47), (3, 29), (16, 14), (29, 17), (28, 1), (6, 17), (2, 26), (32, 38), (11, 17), (35, 43), (21, 31), (40, 42), (1, 40), (14, 32), (1, 41), (5, 14), (11, 33), (29, 2), (4, 23), (30, 42), (33, 1), (9, 4), (3, 4), (30, 26), (19, 36), (8, 34), (30, 36), (11, 42), (34, 5), (37, 25), (25, 24), (33, 14), (0, 20), (7, 29), (20, 31), (3, 22), (39, 35), (20, 41), (9, 18), (15, 17), (17, 19), (28, 30), (2, 15), (28, 15), (14, 16), (17, 46), (37, 22), (7, 14), (38, 39), (28, 6), (17, 41), (21, 14), (21, 26), (9, 31), (6, 8), (35, 38), (18, 38), (9, 21), (35, 37), (8, 11), (1, 2), (20, 12), (30, 33), (20, 9), (37, 24), (17, 42), (38, 37), (12, 17), (0, 38), (33, 38), (28, 0), (17, 40), (1, 20), (15, 0), (34, 45), (19, 26), (10, 26), (0, 45), (38, 43), (21, 15), (34, 20), (36, 20), (20, 10), (32, 29), (12, 29), (17, 1), (37, 10), (10, 29), (32, 24), (1, 13), (2, 23), (9, 34), (32, 1), (33, 15), (9, 0), (24, 41), (5, 18), (2, 24), (28, 7), (9, 32), (12, 5), (38, 5), (19, 12), (33, 3), (14, 2), (38, 14), (26, 21), (36, 30), (29, 14), (35, 30), (33, 26), (2, 43), (25, 32), (4, 36), (34, 36), (34, 17), (14, 35), (33, 23), (19, 7), (20, 1), (28, 21), (3, 0), (20, 34), (35, 33), (4, 16), (14, 44), (27, 4), (12, 0), (1, 19), (3, 20), (18, 5), (30, 45), (10, 17), (26, 1), (29, 47), (6, 43), (27, 8), (6, 20), (11, 38), (9, 14), (36, 34), (33, 29), (14, 38), (36, 43), (15, 6), (16, 23), (7, 43), (38, 22), (12, 16), (15, 22), (27, 20), (6, 7), (24, 4), (4, 3), (5, 9), (6, 6), (3, 5), (6, 30), (34, 16), (13, 22), (18, 8), (13, 41), (23, 26), (15, 1), (27, 26), (5, 19), (28, 13), (8, 23), (11, 7), (4, 13), (20, 24), (5, 27), (39, 13), (5, 11), (22, 35), (9, 38), (9, 8), (40, 28), (3, 38), (29, 43), (25, 33), (40, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 2), (9, 33), (38, 10), (16, 11), (29, 13), (9, 24), (6, 29), (0, 22), (39, 18), (9, 6), (4, 33), (31, 8), (31, 14), (41, 25), (30, 15), (10, 7), (25, 25), (11, 1), (7, 32), (14, 21), (16, 39), (16, 22), (14, 7), (44, 29), (26, 30), (32, 31), (19, 19), (12, 11), (29, 17), (44, 4), (17, 26), (10, 11), (35, 0), (13, 18), (28, 25), (34, 30), (43, 38), (37, 23), (42, 29), (18, 19), (12, 4), (44, 25), (4, 38), (0, 3), (36, 21), (16, 24), (30, 14), (8, 38), (34, 38), (33, 25), (22, 5), (40, 19), (26, 5), (12, 37), (8, 37), (44, 33), (14, 9), (34, 32), (29, 4), (20, 11), (44, 20), (24, 31), (10, 21), (31, 10), (30, 25), (5, 28), (30, 26), (9, 9), (12, 27), (16, 5), (0, 17), (36, 31), (5, 30), (27, 25), (19, 39), (10, 25), (30, 1), (2, 29), (43, 10), (28, 26), (0, 11), (17, 36), (8, 13), (4, 11), (20, 28), (18, 2), (34, 35), (29, 28), (5, 13), (30, 38), (30, 17), (30, 37), (34, 8), (10, 14), (32, 29), (44, 22), (8, 1), (0, 33), (0, 10), (17, 0), (39, 35), (11, 23), (1, 27), (36, 1), (14, 26), (30, 30), (19, 11), (9, 0), (33, 20), (44, 34), (39, 28), (1, 19), (2, 14), (27, 23), (30, 10), (22, 28), (17, 15), (0, 12), (38, 9), (3, 22), (16, 4), (15, 4), (25, 11), (0, 30), (23, 37), (3, 2), (19, 34), (36, 20), (38, 8), (5, 33), (12, 36), (40, 22), (35, 34), (11, 28), (26, 6), (0, 13), (14, 17), (10, 27), (40, 15), (12, 22), (10, 3), (39, 22), (1, 34), (23, 29), (30, 11), (12, 5), (18, 13), (15, 33), (27, 28), (21, 15), (6, 26), (28, 19), (5, 38), (16, 32), (12, 8), (25, 6), (11, 21), (38, 19), (20, 29), (2, 15), (4, 6), (14, 28), (29, 19), (30, 31), (11, 29), (25, 24), (2, 25), (28, 12), (39, 37), (29, 32), (7, 18), (6, 2), (8, 24), (35, 39), (22, 35), (22, 12), (11, 26), (6, 0), (10, 38), (4, 30), (17, 13), (24, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 17), (28, 18), (11, 18), (6, 5), (21, 41), (34, 17), (32, 44), (25, 20), (13, 21), (18, 5), (3, 27), (21, 44), (38, 0), (14, 29), (45, 31), (41, 4), (13, 3), (18, 9), (4, 33), (33, 22), (20, 36), (45, 12), (24, 33), (38, 18), (39, 2), (12, 9), (1, 44), (27, 25), (4, 12), (18, 11), (29, 37), (29, 30), (21, 22), (33, 28), (27, 11), (9, 40), (42, 7), (27, 31), (34, 27), (39, 0), (24, 24), (9, 44), (28, 1), (14, 43), (10, 16), (15, 21), (17, 1), (34, 37), (17, 20), (35, 39), (46, 16), (46, 2), (41, 1), (3, 36), (37, 31), (3, 13), (11, 9), (14, 4), (27, 24), (35, 10), (43, 6), (5, 0), (6, 17), (43, 33), (35, 26), (41, 29), (33, 40), (12, 44), (26, 24), (32, 33), (44, 28), (32, 34), (36, 24), (46, 21), (18, 17), (5, 24), (13, 6), (4, 15), (32, 15), (30, 43), (41, 34), (23, 24), (15, 33), (13, 15), (7, 1), (13, 40), (12, 30), (46, 26), (41, 44), (30, 35), (2, 16), (16, 21), (33, 16), (30, 41), (42, 32), (1, 43), (12, 13), (29, 13), (43, 38), (34, 11), (45, 28), (26, 26), (39, 23), (0, 15), (13, 5), (44, 20), (3, 40), (23, 10), (19, 36), (26, 23), (38, 35), (11, 14), (14, 22), (25, 14), (6, 10), (22, 41), (11, 1), (19, 12), (39, 19), (16, 24), (21, 42), (18, 33), (12, 32), (37, 34), (7, 0), (15, 11), (44, 8), (29, 43), (9, 36), (21, 33), (5, 20), (0, 6), (31, 31), (35, 2), (5, 31), (12, 10), (40, 36), (29, 3), (0, 16), (43, 13), (33, 43), (46, 37), (26, 10), (8, 28), (40, 26), (22, 44), (29, 18), (35, 7), (34, 38), (28, 13), (45, 4), (1, 15), (36, 4), (31, 38), (14, 24), (38, 33), (11, 37), (28, 7), (26, 1), (30, 34), (3, 12), (46, 25), (13, 36), (11, 42), (10, 30), (30, 9), (15, 29), (6, 11), (25, 6), (43, 11), (23, 20), (14, 37), (37, 26), (2, 19), (20, 19), (37, 19), (11, 29), (36, 22), (35, 23), (21, 1), (43, 20), (19, 42), (31, 6), (14, 2), (29, 25), (15, 30), (16, 37), (2, 3), (20, 0), (11, 15), (45, 32), (33, 6), (10, 9), (28, 12), (26, 7), (39, 27), (13, 43), (9, 12), (27, 34), (5, 3), (32, 43), (11, 34), (5, 19), (39, 16), (11, 27), (27, 17), (40, 24), (27, 39), (40, 37), (43, 28), (19, 32), (32, 5), (10, 32), (45, 39), (9, 22), (35, 9), (18, 2), (40, 25), (6, 36), (28, 16), (22, 4), (18, 28), (17, 30), (1, 31), (42, 43), (10, 10), (42, 23), (38, 22), (33, 42), (24, 38), (19, 35), (32, 28), (19, 7), (44, 18), (11, 11), (11, 26), (13, 44), (5, 25), (27, 44), (21, 40), (17, 41), (11, 19), (40, 20), (25, 1), (42, 13), (2, 14), (3, 42), (11, 32), (2, 29), (6, 31), (41, 14), (42, 20), (7, 7), (28, 28), (8, 4), (15, 6), (37, 21), (22, 0), (4, 16), (14, 42), (19, 43), (34, 2), (23, 23), (38, 20), (44, 35), (17, 10), (22, 19), (30, 12), (28, 5), (12, 38), (6, 23), (22, 29), (18, 32), (20, 9), (13, 42), (31, 12), (45, 29), (31, 8), (20, 29), (42, 34), (19, 33), (12, 34), (14, 19), (38, 32), (46, 38), (45, 35), (23, 4), (37, 37), (30, 28), (17, 43), (33, 35), (24, 26), (29, 29), (16, 35), (45, 14), (29, 36), (45, 20), (14, 23), (30, 36), (35, 21), (14, 39), (19, 23), (39, 34), (38, 11), (25, 18), (31, 37), (25, 5), (31, 3), (41, 9), (8, 10), (24, 4), (0, 10), (23, 38), (38, 23), (1, 28), (43, 34), (40, 35), (2, 2), (28, 27), (40, 30), (31, 30), (36, 8), (31, 4), (38, 6), (37, 29), (43, 7), (0, 13), (8, 11), (29, 0), (37, 40), (26, 37), (27, 35), (28, 21), (30, 3), (32, 12), (45, 2), (43, 5), (7, 28), (31, 10), (44, 24), (26, 35), (36, 3), (21, 17), (12, 37), (9, 42), (20, 42), (33, 41), (8, 12), (20, 3), (43, 36), (7, 11), (28, 25), (38, 16), (44, 38), (6, 43), (20, 40), (1, 35), (6, 19), (21, 15), (5, 32), (13, 17), (5, 27), (10, 15), (20, 10), (14, 34), (25, 19), (38, 19), (34, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 39), (12, 27), (8, 10), (29, 22), (22, 33), (13, 21), (29, 9), (4, 18), (24, 28), (33, 19), (7, 37), (8, 17), (21, 42), (2, 31), (6, 34), (32, 22), (8, 34), (16, 28), (9, 10), (18, 4), (3, 38), (36, 4), (0, 23), (35, 36), (41, 34), (10, 33), (37, 6), (21, 22), (9, 11), (10, 10), (29, 28), (39, 10), (13, 6), (37, 42), (16, 13), (20, 26), (4, 19), (10, 20), (9, 14), (7, 8), (27, 21), (32, 7), (24, 36), (36, 13), (39, 5), (33, 2), (29, 31), (24, 15), (14, 42), (30, 5), (11, 32), (36, 35), (19, 2), (12, 3), (15, 10), (23, 9), (11, 12), (19, 39), (1, 41), (17, 12), (30, 12), (39, 23), (13, 25), (16, 39), (5, 16), (5, 37), (38, 8), (30, 14), (24, 8), (22, 42), (33, 8), (19, 21), (23, 33), (32, 24), (20, 2), (19, 30), (30, 26), (37, 22), (41, 40), (9, 36), (6, 7), (7, 1), (17, 31), (30, 29), (40, 43), (6, 37), (8, 41), (32, 0), (3, 41), (3, 42), (3, 2), (16, 29), (2, 1), (5, 13), (10, 35), (1, 16), (41, 27), (26, 16), (10, 13), (31, 8), (35, 29), (33, 42), (21, 14), (31, 7), (8, 38), (20, 40), (7, 14), (9, 0), (30, 36), (37, 24), (19, 34), (12, 20), (9, 7), (7, 41), (9, 34), (38, 11), (2, 38), (31, 32), (35, 1), (18, 1), (4, 29), (34, 22), (33, 35), (3, 26), (29, 35), (2, 0), (39, 34), (27, 5), (37, 32), (8, 18), (2, 22), (22, 23), (37, 17), (18, 32), (20, 7), (11, 42), (18, 0), (31, 13), (4, 15), (8, 31), (24, 27), (18, 11), (30, 42), (1, 42), (17, 27), (20, 12), (4, 39), (21, 39), (15, 2), (25, 22), (10, 42), (31, 21), (3, 20), (26, 43), (11, 28), (9, 20), (38, 40), (28, 18), (4, 24), (24, 39), (22, 16), (36, 12), (1, 0), (7, 20), (13, 18), (6, 32), (0, 15), (19, 22), (31, 41), (0, 10), (41, 2), (13, 23), (41, 29), (32, 43), (22, 36), (3, 24), (8, 12), (6, 12), (12, 41), (31, 25), (37, 37), (15, 40), (17, 15), (31, 39), (3, 27), (8, 7), (38, 43), (13, 38), (21, 31), (7, 38), (27, 26), (27, 15), (9, 8), (39, 39), (21, 41), (38, 15), (23, 3), (1, 11), (32, 41), (28, 10), (12, 8), (5, 5), (27, 20), (3, 39), (38, 26), (41, 31), (5, 14), (28, 28), (32, 18), (1, 22), (34, 2), (26, 22), (4, 21), (0, 21), (4, 22), (27, 19), (9, 39), (5, 34), (3, 5), (20, 5), (9, 31), (41, 6), (15, 31), (14, 22), (40, 2), (35, 6), (3, 17), (32, 37), (11, 14), (19, 43), (7, 17), (4, 14), (6, 14), (36, 5), (5, 32), (12, 7), (38, 4), (15, 29), (40, 9), (27, 40), (36, 0), (5, 4), (7, 3), (41, 37), (34, 20), (9, 32), (34, 16), (24, 12), (19, 16), (6, 36), (35, 25), (35, 15), (35, 27), (15, 27), (26, 19), (10, 11), (13, 19), (40, 25), (23, 35), (38, 0), (7, 12), (32, 29), (33, 18), (4, 9), (3, 16), (36, 22), (36, 11), (37, 8), (17, 8), (40, 15), (1, 18), (22, 40), (2, 30), (7, 42), (5, 15), (1, 21), (22, 0), (6, 4), (3, 35), (32, 19), (38, 35), (29, 41), (1, 24), (14, 7), (15, 17), (27, 3), (32, 35), (20, 39), (26, 34), (30, 32), (34, 21), (0, 25), (31, 43), (17, 6), (7, 5), (41, 17), (38, 34), (14, 28), (39, 36), (36, 20), (33, 38), (30, 21), (11, 3), (39, 41), (17, 22), (35, 7), (5, 6), (31, 11), (41, 22), (39, 25), (39, 9), (5, 12), (30, 8), (37, 13), (22, 11), (37, 43), (11, 13), (21, 21), (4, 35), (41, 0), (41, 26), (30, 4), (7, 13), (24, 43), (5, 19), (17, 24), (10, 22), (5, 7), (8, 8), (3, 11), (30, 33), (0, 28), (31, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 34), (16, 2), (11, 26), (30, 21), (37, 22), (29, 0), (30, 10), (1, 29), (1, 34), (29, 37), (2, 31), (14, 26), (29, 28), (42, 39), (2, 23), (11, 28), (4, 35), (40, 33), (23, 3), (9, 25), (43, 15), (31, 21), (31, 2), (1, 3), (6, 33), (30, 1), (13, 19), (30, 30), (12, 2), (23, 21), (28, 0), (2, 4), (36, 16), (40, 11), (42, 37), (22, 10), (10, 29), (29, 10), (26, 33), (26, 3), (37, 17), (24, 11), (43, 33), (11, 4), (31, 9), (29, 7), (16, 1), (11, 39), (25, 13), (15, 25), (24, 4), (33, 34), (36, 7), (31, 27), (35, 23), (31, 17), (24, 38), (25, 1), (17, 4), (0, 33), (28, 22), (31, 23), (24, 29), (19, 7), (27, 34), (42, 9), (43, 23), (25, 18), (8, 28), (30, 3), (29, 22), (18, 27), (28, 39), (18, 29), (34, 33), (22, 31), (8, 22), (18, 40), (0, 13), (39, 17), (25, 33), (17, 2), (27, 14), (0, 8), (33, 36), (18, 32), (8, 16), (11, 0), (30, 22), (7, 34), (39, 37), (37, 25), (33, 30), (31, 40), (9, 21), (4, 11), (42, 36), (3, 11), (17, 24), (2, 21), (0, 18), (32, 7), (22, 15), (32, 30), (31, 28), (16, 30), (29, 38), (34, 24), (13, 18), (7, 22), (9, 22), (42, 14), (9, 35), (29, 23), (21, 18), (35, 37), (10, 37), (40, 1), (26, 17), (41, 13), (34, 34), (3, 1), (6, 26), (23, 26), (3, 7), (14, 22), (17, 30), (31, 10), (35, 25), (10, 8), (34, 11), (35, 10), (14, 29), (20, 39), (6, 4), (8, 20), (36, 18), (25, 5), (3, 19), (16, 9), (19, 40), (41, 36), (29, 33), (41, 34), (37, 11), (12, 28), (32, 40), (29, 40), (7, 40), (4, 2), (31, 16), (41, 23), (39, 6), (11, 1), (11, 12), (43, 20), (10, 7), (43, 6), (4, 17), (5, 9), (21, 23), (22, 9), (9, 26), (9, 5), (36, 24), (13, 17), (40, 24), (38, 7), (36, 13), (39, 26), (13, 33), (41, 6), (37, 40), (22, 22), (1, 1), (17, 1), (19, 27), (42, 7), (22, 0), (43, 12), (35, 6), (13, 24), (28, 6), (20, 28), (24, 27), (38, 3), (28, 19), (23, 36), (37, 5), (17, 40), (23, 14), (43, 9), (39, 4), (12, 25), (15, 16), (28, 36), (34, 21), (13, 38), (41, 21), (10, 35), (1, 14), (18, 38), (4, 38), (24, 15), (25, 37), (0, 12), (8, 17), (39, 15), (1, 35), (38, 1), (39, 7), (11, 9), (9, 14), (16, 35), (6, 29), (18, 5), (31, 20), (8, 33), (16, 0), (20, 18), (6, 0), (32, 4), (33, 14), (36, 25), (5, 25), (29, 35), (6, 1), (8, 25), (42, 22), (32, 35), (3, 17), (0, 30), (32, 8), (12, 22), (35, 26), (15, 23), (17, 34), (29, 31), (40, 37), (2, 10), (16, 15), (30, 4), (32, 19), (29, 5), (17, 18), (24, 23), (3, 2), (7, 7), (12, 3), (25, 39), (5, 21), (26, 30), (29, 18), (34, 17), (25, 29), (0, 22), (15, 39), (17, 9), (25, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 6), (34, 44), (40, 22), (47, 37), (46, 32), (37, 39), (9, 43), (46, 43), (17, 22), (24, 3), (47, 26), (5, 35), (44, 31), (17, 17), (33, 43), (13, 27), (15, 8), (3, 28), (47, 30), (26, 35), (15, 21), (14, 36), (15, 34), (33, 14), (39, 43), (45, 32), (28, 0), (26, 28), (17, 16), (33, 38), (27, 45), (12, 10), (29, 14), (5, 9), (6, 17), (4, 29), (21, 35), (37, 20), (26, 36), (22, 33), (37, 42), (1, 15), (25, 40), (6, 45), (12, 29), (8, 41), (30, 31), (46, 7), (6, 47), (22, 16), (42, 14), (38, 13), (0, 44), (46, 40), (40, 42), (8, 39), (4, 25), (42, 38), (26, 44), (43, 29), (32, 1), (28, 5), (46, 36), (21, 19), (28, 28), (30, 1), (42, 29), (15, 11), (14, 1), (17, 0), (41, 7), (30, 26), (3, 32), (14, 7), (4, 20), (1, 36), (37, 35), (0, 18), (29, 41), (6, 23), (13, 42), (23, 36), (45, 46), (6, 7), (43, 39), (10, 30), (17, 43), (42, 16), (28, 3), (46, 5), (28, 42), (46, 47), (18, 20), (1, 2), (18, 28), (5, 15), (12, 20), (41, 31), (14, 25), (36, 11), (43, 13), (23, 46), (24, 47), (5, 8), (31, 21), (2, 17), (47, 38), (34, 11), (21, 44), (40, 40), (9, 15), (26, 22), (2, 0), (23, 44), (11, 23), (42, 46), (19, 30), (47, 6), (35, 33), (32, 46), (10, 42), (40, 32), (0, 36), (47, 17), (36, 20), (36, 39), (38, 32), (25, 37), (26, 41), (30, 45), (40, 10), (9, 28), (5, 19), (27, 42), (7, 37), (46, 15), (3, 18), (33, 16), (10, 19), (35, 26), (32, 3), (1, 7), (46, 21), (27, 31), (47, 7), (5, 39), (5, 25), (24, 38), (36, 16), (19, 41), (26, 15), (30, 18), (8, 36), (31, 30), (0, 40), (41, 22), (1, 0), (29, 37), (26, 25), (45, 6), (2, 5), (26, 14), (37, 33), (26, 0), (18, 33), (18, 43), (22, 6), (32, 10), (12, 47), (29, 22), (32, 24), (16, 5), (35, 45), (6, 16), (19, 26), (7, 32), (44, 44), (34, 32), (47, 32), (25, 27), (4, 13), (10, 45), (36, 6), (15, 10), (19, 6), (27, 28), (22, 10), (44, 6), (1, 12), (38, 14), (9, 41), (9, 16), (6, 46), (36, 10), (14, 20), (41, 17), (31, 8), (6, 25), (18, 39), (28, 12), (13, 33), (44, 45), (15, 29), (13, 37), (1, 39), (3, 25), (3, 43), (11, 39), (19, 20), (40, 30), (12, 34), (44, 10), (9, 37), (37, 4), (29, 35), (8, 6), (9, 31), (25, 43), (42, 37), (31, 39), (46, 38), (22, 38), (35, 17), (30, 14), (21, 47), (26, 6), (31, 5), (44, 39), (14, 31), (26, 33), (44, 4), (35, 42), (23, 41), (14, 9), (37, 25), (36, 3), (8, 47), (32, 31), (38, 24), (0, 41), (27, 24), (6, 19), (6, 39), (36, 8), (42, 9), (16, 44), (3, 39), (43, 2), (6, 36), (23, 18), (42, 34), (47, 27), (45, 15), (16, 8), (41, 35), (3, 22), (38, 36), (25, 9), (2, 31), (31, 44), (17, 12), (35, 41), (9, 45), (38, 21), (28, 22), (47, 35), (8, 21), (21, 25), (8, 19), (31, 27), (45, 1), (10, 10), (41, 6), (8, 5), (45, 36), (25, 30), (40, 11), (27, 25), (15, 38), (40, 36), (31, 43), (2, 39), (10, 13), (16, 36), (34, 12), (27, 36), (40, 44), (42, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 10), (26, 6), (25, 18), (26, 11), (8, 14), (12, 6), (11, 26), (14, 33), (19, 11), (34, 5), (34, 30), (1, 2), (17, 18), (7, 12), (11, 20), (8, 29), (8, 3), (29, 20), (29, 28), (13, 14), (19, 37), (16, 9), (23, 18), (32, 34), (3, 10), (1, 10), (20, 14), (14, 18), (8, 32), (30, 32), (27, 23), (16, 36), (33, 0), (7, 8), (15, 10), (10, 0), (27, 6), (3, 16), (26, 15), (35, 18), (25, 17), (2, 40), (20, 39), (12, 10), (33, 31), (29, 5), (24, 6), (39, 1), (13, 3), (20, 1), (5, 24), (27, 3), (32, 1), (11, 22), (18, 24), (13, 38), (20, 34), (0, 9), (20, 12), (30, 39), (1, 39), (9, 11), (24, 40), (29, 23), (14, 21), (35, 11), (10, 29), (1, 12), (10, 22), (23, 34), (1, 1), (11, 36), (16, 18), (36, 7), (5, 0), (6, 17), (24, 25), (17, 37), (18, 37), (22, 14), (30, 37), (33, 27), (36, 13), (25, 16), (38, 23), (21, 2), (39, 23), (3, 38), (31, 24), (1, 3), (12, 21), (20, 7), (23, 15), (20, 25), (5, 16), (11, 28), (38, 30), (36, 10), (8, 16), (38, 5), (10, 17), (17, 20), (32, 9), (25, 0), (39, 10), (35, 6), (17, 31), (14, 11), (17, 14), (4, 31), (26, 3), (31, 39), (26, 16), (26, 12), (11, 8), (0, 10), (23, 39), (11, 2), (1, 4), (11, 32), (15, 8), (8, 21), (30, 25), (21, 9), (5, 35), (16, 17), (22, 16), (39, 30), (4, 26), (16, 32), (21, 12), (8, 11), (27, 21), (2, 6), (7, 11), (38, 10), (2, 5), (24, 4), (29, 36), (18, 17), (25, 6), (5, 1), (20, 29), (11, 10), (34, 32), (6, 2), (4, 2), (40, 21), (0, 33), (20, 32), (40, 20), (33, 35), (22, 10), (28, 17), (15, 39), (0, 27), (40, 22), (40, 26), (9, 23), (30, 15), (37, 40), (14, 16), (35, 7), (25, 13), (27, 12), (30, 6), (3, 31), (35, 24), (36, 27), (39, 35), (3, 22), (31, 1), (15, 11), (14, 9), (19, 21), (0, 22), (6, 14), (2, 2), (16, 39), (3, 34), (6, 11), (28, 39), (9, 31), (2, 36), (33, 25), (40, 38), (34, 14), (31, 40), (21, 37), (1, 37), (15, 19), (4, 5), (4, 21), (15, 16), (8, 26), (7, 20), (19, 8), (1, 6), (28, 8), (26, 10), (6, 29), (31, 17), (12, 35), (33, 38), (14, 28), (36, 24), (35, 5), (20, 21), (21, 23), (24, 10), (21, 6), (5, 28), (40, 4), (20, 11), (5, 17), (32, 40), (39, 40), (9, 7), (33, 4), (16, 14), (5, 37), (36, 26), (25, 3), (38, 31), (21, 26), (22, 7), (22, 2), (33, 3), (40, 36), (30, 23), (34, 20), (1, 18), (18, 18), (38, 39), (15, 15), (26, 38), (40, 27), (2, 32), (0, 26), (1, 34), (8, 25), (24, 13), (31, 27), (37, 10), (20, 10), (17, 15), (34, 19), (27, 18), (22, 0), (25, 28), (4, 6), (16, 27), (32, 39), (36, 33), (0, 13), (35, 1), (40, 32), (1, 5), (3, 18), (9, 18), (10, 40), (10, 2), (34, 33), (4, 30), (36, 22), (39, 34), (14, 32), (1, 7), (27, 16), (3, 25), (28, 13), (1, 25), (24, 2), (7, 18), (21, 13), (21, 28), (33, 6), (25, 27), (39, 18), (24, 17), (1, 38), (12, 25), (15, 14), (22, 24), (0, 8), (7, 29), (20, 0), (22, 34), (21, 24), (17, 23), (2, 22), (11, 40), (7, 19), (26, 19), (28, 0), (26, 24), (4, 11), (37, 7), (31, 21), (5, 25), (27, 29), (18, 33), (37, 34), (2, 20), (14, 40), (28, 24), (32, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 31), (10, 22), (26, 27), (38, 34), (3, 17), (31, 9), (37, 43), (34, 36), (33, 23), (18, 44), (23, 8), (27, 18), (32, 13), (28, 0), (3, 37), (35, 6), (5, 30), (36, 2), (36, 3), (27, 46), (17, 30), (20, 8), (35, 37), (8, 46), (35, 35), (28, 24), (16, 12), (7, 28), (33, 20), (21, 36), (11, 13), (13, 5), (1, 16), (39, 16), (31, 18), (25, 47), (6, 14), (24, 32), (14, 8), (10, 39), (30, 32), (10, 23), (35, 8), (12, 10), (17, 33), (22, 20), (28, 6), (18, 26), (6, 40), (28, 22), (16, 5), (5, 5), (17, 24), (19, 30), (13, 8), (36, 16), (38, 47), (33, 5), (8, 36), (29, 43), (18, 10), (32, 12), (5, 11), (6, 6), (31, 28), (4, 8), (0, 22), (5, 42), (3, 39), (13, 47), (23, 23), (9, 38), (5, 45), (29, 2), (16, 0), (28, 14), (27, 26), (7, 9), (17, 4), (7, 31), (12, 37), (1, 39), (17, 13), (2, 21), (37, 11), (27, 10), (29, 8), (4, 46), (38, 8), (13, 22), (37, 24), (28, 47), (37, 26), (39, 14), (23, 45), (13, 1), (33, 0), (22, 17), (14, 14), (17, 0), (26, 12), (26, 42), (22, 42), (24, 24), (10, 38), (16, 4), (24, 26), (39, 4), (29, 0), (17, 44), (35, 33), (2, 47), (4, 2), (35, 0), (37, 9), (21, 4), (15, 25), (19, 0), (2, 7), (23, 41), (12, 24), (25, 32), (1, 45), (2, 45), (32, 21), (6, 28), (32, 45), (2, 17), (37, 14), (37, 13), (15, 41), (7, 32), (6, 21), (26, 4), (21, 17), (24, 40), (27, 3), (32, 7), (11, 0), (25, 12), (24, 16), (22, 18), (15, 15), (35, 16), (16, 30), (37, 41), (20, 29), (8, 32), (5, 47), (26, 26), (7, 8), (2, 44), (37, 17), (2, 29), (20, 39), (22, 6), (23, 37), (19, 15), (11, 41), (35, 19), (7, 38), (38, 37), (37, 31), (20, 34), (6, 30), (12, 22), (12, 42), (6, 29), (12, 19), (27, 4), (22, 26), (5, 19), (39, 33), (4, 5), (19, 5), (27, 39), (17, 21), (18, 41), (18, 22), (26, 9), (6, 12), (34, 47), (3, 15), (15, 6), (2, 14), (19, 11), (10, 32), (1, 20), (10, 44), (20, 19), (8, 42), (1, 28), (0, 8), (17, 40), (2, 36), (12, 16), (9, 35), (25, 23), (34, 20), (37, 21), (4, 24), (6, 24), (34, 37), (14, 41), (23, 38), (39, 42), (25, 1), (39, 34), (28, 12), (29, 46), (29, 16), (33, 27), (24, 2), (9, 23), (4, 34), (3, 40), (31, 20), (8, 2), (37, 12), (21, 38), (11, 21), (38, 16), (30, 27), (1, 23), (3, 46), (23, 13), (14, 27), (7, 47), (25, 30), (17, 25), (1, 32), (5, 40), (36, 37), (16, 6), (13, 39), (39, 25), (3, 12), (33, 17), (3, 23), (39, 31), (31, 29), (26, 43), (8, 11), (12, 5), (22, 30), (34, 34), (12, 13), (2, 41), (39, 6), (4, 38), (33, 41), (10, 10), (0, 21), (24, 0), (32, 40), (5, 6), (13, 27), (13, 0), (16, 20), (24, 46), (21, 26), (8, 27), (17, 5), (12, 26), (20, 36), (37, 19), (24, 31), (36, 40), (28, 42), (15, 17), (24, 21), (36, 10), (6, 17), (23, 20), (6, 15), (36, 22), (20, 33), (15, 44), (39, 1), (16, 31), (19, 47), (0, 6), (14, 9), (7, 23), (38, 33), (38, 17), (4, 23), (35, 31), (17, 42), (27, 12), (26, 8), (32, 26), (23, 33), (17, 1), (37, 3), (2, 26), (20, 7), (21, 14), (25, 27), (31, 43), (12, 1), (14, 22), (17, 19), (38, 1), (21, 19), (37, 10), (1, 33), (36, 46), (36, 19), (2, 12), (4, 15), (23, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 7), (17, 13), (27, 8), (36, 33), (39, 29), (22, 23), (12, 19), (4, 26), (10, 21), (21, 3), (32, 44), (3, 42), (28, 20), (38, 37), (22, 25), (12, 34), (32, 14), (10, 15), (27, 7), (26, 36), (38, 4), (1, 17), (37, 26), (17, 26), (20, 6), (34, 21), (26, 42), (6, 42), (38, 20), (31, 27), (11, 38), (6, 2), (40, 10), (39, 18), (37, 27), (36, 20), (4, 44), (29, 44), (28, 5), (9, 1), (12, 1), (0, 8), (32, 11), (6, 3), (21, 36), (8, 10), (34, 1), (9, 2), (27, 22), (35, 20), (40, 0), (0, 26), (0, 36), (22, 27), (30, 40), (18, 42), (10, 29), (23, 33), (36, 23), (3, 25), (38, 26), (16, 24), (34, 19), (38, 33), (2, 21), (34, 16), (24, 5), (13, 28), (29, 31), (29, 34), (38, 24), (2, 35), (3, 37), (15, 0), (28, 21), (15, 40), (41, 14), (20, 15), (9, 36), (11, 44), (5, 36), (34, 7), (19, 4), (27, 18), (20, 22), (35, 27), (8, 22), (27, 1), (6, 4), (6, 31), (32, 12), (30, 17), (6, 40), (0, 40), (27, 20), (15, 9), (40, 22), (3, 11), (19, 10), (27, 42), (16, 23), (28, 44), (12, 33), (5, 9), (24, 31), (22, 20), (8, 4), (30, 27), (15, 6), (23, 19), (37, 21), (34, 41), (22, 21), (0, 18), (21, 37), (30, 11), (25, 21), (30, 0), (42, 11), (23, 4), (0, 31), (16, 32), (1, 22), (5, 1), (12, 14), (6, 28), (21, 17), (14, 42), (18, 29), (40, 14), (25, 20), (20, 4), (35, 21), (25, 28), (7, 13), (30, 16), (33, 42), (42, 28), (30, 35), (8, 5), (8, 32), (11, 43), (18, 43), (22, 26), (12, 26), (33, 1), (10, 8), (3, 43), (18, 40), (30, 18), (2, 9), (37, 1), (31, 26), (14, 5), (2, 27), (7, 26), (33, 2), (38, 28), (5, 26), (11, 23), (19, 41), (11, 8), (28, 25), (28, 35), (34, 5), (37, 30), (40, 40), (19, 11), (1, 29), (3, 19), (20, 13), (40, 26), (1, 7), (19, 17), (19, 1), (21, 15), (39, 25), (28, 27), (24, 34), (24, 14), (20, 38), (31, 30), (5, 5), (23, 0), (1, 38), (39, 43), (11, 29), (22, 30), (23, 2), (24, 1), (39, 33), (18, 30), (14, 31), (39, 14), (22, 12), (38, 25), (36, 44), (26, 22), (12, 42), (24, 20), (13, 37), (26, 16), (6, 20), (23, 5), (4, 13), (10, 5), (2, 37), (2, 39), (33, 4), (8, 0), (30, 4), (3, 8), (18, 28), (14, 19), (39, 4), (30, 42), (17, 16), (17, 23), (6, 6), (2, 31), (22, 40), (23, 18), (24, 0), (13, 21), (12, 7), (9, 7), (29, 14), (15, 39), (34, 20), (27, 39), (28, 24), (36, 2), (33, 32), (42, 36), (10, 10), (36, 9), (29, 5), (15, 19), (23, 9), (13, 14), (40, 13), (33, 34), (13, 0), (8, 21), (41, 5), (25, 25), (23, 11), (11, 18), (5, 31), (3, 23), (15, 15), (3, 9), (8, 20), (41, 28), (25, 17), (21, 2), (39, 11), (26, 27), (16, 21), (32, 6), (17, 10), (9, 38), (13, 9), (21, 30), (7, 38), (11, 14), (15, 4), (15, 42), (12, 31), (39, 1), (23, 30), (14, 6), (1, 20), (36, 35), (38, 44), (39, 38), (33, 8), (7, 2), (24, 18), (36, 14), (40, 25), (16, 15), (40, 15), (30, 31), (4, 24), (28, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 13), (29, 2), (12, 26), (37, 40), (27, 14), (22, 22), (3, 28), (18, 35), (10, 2), (13, 3), (40, 19), (31, 32), (17, 34), (9, 35), (3, 23), (5, 23), (6, 37), (16, 26), (35, 37), (26, 40), (36, 3), (9, 17), (5, 8), (22, 14), (5, 38), (24, 20), (31, 23), (38, 31), (38, 30), (15, 34), (26, 6), (28, 38), (7, 7), (5, 22), (32, 9), (6, 27), (24, 30), (4, 29), (5, 34), (0, 33), (8, 8), (34, 16), (27, 25), (27, 40), (8, 2), (0, 18), (10, 16), (1, 21), (18, 29), (33, 34), (1, 22), (32, 7), (25, 32), (28, 22), (25, 35), (19, 26), (35, 33), (26, 28), (38, 8), (6, 7), (28, 6), (13, 11), (32, 30), (17, 17), (8, 33), (38, 16), (17, 28), (8, 28), (31, 31), (28, 17), (30, 38), (3, 34), (25, 25), (41, 19), (15, 23), (23, 33), (31, 41), (19, 13), (6, 39), (19, 22), (8, 7), (41, 30), (28, 11), (27, 5), (29, 21), (12, 4), (37, 26), (15, 22), (26, 16), (6, 38), (39, 2), (29, 3), (13, 25), (15, 5), (40, 16), (31, 5), (26, 21), (34, 38), (32, 42), (12, 19), (28, 32), (3, 4), (24, 21), (14, 23), (27, 10), (29, 38), (33, 19), (15, 30), (20, 38), (19, 1), (16, 41), (30, 19), (39, 33), (4, 4), (2, 29), (25, 16), (25, 41), (34, 20), (18, 13), (41, 24), (19, 21), (19, 41), (23, 2), (29, 33), (10, 12), (14, 31), (25, 8), (4, 16), (5, 18), (27, 27), (41, 17), (7, 21), (19, 5), (35, 25), (35, 3), (20, 37), (32, 5), (23, 13), (38, 24), (5, 37), (9, 6), (41, 35), (9, 0), (8, 40), (33, 35), (15, 20), (28, 7), (39, 15), (39, 27), (33, 38), (10, 30), (27, 26), (32, 35), (8, 39), (30, 16), (16, 28), (27, 8), (37, 20), (10, 24), (1, 39), (1, 36), (24, 14), (8, 14), (1, 6), (25, 13), (13, 19), (35, 4), (37, 13), (31, 35), (26, 7), (36, 32), (6, 25), (13, 33), (9, 25), (0, 16), (41, 16), (17, 14), (22, 8), (29, 6), (36, 35), (10, 9), (31, 27), (20, 29), (24, 16), (10, 38), (21, 7), (22, 32), (37, 15), (16, 10), (41, 15), (11, 34), (30, 6), (28, 9), (30, 21), (35, 7), (4, 14), (14, 28), (8, 25), (12, 16), (36, 14), (23, 25), (0, 1), (15, 1), (15, 3), (7, 15), (5, 9), (12, 22), (37, 9), (24, 5), (12, 21), (16, 38), (27, 29), (5, 17), (30, 42), (32, 11), (35, 22), (4, 33), (14, 36), (31, 39), (31, 6), (26, 20), (41, 0), (25, 42), (21, 0), (4, 32), (32, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 31), (8, 32), (20, 28), (41, 15), (35, 10), (3, 24), (12, 32), (10, 30), (19, 4), (17, 2), (37, 32), (10, 9), (0, 4), (31, 13), (9, 26), (25, 7), (15, 22), (14, 39), (35, 39), (41, 31), (9, 42), (11, 20), (30, 15), (44, 0), (21, 43), (25, 1), (12, 23), (28, 37), (31, 3), (11, 33), (2, 12), (33, 21), (22, 11), (2, 23), (21, 47), (32, 6), (16, 39), (3, 3), (7, 23), (36, 23), (43, 46), (43, 40), (28, 15), (29, 13), (33, 9), (24, 44), (26, 27), (42, 24), (14, 9), (34, 44), (8, 39), (7, 18), (4, 30), (9, 13), (34, 11), (19, 34), (41, 34), (27, 6), (35, 42), (42, 7), (23, 15), (23, 47), (19, 2), (17, 8), (39, 14), (1, 39), (20, 23), (10, 47), (10, 4), (27, 9), (8, 7), (32, 42), (6, 47), (21, 46), (40, 39), (20, 31), (20, 21), (3, 40), (19, 28), (1, 40), (8, 6), (28, 26), (25, 2), (9, 34), (44, 47), (23, 27), (38, 38), (37, 46), (5, 2), (11, 36), (22, 18), (8, 10), (20, 36), (35, 38), (1, 29), (17, 18), (35, 37), (9, 41), (7, 40), (20, 25), (40, 2), (15, 20), (33, 1), (2, 2), (17, 37), (34, 18), (20, 46), (32, 5), (7, 33), (4, 40), (5, 34), (14, 15), (36, 3), (5, 12), (29, 45), (44, 11), (5, 44), (16, 15), (27, 20), (28, 32), (37, 35), (36, 14), (11, 30), (6, 20), (2, 19), (32, 47), (0, 1), (15, 36), (8, 15), (6, 10), (30, 29), (10, 32), (5, 26), (33, 38), (20, 22), (34, 2), (44, 4), (31, 2), (16, 44), (41, 30), (7, 31), (28, 28), (9, 18), (17, 5), (43, 18), (19, 16), (40, 22), (17, 17), (34, 40), (17, 34), (30, 10), (34, 0), (20, 7), (41, 4), (40, 20), (32, 25), (17, 43), (18, 24), (17, 23), (26, 46), (9, 27), (5, 21), (34, 23), (27, 7), (14, 25), (2, 45), (12, 14), (36, 13), (34, 28), (34, 10), (23, 13), (5, 30), (41, 26), (40, 35), (10, 20), (27, 3), (3, 38), (30, 41), (42, 32), (33, 43), (38, 19), (6, 45), (14, 12), (6, 36), (34, 5), (35, 5), (9, 14), (15, 0), (1, 26), (21, 19), (27, 37), (5, 48), (30, 26), (6, 37), (16, 24), (43, 8), (28, 38), (22, 30), (5, 0), (11, 11), (9, 40), (18, 43), (20, 4), (41, 40), (12, 43), (5, 29), (3, 6), (28, 46), (2, 4), (33, 24), (7, 44), (9, 32), (7, 27), (5, 36), (18, 23), (33, 44), (40, 41), (25, 45), (29, 48), (18, 18), (38, 28), (8, 13), (12, 8), (27, 13), (40, 46), (16, 26), (15, 19), (26, 37), (26, 41), (31, 31), (29, 37), (20, 37), (29, 36), (34, 24), (9, 3), (24, 21), (17, 41), (30, 8), (15, 35), (22, 9), (24, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 36), (35, 19), (21, 0), (6, 5), (35, 5), (15, 7), (4, 17), (39, 26), (23, 38), (42, 3), (38, 14), (6, 18), (25, 35), (41, 29), (6, 3), (15, 24), (15, 15), (6, 37), (18, 38), (40, 40), (26, 28), (27, 13), (19, 24), (21, 24), (32, 17), (7, 34), (37, 40), (26, 13), (38, 15), (0, 19), (0, 25), (2, 41), (34, 38), (37, 4), (21, 32), (5, 1), (40, 13), (11, 18), (29, 4), (28, 27), (35, 31), (9, 36), (34, 25), (2, 3), (25, 18), (15, 6), (25, 15), (31, 36), (24, 0), (16, 3), (6, 17), (3, 6), (39, 21), (12, 3), (20, 14), (36, 5), (30, 31), (12, 20), (11, 30), (41, 8), (36, 37), (27, 16), (4, 40), (21, 27), (4, 19), (41, 22), (21, 39), (7, 33), (10, 20), (10, 10), (33, 24), (10, 13), (1, 21), (18, 32), (21, 1), (20, 21), (33, 28), (39, 30), (15, 20), (37, 38), (16, 37), (17, 40), (28, 38), (4, 37), (12, 37), (23, 24), (17, 20), (18, 6), (34, 28), (14, 31), (11, 23), (29, 28), (28, 35), (24, 13), (8, 37), (9, 37), (28, 16), (38, 40), (38, 21), (6, 9), (8, 14), (11, 37), (34, 10), (29, 1), (10, 24), (15, 14), (10, 34), (13, 17), (23, 9), (41, 41), (33, 20), (8, 30), (3, 11), (29, 26), (5, 3), (3, 37), (20, 31), (11, 22), (21, 5), (5, 33), (28, 5), (13, 19), (40, 7), (1, 31), (34, 29), (11, 8), (29, 8), (35, 20), (10, 25), (42, 17), (16, 25), (9, 21), (24, 21), (6, 32), (18, 31), (15, 19), (3, 32), (24, 19), (33, 36), (12, 21), (42, 28), (12, 2), (3, 24), (0, 38), (37, 34), (10, 11), (24, 39), (29, 12), (28, 12), (15, 17), (29, 6), (27, 32), (22, 8), (20, 27), (16, 11), (15, 5), (23, 1), (40, 17), (22, 40), (4, 32), (11, 4), (2, 12), (18, 30), (21, 2), (10, 36), (26, 0), (25, 41), (4, 28), (35, 41), (40, 33), (35, 13), (41, 13), (2, 0), (8, 36), (39, 40), (2, 29), (18, 13), (40, 19), (1, 20), (18, 21), (25, 30), (29, 7), (25, 33), (21, 37), (9, 16), (8, 15), (9, 6), (18, 39), (40, 8), (11, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 27), (35, 19), (27, 21), (1, 27), (26, 23), (0, 18), (15, 26), (29, 2), (7, 22), (32, 7), (25, 7), (22, 13), (20, 13), (28, 13), (7, 38), (14, 22), (3, 0), (13, 6), (35, 32), (39, 3), (26, 20), (15, 25), (31, 9), (12, 11), (14, 34), (34, 0), (21, 23), (12, 36), (13, 24), (12, 39), (38, 25), (37, 10), (13, 17), (21, 42), (37, 7), (18, 7), (12, 1), (14, 39), (30, 2), (3, 42), (29, 31), (17, 5), (16, 33), (36, 32), (15, 23), (12, 15), (17, 8), (4, 37), (3, 38), (2, 9), (8, 16), (10, 38), (33, 6), (36, 4), (16, 35), (11, 21), (10, 18), (33, 11), (10, 1), (25, 29), (23, 32), (20, 31), (33, 18), (25, 9), (6, 5), (13, 35), (4, 39), (6, 36), (0, 40), (19, 34), (3, 4), (30, 40), (25, 19), (11, 1), (27, 1), (6, 41), (21, 1), (0, 21), (7, 3), (39, 27), (34, 26), (29, 24), (28, 23), (27, 17), (38, 13), (31, 34), (37, 2), (1, 23), (19, 33), (36, 1), (4, 15), (24, 38), (37, 40), (26, 10), (29, 17), (33, 22), (37, 42), (2, 21), (38, 5), (7, 32), (31, 32), (17, 0), (26, 41), (10, 30), (19, 22), (38, 31), (17, 24), (2, 18), (26, 18), (29, 5), (3, 9), (16, 41), (17, 41), (9, 15), (39, 26), (8, 21), (15, 10), (13, 33), (0, 36), (9, 7), (5, 35), (35, 8), (26, 26), (11, 2), (12, 40), (16, 27), (6, 12), (11, 6), (37, 20), (2, 29), (0, 27), (9, 32), (20, 18), (30, 14), (21, 8), (34, 27), (28, 15), (11, 26), (36, 22), (23, 8), (19, 23), (36, 41), (33, 38), (17, 6), (7, 23), (23, 14), (6, 22), (36, 40), (13, 7), (22, 26), (14, 11), (20, 36), (7, 13), (15, 4), (33, 27), (14, 26), (25, 36), (11, 39), (1, 41), (15, 19), (34, 9), (17, 25), (27, 2), (17, 36), (15, 3), (1, 7), (38, 28), (0, 38), (31, 20), (32, 26), (34, 29), (22, 22), (18, 2), (30, 41), (6, 31), (7, 15), (19, 35), (8, 39), (2, 10), (10, 33), (12, 34), (12, 41), (32, 11), (32, 5), (34, 32), (20, 15), (15, 1), (0, 25), (34, 3), (15, 2), (37, 12), (33, 36), (4, 36), (1, 42), (17, 34), (18, 4), (6, 0), (36, 16), (12, 10), (20, 33), (15, 11), (21, 19), (3, 35), (34, 21), (37, 36), (25, 17), (39, 17), (15, 31), (35, 41), (19, 2), (6, 3), (27, 31), (33, 32), (16, 8), (5, 40), (19, 27), (8, 34), (24, 1), (39, 1), (10, 39), (27, 3), (19, 30), (39, 24), (6, 10), (2, 6), (26, 8), (35, 25), (16, 7), (10, 19), (30, 0), (1, 20), (33, 24), (11, 0), (1, 36), (26, 1), (24, 30), (9, 6), (23, 33), (18, 28), (21, 34), (28, 40), (9, 33), (22, 16), (23, 16), (16, 0), (5, 4), (1, 22), (20, 9), (5, 28), (29, 12), (39, 29), (36, 5), (1, 18), (3, 20), (24, 37), (33, 3), (3, 24), (26, 30), (4, 32), (39, 35), (18, 24), (30, 24), (29, 1), (39, 13), (20, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 23), (35, 14), (28, 38), (29, 13), (19, 6), (9, 10), (30, 17), (28, 35), (11, 24), (47, 6), (23, 30), (9, 14), (11, 13), (16, 15), (22, 0), (28, 2), (10, 4), (17, 7), (25, 35), (4, 9), (12, 1), (40, 34), (1, 8), (21, 4), (10, 36), (32, 39), (24, 0), (41, 7), (27, 23), (33, 10), (30, 35), (14, 2), (16, 40), (25, 19), (15, 12), (26, 32), (1, 3), (0, 2), (3, 21), (7, 19), (9, 38), (16, 25), (0, 34), (1, 35), (7, 30), (15, 23), (14, 18), (4, 24), (46, 29), (6, 17), (25, 13), (47, 36), (10, 5), (34, 11), (9, 26), (14, 21), (43, 1), (2, 29), (43, 21), (8, 21), (8, 25), (21, 18), (20, 38), (24, 24), (27, 27), (34, 14), (13, 39), (44, 27), (37, 12), (33, 14), (48, 9), (15, 40), (8, 1), (32, 13), (3, 4), (9, 9), (35, 19), (14, 34), (37, 40), (41, 11), (5, 2), (35, 7), (6, 37), (44, 13), (42, 13), (7, 34), (16, 36), (15, 15), (4, 18), (4, 28), (25, 18), (41, 4), (2, 14), (38, 17), (45, 11), (48, 5), (44, 23), (20, 20), (11, 27), (45, 18), (41, 30), (3, 36), (26, 28), (42, 23), (26, 20), (22, 8), (31, 34), (13, 11), (39, 23), (13, 19), (34, 19), (5, 34), (12, 25), (43, 15), (26, 8), (35, 2), (8, 4), (2, 7), (29, 33), (31, 1), (38, 1), (7, 23), (20, 39), (2, 37), (1, 20), (41, 0), (17, 24), (22, 24), (42, 3), (36, 0), (38, 14), (31, 23), (17, 5), (31, 28), (28, 23), (38, 35), (14, 14), (41, 31), (22, 29), (20, 22), (48, 13), (32, 21), (3, 17), (32, 30), (34, 5), (10, 14), (23, 17), (19, 12), (9, 34), (40, 20), (38, 5), (23, 5), (5, 3), (35, 36), (40, 16), (25, 4), (35, 16), (41, 37), (42, 14), (10, 21), (39, 26), (48, 8), (30, 1), (41, 40), (0, 5), (34, 6), (4, 27), (26, 38), (8, 9), (6, 34), (4, 20), (37, 0), (3, 33), (40, 12), (45, 6), (2, 1), (26, 21), (11, 37), (8, 16), (25, 38), (45, 2), (0, 14), (27, 1), (41, 8), (19, 11), (38, 16), (46, 19), (15, 21), (43, 31), (3, 22), (41, 5), (12, 29), (9, 6), (38, 7), (12, 19), (36, 26), (26, 27), (1, 18), (24, 9), (11, 9), (26, 19), (19, 5), (22, 38), (20, 10), (33, 17), (18, 27), (18, 4), (42, 6), (31, 7), (37, 23), (22, 13), (47, 4), (35, 30), (25, 11), (48, 15), (28, 32), (5, 11), (36, 25), (34, 31), (15, 18), (19, 10), (9, 31), (37, 33), (17, 22), (27, 7), (35, 17), (19, 15), (14, 31), (41, 20), (35, 1), (18, 29), (1, 14), (12, 33), (30, 16), (13, 35), (33, 6), (47, 26), (2, 3), (25, 31), (33, 31), (37, 39), (23, 12), (0, 24), (30, 14), (45, 24), (9, 29), (45, 37), (2, 39), (12, 7), (39, 39), (0, 28), (16, 9), (42, 34), (27, 34), (6, 12), (25, 36), (42, 25), (5, 32), (34, 30), (46, 13), (2, 32), (39, 11), (43, 3), (30, 28), (16, 26), (43, 20), (21, 1), (32, 26), (9, 40), (45, 30), (14, 37), (36, 33), (37, 3), (8, 7), (47, 19), (29, 38), (28, 30), (48, 1), (12, 14), (43, 8), (39, 35), (7, 15), (47, 11), (1, 16), (16, 33), (35, 31), (23, 15), (4, 26), (30, 2), (41, 2), (20, 26), (28, 20), (7, 21), (37, 15), (41, 12), (46, 34), (36, 15), (11, 16), (28, 24), (45, 19), (7, 32), (6, 15), (22, 27), (45, 40), (46, 22), (36, 37), (12, 27), (32, 40), (31, 6), (23, 0), (32, 5), (41, 26), (1, 1), (12, 26), (41, 17), (1, 11), (14, 27), (0, 22), (18, 15), (24, 10), (44, 6), (0, 1), (36, 31), (3, 35), (1, 6), (31, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 7), (9, 32), (0, 20), (13, 18), (32, 30), (28, 36), (27, 3), (23, 4), (42, 28), (29, 42), (18, 21), (38, 19), (0, 26), (28, 2), (27, 15), (22, 24), (38, 36), (37, 37), (12, 29), (18, 25), (25, 24), (16, 40), (15, 37), (12, 16), (33, 17), (3, 33), (28, 19), (22, 40), (28, 35), (43, 0), (36, 6), (8, 36), (12, 13), (19, 39), (36, 34), (41, 22), (26, 0), (13, 35), (18, 36), (29, 11), (17, 17), (22, 34), (29, 9), (26, 36), (37, 42), (34, 32), (32, 27), (14, 9), (14, 32), (25, 38), (5, 40), (40, 16), (18, 9), (12, 42), (10, 14), (3, 3), (30, 10), (30, 36), (30, 0), (25, 29), (34, 5), (14, 14), (39, 33), (28, 21), (34, 1), (27, 21), (21, 4), (12, 10), (39, 19), (42, 25), (10, 8), (1, 28), (22, 6), (3, 7), (7, 35), (42, 33), (30, 20), (35, 9), (20, 22), (41, 2), (11, 5), (43, 35), (42, 35), (22, 10), (6, 8), (25, 28), (36, 15), (37, 30), (38, 31), (8, 38), (9, 18), (31, 3), (3, 25), (14, 16), (37, 26), (27, 16), (24, 31), (32, 22), (32, 5), (15, 36), (8, 34), (32, 7), (4, 33), (25, 10), (6, 12), (39, 24), (16, 15), (42, 32), (10, 9), (3, 26), (30, 41), (5, 36), (15, 12), (21, 17), (13, 16), (33, 37), (22, 23), (27, 8), (10, 10), (35, 6), (35, 23), (15, 23), (27, 11), (3, 23), (0, 9), (3, 2), (26, 24), (30, 2), (37, 20), (19, 40), (43, 38), (7, 16), (33, 26), (19, 8), (21, 31), (8, 28), (43, 3), (39, 36), (12, 14), (41, 24), (22, 42), (8, 42), (19, 18), (5, 25), (18, 38), (38, 5), (11, 40), (40, 41), (36, 28), (36, 40), (1, 24), (21, 23), (30, 23), (25, 12), (11, 4), (7, 34), (16, 35), (27, 2), (5, 15), (42, 3), (34, 14), (40, 11), (15, 3), (8, 21), (31, 25), (19, 10), (38, 41), (37, 25), (2, 14), (0, 1), (30, 7), (1, 23), (10, 21), (13, 0), (41, 29), (30, 31), (11, 0), (33, 40), (30, 35), (24, 18), (29, 31), (22, 2), (19, 22), (16, 23), (3, 43), (6, 28), (24, 37), (3, 30), (26, 3), (19, 13), (2, 39), (21, 15), (2, 28), (26, 12), (13, 41), (12, 3), (28, 6), (18, 0), (41, 17), (25, 13), (7, 36), (8, 15), (25, 40), (32, 17), (37, 40), (15, 8), (2, 9), (16, 20), (29, 27), (30, 19), (10, 12), (13, 10), (9, 28), (24, 17), (30, 33), (35, 39), (23, 43), (2, 32), (34, 33), (29, 39), (28, 22), (41, 25), (33, 1), (14, 15), (21, 1), (3, 5), (18, 28), (24, 7), (12, 18), (19, 23), (37, 16), (42, 2), (13, 7), (0, 10), (36, 42), (19, 38), (6, 15), (33, 31), (10, 18), (34, 24), (9, 15), (24, 9), (32, 3), (18, 15), (29, 37), (37, 41), (30, 8), (24, 22), (0, 37), (21, 24), (7, 17), (11, 10), (28, 43), (42, 15), (15, 29), (31, 1), (39, 5), (25, 35), (32, 42), (14, 30), (20, 37), (16, 30), (17, 38), (24, 29), (24, 13), (27, 40), (35, 2), (43, 7), (30, 24), (0, 29), (30, 9), (33, 32), (34, 12), (37, 43), (27, 1), (18, 42), (32, 33), (10, 24), (6, 23), (41, 18), (2, 5), (33, 10), (6, 18), (16, 29), (17, 3), (36, 27), (1, 30), (29, 24), (6, 34), (28, 13), (4, 43), (38, 32), (13, 24), (24, 43), (12, 24), (1, 27), (20, 9), (9, 36), (35, 17), (40, 0), (35, 25), (23, 22), (28, 27), (9, 0), (18, 24), (31, 33), (35, 34), (20, 36), (12, 7), (36, 1), (35, 1), (30, 37), (27, 42), (22, 38), (11, 16), (23, 7), (39, 28), (26, 40), (30, 12), (19, 20), (24, 27), (1, 20), (28, 11), (19, 5), (29, 6), (13, 19), (25, 41), (8, 13), (41, 30), (24, 15), (19, 34), (1, 9), (12, 23), (34, 4), (15, 26), (42, 29), (6, 25), (15, 17), (8, 24), (22, 5), (33, 3), (33, 29), (31, 31), (23, 2), (40, 26), (10, 17), (2, 0), (20, 12), (32, 36), (22, 28), (8, 9), (38, 28), (20, 32), (4, 2), (20, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 4), (23, 35), (34, 23), (14, 2), (22, 30), (7, 40), (17, 5), (13, 2), (4, 11), (4, 12), (32, 28), (8, 13), (29, 4), (17, 26), (38, 22), (13, 0), (25, 7), (40, 13), (16, 12), (23, 37), (5, 8), (25, 0), (5, 35), (2, 33), (21, 20), (27, 11), (33, 34), (12, 8), (43, 3), (0, 16), (37, 34), (21, 35), (0, 31), (31, 9), (27, 26), (31, 13), (26, 23), (4, 27), (20, 3), (18, 37), (3, 0), (30, 10), (5, 2), (34, 8), (0, 39), (41, 8), (6, 7), (43, 24), (22, 24), (28, 13), (36, 34), (11, 14), (2, 21), (5, 28), (5, 9), (7, 26), (14, 16), (8, 33), (28, 29), (36, 6), (20, 23), (24, 7), (17, 21), (21, 32), (0, 40), (32, 12), (8, 11), (38, 0), (7, 19), (34, 35), (6, 25), (41, 17), (40, 14), (41, 33), (23, 41), (10, 16), (13, 32), (39, 21), (42, 41), (43, 9), (23, 7), (34, 16), (41, 25), (24, 5), (36, 35), (42, 17), (37, 7), (8, 31), (40, 1), (27, 7), (40, 9), (18, 25), (25, 40), (25, 38), (2, 24), (35, 11), (15, 22), (25, 16), (19, 33), (8, 35), (25, 9), (40, 16), (27, 38), (8, 6), (15, 33), (4, 37), (17, 4), (13, 27), (32, 30), (25, 36), (42, 28), (41, 19), (1, 2), (17, 2), (11, 5), (11, 0), (14, 40), (28, 28), (5, 0), (30, 17), (43, 34), (23, 23), (0, 24), (25, 21), (37, 20), (8, 40), (18, 5), (8, 2), (23, 38), (33, 9), (33, 19), (37, 15), (26, 18), (22, 38), (39, 27), (27, 16), (21, 22), (31, 33), (10, 36), (6, 40), (9, 28), (1, 36), (42, 35), (26, 10), (43, 35), (6, 18), (15, 4), (32, 25), (35, 18), (6, 41), (2, 8), (25, 23), (19, 13), (37, 30), (42, 16), (12, 27), (18, 7), (20, 20), (40, 34), (24, 16), (7, 39), (31, 28), (7, 10), (4, 21), (32, 9), (2, 38), (2, 17), (17, 36), (30, 18), (34, 18), (17, 1), (33, 21), (3, 28), (18, 38), (1, 4), (31, 31), (29, 21), (6, 28), (37, 41), (21, 13), (16, 4), (19, 9), (1, 27), (28, 26), (28, 4), (3, 13), (29, 38), (42, 26), (35, 9), (35, 20), (12, 25), (4, 30), (24, 6), (13, 30), (2, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 48x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 26), (4, 9), (1, 4), (16, 38), (1, 42), (37, 34), (40, 2), (3, 3), (35, 31), (7, 13), (27, 15), (7, 19), (12, 19), (19, 2), (8, 4), (18, 19), (16, 22), (21, 35), (4, 17), (6, 22), (39, 41), (19, 5), (40, 40), (14, 19), (24, 40), (18, 26), (9, 5), (24, 4), (30, 19), (4, 15), (29, 26), (0, 18), (17, 24), (9, 21), (43, 17), (11, 40), (5, 22), (23, 34), (2, 12), (13, 12), (11, 7), (37, 39), (6, 2), (3, 13), (0, 35), (40, 29), (6, 26), (3, 7), (15, 0), (5, 35), (44, 40), (47, 28), (2, 26), (12, 24), (27, 31), (22, 14), (38, 26), (42, 6), (0, 28), (1, 9), (8, 33), (31, 1), (38, 31), (46, 8), (45, 19), (34, 39), (35, 29), (44, 15), (45, 7), (40, 18), (26, 2), (40, 16), (37, 33), (40, 42), (21, 37), (42, 13), (19, 32), (29, 1), (14, 25), (28, 2), (39, 22), (2, 27), (0, 33), (6, 29), (1, 18), (34, 12), (9, 37), (34, 5), (29, 22), (14, 34), (13, 4), (40, 34), (31, 32), (42, 16), (3, 38), (20, 7), (44, 20), (12, 4), (31, 9), (5, 25), (10, 29), (18, 33), (5, 5), (29, 33), (26, 34), (4, 4), (8, 10), (36, 32), (32, 38), (7, 30), (2, 24), (8, 18), (22, 36), (33, 13), (44, 8), (23, 25), (40, 5), (37, 3), (36, 4), (5, 12), (13, 0), (25, 22), (2, 33), (10, 18), (20, 22), (40, 10), (15, 16), (6, 35), (9, 42), (23, 14), (14, 18), (3, 24), (43, 34), (0, 23), (5, 1), (1, 7), (16, 20), (3, 2), (11, 10), (40, 3), (36, 7), (23, 36), (17, 20), (16, 41), (28, 40), (4, 12), (40, 1), (25, 36), (26, 41), (16, 35), (32, 17), (12, 28), (17, 41), (35, 37), (33, 1), (13, 42), (40, 12), (15, 37), (34, 1), (14, 35), (21, 34), (46, 7), (8, 2), (45, 32), (34, 41), (4, 11), (19, 29), (28, 24), (3, 32), (41, 37), (4, 36), (44, 25), (17, 15), (20, 28), (13, 11), (43, 8), (44, 4), (13, 27), (30, 42), (45, 13), (28, 23), (4, 42), (22, 29), (38, 3), (47, 14), (11, 0), (26, 1), (43, 38), (41, 3), (13, 1), (43, 18), (3, 10), (45, 35), (35, 10), (35, 5), (34, 13), (21, 31), (15, 10), (7, 42), (16, 25), (35, 16), (3, 30), (16, 18), (42, 20), (10, 0), (42, 2), (19, 40), (13, 38), (18, 20), (14, 27), (21, 22), (46, 29), (43, 2), (5, 20), (24, 41), (14, 14), (27, 10), (23, 6), (2, 30), (9, 0), (38, 39), (21, 14), (18, 16), (10, 16), (5, 39), (18, 17), (9, 36), (5, 30), (33, 2), (27, 14), (1, 17), (30, 6), (41, 42), (38, 5), (5, 7), (10, 21), (22, 32), (20, 9), (4, 8), (13, 24), (0, 15), (8, 5), (4, 25), (27, 28), (6, 36), (40, 19), (16, 24), (26, 28), (25, 7), (14, 15), (25, 10), (41, 39), (18, 31), (25, 20), (29, 23), (1, 19), (20, 1), (17, 31), (10, 37), (15, 29), (45, 1), (44, 34), (41, 41), (24, 15), (39, 26), (15, 23), (11, 17), (20, 20), (47, 10), (23, 16), (25, 0), (22, 9), (27, 19), (0, 42), (0, 37), (41, 14), (6, 6), (35, 14), (36, 38), (30, 27), (11, 1), (0, 9), (9, 32), (7, 20), (22, 1), (3, 18), (10, 12), (6, 37), (31, 33), (18, 0), (25, 23), (37, 8), (46, 35), (27, 25), (40, 7), (13, 19), (38, 20), (7, 18), (9, 29), (47, 37), (46, 12), (37, 15), (3, 8), (11, 39), (22, 8), (15, 41), (18, 2), (2, 9), (47, 8), (41, 18), (15, 3), (4, 31), (4, 5), (8, 41), (17, 9), (26, 25), (27, 30), (37, 20), (30, 37), (15, 27), (25, 38), (17, 25), (18, 41), (28, 37), (13, 29), (33, 0), (27, 26), (41, 29), (15, 22), (25, 2), (16, 33), (0, 2), (31, 24), (9, 40), (30, 18), (22, 19), (31, 23), (19, 14), (14, 10), (9, 19), (43, 14), (23, 1), (20, 21), (17, 5), (45, 0), (20, 4), (40, 25), (28, 25), (44, 39), (29, 20), (16, 36), (31, 35), (2, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 20), (3, 14), (24, 11), (18, 21), (29, 13), (19, 26), (27, 15), (39, 35), (29, 16), (22, 29), (32, 25), (26, 26), (24, 31), (40, 9), (44, 22), (7, 39), (20, 1), (0, 40), (6, 34), (12, 36), (36, 25), (42, 2), (20, 4), (10, 38), (8, 18), (7, 2), (32, 4), (5, 4), (41, 7), (14, 20), (43, 25), (17, 20), (36, 8), (28, 33), (12, 1), (18, 38), (28, 17), (0, 30), (23, 40), (19, 23), (17, 9), (45, 16), (4, 5), (0, 26), (32, 2), (8, 32), (38, 13), (44, 35), (30, 36), (9, 4), (13, 14), (16, 23), (35, 25), (34, 36), (11, 32), (3, 27), (45, 35), (29, 5), (3, 12), (19, 21), (39, 42), (42, 17), (39, 11), (23, 31), (43, 31), (19, 27), (31, 18), (38, 16), (37, 37), (17, 39), (35, 10), (28, 42), (5, 22), (2, 10), (43, 18), (2, 41), (1, 29), (31, 28), (33, 31), (15, 25), (23, 12), (19, 25), (14, 36), (18, 19), (6, 29), (10, 40), (9, 29), (13, 30), (41, 32), (18, 22), (10, 17), (34, 35), (21, 3), (19, 41), (24, 2), (41, 9), (0, 25), (4, 18), (40, 24), (19, 4), (45, 29), (22, 25), (18, 13), (15, 27), (34, 38), (42, 7), (36, 38), (1, 32), (12, 35), (17, 15), (8, 17), (37, 35), (37, 42), (30, 5), (37, 32), (4, 1), (35, 9), (42, 39), (12, 21), (40, 15), (27, 37), (38, 23), (24, 16), (35, 42), (8, 14), (15, 24), (43, 32), (35, 5), (9, 0), (19, 38), (6, 25), (6, 20), (19, 37), (29, 6), (3, 29), (40, 20), (32, 18), (40, 0), (8, 22), (39, 34), (20, 17), (11, 39), (1, 9), (8, 31), (9, 13), (9, 14), (12, 13), (35, 8), (16, 1), (35, 33), (36, 3), (10, 30), (38, 34), (42, 18), (15, 10), (14, 31), (0, 21), (34, 34), (35, 36), (30, 35), (7, 23), (33, 11), (41, 14), (0, 14), (9, 30), (41, 10), (45, 12), (35, 4), (16, 35), (5, 20), (24, 12), (15, 30), (20, 22), (14, 11), (1, 18), (28, 3), (2, 23), (14, 9), (25, 39), (2, 37), (41, 19), (30, 38), (15, 40), (15, 12), (1, 31), (9, 18), (3, 15), (20, 32), (21, 20), (22, 19), (18, 14), (34, 0), (31, 2), (42, 16), (44, 21), (1, 3), (36, 29), (26, 3), (34, 33), (7, 15), (17, 24), (26, 2), (6, 15), (21, 22), (0, 19), (2, 22), (1, 37), (34, 20), (27, 22), (23, 23), (32, 31), (18, 26), (19, 34), (38, 10), (39, 16), (11, 36), (30, 41), (37, 15), (1, 10), (15, 28), (45, 21), (24, 4), (17, 8), (23, 11), (29, 20), (31, 27), (28, 38), (21, 21), (27, 16), (11, 12), (42, 6), (45, 28), (43, 42), (6, 31), (9, 33), (25, 18), (0, 37), (1, 5), (36, 6), (20, 41), (18, 6), (21, 26), (44, 7), (25, 22), (28, 5), (41, 20), (23, 13), (20, 30), (17, 3), (19, 0), (20, 16), (20, 10), (4, 19), (2, 5), (23, 4), (40, 22), (26, 36), (34, 3), (2, 24), (22, 17), (18, 4), (27, 5), (12, 17), (36, 16), (30, 32), (21, 8), (16, 39), (44, 1), (35, 28), (22, 24), (25, 6), (7, 10), (34, 37), (11, 4), (14, 0), (30, 25), (25, 14), (23, 9), (29, 32), (23, 20), (39, 33), (40, 32), (35, 13), (41, 1), (32, 5), (0, 29), (12, 3), (21, 6), (19, 7), (1, 36), (25, 11), (11, 2), (6, 7), (18, 28), (2, 14), (24, 39), (13, 24), (25, 5), (7, 22), (45, 18), (3, 26), (5, 33), (19, 33), (11, 19), (13, 1), (21, 36), (17, 42), (31, 20), (43, 35), (30, 12), (32, 41), (16, 42), (37, 12), (41, 2), (34, 10), (45, 24), (34, 16), (45, 17), (10, 41), (3, 2), (43, 0), (24, 23), (15, 7), (29, 42), (22, 9), (15, 34), (23, 6), (39, 8), (27, 33), (2, 21), (36, 27), (22, 7), (21, 13), (22, 38), (4, 14), (17, 30), (21, 33), (12, 22), (41, 16), (34, 23), (26, 8), (21, 15), (30, 7), (40, 5), (13, 18), (2, 16), (38, 41), (6, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 3), (44, 31), (27, 34), (45, 44), (40, 37), (32, 21), (17, 16), (1, 11), (0, 41), (0, 10), (10, 41), (2, 33), (28, 16), (1, 45), (45, 23), (30, 5), (45, 28), (35, 14), (23, 45), (21, 42), (11, 15), (19, 43), (11, 34), (14, 31), (42, 29), (37, 22), (23, 30), (15, 21), (6, 4), (12, 0), (0, 28), (5, 39), (4, 44), (32, 0), (25, 31), (32, 25), (2, 38), (21, 7), (36, 35), (16, 29), (20, 28), (16, 34), (41, 6), (14, 0), (33, 6), (41, 11), (11, 43), (25, 24), (15, 20), (4, 18), (4, 39), (37, 29), (7, 27), (11, 0), (24, 14), (1, 21), (20, 27), (23, 41), (45, 20), (24, 24), (10, 17), (33, 46), (43, 24), (32, 13), (29, 17), (44, 43), (30, 26), (18, 9), (6, 39), (3, 3), (36, 38), (10, 30), (35, 26), (12, 18), (31, 36), (44, 3), (13, 41), (6, 43), (43, 26), (35, 12), (24, 15), (14, 28), (7, 19), (25, 6), (8, 22), (24, 7), (44, 18), (18, 12), (6, 22), (12, 13), (12, 42), (19, 30), (30, 14), (10, 29), (18, 26), (41, 4), (40, 19), (24, 26), (8, 25), (5, 3), (3, 45), (42, 22), (10, 15), (45, 32), (12, 46), (39, 4), (13, 21), (34, 32), (1, 1), (5, 14), (37, 15), (36, 37), (0, 37), (32, 44), (25, 40), (27, 14), (4, 10), (23, 46), (13, 5), (2, 17), (31, 38), (26, 3), (9, 17), (43, 8), (27, 36), (26, 4), (18, 40), (2, 12), (31, 25), (44, 13), (36, 46), (36, 19), (29, 37), (39, 36), (24, 28), (41, 21), (17, 7), (1, 20), (21, 21), (15, 10), (2, 22), (8, 12), (44, 6), (27, 6), (33, 16), (15, 27), (40, 21), (45, 33), (1, 3), (24, 38), (19, 2), (42, 1), (34, 2), (15, 6), (1, 0), (40, 11), (15, 38), (28, 40), (10, 1), (24, 0), (8, 26), (33, 19), (8, 23), (0, 19), (44, 39), (19, 36), (26, 29), (41, 18), (38, 2), (12, 15), (39, 45), (8, 9), (5, 38), (39, 9), (36, 18), (25, 15), (30, 43), (10, 23), (42, 44), (29, 44), (3, 30), (37, 6), (39, 33), (17, 15), (7, 18), (8, 43), (9, 39), (27, 45), (25, 23), (28, 5), (24, 31), (19, 7), (10, 13), (43, 3), (35, 24), (1, 10), (29, 42), (43, 31), (6, 24), (17, 20), (40, 5), (28, 31), (36, 26), (31, 15), (22, 5), (4, 0), (27, 27), (19, 32), (7, 43), (42, 12), (31, 30), (40, 39), (36, 31), (44, 34), (20, 1), (0, 22), (2, 29), (25, 45), (40, 10), (30, 23), (5, 5), (40, 18), (26, 21), (26, 41), (43, 2), (40, 1), (3, 14), (13, 3), (19, 17), (44, 15), (25, 1), (13, 2), (28, 34), (26, 17), (22, 19), (41, 25), (28, 36), (19, 44), (8, 27), (6, 29), (23, 20), (30, 4), (36, 7), (29, 43), (42, 39), (38, 37), (25, 39), (13, 0), (14, 9), (27, 25), (22, 3), (45, 22), (36, 27), (19, 4), (14, 16), (13, 20), (1, 39), (34, 7), (17, 31), (22, 11), (26, 14), (27, 7), (24, 18), (5, 9), (27, 22), (25, 11), (15, 1), (7, 1), (28, 9), (23, 23), (8, 4), (32, 11), (29, 32), (15, 28), (15, 36), (11, 16), (45, 35), (4, 21), (16, 45), (27, 30), (3, 42), (40, 3), (22, 28), (31, 22), (3, 21), (1, 15), (9, 2), (1, 37), (42, 19), (25, 10), (14, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 10), (23, 27), (3, 4), (22, 24), (26, 5), (31, 30), (23, 25), (28, 19), (29, 31), (44, 22), (39, 16), (39, 19), (28, 36), (10, 31), (28, 23), (44, 3), (16, 33), (41, 39), (33, 9), (11, 13), (13, 14), (36, 18), (22, 6), (29, 7), (6, 34), (17, 9), (1, 5), (13, 20), (15, 4), (21, 12), (44, 18), (10, 8), (38, 10), (26, 39), (14, 25), (26, 23), (13, 13), (28, 27), (10, 39), (16, 0), (34, 32), (40, 37), (33, 1), (7, 8), (7, 5), (8, 27), (25, 26), (9, 0), (6, 39), (7, 35), (23, 7), (5, 13), (13, 0), (19, 28), (11, 2), (16, 17), (30, 15), (14, 27), (30, 26), (41, 23), (20, 25), (2, 30), (32, 32), (45, 0), (8, 33), (8, 8), (17, 16), (1, 14), (15, 16), (6, 21), (24, 4), (25, 1), (33, 0), (29, 6), (36, 39), (40, 38), (26, 26), (26, 1), (43, 39), (38, 6), (29, 9), (30, 12), (8, 29), (42, 23), (17, 12), (10, 0), (23, 11), (42, 25), (2, 31), (16, 22), (21, 22), (40, 25), (37, 22), (23, 30), (30, 36), (1, 19), (37, 36), (22, 26), (22, 18), (12, 19), (35, 15), (14, 0), (11, 24), (42, 39), (36, 22), (9, 7), (42, 29), (21, 15), (32, 9), (22, 3), (18, 2), (38, 29), (6, 17), (31, 8), (18, 18), (4, 13), (8, 38), (13, 17), (40, 17), (27, 7), (10, 7), (10, 9), (19, 27), (21, 8), (13, 36), (8, 10), (33, 18), (5, 25), (19, 7), (37, 7), (35, 35), (3, 33), (16, 5), (28, 39), (12, 38), (5, 20), (26, 33), (0, 26), (38, 26), (24, 23), (27, 37), (22, 8), (20, 17), (13, 10), (16, 29), (27, 35), (30, 18), (46, 8), (34, 14), (25, 34), (45, 3), (3, 25), (27, 15), (40, 24), (28, 12), (4, 9), (28, 28), (24, 31), (39, 0), (35, 22), (0, 22), (9, 2), (23, 24), (39, 12), (0, 8), (1, 6), (3, 32), (42, 3), (7, 14), (35, 38), (1, 23), (13, 30), (1, 1), (17, 29), (38, 17), (26, 7), (25, 33), (46, 7), (39, 9), (39, 39), (6, 3), (31, 27), (1, 28), (7, 18), (42, 16), (2, 1), (14, 39), (5, 28), (37, 32), (21, 23), (15, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 37), (28, 0), (9, 43), (23, 5), (36, 42), (17, 28), (6, 10), (31, 19), (24, 1), (24, 37), (6, 21), (12, 19), (7, 37), (40, 26), (41, 37), (19, 8), (1, 5), (9, 1), (34, 0), (28, 21), (13, 3), (8, 14), (17, 40), (15, 36), (4, 0), (21, 38), (33, 6), (39, 30), (37, 11), (7, 5), (19, 6), (32, 38), (32, 21), (26, 33), (41, 25), (27, 29), (36, 33), (3, 14), (9, 30), (12, 3), (24, 8), (6, 12), (24, 39), (43, 20), (14, 38), (4, 20), (42, 7), (13, 24), (0, 9), (43, 37), (36, 30), (28, 7), (7, 44), (29, 22), (39, 39), (8, 34), (12, 43), (36, 16), (8, 44), (9, 13), (21, 26), (20, 39), (4, 19), (25, 11), (31, 30), (40, 22), (31, 14), (28, 42), (34, 30), (38, 16), (18, 14), (19, 22), (14, 4), (2, 23), (5, 35), (19, 29), (32, 6), (37, 6), (18, 27), (24, 22), (20, 2), (12, 8), (38, 32), (37, 0), (41, 14), (27, 19), (39, 12), (18, 31), (16, 13), (36, 20), (20, 35), (42, 21), (29, 34), (20, 18), (12, 32), (3, 0), (43, 36), (16, 3), (34, 12), (0, 12), (5, 11), (11, 27), (14, 34), (10, 43), (6, 28), (30, 3), (2, 14), (0, 17), (14, 19), (2, 16), (39, 7), (13, 10), (8, 10), (12, 33), (33, 14), (17, 36), (18, 17), (25, 7), (33, 24), (8, 15), (32, 8), (4, 43), (34, 1), (14, 14), (15, 33), (29, 0), (31, 44), (19, 44), (16, 20), (38, 0), (6, 24), (0, 11), (28, 2), (38, 5), (36, 27), (25, 18), (20, 4), (2, 37), (19, 24), (30, 34), (27, 25), (2, 26), (31, 8), (19, 3), (31, 1), (30, 11), (43, 29), (30, 36), (11, 10), (43, 16), (2, 24), (4, 11), (26, 7), (13, 22), (27, 2), (42, 15), (2, 42), (38, 12), (33, 33), (34, 44), (3, 8), (42, 40), (27, 11), (19, 25), (21, 44), (3, 35), (5, 32), (29, 4), (34, 8), (0, 27), (12, 4), (28, 8), (13, 39), (22, 33), (16, 38), (42, 18), (2, 44), (25, 26), (15, 44), (13, 15), (12, 5), (23, 23), (1, 32), (15, 32), (14, 20), (24, 20), (37, 30), (17, 4), (21, 14), (14, 39), (32, 27), (3, 2), (43, 38), (42, 20), (11, 22), (8, 11), (6, 1), (2, 39), (1, 28), (9, 42), (8, 24), (3, 41), (21, 4), (24, 11), (1, 20), (11, 42), (18, 39), (19, 10), (11, 0), (21, 25), (22, 4), (32, 18), (22, 1), (1, 12), (39, 3), (5, 25), (38, 2), (28, 29), (31, 11), (5, 29), (21, 35), (33, 27), (40, 11), (35, 12), (35, 40), (5, 4), (20, 22), (31, 10), (31, 35), (23, 18), (36, 39), (7, 32), (42, 10), (33, 1), (42, 5), (19, 23), (35, 0), (40, 21), (26, 41), (11, 14), (36, 21), (9, 34), (32, 13), (30, 17), (26, 24), (1, 26), (4, 41), (29, 8), (26, 43), (37, 38), (3, 43), (27, 1), (10, 37), (28, 3), (12, 34), (15, 43), (7, 11), (40, 44), (1, 31), (35, 34), (40, 33), (5, 18), (1, 13), (24, 9), (15, 28), (23, 33), (10, 12), (24, 12), (2, 15), (40, 29), (12, 21), (36, 29), (30, 39), (5, 41), (39, 10), (12, 38), (38, 38), (31, 12), (15, 21), (33, 35), (23, 31), (6, 42), (29, 14), (42, 29), (18, 15), (32, 44), (20, 23), (9, 7), (23, 43), (37, 4), (9, 17), (4, 32), (9, 23), (23, 0), (17, 39), (22, 6), (7, 23), (14, 29), (23, 35), (38, 6), (27, 18), (28, 37), (34, 22), (8, 39), (29, 25), (41, 32), (43, 2), (22, 21), (11, 12), (41, 3), (28, 39), (4, 2), (37, 22), (36, 9), (0, 25), (27, 35), (15, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 38), (10, 24), (29, 39), (16, 15), (23, 36), (27, 31), (31, 23), (31, 6), (17, 0), (38, 39), (26, 9), (45, 36), (7, 14), (31, 20), (39, 2), (16, 22), (9, 29), (21, 29), (10, 30), (20, 9), (18, 37), (38, 33), (40, 27), (39, 32), (13, 24), (23, 23), (26, 13), (7, 17), (30, 2), (15, 36), (5, 30), (8, 5), (2, 23), (11, 26), (11, 6), (20, 12), (26, 1), (12, 8), (36, 5), (36, 33), (24, 8), (41, 4), (22, 35), (13, 34), (42, 24), (3, 12), (12, 5), (15, 1), (20, 35), (11, 37), (0, 33), (36, 38), (29, 21), (4, 29), (3, 7), (12, 25), (14, 14), (25, 16), (44, 14), (43, 9), (41, 24), (4, 36), (35, 4), (41, 27), (26, 18), (42, 12), (41, 28), (40, 31), (19, 20), (5, 11), (29, 30), (32, 27), (33, 6), (13, 11), (8, 32), (38, 15), (8, 28), (6, 23), (16, 27), (37, 15), (41, 19), (14, 9), (39, 7), (13, 26), (20, 8), (23, 29), (16, 29), (33, 39), (2, 22), (21, 4), (3, 37), (38, 12), (42, 20), (0, 13), (33, 5), (2, 6), (14, 39), (39, 39), (30, 38), (8, 35), (40, 18), (32, 2), (41, 13), (0, 27), (0, 21), (7, 10), (35, 6), (1, 32), (0, 20), (17, 32), (1, 9), (40, 28), (13, 6), (26, 21), (25, 12), (2, 7), (15, 31), (27, 13), (13, 32), (18, 29), (15, 20), (37, 14), (43, 0), (16, 10), (28, 3), (24, 1), (22, 36), (12, 10), (29, 9), (43, 10), (40, 30), (11, 3), (31, 26), (1, 38), (43, 29), (21, 37), (10, 23), (28, 15), (22, 8), (22, 0), (28, 6), (4, 32), (15, 10), (34, 28), (15, 39), (22, 20), (20, 24), (16, 18), (14, 23), (45, 33), (40, 19), (37, 30), (22, 32), (0, 31), (13, 33), (21, 23), (37, 31), (45, 6), (10, 18), (16, 24), (23, 24), (43, 38), (8, 11), (14, 32), (33, 18), (26, 38), (42, 2), (5, 14), (42, 14), (31, 9), (28, 23), (7, 2), (12, 0), (1, 27), (37, 10), (37, 19), (21, 35), (1, 14), (20, 19), (25, 32), (45, 10), (25, 7), (40, 16), (30, 29), (14, 11), (8, 26), (45, 13), (27, 6), (39, 35), (26, 14), (39, 24), (26, 35), (38, 31), (12, 2), (7, 22), (21, 2), (31, 13), (3, 17), (6, 3), (10, 27), (10, 25), (1, 23), (6, 5), (19, 13), (13, 9), (44, 20), (11, 38), (17, 8), (6, 28), (5, 26), (34, 3), (17, 24), (40, 23), (38, 23), (22, 11), (35, 2), (44, 7), (41, 12), (4, 21), (34, 30), (4, 5), (7, 15), (0, 12), (26, 31), (1, 19), (42, 30), (25, 25), (23, 34), (4, 33), (17, 15), (7, 13), (10, 7), (31, 3), (8, 8), (21, 27), (0, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 31), (35, 5), (2, 13), (44, 5), (32, 2), (31, 38), (12, 18), (23, 37), (1, 17), (3, 40), (34, 7), (22, 19), (27, 37), (37, 16), (44, 28), (30, 7), (43, 6), (33, 37), (29, 32), (41, 16), (35, 2), (6, 4), (31, 9), (16, 41), (3, 33), (31, 22), (11, 2), (36, 33), (33, 21), (8, 16), (41, 14), (33, 12), (19, 10), (19, 24), (15, 32), (3, 4), (43, 12), (22, 31), (39, 5), (36, 34), (36, 12), (19, 9), (9, 29), (27, 38), (25, 6), (30, 29), (44, 13), (38, 17), (19, 35), (42, 5), (43, 22), (36, 15), (13, 34), (39, 30), (29, 20), (2, 8), (16, 21), (25, 21), (32, 42), (27, 15), (17, 5), (21, 11), (42, 42), (21, 21), (17, 29), (39, 1), (43, 24), (28, 11), (17, 33), (43, 15), (11, 35), (3, 12), (9, 30), (15, 28), (32, 32), (41, 18), (32, 35), (24, 4), (0, 3), (41, 17), (5, 14), (26, 27), (40, 33), (13, 3), (6, 23), (4, 38), (19, 25), (43, 36), (10, 33), (13, 41), (35, 42), (19, 13), (15, 24), (26, 29), (38, 15), (28, 18), (1, 40), (41, 30), (25, 42), (44, 31), (5, 7), (5, 33), (1, 4), (28, 26), (21, 24), (11, 28), (28, 31), (36, 37), (34, 15), (23, 24), (28, 38), (13, 36), (14, 10), (31, 21), (14, 42), (29, 36), (28, 1), (42, 36), (4, 30), (9, 14), (26, 31), (21, 32), (9, 27), (23, 15), (1, 19), (37, 5), (5, 8), (12, 11), (12, 42), (35, 40), (36, 32), (25, 29), (33, 42), (23, 26), (17, 16), (17, 2), (20, 19), (18, 28), (13, 24), (10, 22), (10, 0), (26, 13), (34, 30), (34, 40), (13, 28), (23, 33), (0, 25), (28, 30), (31, 30), (21, 3), (4, 22), (23, 1), (24, 37), (25, 38), (29, 11), (24, 7), (19, 18), (14, 16), (19, 16), (2, 24), (3, 36), (1, 7), (8, 40), (18, 4), (7, 26), (44, 41), (40, 23), (44, 6), (19, 4), (31, 19), (35, 27), (2, 4), (35, 13), (19, 27), (41, 8), (33, 19), (33, 6), (29, 28), (18, 20), (6, 3), (23, 19), (0, 7), (18, 15), (6, 14), (29, 14), (11, 24), (36, 38), (25, 19), (5, 34), (10, 30), (43, 25), (21, 40), (2, 34), (21, 6), (9, 6), (0, 18), (3, 8), (36, 2), (32, 41), (11, 41), (23, 36), (10, 31), (40, 29), (28, 40), (21, 35), (35, 26), (3, 31), (9, 5), (11, 32), (6, 21), (15, 23), (14, 9), (42, 1), (37, 9), (13, 0), (43, 34), (44, 8), (7, 38), (9, 1), (41, 1), (7, 2), (41, 38), (8, 39), (36, 31), (40, 22), (25, 30), (4, 36), (4, 40), (7, 15), (12, 23), (0, 20), (0, 31), (19, 42), (40, 26), (21, 34), (19, 1), (16, 28), (5, 11), (25, 4), (42, 30), (11, 15), (40, 12), (10, 24), (8, 14), (1, 38), (41, 6), (14, 19), (10, 40), (0, 27), (3, 26), (11, 31), (26, 1), (16, 20), (9, 36), (37, 17), (30, 24), (43, 16), (18, 10), (23, 23), (0, 29), (18, 12), (35, 20), (19, 36), (14, 24), (20, 17), (6, 7), (26, 26), (16, 24), (13, 32), (25, 27), (22, 20), (18, 37), (12, 3), (29, 38), (37, 11), (39, 15), (19, 14), (34, 41), (24, 21), (29, 17), (16, 10), (33, 7), (38, 4), (6, 10), (12, 12), (36, 26), (29, 15), (27, 31), (38, 14), (38, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 1), (43, 45), (45, 43), (28, 30), (13, 44), (7, 11), (23, 43), (41, 13), (24, 2), (18, 32), (30, 34), (11, 24), (42, 30), (26, 34), (17, 34), (40, 30), (25, 19), (26, 31), (4, 46), (27, 40), (9, 37), (34, 44), (0, 1), (23, 18), (14, 29), (13, 16), (6, 20), (9, 12), (6, 11), (23, 3), (27, 21), (21, 45), (37, 19), (18, 42), (18, 14), (46, 38), (43, 19), (5, 3), (33, 41), (23, 33), (3, 30), (40, 12), (12, 31), (2, 41), (14, 9), (1, 36), (26, 20), (16, 38), (30, 45), (32, 26), (18, 36), (11, 45), (22, 6), (8, 4), (1, 13), (45, 9), (4, 17), (36, 20), (25, 1), (12, 4), (33, 33), (21, 30), (4, 6), (5, 23), (25, 17), (44, 32), (32, 41), (46, 33), (22, 3), (25, 26), (32, 9), (22, 46), (3, 0), (45, 24), (40, 22), (44, 45), (25, 9), (8, 24), (18, 27), (17, 22), (7, 27), (39, 40), (0, 5), (8, 29), (19, 11), (14, 17), (20, 8), (9, 22), (17, 3), (27, 16), (38, 1), (3, 9), (2, 7), (42, 29), (3, 18), (36, 28), (43, 25), (14, 46), (29, 10), (40, 0), (25, 5), (33, 26), (1, 24), (47, 42), (8, 11), (46, 9), (6, 38), (47, 39), (10, 36), (35, 3), (12, 42), (16, 37), (14, 3), (33, 39), (22, 1), (44, 37), (30, 6), (10, 10), (15, 5), (9, 16), (14, 27), (31, 16), (33, 21), (4, 42), (42, 42), (45, 46), (34, 20), (10, 38), (43, 1), (39, 7), (26, 7), (20, 35), (26, 14), (7, 38), (31, 31), (42, 39), (27, 22), (27, 13), (5, 35), (20, 26), (28, 31), (0, 12), (1, 29), (30, 43), (8, 30), (28, 44), (0, 24), (43, 5), (46, 30), (26, 29), (21, 34), (7, 18), (39, 26), (32, 6), (33, 19), (39, 46), (25, 14), (36, 40), (8, 33), (32, 31), (22, 18), (20, 18), (28, 1), (12, 32), (19, 7), (16, 14), (37, 36), (4, 41), (26, 10), (31, 42), (19, 26), (46, 25), (46, 27), (10, 19), (21, 23), (44, 42), (4, 36), (10, 34), (46, 4), (44, 44), (41, 30), (24, 43), (1, 21), (13, 12), (23, 30), (26, 11), (3, 7), (10, 18), (34, 11), (40, 9), (2, 27), (38, 33), (21, 22), (31, 35), (35, 21), (8, 34), (29, 43), (26, 46), (26, 9), (17, 21), (0, 14), (6, 17), (9, 18), (14, 7), (34, 24), (4, 23), (39, 9), (38, 19), (47, 41), (27, 20), (9, 20), (20, 33), (34, 38), (36, 7), (28, 26), (33, 34), (1, 7), (4, 11), (16, 30), (39, 30), (28, 19), (16, 11), (42, 27), (27, 38), (4, 18), (28, 32), (29, 12), (29, 19), (1, 4), (45, 33), (37, 25), (33, 46), (2, 3), (2, 25), (44, 8), (37, 16), (15, 23), (36, 15), (19, 38), (9, 17), (35, 27), (13, 7), (22, 38), (9, 9), (45, 32), (41, 3), (44, 15), (13, 5), (16, 2), (3, 42), (7, 7), (14, 25), (42, 16), (26, 41), (47, 30), (1, 25), (17, 37), (0, 41), (38, 21), (46, 2), (16, 36), (18, 41), (32, 12), (12, 2), (2, 36), (16, 0), (29, 8), (2, 38), (33, 8), (42, 10), (29, 36), (2, 20), (34, 13), (9, 3), (19, 41), (44, 16), (8, 42), (33, 13), (36, 12), (10, 30), (25, 6), (34, 7), (38, 35), (29, 21), (33, 20), (28, 12), (12, 46), (9, 40), (20, 38), (33, 4), (9, 25), (31, 12), (21, 14), (38, 26), (38, 43), (21, 33), (28, 17), (41, 46), (5, 4), (45, 44), (35, 4), (35, 11), (34, 5), (46, 28), (15, 44), (13, 45), (12, 20), (3, 36), (42, 6), (6, 41), (46, 5), (2, 17), (3, 8), (17, 20), (14, 30), (11, 7), (13, 37), (42, 5), (26, 21), (12, 9), (29, 2), (35, 18), (26, 35), (25, 30), (30, 0), (28, 4), (30, 26), (24, 1), (31, 29), (13, 31), (31, 7), (35, 15), (10, 0), (34, 19), (24, 6), (11, 6), (10, 27), (5, 16), (26, 28), (40, 14), (42, 15), (32, 8), (13, 6), (7, 43), (10, 3), (38, 12), (7, 28), (39, 31), (29, 44), (33, 11), (4, 38), (22, 5), (18, 16), (15, 11), (7, 5), (47, 20), (14, 32), (17, 45), (44, 27), (8, 45), (23, 42), (42, 20), (22, 14), (20, 32), (18, 6), (24, 33), (43, 14), (37, 40), (31, 38), (4, 26), (46, 0), (35, 17), (4, 0), (28, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 40), (15, 26), (8, 33), (3, 23), (5, 10), (31, 24), (9, 33), (33, 8), (39, 41), (13, 13), (28, 46), (29, 11), (36, 20), (22, 38), (39, 33), (7, 33), (23, 18), (38, 13), (6, 27), (35, 44), (18, 20), (21, 0), (35, 12), (14, 23), (30, 34), (15, 20), (21, 17), (3, 38), (36, 4), (20, 15), (39, 46), (17, 15), (36, 21), (13, 23), (12, 8), (4, 46), (7, 14), (18, 39), (29, 5), (36, 8), (10, 9), (31, 45), (15, 8), (36, 7), (35, 3), (36, 15), (27, 28), (4, 4), (9, 37), (36, 34), (21, 4), (32, 15), (4, 14), (31, 29), (15, 1), (16, 43), (33, 22), (40, 20), (21, 44), (7, 32), (24, 35), (23, 46), (38, 33), (15, 44), (6, 38), (17, 16), (13, 40), (9, 24), (33, 12), (19, 31), (39, 36), (28, 38), (27, 31), (26, 24), (8, 19), (21, 21), (28, 28), (17, 20), (0, 36), (28, 34), (41, 35), (5, 25), (20, 41), (8, 3), (31, 42), (8, 46), (17, 36), (40, 19), (8, 34), (23, 21), (39, 18), (2, 9), (10, 19), (30, 45), (26, 33), (35, 43), (35, 21), (28, 36), (1, 19), (36, 30), (0, 7), (18, 17), (38, 14), (36, 39), (40, 16), (37, 29), (17, 4), (18, 7), (8, 45), (2, 42), (4, 17), (10, 43), (40, 42), (28, 42), (14, 14), (18, 45), (1, 7), (31, 32), (39, 24), (34, 25), (7, 2), (8, 11), (8, 38), (2, 24), (30, 43), (29, 18), (38, 43), (32, 37), (1, 22), (2, 18), (25, 3), (8, 41), (30, 32), (33, 19), (13, 27), (7, 29), (38, 40), (26, 42), (24, 27), (4, 32), (23, 20), (5, 2), (34, 14), (33, 23), (0, 38), (16, 46), (25, 28), (36, 14), (28, 18), (27, 24), (23, 2), (22, 23), (36, 43), (16, 10), (26, 39), (35, 2), (2, 35), (27, 15), (9, 19), (36, 5), (35, 32), (1, 25), (11, 13), (29, 32), (24, 44), (30, 22), (41, 42), (24, 34), (0, 32), (21, 35), (21, 46), (28, 24), (23, 6), (38, 12), (13, 39), (0, 22), (3, 2), (31, 13), (16, 1), (23, 10), (1, 8), (28, 23), (21, 31), (18, 6), (1, 32), (35, 38), (36, 2), (21, 23), (26, 43), (14, 42), (7, 36), (14, 16), (15, 30), (32, 33), (27, 46), (23, 22), (29, 45), (34, 17), (5, 6), (8, 0), (39, 34), (22, 43), (34, 8), (17, 28), (27, 1), (29, 44), (9, 46), (5, 40), (25, 14), (40, 44), (17, 11), (12, 0), (24, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (35, 12), (38, 22), (20, 32), (33, 27), (8, 6), (40, 20), (16, 39), (12, 41), (40, 34), (36, 23), (21, 1), (16, 12), (13, 22), (19, 20), (32, 37), (20, 1), (33, 20), (38, 0), (19, 42), (23, 25), (35, 20), (1, 22), (23, 11), (26, 30), (7, 10), (20, 29), (32, 25), (5, 35), (11, 22), (17, 2), (18, 19), (18, 1), (19, 41), (8, 0), (42, 9), (24, 33), (12, 14), (35, 37), (9, 25), (34, 6), (36, 20), (25, 8), (1, 1), (7, 11), (9, 24), (24, 37), (33, 5), (33, 22), (43, 29), (43, 7), (27, 36), (33, 28), (26, 17), (12, 30), (6, 33), (11, 1), (38, 18), (36, 15), (24, 36), (1, 13), (22, 33), (26, 2), (2, 24), (26, 0), (27, 32), (6, 35), (23, 43), (31, 39), (15, 2), (25, 34), (13, 9), (16, 33), (41, 17), (10, 36), (24, 2), (0, 34), (13, 43), (41, 22), (20, 31), (28, 28), (3, 32), (6, 36), (11, 18), (21, 2), (2, 1), (8, 14), (6, 34), (8, 18), (11, 43), (5, 13), (23, 14), (8, 41), (21, 30), (3, 8), (0, 21), (30, 43), (30, 30), (22, 9), (14, 25), (21, 40), (40, 24), (11, 27), (40, 33), (31, 38), (3, 7), (18, 38), (6, 7), (14, 36), (3, 25), (13, 37), (37, 9), (18, 43), (33, 4), (23, 35), (31, 13), (27, 8), (40, 11), (10, 39), (10, 29), (1, 27), (2, 9), (4, 33), (35, 23), (19, 33), (2, 2), (17, 5), (10, 28), (23, 7), (0, 19), (27, 5), (6, 29), (13, 30), (43, 41), (8, 11), (26, 27), (42, 36), (13, 33), (21, 10), (27, 37), (13, 32), (10, 41), (43, 35), (38, 20), (22, 15), (32, 20), (2, 31), (12, 27), (43, 28), (14, 23), (36, 0), (35, 13), (17, 19), (27, 11), (5, 27), (8, 32), (12, 26), (35, 28), (33, 26), (1, 33), (39, 17), (9, 2), (32, 11), (5, 31), (9, 26), (31, 29), (19, 36), (9, 39), (11, 11), (43, 16), (42, 14), (20, 6), (14, 21), (0, 36), (21, 39), (43, 34), (43, 33), (20, 20), (27, 40), (39, 40), (15, 36), (16, 4), (17, 37), (34, 3), (21, 3), (29, 5), (5, 34), (32, 42), (9, 28), (42, 0), (17, 34), (30, 40), (22, 36), (13, 23), (28, 36), (28, 31), (24, 43), (21, 24), (17, 20), (29, 28), (41, 26), (9, 5), (30, 7), (41, 4), (10, 5), (26, 41), (4, 26), (32, 15), (2, 27), (38, 43), (4, 41), (29, 32), (16, 8), (9, 43), (36, 36), (36, 8), (7, 9), (19, 28), (11, 0), (8, 23), (36, 28), (38, 19), (34, 4), (39, 37), (35, 14), (0, 14), (38, 9), (15, 24), (6, 26), (34, 38), (24, 6), (3, 36), (8, 24), (33, 21), (30, 16), (3, 43), (41, 41), (18, 27), (8, 26), (19, 9), (42, 33), (24, 24), (30, 39), (21, 18), (27, 4), (5, 14), (3, 41), (25, 33), (15, 29), (19, 27), (19, 30), (6, 13), (34, 25), (39, 39), (40, 13), (22, 41), (29, 22), (9, 40), (20, 23), (6, 39), (29, 16), (20, 36), (41, 16), (32, 19), (13, 39), (39, 3), (34, 30), (7, 25), (42, 8), (1, 10), (12, 31), (34, 12), (6, 1), (22, 17), (31, 26), (34, 23), (24, 10), (39, 11), (37, 0), (3, 21), (7, 2), (16, 25), (23, 27), (7, 16), (4, 8), (43, 32), (11, 30), (42, 6), (17, 8), (33, 41), (18, 7), (42, 41), (23, 30), (20, 38), (22, 8), (2, 26), (9, 34), (38, 31), (6, 19), (24, 8), (25, 43), (37, 19), (36, 34), (12, 23), (8, 7), (18, 32), (29, 17), (12, 3), (1, 15), (30, 3), (34, 9), (11, 34), (23, 34), (36, 41), (29, 29), (39, 38), (35, 9), (36, 21), (41, 13), (37, 22), (2, 21), (10, 18), (28, 8), (9, 35), (7, 19), (40, 27), (7, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 31), (22, 35), (8, 0), (32, 25), (33, 19), (41, 5), (41, 47), (48, 26), (13, 20), (10, 8), (29, 35), (3, 12), (38, 38), (31, 7), (26, 45), (8, 7), (5, 39), (19, 27), (14, 25), (36, 12), (24, 39), (16, 46), (42, 13), (16, 39), (38, 20), (35, 23), (34, 39), (1, 7), (42, 7), (15, 17), (20, 4), (20, 42), (15, 10), (9, 47), (13, 24), (13, 45), (39, 1), (23, 25), (28, 14), (4, 40), (37, 23), (11, 6), (6, 29), (16, 27), (15, 19), (17, 1), (14, 30), (24, 3), (21, 20), (44, 13), (11, 2), (46, 19), (42, 29), (39, 9), (41, 16), (46, 47), (17, 41), (17, 27), (9, 46), (2, 4), (30, 36), (39, 24), (1, 11), (42, 12), (36, 39), (14, 41), (23, 14), (24, 37), (42, 42), (4, 29), (18, 42), (32, 28), (21, 8), (10, 7), (44, 22), (1, 10), (20, 21), (44, 39), (3, 14), (39, 21), (19, 28), (0, 8), (43, 45), (3, 33), (26, 17), (45, 5), (18, 25), (37, 29), (4, 6), (34, 16), (35, 18), (1, 43), (41, 44), (4, 31), (43, 0), (27, 4), (30, 0), (13, 46), (31, 25), (38, 14), (30, 30), (28, 13), (25, 22), (32, 29), (6, 5), (44, 45), (7, 42), (32, 10), (22, 4), (8, 8), (3, 31), (11, 43), (46, 38), (7, 38), (14, 1), (13, 37), (9, 40), (48, 8), (47, 28), (16, 14), (13, 4), (48, 6), (46, 2), (44, 15), (19, 30), (14, 19), (5, 42), (38, 42), (46, 36), (10, 10), (7, 31), (13, 26), (38, 2), (11, 18), (23, 32), (2, 3), (34, 38), (45, 29), (37, 32), (18, 3), (48, 17), (23, 37), (38, 26), (31, 36), (38, 21), (29, 28), (1, 35), (37, 44), (44, 4), (28, 41), (31, 38), (23, 33), (46, 45), (22, 32), (28, 0), (31, 18), (34, 11), (45, 35), (39, 46), (34, 35), (24, 29), (20, 28), (20, 20), (8, 27), (13, 10), (6, 39), (11, 16), (0, 39), (19, 10), (17, 35), (0, 31), (6, 20), (16, 21), (42, 47), (0, 33), (38, 40), (12, 27), (23, 22), (9, 6), (31, 20), (38, 7), (12, 18), (1, 0), (33, 44), (21, 37), (21, 9), (6, 37), (36, 34), (27, 14), (39, 6), (18, 26), (21, 5), (26, 13), (24, 1), (26, 7), (36, 38), (5, 6), (44, 23), (18, 10), (1, 33), (41, 29), (48, 37), (4, 4), (4, 46), (1, 41), (9, 9), (28, 32), (1, 21), (13, 23), (25, 45), (36, 23), (48, 40), (35, 9), (43, 5), (36, 47), (18, 9), (47, 43), (17, 23), (20, 39), (3, 13), (35, 46), (34, 22), (44, 2), (8, 1), (36, 17), (40, 35), (24, 11), (38, 46), (40, 41), (46, 14), (3, 1), (15, 20), (21, 18), (37, 13), (12, 19), (34, 23), (46, 26), (21, 35), (41, 8), (17, 40), (9, 23), (4, 22), (13, 43), (13, 19), (23, 23), (18, 1), (37, 12), (25, 23), (34, 30), (2, 19), (48, 15), (16, 20), (32, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 26), (21, 38), (38, 10), (43, 15), (20, 2), (40, 10), (11, 24), (23, 16), (20, 14), (23, 34), (7, 20), (4, 8), (8, 30), (44, 24), (37, 24), (1, 30), (44, 19), (23, 28), (26, 42), (10, 35), (2, 31), (5, 20), (3, 20), (22, 23), (27, 14), (13, 2), (20, 44), (8, 41), (34, 20), (0, 22), (8, 28), (4, 30), (23, 23), (13, 38), (31, 17), (16, 6), (4, 33), (38, 21), (43, 22), (7, 41), (26, 28), (9, 37), (9, 0), (44, 36), (40, 8), (19, 21), (32, 27), (2, 11), (25, 12), (27, 24), (4, 9), (28, 4), (14, 16), (12, 33), (7, 27), (31, 45), (25, 40), (43, 26), (14, 24), (46, 23), (8, 22), (15, 27), (35, 30), (34, 28), (45, 15), (7, 32), (33, 22), (42, 9), (7, 22), (38, 35), (2, 34), (21, 36), (46, 16), (11, 5), (19, 37), (17, 27), (7, 12), (21, 6), (33, 2), (7, 2), (0, 1), (7, 44), (16, 32), (24, 4), (17, 38), (46, 39), (42, 23), (20, 11), (32, 3), (28, 28), (45, 1), (1, 43), (15, 32), (28, 16), (19, 14), (35, 29), (2, 23), (46, 44), (44, 13), (41, 23), (46, 8), (22, 16), (9, 16), (37, 14), (27, 17), (3, 25), (11, 25), (26, 3), (27, 29), (34, 17), (2, 38), (9, 12), (39, 21), (16, 16), (6, 25), (11, 41), (24, 17), (1, 31), (9, 18), (1, 24), (8, 17), (3, 7), (37, 19), (39, 14), (45, 20), (34, 6), (3, 42), (28, 8), (5, 26), (32, 29), (23, 24), (24, 27), (29, 34), (19, 28), (46, 37), (39, 33), (39, 13), (13, 15), (34, 0), (9, 32), (6, 21), (26, 39), (26, 9), (38, 29), (11, 7), (40, 40), (13, 6), (42, 35), (10, 2), (41, 41), (20, 43), (14, 36), (43, 35), (22, 21), (9, 40), (40, 41), (7, 14), (30, 2), (23, 4), (22, 42), (31, 38), (34, 4), (3, 28), (22, 10), (32, 39), (28, 45), (4, 12), (40, 22), (45, 22), (0, 44), (9, 34), (19, 25), (36, 3), (30, 27), (44, 18), (4, 31), (17, 1), (31, 11), (22, 36), (46, 14), (40, 42), (38, 7), (9, 14), (0, 38), (12, 7), (15, 13), (31, 29), (21, 15), (27, 42), (4, 13), (41, 17), (35, 19), (16, 38), (7, 16), (22, 40), (6, 38), (31, 15), (22, 29), (39, 34), (7, 38), (14, 32), (25, 4), (43, 12), (17, 2), (16, 26), (13, 22), (23, 32), (19, 35), (26, 43), (45, 44), (10, 3), (8, 21), (18, 40), (10, 9), (26, 44), (21, 12), (9, 9), (40, 12), (45, 23), (23, 12), (30, 40), (40, 23), (25, 13), (31, 42), (19, 9), (19, 24), (45, 14), (44, 1), (43, 31), (27, 3), (21, 30), (7, 19), (43, 7), (20, 29), (23, 33), (38, 33), (34, 43), (2, 7), (29, 10), (16, 4), (34, 10), (1, 33), (22, 24), (41, 40), (43, 37), (43, 2), (22, 11), (43, 38), (14, 28), (9, 39), (23, 36), (38, 18), (12, 18), (33, 8), (23, 7), (14, 23), (1, 32), (5, 10), (42, 17), (25, 2), (22, 17), (35, 27), (6, 26), (34, 31), (17, 3), (26, 38), (1, 6), (3, 40), (16, 8), (1, 35), (28, 18), (14, 13), (6, 43), (32, 23), (24, 10), (34, 11), (32, 19), (36, 19), (40, 5), (8, 10), (35, 2), (40, 45), (45, 29), (21, 16), (21, 8), (15, 10), (41, 3), (30, 8), (9, 22), (2, 4), (5, 13), (9, 27), (46, 26), (42, 18), (41, 5), (34, 13), (3, 12), (37, 41), (10, 12), (36, 9), (21, 13), (30, 20), (31, 4), (14, 35), (17, 40), (20, 6), (12, 25), (1, 36), (35, 38), (18, 9), (29, 9), (31, 44), (39, 7), (32, 30), (6, 28), (39, 20), (31, 34), (12, 36), (6, 14), (44, 27), (3, 33), (36, 0), (25, 1), (46, 10), (12, 37), (10, 24), (22, 25), (41, 25), (36, 28), (23, 41), (42, 16), (29, 0), (28, 0), (10, 19), (38, 12), (35, 23), (38, 27), (22, 45), (4, 34), (12, 35), (24, 14), (35, 21), (27, 23), (20, 7), (20, 5), (17, 13), (12, 34), (19, 43), (23, 42), (0, 2), (30, 29), (43, 4), (25, 3), (5, 40), (19, 33), (23, 15), (33, 13), (38, 25), (14, 19), (7, 35), (33, 26), (42, 28), (17, 0), (14, 31), (26, 22), (15, 8), (10, 18), (46, 7), (16, 35), (13, 42), (27, 30), (14, 44), (25, 38), (24, 12), (15, 20), (9, 41), (26, 18), (5, 29), (16, 3), (26, 2), (19, 40), (5, 4), (11, 19), (2, 39), (26, 36), (25, 17), (39, 4), (0, 36), (46, 13), (39, 2), (28, 11), (27, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 37), (40, 20), (14, 9), (41, 4), (6, 12), (1, 27), (15, 37), (24, 27), (17, 3), (31, 6), (20, 27), (14, 30), (15, 18), (16, 28), (14, 31), (27, 36), (25, 34), (10, 29), (13, 29), (20, 16), (31, 3), (13, 9), (28, 36), (35, 27), (35, 22), (1, 13), (10, 7), (15, 31), (37, 34), (5, 29), (39, 27), (19, 33), (20, 14), (22, 31), (16, 37), (18, 2), (42, 5), (24, 3), (0, 8), (29, 1), (37, 29), (4, 16), (28, 16), (3, 20), (4, 8), (36, 10), (41, 21), (32, 32), (33, 2), (40, 36), (34, 24), (10, 27), (40, 0), (39, 35), (2, 39), (12, 22), (36, 15), (12, 19), (18, 5), (19, 0), (5, 8), (8, 2), (35, 17), (38, 13), (27, 12), (4, 23), (20, 1), (40, 19), (29, 32), (25, 17), (43, 3), (1, 1), (43, 1), (17, 20), (22, 20), (40, 14), (25, 13), (4, 18), (6, 25), (15, 1), (11, 33), (19, 28), (1, 38), (35, 18), (32, 36), (34, 7), (32, 34), (40, 6), (34, 17), (2, 15), (38, 14), (41, 15), (35, 0), (21, 20), (2, 8), (21, 2), (27, 2), (3, 0), (6, 33), (32, 11), (24, 37), (7, 19), (11, 12), (25, 1), (25, 20), (33, 16), (24, 14), (2, 27), (42, 8), (21, 32), (36, 31), (38, 6), (20, 37), (22, 3), (14, 6), (20, 4), (42, 37), (6, 35), (28, 18), (20, 26), (30, 4), (17, 19), (1, 17), (1, 10), (39, 2), (25, 27), (21, 24), (28, 29), (43, 13), (29, 30), (35, 9), (22, 8), (11, 24), (8, 11), (21, 26), (7, 22), (20, 5), (32, 18), (39, 25), (13, 38), (4, 11), (20, 38), (17, 39), (32, 15), (42, 35), (32, 6), (22, 17), (27, 18), (20, 33), (36, 0), (23, 27), (17, 32), (24, 0), (10, 37), (39, 29), (27, 21), (23, 37), (39, 21), (10, 12), (39, 4), (14, 16), (0, 3), (34, 4), (11, 35), (40, 32), (3, 15), (40, 38), (13, 24), (26, 5), (42, 6), (25, 10), (16, 26), (12, 14), (31, 36), (36, 12), (43, 9), (29, 33), (38, 26), (14, 7), (17, 34), (34, 36), (29, 25), (21, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 29), (11, 34), (7, 23), (1, 5), (31, 31), (31, 18), (35, 32), (6, 13), (15, 23), (22, 40), (24, 9), (35, 35), (11, 24), (14, 6), (1, 37), (40, 38), (28, 39), (5, 30), (37, 17), (21, 30), (9, 4), (40, 8), (12, 15), (27, 5), (39, 37), (17, 25), (29, 7), (33, 27), (6, 3), (27, 27), (6, 6), (1, 19), (20, 41), (30, 18), (19, 31), (19, 18), (19, 2), (9, 15), (6, 35), (39, 9), (27, 12), (23, 35), (10, 32), (31, 24), (15, 20), (0, 4), (4, 10), (5, 33), (25, 23), (27, 9), (4, 6), (25, 3), (0, 34), (8, 4), (33, 14), (1, 30), (14, 7), (25, 33), (9, 18), (3, 2), (2, 9), (27, 19), (29, 2), (29, 26), (38, 36), (35, 22), (23, 31), (27, 14), (16, 26), (3, 13), (1, 34), (37, 37), (31, 35), (21, 31), (23, 17), (16, 22), (16, 0), (34, 33), (13, 36), (37, 8), (39, 29), (36, 11), (12, 39), (6, 36), (39, 30), (37, 3), (12, 28), (20, 6), (0, 38), (15, 4), (8, 1), (35, 30), (17, 15), (3, 28), (17, 35), (16, 8), (15, 6), (16, 17), (10, 21), (17, 23), (26, 27), (40, 39), (3, 16), (32, 14), (13, 11), (6, 11), (20, 34), (33, 3), (28, 21), (36, 39), (15, 36), (9, 13), (2, 20), (28, 23), (25, 4), (26, 40), (14, 38), (17, 7), (7, 28), (26, 9), (17, 16), (24, 21), (27, 39), (22, 31), (8, 0), (39, 7), (16, 27), (36, 32), (15, 9), (23, 11), (29, 39), (15, 3), (29, 17), (29, 15), (9, 5), (16, 5), (27, 13), (28, 41), (29, 1), (9, 32), (12, 8), (20, 12), (4, 25), (20, 22), (12, 16), (22, 1), (13, 23), (29, 13), (22, 18), (28, 11), (21, 7), (7, 25), (22, 28), (26, 34), (13, 34), (17, 19), (27, 26), (31, 6), (28, 9), (12, 10), (9, 0), (33, 0), (11, 25), (14, 17), (8, 8), (35, 13), (31, 11), (19, 22), (27, 20), (16, 33), (11, 11), (29, 20), (34, 3), (27, 10), (40, 33), (3, 11), (34, 27), (33, 2), (33, 25), (22, 5), (25, 34), (30, 14), (20, 0), (30, 25), (27, 1), (27, 21), (31, 25), (19, 12), (24, 5), (6, 15), (5, 28), (0, 15), (0, 8), (8, 15), (32, 23), (28, 10), (17, 5), (8, 18), (11, 8), (10, 22), (33, 37), (13, 17), (19, 33), (4, 17), (4, 41), (2, 10), (13, 7), (18, 32), (28, 19), (33, 15), (39, 25), (39, 39), (2, 32), (6, 29), (12, 33), (20, 39), (4, 28), (21, 1), (13, 31), (8, 6), (30, 8), (27, 22), (16, 7), (0, 37), (38, 26), (27, 29), (16, 20), (25, 41), (15, 2), (11, 39), (32, 38), (38, 24), (20, 24), (10, 40), (34, 11), (32, 6), (8, 27), (9, 21), (35, 8), (9, 40), (40, 7), (32, 0), (11, 22), (11, 38), (19, 0), (15, 17), (9, 27), (19, 30), (21, 26), (11, 26), (14, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 41), (24, 38), (32, 17), (11, 17), (16, 3), (39, 15), (21, 15), (38, 23), (45, 16), (16, 18), (30, 13), (20, 40), (1, 23), (28, 1), (45, 32), (7, 36), (13, 24), (43, 43), (27, 28), (27, 39), (48, 35), (42, 17), (27, 0), (36, 8), (43, 35), (46, 0), (5, 2), (48, 5), (10, 30), (48, 26), (3, 7), (22, 0), (43, 39), (16, 35), (16, 24), (34, 25), (13, 39), (25, 36), (25, 19), (14, 9), (41, 23), (41, 12), (5, 12), (36, 34), (34, 7), (22, 6), (28, 25), (12, 18), (20, 27), (11, 8), (41, 10), (19, 16), (12, 35), (44, 6), (9, 35), (31, 14), (41, 8), (39, 38), (23, 4), (29, 5), (48, 42), (44, 9), (45, 39), (43, 33), (14, 32), (3, 24), (43, 30), (30, 38), (36, 16), (37, 43), (2, 31), (23, 5), (31, 12), (8, 20), (12, 42), (37, 1), (42, 11), (32, 23), (25, 37), (11, 26), (9, 22), (24, 27), (19, 3), (28, 10), (19, 19), (9, 15), (11, 15), (19, 22), (3, 30), (35, 26), (7, 34), (39, 2), (12, 7), (38, 0), (36, 24), (0, 41), (46, 32), (23, 8), (30, 26), (3, 21), (14, 4), (41, 38), (13, 27), (34, 20), (19, 29), (7, 6), (34, 34), (41, 39), (45, 17), (28, 5), (48, 30), (19, 34), (15, 32), (19, 12), (36, 29), (9, 3), (32, 37), (21, 3), (12, 36), (45, 8), (31, 25), (24, 15), (30, 27), (22, 2), (30, 34), (30, 2), (16, 11), (9, 16), (12, 21), (36, 27), (43, 32), (39, 12), (8, 0), (25, 3), (46, 13), (2, 6), (36, 32), (31, 23), (12, 14), (25, 8), (47, 26), (21, 38), (1, 9), (10, 24), (12, 39), (26, 33), (27, 40), (3, 27), (0, 30), (35, 43), (32, 38), (21, 16), (8, 18), (13, 22), (38, 5), (43, 40), (20, 43), (27, 32), (17, 23), (43, 41), (15, 25), (11, 42), (48, 19), (25, 20), (0, 26), (13, 25), (16, 0), (27, 3), (36, 10), (48, 32), (11, 28), (8, 37), (38, 15), (10, 11), (24, 12), (18, 6), (10, 12), (3, 36), (13, 41), (7, 40), (28, 28), (7, 26), (0, 27), (46, 42), (42, 23), (10, 18), (18, 25), (42, 0), (27, 5), (45, 24), (40, 7), (39, 6), (41, 24), (5, 26), (15, 31), (43, 34), (40, 41), (37, 31), (34, 28), (6, 32), (32, 14), (25, 33), (8, 17), (2, 17), (33, 11), (40, 31), (25, 14), (11, 4), (10, 31), (9, 21), (9, 20), (9, 12), (33, 2), (27, 15), (30, 1), (45, 42), (35, 7), (45, 4), (32, 27), (19, 14), (13, 30), (20, 41), (8, 35), (26, 24), (32, 12), (20, 7), (48, 23), (5, 39), (29, 17), (48, 13), (4, 18), (40, 43), (36, 25), (46, 43), (0, 4), (18, 20), (36, 43), (19, 37), (28, 37), (39, 27), (44, 0), (36, 5), (18, 19), (6, 25), (16, 36), (6, 3), (47, 13), (3, 37), (43, 27), (35, 4), (14, 41), (23, 19), (3, 38), (20, 32), (23, 20), (21, 11), (29, 23), (8, 22), (42, 20), (26, 14), (6, 7), (5, 1), (17, 18), (30, 32), (2, 21), (26, 13), (8, 19), (12, 30), (25, 23), (5, 0), (33, 35), (7, 28), (0, 28), (4, 7), (41, 25), (20, 19), (11, 9), (31, 22), (7, 39), (17, 38), (33, 13), (43, 2), (43, 8), (46, 5), (45, 9), (42, 39), (5, 3), (13, 15), (28, 43), (3, 6), (2, 19), (21, 24), (7, 30), (33, 32), (27, 21), (36, 38), (0, 17), (28, 6), (30, 22), (35, 12), (6, 42), (17, 27), (30, 8), (22, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 32), (37, 10), (2, 33), (11, 42), (33, 41), (16, 26), (26, 22), (39, 3), (25, 22), (17, 22), (2, 22), (42, 10), (18, 18), (14, 20), (18, 28), (25, 29), (42, 39), (18, 7), (10, 13), (37, 26), (26, 26), (22, 9), (3, 19), (13, 21), (39, 32), (37, 3), (29, 14), (41, 13), (0, 5), (31, 28), (2, 2), (8, 15), (15, 23), (32, 9), (22, 8), (32, 26), (19, 10), (23, 4), (3, 13), (35, 36), (33, 3), (31, 6), (31, 41), (6, 26), (37, 32), (39, 5), (3, 5), (17, 3), (24, 32), (26, 2), (3, 7), (36, 32), (38, 9), (11, 39), (38, 35), (29, 10), (28, 1), (27, 36), (5, 39), (6, 12), (13, 15), (15, 19), (41, 11), (5, 34), (6, 40), (9, 15), (42, 27), (39, 37), (41, 35), (29, 29), (41, 29), (34, 22), (41, 31), (22, 41), (20, 11), (10, 19), (18, 30), (35, 42), (4, 9), (0, 16), (6, 29), (34, 14), (8, 31), (13, 17), (27, 38), (26, 40), (26, 25), (26, 13), (4, 41), (8, 17), (35, 8), (24, 28), (28, 12), (3, 16), (5, 31), (25, 26), (41, 22), (32, 19), (7, 25), (20, 12), (35, 14), (4, 19), (13, 18), (3, 22), (15, 25), (6, 9), (11, 21), (1, 4), (38, 20), (37, 14), (2, 35), (12, 9), (9, 9), (35, 17), (35, 21), (30, 18), (36, 28), (24, 37), (33, 6), (21, 20), (21, 8), (17, 9), (7, 28), (4, 12), (7, 31), (20, 16), (9, 19), (8, 22), (25, 32), (12, 23), (21, 42), (41, 12), (9, 3), (1, 3), (24, 40), (42, 38), (35, 32), (2, 41), (29, 42), (38, 33), (25, 40), (26, 19), (15, 14), (39, 29), (35, 5), (37, 23), (18, 5), (12, 12), (42, 17), (3, 8), (41, 25), (39, 19), (8, 19), (25, 7), (3, 41), (27, 5), (41, 9), (32, 22), (16, 3), (12, 8), (24, 21), (4, 3), (42, 12), (3, 9), (10, 17), (3, 38), (33, 17), (13, 9), (6, 34), (32, 27), (40, 42), (15, 30), (28, 13), (29, 26), (3, 4), (38, 38), (1, 31), (41, 0), (7, 13), (28, 25), (41, 42), (19, 34), (33, 32), (37, 16), (3, 32), (40, 17), (27, 1), (15, 0), (12, 15), (38, 21), (33, 33), (3, 31), (23, 21), (35, 2), (37, 42), (11, 11), (39, 33), (17, 42), (36, 11), (21, 23), (15, 36), (20, 29), (9, 34), (38, 4), (13, 28), (22, 28), (2, 12), (7, 3), (3, 42), (8, 16), (39, 42), (42, 34), (32, 40), (2, 18), (28, 33), (0, 39), (1, 42), (18, 8), (25, 17), (8, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (11, 1), (37, 1), (4, 12), (18, 36), (27, 22), (26, 6), (12, 28), (19, 22), (38, 18), (0, 35), (27, 24), (40, 27), (13, 32), (22, 20), (36, 16), (13, 10), (20, 22), (9, 32), (28, 9), (4, 34), (9, 23), (2, 26), (0, 22), (14, 22), (40, 36), (26, 7), (33, 2), (16, 37), (12, 8), (14, 39), (23, 25), (24, 39), (20, 12), (36, 1), (28, 30), (13, 31), (17, 26), (37, 34), (23, 4), (1, 11), (11, 26), (16, 23), (15, 26), (2, 0), (41, 14), (5, 7), (35, 15), (41, 19), (10, 21), (16, 7), (17, 27), (19, 12), (11, 20), (22, 12), (11, 37), (16, 34), (4, 8), (11, 31), (5, 21), (21, 19), (32, 8), (22, 18), (0, 26), (18, 12), (9, 34), (12, 26), (2, 31), (27, 19), (35, 2), (29, 14), (31, 36), (26, 4), (27, 0), (10, 27), (31, 14), (15, 15), (15, 34), (30, 7), (2, 13), (33, 25), (33, 24), (32, 1), (6, 10), (24, 28), (21, 36), (15, 28), (3, 24), (31, 20), (1, 36), (17, 5), (39, 22), (26, 1), (13, 4), (28, 14), (14, 13), (16, 16), (26, 11), (11, 4), (27, 21), (17, 6), (10, 35), (32, 39), (7, 8), (10, 34), (15, 25), (3, 34), (20, 21), (14, 30), (18, 11), (40, 38), (9, 15), (40, 37), (37, 25), (31, 28), (1, 25), (23, 33), (1, 2), (26, 39), (11, 36), (27, 17), (39, 5), (5, 38), (20, 20), (7, 36), (22, 15), (6, 16), (4, 2), (12, 12), (36, 3), (3, 2), (18, 8), (23, 26), (12, 17), (15, 20), (7, 33), (1, 5), (40, 24), (37, 8), (40, 31), (9, 28), (10, 5), (33, 18), (15, 2), (31, 15), (13, 2), (5, 25), (41, 18), (4, 6), (22, 7), (1, 28), (38, 38), (25, 31), (3, 13), (21, 35), (36, 23), (20, 28), (38, 20), (24, 26), (5, 11), (28, 33), (23, 31), (16, 30), (1, 10), (30, 36), (14, 24), (38, 35), (24, 29), (32, 28), (30, 32), (34, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 10), (22, 20), (6, 1), (18, 27), (0, 11), (36, 7), (32, 1), (5, 15), (22, 36), (36, 5), (38, 37), (26, 3), (28, 22), (16, 11), (23, 24), (37, 34), (3, 24), (34, 23), (25, 38), (2, 29), (31, 26), (8, 12), (22, 15), (31, 24), (10, 2), (43, 34), (25, 24), (15, 39), (38, 12), (29, 19), (2, 24), (1, 7), (11, 6), (29, 24), (8, 37), (6, 21), (14, 10), (42, 14), (22, 24), (11, 16), (16, 12), (14, 12), (16, 28), (29, 16), (37, 18), (20, 18), (9, 1), (36, 11), (3, 20), (11, 21), (0, 33), (6, 22), (7, 39), (21, 38), (0, 25), (22, 33), (17, 27), (29, 37), (28, 29), (17, 38), (2, 4), (8, 31), (24, 17), (29, 27), (7, 16), (16, 5), (8, 0), (37, 36), (18, 36), (8, 17), (25, 21), (6, 14), (20, 38), (1, 35), (38, 32), (34, 25), (41, 32), (31, 8), (1, 29), (39, 0), (5, 23), (5, 0), (13, 30), (24, 15), (1, 18), (4, 28), (37, 35), (32, 13), (13, 19), (41, 5), (27, 22), (39, 14), (26, 20), (40, 3), (29, 2), (36, 19), (8, 26), (3, 4), (14, 1), (25, 32), (21, 9), (9, 12), (22, 1), (14, 36), (19, 10), (9, 24), (9, 22), (35, 10), (11, 36), (31, 14), (39, 21), (21, 36), (34, 38), (5, 38), (24, 33), (41, 9), (24, 0), (39, 15), (8, 32), (17, 12), (43, 33), (6, 29), (32, 38), (3, 37), (39, 18), (36, 25), (29, 28), (43, 17), (25, 29), (7, 6), (39, 5), (32, 3), (22, 10), (21, 33), (10, 1), (41, 30), (25, 4), (25, 14), (30, 8), (6, 16), (28, 36), (36, 27), (20, 7), (2, 14), (23, 36), (26, 12), (17, 34), (37, 9), (31, 11), (30, 36), (16, 21), (22, 35), (35, 34), (32, 21), (25, 16), (5, 11), (20, 15), (14, 24), (10, 7), (0, 7), (29, 31), (12, 25), (34, 6), (40, 29), (12, 34), (12, 21), (26, 29), (8, 4), (22, 32), (27, 2), (2, 35), (28, 1), (0, 34), (32, 35), (31, 23), (33, 32), (13, 36), (33, 10), (8, 3), (12, 5), (1, 36), (11, 17), (31, 35), (30, 1), (42, 27), (9, 25), (29, 14), (18, 12), (4, 37), (19, 2), (26, 2), (31, 13), (16, 26), (37, 29), (22, 14), (33, 13), (9, 39), (38, 31), (25, 0), (27, 27), (35, 36), (3, 25), (27, 38), (0, 37), (36, 20), (15, 35), (33, 9), (17, 17), (42, 35), (9, 27), (13, 1), (23, 12), (0, 3), (26, 39), (7, 7), (29, 36), (36, 0), (20, 10), (1, 19), (42, 18), (0, 2), (13, 39), (12, 7), (42, 0), (38, 6), (36, 10), (31, 3), (22, 28), (31, 22), (1, 12), (33, 3), (26, 8), (41, 25), (40, 4), (11, 22), (33, 7), (8, 15), (19, 1), (6, 15), (1, 32), (26, 21), (42, 17), (17, 30), (23, 8), (4, 32), (6, 0), (31, 18), (19, 17), (15, 34), (8, 33), (30, 14), (16, 19), (6, 31), (25, 19), (32, 8), (1, 15), (22, 12), (32, 22), (13, 13), (21, 2), (7, 3), (11, 25), (25, 30), (39, 7), (4, 7), (24, 36), (18, 6), (29, 1), (35, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 17), (5, 44), (39, 44), (35, 26), (13, 0), (37, 3), (38, 25), (32, 30), (26, 13), (17, 19), (3, 5), (6, 24), (33, 7), (25, 42), (2, 31), (23, 3), (27, 31), (36, 21), (41, 23), (40, 33), (22, 9), (31, 21), (42, 39), (3, 15), (42, 3), (14, 20), (19, 3), (43, 18), (0, 27), (33, 39), (11, 26), (38, 31), (7, 35), (37, 22), (11, 31), (9, 2), (8, 40), (35, 14), (15, 14), (41, 9), (16, 0), (13, 5), (17, 3), (31, 46), (1, 33), (19, 22), (34, 33), (31, 6), (42, 1), (32, 38), (29, 4), (40, 8), (6, 27), (43, 38), (6, 19), (8, 37), (33, 3), (27, 43), (32, 36), (37, 27), (8, 10), (18, 32), (12, 45), (33, 26), (26, 2), (41, 13), (13, 23), (10, 6), (2, 28), (15, 15), (35, 1), (37, 45), (12, 26), (20, 14), (21, 24), (13, 1), (27, 15), (29, 42), (7, 20), (1, 47), (12, 41), (25, 19), (26, 12), (8, 43), (5, 3), (3, 22), (10, 42), (35, 28), (2, 46), (2, 9), (18, 46), (18, 14), (23, 8), (36, 4), (9, 41), (35, 23), (17, 32), (42, 6), (23, 26), (14, 8), (13, 46), (4, 31), (14, 36), (42, 16), (15, 23), (29, 1), (5, 1), (25, 33), (12, 3), (28, 36), (6, 40), (42, 40), (41, 6), (13, 43), (33, 17), (37, 43), (0, 32), (19, 15), (17, 27), (25, 10), (18, 17), (13, 10), (6, 33), (1, 5), (38, 41), (12, 0), (7, 24), (13, 4), (22, 33), (28, 27), (36, 29), (42, 10), (1, 41), (15, 8), (3, 18), (23, 9), (4, 16), (43, 13), (11, 34), (39, 13), (17, 15), (6, 39), (3, 31), (22, 27), (40, 47), (31, 24), (21, 35), (4, 3), (18, 21), (7, 12), (33, 38), (20, 24), (8, 11), (33, 25), (27, 36), (6, 43), (11, 1), (13, 30), (18, 8), (33, 18), (41, 25), (38, 10), (44, 9), (39, 4), (31, 47), (7, 29), (17, 17), (26, 37), (13, 44), (16, 18), (39, 26), (28, 22), (12, 29), (39, 47), (20, 13), (21, 7), (35, 33), (41, 12), (14, 42), (4, 18), (30, 18), (1, 16), (43, 19), (36, 40), (40, 42), (32, 31), (44, 24), (39, 25), (11, 28), (28, 18), (32, 16), (1, 46), (5, 16), (34, 15), (38, 7), (19, 37), (16, 42), (24, 2), (7, 36), (42, 29), (9, 23), (25, 21), (8, 1), (14, 2), (14, 12), (38, 26), (11, 7), (14, 30), (19, 18), (2, 36), (2, 38), (10, 2), (7, 42), (5, 21), (41, 39), (11, 19), (28, 3), (28, 14), (36, 18), (28, 12), (32, 21), (44, 35), (4, 42), (32, 45), (30, 45), (20, 7), (21, 30), (29, 2), (11, 46), (30, 17), (17, 40), (12, 15), (25, 39), (44, 32), (18, 7), (25, 7), (40, 38), (5, 30), (2, 15), (30, 42), (1, 6), (8, 12), (20, 21), (19, 24), (10, 13), (23, 41), (28, 16), (31, 27), (29, 21), (25, 44), (42, 35), (23, 6), (36, 22), (29, 35), (28, 42), (37, 44), (31, 33), (5, 18), (14, 7), (4, 34), (11, 30), (15, 30), (38, 35), (34, 17), (43, 43), (26, 0), (1, 44), (44, 19), (5, 46), (23, 25), (1, 2), (14, 27), (38, 40), (39, 0), (30, 5), (34, 20), (25, 29), (33, 24), (19, 47), (10, 29), (17, 23), (27, 22), (29, 15), (12, 47), (43, 3), (19, 32), (42, 22), (22, 47), (39, 5), (4, 28), (9, 1), (26, 4), (3, 13), (38, 39), (11, 4), (42, 0), (37, 17), (39, 36), (31, 40), (24, 38), (38, 37), (34, 4), (43, 7), (18, 12), (42, 19), (1, 23), (35, 3), (10, 19), (0, 13), (26, 31), (19, 4), (26, 1), (6, 41), (39, 37), (22, 25), (28, 28), (22, 15), (35, 47), (43, 12), (44, 27), (32, 42), (42, 30), (40, 26), (38, 11), (11, 23), (20, 34), (24, 26), (30, 14), (21, 5), (20, 42), (10, 38), (41, 5), (10, 1), (40, 44), (4, 41), (35, 25), (34, 12), (10, 32), (24, 28), (23, 42), (41, 26), (16, 37), (8, 14), (40, 12), (35, 16), (31, 11), (12, 9), (2, 14), (9, 11), (21, 17), (16, 29), (8, 2), (12, 35), (3, 6), (28, 39), (38, 13), (17, 43), (28, 10), (9, 30), (8, 45), (10, 10), (20, 28), (11, 11), (26, 15), (5, 15), (11, 35), (21, 33), (39, 11), (25, 32), (12, 20), (15, 1), (44, 1), (15, 26), (30, 1), (41, 11), (44, 25), (6, 44), (35, 32), (32, 17), (21, 27), (42, 15), (36, 25), (2, 6), (29, 9), (18, 43), (15, 21), (22, 4), (17, 8), (39, 32), (12, 24), (17, 22), (10, 21), (36, 47), (21, 4), (14, 41), (2, 18), (3, 45), (3, 26), (38, 33), (23, 22), (20, 27), (17, 13), (24, 10), (32, 39), (0, 41), (16, 22), (10, 43), (15, 13), (15, 28), (27, 4), (31, 28), (8, 44), (18, 20), (2, 3), (28, 47), (30, 7), (6, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 21), (34, 26), (10, 30), (3, 44), (23, 4), (37, 26), (35, 23), (35, 10), (25, 33), (11, 35), (24, 23), (34, 33), (2, 37), (33, 42), (41, 46), (11, 1), (19, 20), (38, 35), (42, 0), (39, 34), (12, 27), (19, 38), (41, 3), (25, 23), (26, 16), (43, 33), (35, 36), (13, 11), (24, 32), (4, 16), (6, 12), (18, 17), (32, 27), (5, 43), (15, 16), (32, 26), (9, 27), (38, 31), (31, 11), (15, 38), (30, 25), (31, 26), (21, 10), (2, 26), (8, 45), (6, 25), (33, 17), (25, 5), (7, 39), (37, 5), (2, 43), (13, 13), (31, 19), (27, 38), (19, 35), (9, 5), (34, 27), (38, 14), (8, 19), (29, 32), (40, 2), (24, 38), (3, 9), (38, 36), (0, 38), (35, 31), (7, 41), (23, 29), (45, 4), (43, 2), (14, 19), (28, 18), (10, 33), (8, 39), (3, 28), (33, 11), (43, 8), (5, 13), (1, 12), (0, 14), (7, 25), (4, 35), (16, 22), (43, 43), (13, 42), (43, 37), (41, 8), (6, 42), (26, 0), (35, 45), (0, 32), (36, 18), (21, 32), (32, 34), (17, 28), (23, 18), (36, 15), (5, 19), (36, 24), (43, 18), (12, 28), (10, 19), (41, 37), (27, 44), (2, 12), (22, 38), (22, 23), (19, 43), (8, 24), (7, 20), (27, 21), (30, 16), (44, 15), (31, 43), (33, 20), (43, 5), (17, 5), (3, 43), (5, 38), (1, 14), (43, 45), (18, 9), (43, 39), (30, 28), (4, 19), (7, 8), (28, 41), (8, 11), (17, 44), (2, 25), (19, 23), (30, 5), (33, 33), (0, 23), (24, 24), (22, 18), (21, 2), (9, 7), (36, 40), (42, 27), (20, 31), (9, 39), (14, 40), (29, 34), (30, 30), (15, 33), (41, 42), (36, 35), (3, 2), (26, 32), (41, 2), (5, 3), (15, 6), (1, 2), (23, 9), (21, 26), (26, 44), (37, 33), (31, 31), (26, 22), (42, 18), (14, 0), (8, 4), (34, 12), (0, 7), (21, 12), (42, 45), (16, 43), (43, 3), (15, 46), (39, 33), (14, 39), (0, 5), (25, 14), (12, 32), (9, 21), (25, 9), (16, 31), (11, 17), (2, 6), (23, 20), (30, 10), (16, 30), (7, 16), (30, 11), (34, 14), (22, 44), (19, 17), (6, 20), (4, 24), (30, 38), (41, 19), (7, 13), (9, 15), (3, 37), (33, 28), (28, 31), (21, 28), (20, 4), (45, 2), (2, 7), (19, 9), (17, 39), (2, 2), (14, 11), (1, 15), (21, 42), (2, 42), (27, 10), (17, 15), (3, 11), (20, 11), (10, 14), (30, 17), (9, 36), (38, 11), (15, 19), (2, 17), (1, 32), (23, 6), (31, 32), (10, 11), (44, 37), (44, 22), (42, 1), (24, 19), (27, 36), (18, 40), (24, 17), (6, 45), (25, 0), (11, 11), (22, 29), (8, 34), (2, 15), (38, 20), (15, 34), (29, 24), (11, 0), (34, 45), (10, 31), (12, 16), (11, 29), (21, 38), (12, 46), (4, 46), (12, 45), (0, 36), (20, 42), (38, 43), (20, 36), (6, 0), (8, 20), (17, 37), (20, 29), (10, 6), (35, 38), (4, 0), (36, 21), (14, 45), (26, 5), (6, 19), (18, 41), (32, 20), (26, 23), (20, 13), (32, 32), (16, 17), (29, 12), (9, 35), (13, 1), (26, 14), (26, 8), (32, 23), (42, 17), (9, 0), (0, 11), (13, 9), (4, 37), (40, 7), (20, 19), (39, 43), (27, 7), (42, 14), (12, 8), (8, 16), (9, 14), (3, 7), (26, 39), (3, 35), (35, 42), (19, 29), (20, 30), (25, 2), (10, 0), (10, 7), (37, 35), (14, 33), (35, 33), (15, 41), (1, 39), (37, 11), (12, 13), (7, 14), (4, 42), (29, 29), (9, 42), (27, 3), (39, 20), (18, 21), (44, 12), (37, 42), (43, 21), (14, 42), (19, 7), (37, 21), (14, 5), (5, 15), (3, 3), (14, 13), (31, 7), (8, 12), (0, 2), (27, 26), (29, 15), (17, 9), (32, 28), (32, 22), (30, 26), (11, 5), (6, 40), (22, 21), (40, 38), (41, 14), (0, 31), (19, 14), (39, 25), (6, 4), (12, 39), (41, 34), (23, 35), (4, 14), (38, 16), (32, 40), (41, 40), (38, 9), (11, 37), (36, 9), (4, 5), (45, 1), (24, 9), (20, 0), (4, 26), (34, 9), (2, 35), (20, 21), (40, 8), (45, 33), (24, 14), (18, 6), (23, 45), (44, 18), (36, 29), (11, 13), (29, 5), (10, 45), (37, 44), (11, 19), (36, 1), (28, 45), (14, 7), (32, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 33), (43, 1), (10, 38), (26, 2), (11, 12), (7, 38), (28, 24), (29, 39), (11, 14), (13, 16), (4, 28), (35, 40), (25, 6), (40, 34), (0, 13), (28, 27), (36, 37), (15, 7), (40, 6), (0, 32), (43, 16), (35, 44), (48, 34), (35, 34), (8, 13), (22, 25), (30, 10), (37, 0), (12, 5), (42, 6), (48, 25), (10, 40), (3, 22), (10, 15), (1, 4), (14, 37), (0, 37), (16, 2), (35, 31), (32, 5), (9, 37), (44, 30), (41, 46), (30, 22), (44, 3), (37, 42), (19, 35), (23, 33), (32, 6), (16, 35), (8, 4), (30, 27), (29, 6), (32, 7), (18, 22), (9, 27), (36, 36), (4, 10), (32, 37), (42, 43), (8, 21), (28, 29), (32, 24), (26, 22), (19, 40), (47, 17), (47, 34), (25, 42), (37, 27), (9, 35), (8, 25), (48, 40), (24, 9), (23, 28), (33, 33), (12, 28), (34, 11), (3, 21), (42, 33), (17, 18), (46, 28), (43, 7), (13, 7), (2, 6), (42, 35), (31, 15), (18, 26), (7, 44), (12, 31), (11, 20), (40, 2), (15, 39), (43, 46), (45, 2), (5, 28), (32, 43), (48, 45), (26, 12), (14, 20), (1, 42), (46, 43), (36, 24), (29, 23), (3, 11), (22, 18), (8, 39), (39, 1), (37, 14), (24, 33), (30, 21), (14, 27), (23, 22), (17, 33), (44, 39), (7, 33), (35, 28), (6, 37), (27, 38), (41, 36), (17, 20), (47, 23), (1, 41), (1, 10), (24, 18), (13, 34), (11, 11), (10, 21), (21, 19), (1, 8), (46, 33), (29, 33), (14, 33), (20, 21), (41, 4), (42, 30), (9, 10), (0, 6), (31, 32), (28, 33), (30, 34), (24, 25), (45, 17), (32, 44), (3, 37), (36, 0), (47, 16), (0, 18), (16, 40), (7, 10), (18, 28), (13, 2), (14, 1), (36, 1), (24, 17), (18, 31), (36, 6), (32, 10), (31, 19), (40, 33), (9, 33), (36, 8), (26, 38), (20, 17), (9, 43), (19, 10), (11, 6), (10, 17), (46, 25), (33, 5), (40, 10), (39, 30), (2, 22), (29, 12), (13, 36), (6, 10), (44, 17), (33, 19), (15, 30), (48, 3), (17, 1), (35, 3), (0, 44), (48, 33), (16, 41), (17, 4), (1, 21), (37, 37), (0, 2), (32, 9), (46, 34), (16, 10), (41, 26), (41, 9), (32, 18), (46, 21), (34, 21), (7, 17), (24, 27), (38, 44), (5, 22), (32, 30), (27, 29), (7, 6), (29, 2), (35, 38), (37, 1), (28, 30), (43, 32), (1, 43), (13, 41), (44, 26), (29, 41), (20, 0), (3, 38), (5, 36), (5, 6), (10, 43), (8, 46), (44, 23), (22, 43), (7, 2), (46, 13), (0, 41), (22, 26), (28, 11), (32, 11), (40, 44), (28, 42), (7, 40), (21, 32), (47, 19), (35, 39), (37, 17), (27, 31), (37, 6), (37, 13), (1, 24), (42, 26), (1, 2), (6, 42), (23, 46), (45, 18), (7, 37), (18, 43), (48, 42), (16, 12), (17, 11), (25, 39), (17, 0), (38, 6), (16, 31), (24, 20), (30, 46), (34, 15), (2, 14), (8, 7), (35, 27), (9, 22), (25, 23), (39, 0), (22, 2), (15, 9), (48, 2), (10, 35), (39, 32), (45, 4), (30, 31), (21, 11), (38, 11), (8, 27), (10, 42), (43, 14), (41, 29), (30, 41), (22, 27), (14, 29), (24, 38), (48, 23), (1, 13), (21, 2), (24, 39), (25, 17), (48, 30), (36, 35), (47, 39), (16, 5), (10, 5), (40, 28), (33, 44), (10, 7), (47, 0), (5, 12), (27, 45), (9, 46), (48, 31), (37, 40), (44, 41), (25, 44), (35, 15), (44, 46), (48, 9), (19, 34), (22, 11), (13, 46), (31, 10), (24, 28), (47, 11), (39, 34), (39, 14), (24, 1), (45, 6), (31, 38), (41, 19), (25, 15), (12, 34), (40, 19), (5, 7), (44, 5), (11, 38), (3, 46), (43, 2), (11, 34), (36, 13), (4, 42), (26, 5), (15, 13), (38, 38), (46, 19), (42, 25), (41, 16), (0, 14), (25, 4), (20, 4), (37, 15), (7, 25), (9, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 25), (23, 13), (17, 28), (32, 23), (2, 1), (15, 32), (29, 7), (14, 25), (8, 24), (4, 20), (36, 21), (9, 10), (40, 36), (35, 13), (34, 15), (33, 6), (8, 7), (39, 17), (1, 8), (2, 33), (22, 1), (22, 27), (37, 2), (36, 32), (16, 41), (37, 17), (23, 22), (39, 31), (2, 42), (18, 37), (22, 26), (27, 38), (23, 38), (14, 18), (12, 21), (3, 1), (12, 28), (7, 23), (4, 28), (20, 7), (0, 14), (39, 22), (25, 2), (35, 3), (1, 6), (14, 9), (29, 17), (25, 24), (21, 30), (7, 37), (38, 41), (4, 13), (14, 28), (6, 24), (17, 22), (24, 26), (6, 31), (3, 3), (11, 24), (30, 40), (27, 31), (24, 29), (38, 40), (35, 23), (19, 21), (9, 34), (40, 34), (37, 42), (11, 15), (17, 8), (8, 27), (35, 5), (20, 21), (18, 21), (10, 23), (39, 20), (17, 11), (39, 9), (26, 18), (13, 0), (3, 7), (14, 41), (7, 14), (22, 5), (35, 18), (2, 40), (16, 3), (26, 22), (18, 30), (1, 30), (39, 7), (6, 15), (30, 7), (12, 14), (33, 21), (21, 17), (0, 31), (37, 22), (33, 17), (28, 25), (31, 22), (30, 20), (29, 38), (16, 39), (1, 17), (12, 38), (4, 37), (3, 12), (3, 4), (35, 6), (25, 29), (16, 13), (3, 8), (25, 35), (5, 5), (16, 24), (13, 40), (5, 37), (31, 19), (34, 17), (33, 5), (1, 37), (21, 11), (24, 19), (36, 10), (28, 37), (35, 10), (27, 20), (19, 11), (8, 15), (40, 14), (26, 39), (1, 1), (16, 36), (24, 12), (26, 3), (22, 28), (11, 34), (16, 27), (25, 41), (7, 6), (11, 13), (40, 13), (12, 11), (12, 6), (11, 17), (4, 2), (21, 36), (16, 2), (9, 8), (27, 6), (16, 20), (8, 5), (20, 10), (40, 27), (11, 0), (13, 27), (6, 27), (22, 12), (35, 25), (14, 26), (16, 15), (8, 2), (17, 2), (3, 27), (18, 39), (26, 42), (20, 33), (36, 1), (0, 12), (23, 35), (23, 41), (40, 31), (12, 35), (1, 31), (37, 30), (11, 41), (3, 11), (34, 14), (14, 13), (35, 0), (12, 20), (24, 40), (13, 32), (8, 13), (32, 2), (13, 15), (31, 36), (17, 35), (33, 37), (14, 8), (27, 41), (10, 16), (25, 40), (9, 23), (36, 0), (28, 30), (26, 24), (8, 14), (19, 9), (23, 17), (13, 21), (27, 26), (2, 18), (13, 17), (5, 11), (30, 9), (27, 11), (9, 0), (13, 12), (20, 19), (24, 14), (1, 20), (9, 31), (34, 19), (4, 34), (9, 3), (10, 18), (2, 37), (37, 12), (11, 11), (15, 25), (32, 34), (28, 12), (1, 4), (23, 12), (29, 23), (22, 18), (40, 11), (24, 32), (6, 12), (21, 40), (19, 1), (14, 36), (23, 34), (31, 30), (20, 37), (17, 7), (28, 14), (10, 34), (35, 37), (28, 42), (10, 42), (28, 0), (8, 10), (21, 15), (6, 39), (7, 27), (12, 19), (24, 10), (10, 20), (25, 18), (28, 16), (1, 34), (0, 26), (5, 0), (16, 40), (2, 23), (20, 15), (5, 40), (15, 20), (36, 15), (20, 22), (32, 10), (22, 14), (19, 13), (10, 28), (10, 41), (28, 11), (10, 36), (39, 38), (24, 23), (38, 29), (7, 41), (32, 26), (26, 11), (32, 25), (11, 6), (7, 13), (29, 29), (40, 32), (4, 21), (15, 22), (30, 41), (30, 3), (30, 23), (6, 3), (33, 26), (36, 11), (5, 24), (19, 15), (35, 30), (33, 31), (35, 12), (11, 5), (8, 28), (29, 6), (29, 31), (32, 19), (16, 4), (26, 5), (3, 19), (3, 40), (36, 19), (38, 12), (10, 33), (15, 29), (11, 29), (11, 36), (21, 0), (13, 2), (31, 9), (36, 16), (5, 21), (19, 16), (1, 39), (39, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 21), (21, 0), (10, 3), (7, 6), (20, 14), (43, 16), (11, 9), (1, 42), (21, 34), (29, 37), (19, 45), (2, 25), (35, 29), (41, 26), (1, 29), (7, 37), (39, 19), (25, 32), (39, 30), (12, 40), (0, 6), (29, 36), (30, 10), (29, 30), (37, 44), (10, 32), (12, 10), (15, 34), (3, 46), (5, 36), (7, 5), (8, 5), (10, 12), (18, 6), (19, 4), (28, 45), (4, 22), (14, 17), (15, 25), (15, 0), (6, 39), (13, 33), (43, 24), (38, 11), (25, 16), (41, 28), (36, 21), (39, 24), (27, 22), (43, 18), (15, 31), (43, 25), (26, 23), (19, 6), (8, 24), (31, 32), (33, 14), (20, 40), (19, 42), (36, 4), (9, 9), (26, 15), (23, 42), (11, 32), (16, 32), (26, 22), (26, 7), (13, 40), (9, 35), (1, 43), (28, 12), (33, 39), (8, 10), (38, 3), (20, 33), (8, 32), (34, 29), (27, 0), (39, 45), (36, 33), (2, 41), (15, 36), (24, 24), (17, 10), (24, 37), (37, 32), (20, 41), (13, 12), (34, 14), (31, 43), (38, 24), (20, 45), (1, 19), (5, 2), (26, 40), (24, 17), (20, 46), (41, 38), (20, 4), (6, 10), (20, 3), (14, 46), (36, 9), (11, 20), (39, 18), (32, 0), (18, 35), (30, 17), (14, 23), (41, 3), (0, 23), (6, 25), (25, 30), (6, 42), (25, 43), (28, 41), (21, 11), (30, 24), (42, 42), (3, 33), (12, 24), (8, 38), (37, 12), (34, 9), (29, 33), (43, 11), (38, 37), (12, 18), (29, 34), (24, 22), (33, 45), (33, 8), (15, 9), (43, 17), (31, 24), (2, 28), (20, 16), (4, 16), (19, 10), (33, 10), (18, 42), (39, 8), (33, 32), (1, 17), (3, 44), (38, 38), (16, 4), (18, 37), (10, 22), (10, 0), (24, 2), (3, 7), (21, 17), (2, 0), (34, 12), (1, 16), (3, 32), (8, 1), (38, 34), (4, 2), (11, 26), (39, 20), (16, 18), (30, 41), (27, 19), (19, 3), (36, 26), (6, 34), (7, 31), (27, 13), (2, 17), (34, 13), (16, 37), (6, 21), (33, 2), (7, 2), (4, 23), (23, 17), (17, 16), (5, 22), (27, 24), (19, 34), (23, 0), (39, 10), (8, 22), (9, 7), (35, 23), (6, 43), (32, 31), (13, 21), (19, 26), (21, 5), (13, 3), (32, 20), (29, 35), (43, 7), (34, 18), (16, 29), (5, 5), (11, 4), (3, 21), (2, 19), (34, 27), (4, 32), (10, 11), (1, 11), (25, 22), (37, 34), (13, 29), (29, 0), (32, 15), (20, 36), (19, 7), (7, 0), (19, 35), (29, 3), (12, 28), (35, 0), (2, 22), (30, 14), (5, 0), (34, 17), (36, 11), (39, 39), (2, 37), (20, 42), (40, 30), (11, 11), (26, 25), (22, 10), (36, 43), (34, 10), (39, 29), (4, 37), (24, 26), (29, 21), (39, 17), (20, 25), (24, 27), (29, 39), (32, 27), (43, 0), (16, 15), (11, 39), (37, 6), (38, 22), (25, 12), (40, 4), (39, 26), (42, 26), (2, 15), (16, 26), (36, 5), (43, 43), (10, 14), (1, 37), (0, 38), (0, 3), (10, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 32), (1, 8), (8, 42), (10, 15), (9, 5), (38, 30), (26, 41), (27, 25), (9, 13), (0, 18), (3, 9), (14, 38), (22, 34), (39, 9), (2, 24), (16, 24), (1, 32), (4, 11), (16, 36), (22, 23), (6, 27), (15, 10), (21, 35), (4, 26), (4, 7), (0, 5), (10, 19), (28, 18), (29, 29), (25, 34), (32, 17), (27, 24), (35, 5), (37, 31), (16, 8), (25, 19), (11, 10), (17, 43), (26, 15), (31, 6), (39, 42), (10, 7), (32, 0), (23, 31), (7, 11), (13, 7), (39, 31), (21, 36), (23, 22), (9, 3), (35, 41), (36, 32), (32, 42), (1, 30), (8, 0), (8, 35), (32, 12), (3, 20), (2, 34), (31, 10), (2, 23), (28, 9), (14, 20), (32, 32), (29, 28), (2, 0), (17, 15), (30, 9), (12, 1), (29, 14), (31, 14), (34, 20), (36, 43), (16, 17), (1, 28), (18, 32), (23, 41), (23, 4), (14, 33), (35, 13), (31, 39), (0, 26), (1, 6), (0, 22), (36, 1), (14, 17), (10, 33), (16, 35), (5, 33), (4, 36), (13, 43), (3, 12), (12, 7), (14, 35), (16, 10), (7, 22), (37, 15), (34, 43), (0, 27), (23, 21), (4, 29), (24, 37), (17, 0), (37, 37), (13, 28), (18, 18), (4, 41), (8, 20), (22, 12), (37, 30), (31, 20), (8, 18), (3, 1), (27, 38), (16, 7), (36, 28), (39, 12), (3, 34), (37, 10), (24, 3), (9, 38), (29, 33), (16, 19), (29, 39), (1, 33), (35, 20), (6, 11), (15, 32), (24, 17), (30, 39), (30, 37), (38, 36), (25, 9), (14, 9), (35, 1), (18, 17), (11, 18), (8, 34), (10, 38), (9, 29), (19, 20), (25, 7), (30, 15), (2, 1), (14, 25), (39, 10), (35, 7), (34, 4), (14, 36), (5, 10), (38, 32), (17, 27), (15, 17), (18, 15), (2, 39), (28, 2), (37, 16), (0, 11), (29, 7), (13, 36), (20, 16), (17, 32), (35, 8), (24, 8), (3, 22), (19, 14), (18, 34), (24, 41), (38, 5), (38, 37), (27, 8), (16, 9), (3, 21), (39, 2), (2, 12), (22, 21), (29, 17), (7, 18), (15, 35), (19, 17), (8, 9), (3, 11), (18, 4), (17, 23), (31, 34), (4, 37), (14, 40), (11, 24), (30, 8), (16, 5), (17, 19), (7, 5), (5, 16), (14, 22), (33, 38), (18, 36), (11, 43), (12, 24), (36, 9), (15, 14), (38, 3), (25, 42), (21, 10), (16, 32), (36, 40), (18, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 23), (12, 27), (15, 33), (12, 36), (16, 4), (37, 26), (39, 31), (20, 10), (25, 10), (36, 10), (21, 10), (9, 2), (0, 31), (38, 22), (35, 22), (34, 22), (29, 12), (6, 24), (24, 33), (5, 3), (14, 37), (18, 11), (26, 11), (35, 12), (16, 0), (40, 22), (12, 24), (15, 40), (3, 19), (32, 11), (20, 2), (23, 24), (33, 15), (36, 21), (26, 18), (22, 15), (17, 2), (21, 8), (13, 33), (38, 25), (16, 40), (10, 38), (0, 33), (3, 23), (7, 11), (38, 33), (25, 1), (28, 26), (35, 38), (9, 34), (38, 10), (40, 38), (40, 9), (32, 1), (18, 9), (17, 38), (29, 2), (7, 33), (36, 23), (10, 11), (26, 0), (1, 15), (8, 26), (32, 35), (37, 19), (19, 19), (11, 6), (25, 21), (0, 27), (11, 14), (6, 18), (33, 34), (37, 32), (27, 12), (39, 24), (26, 29), (27, 31), (29, 16), (36, 40), (21, 18), (0, 34), (3, 28), (20, 25), (10, 3), (4, 23), (2, 1), (24, 24), (3, 6), (19, 3), (7, 35), (35, 20), (31, 7), (21, 41), (8, 25), (34, 39), (11, 4), (23, 22), (7, 8), (31, 0), (13, 24), (5, 35), (38, 11), (17, 3), (1, 13), (31, 21), (35, 35), (30, 38), (26, 41), (38, 34), (19, 11), (38, 16), (35, 39), (20, 9), (23, 28), (31, 33), (19, 15), (17, 37), (30, 13), (14, 1), (29, 32), (10, 41), (28, 10), (12, 13), (20, 15), (9, 21), (38, 12), (16, 37), (15, 12), (0, 17), (1, 23), (19, 5), (39, 23), (25, 30), (6, 19), (4, 33), (17, 16), (35, 10), (23, 37), (15, 6), (39, 16), (6, 9), (6, 35), (26, 16), (6, 25), (10, 1), (17, 21), (32, 40), (11, 32), (10, 39), (9, 33), (39, 20), (32, 34), (1, 17), (34, 36), (4, 21), (17, 4), (12, 31), (18, 10), (38, 8), (5, 10), (7, 12), (30, 21), (28, 8), (24, 17), (30, 14), (28, 1), (30, 22), (22, 34), (1, 16), (22, 12), (38, 6), (14, 33), (15, 21), (22, 6), (3, 35), (17, 15), (20, 21), (12, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 33), (3, 16), (0, 12), (27, 31), (42, 38), (1, 11), (24, 29), (29, 36), (28, 37), (5, 23), (4, 29), (9, 27), (31, 20), (19, 22), (21, 43), (43, 14), (19, 10), (16, 8), (4, 8), (24, 30), (16, 5), (3, 23), (31, 15), (14, 28), (2, 37), (9, 16), (2, 20), (28, 12), (38, 45), (17, 5), (19, 31), (15, 18), (3, 0), (15, 11), (21, 17), (28, 5), (22, 20), (39, 5), (0, 29), (22, 32), (25, 28), (14, 4), (0, 16), (36, 15), (36, 36), (18, 36), (17, 43), (18, 21), (24, 1), (24, 10), (32, 29), (33, 35), (35, 39), (30, 39), (19, 36), (18, 35), (43, 38), (21, 18), (42, 43), (10, 41), (34, 29), (2, 33), (12, 33), (21, 44), (17, 41), (26, 22), (36, 26), (0, 2), (43, 1), (21, 28), (26, 20), (6, 25), (24, 21), (36, 30), (32, 3), (41, 43), (5, 35), (31, 41), (43, 43), (38, 33), (1, 1), (5, 29), (8, 8), (29, 7), (23, 15), (37, 15), (36, 23), (4, 39), (20, 28), (32, 4), (8, 15), (6, 37), (23, 5), (30, 25), (7, 20), (11, 29), (15, 1), (44, 6), (34, 7), (3, 1), (18, 40), (15, 45), (37, 27), (8, 2), (5, 41), (31, 1), (15, 37), (0, 43), (29, 27), (10, 8), (23, 31), (9, 13), (12, 29), (31, 11), (0, 34), (6, 4), (5, 19), (20, 41), (24, 11), (28, 33), (30, 13), (11, 5), (43, 15), (0, 35), (28, 24), (19, 6), (41, 37), (31, 44), (26, 17), (42, 24), (24, 0), (20, 37), (9, 41), (1, 4), (9, 29), (12, 41), (40, 38), (0, 22), (38, 29), (16, 45), (3, 11), (3, 36), (22, 43), (13, 23), (17, 44), (28, 44), (17, 2), (0, 20), (14, 3), (34, 31), (13, 7), (42, 11), (41, 41), (2, 11), (41, 16), (14, 34), (36, 42), (16, 15), (27, 33), (36, 40), (39, 30), (27, 38), (18, 38), (32, 20), (30, 1), (14, 8), (43, 18), (31, 3), (19, 23), (13, 36), (5, 15), (26, 32), (12, 38), (2, 34), (44, 33), (0, 31), (22, 10), (6, 11), (40, 7), (24, 44), (39, 23), (23, 45), (17, 11), (26, 42), (10, 29), (38, 12), (2, 42), (20, 4), (1, 2), (34, 36), (1, 30), (38, 3), (2, 4), (18, 2), (38, 35), (2, 40), (33, 20), (19, 44), (21, 21), (23, 29), (25, 25), (31, 0), (44, 21), (26, 45), (4, 4), (38, 37), (27, 17), (1, 29), (33, 17), (42, 14), (11, 40), (6, 43), (1, 43), (13, 45), (41, 15), (37, 21), (29, 28), (6, 13), (9, 45), (23, 26), (21, 2), (24, 17), (17, 19), (30, 36), (12, 19), (14, 38), (24, 27), (6, 10), (21, 32), (24, 45), (11, 37), (44, 20), (16, 16), (6, 19), (40, 39), (18, 9), (22, 35), (32, 39), (9, 18), (7, 32), (27, 35), (2, 32), (20, 16), (33, 13), (7, 35), (1, 45), (15, 7), (30, 28), (5, 43), (31, 25), (4, 9), (39, 14), (20, 5), (26, 28), (11, 7), (42, 10), (14, 42), (11, 8), (0, 21), (34, 26), (14, 26), (15, 31), (3, 2), (4, 31), (42, 5), (31, 30), (22, 23), (32, 22), (11, 45), (22, 17), (36, 17), (29, 42), (7, 40), (15, 17), (42, 15), (26, 15), (36, 41), (14, 32), (4, 24), (40, 31), (22, 8), (11, 39), (23, 23), (34, 20), (39, 33), (12, 15), (18, 18), (8, 32), (21, 0), (31, 35), (28, 29), (5, 6), (27, 42), (11, 43), (27, 12), (10, 43), (17, 27), (14, 30), (30, 21), (30, 12), (4, 19), (41, 24), (26, 5), (7, 7), (11, 34), (40, 37), (42, 39), (37, 5), (21, 29), (34, 3), (40, 2), (31, 6), (34, 9), (36, 18), (44, 3), (12, 5), (40, 0), (9, 35), (7, 9), (37, 1), (32, 10), (40, 25), (19, 14), (15, 13), (6, 34), (19, 42), (11, 32), (6, 5), (2, 36), (10, 28), (43, 37), (23, 9), (37, 34), (20, 36), (8, 38), (5, 18), (33, 23), (28, 25), (16, 14), (8, 19), (12, 4), (0, 36), (32, 7), (21, 16), (24, 43), (43, 34), (36, 16), (12, 43), (20, 24), (5, 1), (19, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 16), (29, 35), (16, 22), (22, 7), (42, 23), (8, 15), (3, 34), (26, 40), (25, 28), (33, 34), (36, 4), (29, 1), (17, 23), (34, 31), (46, 23), (43, 19), (33, 10), (20, 35), (22, 34), (36, 14), (28, 7), (10, 37), (23, 34), (13, 21), (40, 29), (14, 32), (4, 2), (21, 1), (1, 12), (24, 0), (42, 27), (29, 3), (30, 31), (11, 30), (47, 14), (16, 32), (33, 24), (44, 16), (37, 36), (7, 15), (48, 31), (21, 31), (41, 9), (3, 7), (30, 7), (24, 4), (34, 33), (40, 5), (43, 8), (46, 17), (45, 15), (3, 32), (17, 37), (46, 20), (5, 28), (2, 9), (12, 20), (27, 1), (20, 24), (5, 16), (31, 18), (45, 9), (4, 33), (44, 35), (8, 14), (36, 1), (23, 6), (17, 14), (11, 19), (40, 8), (15, 6), (21, 28), (18, 20), (30, 22), (41, 23), (38, 37), (12, 10), (20, 8), (7, 22), (3, 37), (12, 30), (1, 30), (22, 12), (11, 8), (30, 20), (41, 32), (16, 15), (23, 28), (31, 15), (3, 4), (32, 2), (34, 14), (47, 2), (7, 40), (15, 0), (14, 34), (5, 39), (2, 30), (39, 12), (30, 28), (18, 27), (33, 36), (19, 20), (5, 31), (48, 35), (21, 7), (8, 36), (47, 21), (1, 22), (47, 18), (11, 34), (1, 25), (18, 12), (22, 39), (32, 32), (33, 12), (16, 25), (38, 26), (29, 36), (46, 22), (38, 6), (0, 31), (35, 19), (26, 0), (23, 14), (14, 26), (44, 7), (15, 21), (33, 11), (2, 32), (38, 23), (35, 5), (21, 11), (9, 1), (39, 37), (11, 28), (41, 13), (1, 1), (45, 23), (47, 8), (35, 4), (26, 24), (38, 10), (48, 28), (23, 31), (13, 2), (19, 35), (29, 29), (43, 26), (36, 39), (7, 32), (24, 39), (2, 38), (42, 16), (12, 28), (32, 36), (21, 8), (7, 26), (5, 21), (16, 24), (22, 19), (46, 29), (9, 11), (8, 1), (18, 29), (32, 29), (22, 25), (29, 22), (34, 37), (18, 19), (19, 22), (15, 1), (5, 38), (31, 31), (31, 20), (11, 21), (29, 31), (13, 35), (16, 36), (16, 31), (38, 28), (31, 21), (2, 12), (2, 1), (14, 6), (42, 26), (21, 6), (44, 2), (19, 9), (36, 16), (4, 9), (35, 3), (34, 20), (8, 26), (9, 7), (39, 36), (10, 12), (33, 30), (29, 33), (35, 39), (41, 38), (9, 40), (10, 9), (43, 22), (8, 25), (20, 5), (23, 15), (38, 21), (7, 39), (19, 3), (1, 34), (30, 10), (16, 38), (45, 33), (23, 18), (35, 37), (3, 12), (28, 23), (28, 19), (34, 28), (11, 17), (10, 40), (6, 19), (32, 22), (6, 28), (37, 3), (13, 13), (9, 34), (0, 20), (39, 39), (1, 17), (30, 12), (47, 23), (26, 5), (3, 33), (13, 18), (13, 16), (7, 30), (3, 31), (45, 1), (31, 38), (21, 34), (1, 5), (7, 27), (35, 34), (12, 27), (25, 20), (17, 10), (2, 17), (36, 9), (34, 27), (43, 32), (38, 35), (46, 33), (8, 18), (6, 10), (27, 40), (15, 13), (48, 37), (3, 13), (14, 5), (30, 38), (9, 16), (25, 40), (21, 26), (44, 22), (15, 25), (33, 38), (20, 28), (10, 25), (29, 30), (14, 25), (47, 1), (7, 37), (44, 3), (0, 17), (30, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 29), (34, 22), (1, 9), (22, 17), (16, 26), (41, 35), (41, 43), (28, 35), (33, 25), (29, 7), (16, 35), (31, 35), (16, 37), (23, 1), (3, 19), (5, 11), (3, 47), (36, 40), (24, 11), (15, 34), (40, 41), (5, 12), (16, 11), (39, 18), (9, 10), (9, 4), (17, 28), (18, 32), (32, 46), (19, 32), (23, 29), (3, 10), (35, 13), (38, 27), (41, 2), (0, 47), (24, 17), (10, 9), (15, 48), (16, 34), (37, 30), (9, 18), (30, 1), (10, 8), (39, 30), (41, 33), (9, 9), (13, 6), (22, 31), (14, 8), (14, 34), (35, 14), (19, 22), (3, 18), (22, 13), (10, 22), (30, 46), (29, 1), (38, 0), (38, 16), (13, 39), (7, 30), (22, 30), (29, 27), (17, 3), (15, 7), (5, 16), (34, 0), (19, 10), (4, 12), (3, 20), (8, 35), (29, 30), (30, 15), (32, 4), (30, 12), (10, 25), (24, 18), (16, 38), (26, 18), (12, 18), (40, 20), (9, 22), (3, 40), (18, 48), (20, 37), (25, 3), (18, 35), (22, 19), (19, 0), (37, 6), (33, 5), (20, 41), (6, 18), (20, 32), (40, 2), (27, 39), (14, 4), (12, 20), (20, 31), (7, 9), (11, 34), (41, 0), (23, 25), (9, 34), (2, 25), (31, 0), (32, 25), (39, 5), (0, 46), (14, 3), (23, 0), (35, 8), (13, 48), (33, 13), (2, 26), (22, 4), (34, 21), (10, 20), (37, 11), (1, 2), (7, 41), (12, 19), (4, 15), (18, 20), (30, 3), (9, 0), (26, 45), (40, 39), (12, 13), (9, 45), (37, 22), (12, 14), (4, 21), (6, 27), (41, 6), (5, 9), (23, 45), (8, 37), (32, 15), (16, 7), (39, 0), (11, 25), (26, 6), (24, 7), (41, 41), (0, 42), (21, 25), (10, 11), (5, 46), (5, 1), (21, 48), (39, 9), (39, 32), (25, 21), (26, 41), (36, 48), (19, 36), (26, 36), (10, 46), (9, 46), (19, 25), (35, 24), (13, 10), (17, 39), (20, 24), (35, 35), (25, 28), (36, 33), (15, 18), (33, 21), (18, 24), (12, 7), (21, 29), (12, 24), (35, 45), (13, 7), (31, 1), (31, 29), (33, 47), (12, 31), (9, 11), (40, 10), (41, 42), (6, 47), (17, 33), (10, 23), (4, 3), (24, 29), (24, 24), (38, 46), (17, 1), (12, 42), (0, 21), (0, 5), (13, 23), (34, 36), (1, 24), (19, 40), (21, 31), (36, 1), (17, 17), (38, 10), (25, 27), (19, 11), (27, 32), (1, 17), (21, 35), (36, 8), (35, 36), (5, 27), (30, 8), (9, 38), (24, 15), (14, 20), (5, 6), (5, 44), (25, 48), (20, 40), (1, 43), (41, 29), (28, 36), (0, 41), (27, 28), (40, 24), (36, 0), (24, 14), (3, 8), (30, 48), (4, 29), (2, 6), (7, 16), (37, 28), (31, 20), (2, 16), (12, 27), (27, 5), (11, 40), (25, 18), (7, 18), (7, 38), (0, 31), (14, 14), (33, 27), (9, 6), (28, 5), (35, 47), (17, 13), (40, 31), (29, 48), (38, 15), (9, 16), (26, 27), (39, 22), (34, 23), (0, 30), (34, 37), (35, 29), (16, 6), (21, 19), (8, 6), (25, 9), (8, 36), (30, 40), (9, 24), (22, 9), (3, 1), (0, 11), (7, 11), (25, 25), (32, 27), (20, 9), (23, 3), (23, 42), (26, 7), (4, 26), (18, 5), (12, 1), (24, 1), (20, 47), (18, 23), (34, 10), (19, 12), (13, 47), (4, 31), (18, 42), (28, 39), (18, 13), (25, 24), (34, 32), (0, 36), (17, 42), (40, 35), (30, 31), (24, 42), (31, 37), (38, 47), (37, 39), (27, 42), (17, 38), (37, 33), (6, 10), (7, 40), (35, 7), (12, 39), (20, 0), (37, 9), (25, 6), (11, 39), (3, 11), (2, 10), (13, 1), (25, 46), (19, 38), (33, 2), (1, 25), (38, 36), (1, 6), (25, 35), (13, 5), (28, 2), (37, 10), (14, 47), (1, 27), (27, 13), (20, 29), (22, 32), (6, 25), (19, 24), (19, 19), (6, 6), (18, 34), (18, 18), (28, 19), (6, 43), (27, 11), (4, 2), (10, 40), (21, 2), (20, 10), (3, 25), (34, 17), (26, 40), (34, 15), (28, 31), (24, 46), (40, 47), (40, 25), (26, 2), (15, 44), (16, 43), (38, 21), (22, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 20), (19, 6), (12, 12), (17, 30), (35, 4), (20, 18), (24, 0), (24, 22), (32, 10), (20, 40), (15, 2), (30, 25), (6, 38), (31, 27), (27, 27), (24, 42), (28, 2), (37, 31), (24, 38), (21, 18), (20, 24), (39, 42), (5, 22), (19, 27), (19, 3), (17, 29), (35, 19), (18, 37), (7, 28), (10, 0), (33, 8), (30, 24), (13, 6), (7, 5), (29, 19), (33, 19), (11, 7), (43, 12), (39, 21), (6, 25), (32, 28), (0, 25), (25, 43), (28, 29), (23, 39), (21, 26), (40, 24), (29, 10), (26, 7), (9, 27), (20, 0), (36, 31), (37, 39), (3, 31), (21, 38), (38, 18), (40, 43), (26, 36), (8, 34), (29, 30), (0, 6), (4, 8), (20, 27), (40, 8), (19, 9), (10, 10), (22, 40), (43, 22), (4, 30), (39, 8), (29, 0), (37, 7), (38, 9), (25, 15), (39, 17), (41, 33), (14, 14), (39, 28), (20, 25), (5, 36), (22, 24), (8, 29), (42, 2), (20, 38), (25, 4), (0, 22), (37, 24), (18, 11), (2, 26), (38, 37), (37, 22), (15, 17), (16, 6), (35, 2), (41, 27), (35, 16), (25, 11), (1, 0), (35, 5), (16, 30), (4, 19), (19, 32), (12, 1), (0, 8), (19, 31), (32, 23), (9, 32), (22, 17), (1, 39), (11, 28), (33, 35), (33, 36), (24, 28), (35, 9), (27, 38), (28, 33), (38, 29), (38, 6), (39, 25), (34, 30), (29, 7), (6, 1), (28, 44), (33, 43), (1, 11), (29, 20), (2, 15), (2, 38), (2, 30), (18, 7), (11, 26), (13, 2), (38, 39), (21, 36), (13, 38), (26, 9), (23, 26), (42, 4), (40, 5), (25, 6), (29, 41), (12, 17), (18, 43), (4, 35), (26, 19), (44, 5), (23, 43), (28, 20), (22, 22), (21, 31), (41, 5), (42, 42), (5, 17), (4, 10), (19, 41), (25, 8), (32, 20), (22, 35), (32, 15), (20, 28), (16, 1), (13, 13), (26, 27), (34, 28), (35, 41), (38, 32), (31, 3), (32, 41), (39, 26), (28, 30), (42, 20), (8, 20), (37, 32), (31, 44), (17, 0), (27, 32), (5, 4), (27, 7), (29, 25), (34, 34), (8, 10), (23, 34), (36, 1), (43, 28), (13, 30), (19, 28), (8, 16), (30, 44), (28, 37), (29, 5), (8, 22), (42, 28), (33, 23), (26, 35), (4, 17), (23, 21), (1, 44), (9, 42), (8, 33), (37, 37), (44, 20), (27, 4), (33, 38), (3, 3), (41, 16), (36, 26), (14, 43), (39, 9), (44, 3), (27, 43), (5, 38), (44, 26), (34, 0), (12, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 3), (32, 32), (25, 17), (27, 23), (16, 35), (24, 0), (1, 26), (4, 23), (31, 16), (27, 37), (5, 14), (29, 35), (32, 3), (23, 0), (28, 17), (5, 35), (30, 21), (8, 19), (8, 1), (45, 14), (41, 5), (36, 27), (40, 23), (7, 25), (30, 40), (1, 16), (10, 3), (3, 39), (24, 26), (40, 16), (40, 5), (29, 19), (20, 19), (30, 29), (39, 34), (18, 16), (15, 19), (8, 16), (30, 9), (0, 40), (32, 6), (37, 37), (19, 2), (34, 2), (38, 14), (11, 34), (21, 24), (43, 3), (14, 20), (41, 13), (37, 38), (11, 40), (26, 20), (19, 26), (22, 29), (31, 22), (30, 32), (38, 3), (15, 39), (9, 36), (32, 2), (19, 33), (19, 13), (8, 30), (20, 37), (40, 32), (33, 6), (2, 15), (35, 9), (9, 9), (23, 15), (1, 21), (15, 37), (15, 4), (29, 12), (28, 33), (32, 20), (2, 16), (1, 4), (35, 27), (0, 37), (6, 26), (6, 5), (17, 24), (7, 17), (7, 36), (7, 6), (24, 30), (24, 35), (19, 6), (14, 0), (32, 8), (21, 12), (18, 29), (3, 29), (39, 23), (20, 39), (43, 12), (30, 37), (35, 14), (34, 24), (19, 38), (28, 36), (10, 19), (18, 32), (29, 37), (18, 14), (45, 27), (11, 7), (15, 29), (15, 25), (41, 21), (17, 6), (25, 28), (29, 22), (40, 27), (38, 5), (33, 5), (39, 2), (24, 20), (7, 38), (16, 32), (30, 36), (0, 12), (6, 19), (12, 7), (15, 18), (21, 9), (38, 29), (18, 12), (22, 39), (21, 31), (28, 16), (11, 2), (32, 24), (31, 36), (24, 6), (28, 32), (20, 15), (30, 0), (4, 19), (4, 24), (14, 3), (41, 29), (31, 39), (19, 34), (36, 14), (22, 37), (8, 9), (36, 8), (19, 11), (44, 10), (23, 31), (9, 19), (25, 19), (30, 27), (20, 36), (26, 31), (5, 1), (4, 9), (40, 17), (13, 3), (6, 17), (14, 13), (16, 13), (35, 24), (13, 32), (42, 2), (19, 4), (6, 8), (5, 33), (12, 9), (38, 24), (13, 40), (17, 29), (26, 13), (10, 35), (6, 9), (33, 15), (26, 9), (15, 2), (28, 28), (36, 40), (12, 13), (24, 2), (40, 9), (36, 38), (12, 3), (11, 11), (41, 2), (13, 9), (4, 30), (18, 30), (9, 1), (13, 12), (8, 0), (28, 26), (7, 29), (11, 13), (38, 40), (43, 16), (5, 8), (19, 15), (33, 22), (43, 9), (41, 39), (29, 5), (45, 29), (44, 13), (12, 26), (4, 22), (30, 28), (29, 23), (30, 7), (20, 32), (36, 23), (42, 34), (40, 20), (42, 1), (8, 25), (9, 2), (44, 11), (21, 23), (5, 17), (4, 36), (5, 34), (41, 0), (3, 34), (33, 4), (22, 14), (10, 28), (10, 26), (31, 23), (4, 38), (6, 36), (21, 5), (14, 14), (38, 26), (16, 27), (40, 33), (18, 11), (16, 25), (3, 4), (45, 8), (43, 20), (17, 40), (36, 0), (34, 23), (28, 4), (34, 1), (29, 29), (10, 31), (27, 19), (39, 19), (26, 36), (0, 31), (37, 31), (40, 26), (30, 5), (21, 15), (39, 7), (10, 9), (44, 18), (12, 29), (13, 29), (15, 12), (18, 40), (38, 32), (14, 26), (3, 33), (13, 2), (5, 31), (3, 35), (0, 1), (37, 34), (41, 35), (39, 29), (6, 6), (17, 13), (34, 19), (41, 8), (27, 33), (2, 7), (28, 11), (32, 23), (37, 1), (5, 10), (26, 25), (34, 34), (9, 37), (45, 15), (42, 22), (2, 33), (22, 32), (0, 11), (12, 22), (31, 5), (20, 40), (21, 30), (3, 7), (32, 13), (17, 0), (37, 39), (21, 37), (32, 14), (41, 19), (32, 11), (10, 5), (38, 28), (22, 15), (26, 27), (27, 20), (3, 37), (40, 25), (10, 38), (16, 12), (4, 8), (39, 17), (44, 2), (14, 7), (27, 8), (26, 5), (20, 6), (20, 11), (28, 21), (37, 17), (32, 29), (28, 37), (24, 31), (28, 6), (41, 40), (24, 10), (7, 10), (22, 17), (22, 34), (35, 28), (37, 27), (15, 40), (17, 36), (38, 10), (13, 34), (2, 39), (27, 25), (41, 36), (35, 15), (45, 12), (39, 4), (30, 16), (2, 26), (35, 10), (11, 37), (23, 10), (11, 16), (38, 11), (5, 0), (17, 31), (9, 16), (9, 8), (1, 30), (1, 24), (11, 39), (9, 7), (3, 10), (21, 25), (31, 3), (3, 0), (3, 31), (24, 9), (9, 20), (40, 2), (16, 40), (40, 21), (23, 28), (0, 2), (6, 2), (17, 5), (30, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 37), (20, 15), (5, 12), (25, 5), (7, 18), (17, 34), (17, 33), (28, 23), (7, 22), (39, 21), (20, 11), (6, 7), (40, 31), (11, 33), (39, 37), (27, 42), (9, 17), (40, 39), (26, 23), (19, 28), (13, 13), (37, 18), (41, 9), (14, 41), (4, 34), (11, 1), (17, 31), (19, 35), (30, 12), (17, 22), (39, 34), (19, 20), (31, 21), (26, 15), (2, 2), (29, 41), (22, 38), (30, 14), (34, 6), (26, 21), (31, 30), (28, 39), (37, 25), (15, 42), (23, 37), (28, 34), (24, 10), (3, 10), (30, 33), (21, 24), (17, 39), (4, 40), (31, 36), (18, 22), (5, 19), (15, 14), (38, 28), (16, 20), (29, 42), (22, 1), (37, 22), (31, 40), (29, 26), (1, 41), (7, 5), (3, 1), (11, 12), (25, 21), (36, 13), (36, 31), (18, 33), (5, 24), (3, 28), (25, 20), (6, 11), (38, 18), (31, 29), (0, 24), (22, 17), (40, 29), (31, 2), (14, 3), (22, 6), (15, 25), (36, 18), (22, 37), (14, 35), (37, 36), (25, 38), (41, 22), (39, 1), (22, 34), (32, 6), (5, 40), (19, 19), (9, 9), (22, 10), (29, 37), (12, 18), (16, 1), (35, 33), (15, 2), (7, 27), (15, 10), (28, 0), (17, 19), (36, 26), (24, 19), (33, 10), (25, 32), (23, 1), (37, 7), (13, 32), (2, 30), (22, 5), (39, 6), (17, 30), (9, 7), (40, 10), (28, 5), (34, 35), (26, 0), (33, 17), (36, 28), (34, 33), (7, 17), (13, 22), (4, 9), (0, 10), (29, 18), (9, 18), (35, 19), (41, 16), (36, 16), (2, 40), (29, 21), (25, 39), (2, 19), (13, 21), (33, 14), (17, 32), (38, 16), (39, 27), (39, 2), (35, 36), (12, 29), (25, 2), (40, 20), (41, 13), (10, 8), (5, 17), (9, 13), (40, 15), (3, 13), (24, 15), (2, 32), (7, 29), (7, 33), (14, 11), (8, 17), (14, 7), (39, 8), (41, 11), (14, 6), (34, 29), (7, 32), (34, 5), (38, 29), (21, 9), (36, 7), (1, 21), (22, 15), (29, 36), (15, 15), (24, 42), (10, 12), (19, 25), (14, 24), (4, 27), (10, 4), (21, 36), (32, 24), (38, 15), (22, 29), (26, 24), (15, 34), (7, 23), (14, 18), (4, 10), (13, 7), (40, 13), (7, 41), (2, 27), (24, 14), (17, 37), (31, 28), (27, 10), (33, 13), (8, 27), (16, 3), (28, 28), (30, 17), (32, 41), (1, 6), (37, 30), (1, 36), (15, 29), (33, 28), (13, 19), (1, 5), (26, 8), (41, 14), (21, 20), (10, 17), (21, 10), (35, 38), (38, 30), (11, 28), (16, 26), (2, 13), (7, 3), (14, 23), (14, 5), (36, 20), (1, 14), (22, 18), (27, 6), (30, 25), (33, 15), (2, 3), (25, 15), (28, 17), (9, 14), (30, 1), (40, 7), (8, 11), (28, 30), (4, 25), (14, 0), (23, 7), (20, 36), (16, 17), (29, 30), (15, 30), (18, 14), (19, 13), (39, 29), (33, 7), (28, 19), (37, 13), (30, 9), (15, 38), (0, 18), (6, 19), (32, 26), (28, 20), (25, 19), (33, 39), (17, 11), (1, 23), (41, 24), (13, 5), (1, 34), (27, 41), (37, 37), (41, 18), (14, 21), (25, 33), (13, 8), (8, 0), (5, 3), (23, 3), (29, 25), (27, 31), (38, 24), (40, 34), (4, 22), (8, 33), (40, 2), (34, 7), (1, 19), (39, 42), (15, 40), (28, 32), (6, 28), (13, 34), (6, 39), (4, 5), (3, 21), (11, 16), (13, 23), (5, 23), (1, 7), (22, 11), (40, 3), (40, 1), (19, 26), (29, 2), (40, 14), (29, 28), (22, 39), (40, 16), (40, 36), (29, 9), (3, 2), (17, 29), (20, 40), (23, 24), (2, 15), (4, 30), (27, 30), (39, 39), (18, 26), (29, 35), (32, 5), (25, 12), (5, 4), (19, 15), (31, 41), (39, 36), (5, 26), (4, 13), (16, 35), (15, 3), (40, 40), (13, 9), (9, 28), (30, 24), (13, 35), (35, 7), (11, 4), (4, 28), (7, 34), (0, 35), (16, 25), (20, 5), (11, 5), (17, 1), (32, 31), (21, 15), (10, 23), (37, 14), (35, 39), (27, 7), (35, 1), (19, 17), (32, 36), (31, 0), (29, 15), (15, 21), (39, 11), (20, 31), (24, 6), (32, 34), (10, 25), (4, 41), (2, 28), (25, 13), (12, 11), (39, 32), (6, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 2), (31, 46), (41, 18), (32, 32), (15, 35), (28, 35), (27, 28), (16, 14), (0, 41), (23, 29), (40, 12), (40, 42), (10, 13), (10, 2), (2, 41), (28, 3), (5, 5), (7, 16), (30, 30), (7, 42), (12, 33), (8, 18), (16, 34), (26, 14), (40, 1), (23, 34), (37, 30), (24, 21), (20, 14), (12, 20), (33, 5), (38, 28), (21, 18), (5, 47), (17, 10), (29, 23), (21, 7), (40, 29), (41, 10), (10, 11), (17, 26), (34, 30), (10, 16), (34, 31), (22, 29), (1, 8), (18, 32), (23, 40), (36, 46), (38, 34), (29, 14), (31, 7), (36, 4), (5, 8), (9, 1), (6, 5), (13, 30), (37, 15), (23, 1), (8, 1), (3, 19), (11, 16), (1, 42), (20, 12), (32, 33), (28, 36), (18, 4), (36, 44), (28, 47), (27, 24), (22, 28), (23, 15), (29, 31), (29, 16), (3, 13), (19, 39), (3, 47), (37, 27), (40, 6), (21, 40), (15, 47), (10, 7), (9, 9), (16, 33), (24, 44), (6, 41), (7, 41), (34, 28), (31, 22), (4, 16), (1, 44), (23, 6), (34, 3), (17, 38), (34, 4), (27, 44), (24, 11), (8, 6), (23, 32), (13, 16), (41, 27), (0, 38), (11, 8), (9, 42), (14, 0), (4, 45), (33, 42), (4, 10), (8, 27), (6, 46), (31, 40), (28, 31), (34, 8), (17, 34), (30, 1), (1, 41), (5, 23), (21, 30), (15, 43), (10, 26), (40, 14), (1, 3), (27, 4), (16, 40), (24, 14), (9, 24), (25, 32), (30, 9), (39, 28), (33, 14), (14, 3), (10, 8), (29, 33), (19, 45), (6, 43), (16, 29), (18, 42), (20, 45), (8, 14), (24, 19), (26, 13), (15, 37), (19, 44), (9, 27), (22, 35), (16, 6), (18, 39), (2, 3), (3, 41), (14, 10), (39, 25), (20, 28), (7, 31), (39, 6), (20, 39), (9, 41), (30, 13), (8, 28), (18, 12), (34, 32), (29, 17), (22, 13), (40, 26), (10, 6), (33, 39), (18, 43), (10, 41), (39, 9), (18, 21), (22, 8), (26, 1), (38, 10), (23, 8), (40, 40), (28, 26), (21, 0), (41, 44), (36, 22), (0, 35), (32, 29), (7, 43), (24, 33), (6, 36), (10, 23), (26, 6), (40, 20), (32, 30), (25, 3), (9, 29), (41, 3), (18, 41), (13, 23), (38, 44), (20, 24), (27, 3), (12, 1), (29, 21), (39, 2), (22, 32), (39, 26), (39, 21), (11, 40), (14, 27), (29, 38), (40, 15), (36, 45), (38, 47), (26, 39), (34, 16), (11, 24), (21, 29), (35, 10), (34, 33), (14, 4), (25, 44), (0, 9), (19, 15), (2, 26), (32, 13), (35, 11), (35, 12), (24, 15), (14, 31), (19, 46), (7, 3), (17, 8), (22, 17), (24, 25), (29, 2), (6, 14), (28, 1), (34, 35), (37, 31), (29, 22), (21, 19), (20, 27), (16, 7), (30, 42), (2, 33), (15, 23), (34, 36), (22, 7), (3, 18), (22, 1), (23, 43), (2, 44), (1, 40), (29, 6), (9, 3), (36, 32), (20, 42), (33, 23), (38, 29), (34, 10), (19, 3), (30, 26), (13, 47), (8, 36), (33, 1), (30, 29), (1, 16), (17, 32), (34, 38), (35, 4), (34, 5), (16, 37), (27, 46), (13, 29), (22, 15), (17, 37), (30, 10), (17, 12), (31, 27), (16, 22), (35, 3), (31, 13), (6, 16), (1, 17), (32, 40), (31, 21), (18, 24), (37, 17), (6, 1), (6, 45), (23, 23), (30, 38), (19, 10), (4, 44), (39, 11), (41, 16), (11, 9), (23, 16), (37, 3), (0, 20), (40, 34), (23, 9), (14, 47), (26, 19), (40, 28), (38, 3), (24, 36), (11, 29), (4, 17), (9, 0), (39, 42), (4, 4), (24, 28), (3, 9), (41, 7), (23, 0), (11, 33), (10, 24), (2, 30), (4, 21), (34, 7), (3, 30), (33, 31), (29, 42), (1, 18), (10, 34), (18, 25), (25, 41), (31, 3), (27, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 1), (10, 20), (31, 31), (9, 33), (39, 5), (20, 13), (32, 25), (34, 6), (3, 28), (15, 34), (0, 11), (44, 18), (28, 26), (17, 29), (34, 24), (44, 36), (37, 10), (43, 29), (32, 8), (10, 17), (28, 6), (30, 29), (34, 35), (16, 38), (29, 15), (35, 16), (38, 26), (43, 9), (16, 22), (45, 1), (9, 39), (6, 34), (15, 0), (22, 39), (12, 29), (9, 3), (6, 30), (3, 13), (13, 1), (14, 13), (46, 16), (4, 12), (27, 31), (9, 1), (45, 28), (4, 6), (32, 3), (34, 1), (0, 40), (4, 17), (2, 15), (30, 1), (6, 23), (24, 25), (20, 14), (10, 21), (1, 11), (17, 34), (19, 32), (13, 14), (23, 37), (26, 4), (30, 28), (36, 0), (19, 39), (23, 1), (21, 34), (3, 29), (18, 10), (22, 16), (43, 35), (15, 13), (43, 34), (26, 35), (9, 36), (25, 26), (23, 13), (42, 19), (32, 16), (9, 7), (4, 23), (37, 16), (3, 30), (16, 39), (29, 29), (4, 21), (41, 3), (37, 32), (32, 15), (16, 28), (30, 19), (15, 36), (2, 14), (4, 18), (45, 2), (45, 27), (1, 37), (41, 40), (10, 0), (39, 23), (34, 10), (1, 9), (40, 28), (14, 39), (40, 34), (10, 19), (14, 40), (7, 34), (31, 5), (7, 13), (42, 15), (22, 18), (29, 12), (32, 20), (32, 31), (21, 10), (25, 20), (20, 11), (18, 33), (3, 1), (26, 40), (19, 3), (25, 32), (35, 18), (23, 12), (33, 17), (6, 12), (5, 17), (11, 13), (25, 25), (42, 7), (29, 17), (30, 27), (13, 4), (29, 27), (18, 35), (30, 30), (32, 0), (42, 14), (42, 18), (6, 14), (33, 30), (46, 39), (26, 38), (15, 7), (25, 3), (25, 15), (31, 27), (2, 7), (33, 13), (9, 35), (14, 16), (4, 9), (28, 39), (11, 8), (0, 28), (41, 15), (34, 38), (8, 31), (30, 3), (18, 21), (22, 7), (7, 25), (31, 30), (0, 19), (29, 36), (10, 11), (15, 14), (14, 28), (20, 18), (16, 6), (7, 9), (43, 11), (24, 13), (35, 4), (33, 2), (42, 20), (12, 34), (45, 35), (43, 13), (44, 19), (40, 6), (32, 14), (1, 38), (43, 5), (18, 12), (41, 14), (24, 31), (45, 26), (30, 7), (41, 37), (3, 38), (45, 30), (43, 16), (9, 15), (41, 23), (38, 24), (34, 34), (7, 35), (20, 21), (27, 0), (23, 11), (36, 14), (44, 30), (31, 7), (22, 32), (37, 12), (11, 23), (9, 14), (30, 6), (27, 39), (9, 18), (37, 8), (14, 37), (27, 40), (3, 21), (29, 10), (19, 9), (2, 9), (21, 16), (25, 36), (9, 4), (38, 8), (23, 39), (19, 4), (7, 19), (34, 12), (14, 30), (2, 30), (42, 35), (43, 26), (11, 37), (44, 0), (40, 25), (37, 5), (18, 8), (29, 11), (39, 17), (1, 23), (8, 11), (18, 39), (18, 27), (23, 2), (44, 33), (2, 33), (40, 33), (37, 39), (44, 29), (46, 18), (40, 29), (11, 29), (37, 20), (15, 25), (19, 17), (27, 28), (3, 17), (17, 3), (20, 0), (40, 3), (46, 8), (31, 8), (37, 7), (27, 4), (20, 16), (13, 6), (34, 27), (6, 1), (10, 7), (30, 0), (32, 18), (25, 0), (40, 18), (44, 7), (4, 24), (32, 22), (20, 25), (27, 20), (33, 18), (37, 26), (46, 38), (17, 2), (45, 0), (41, 9), (23, 30), (18, 26), (3, 10), (5, 15), (14, 21), (5, 37), (9, 32), (9, 40), (9, 2), (22, 17), (33, 29), (21, 20), (39, 35), (31, 2), (13, 25), (3, 37), (3, 5), (25, 16), (2, 23), (20, 9), (30, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 20), (22, 29), (8, 14), (8, 18), (9, 13), (43, 3), (6, 13), (22, 31), (22, 4), (44, 18), (19, 40), (45, 17), (32, 39), (29, 37), (3, 27), (4, 11), (34, 6), (8, 30), (4, 22), (42, 3), (7, 11), (28, 14), (33, 39), (7, 7), (2, 35), (9, 40), (28, 21), (17, 9), (5, 32), (12, 19), (22, 27), (18, 28), (21, 24), (34, 23), (19, 12), (22, 19), (15, 31), (39, 33), (10, 36), (16, 0), (15, 19), (33, 31), (9, 26), (41, 8), (11, 26), (25, 29), (35, 27), (46, 6), (34, 2), (39, 23), (46, 21), (46, 11), (36, 38), (34, 11), (37, 12), (10, 35), (13, 28), (0, 34), (2, 28), (38, 38), (34, 8), (18, 18), (13, 15), (2, 30), (19, 9), (39, 0), (31, 27), (10, 5), (11, 30), (2, 36), (6, 23), (24, 31), (17, 8), (8, 40), (39, 39), (25, 20), (7, 16), (6, 9), (47, 39), (41, 10), (18, 12), (8, 39), (1, 10), (31, 21), (22, 0), (3, 19), (23, 6), (35, 35), (29, 27), (32, 6), (35, 39), (9, 27), (24, 33), (2, 37), (20, 12), (17, 7), (1, 34), (21, 0), (3, 38), (33, 18), (27, 36), (20, 15), (20, 24), (5, 5), (6, 29), (21, 8), (1, 5), (47, 11), (28, 27), (3, 8), (47, 0), (0, 2), (47, 37), (36, 35), (45, 14), (6, 39), (21, 19), (0, 28), (16, 4), (7, 6), (18, 6), (45, 23), (46, 31), (44, 24), (29, 32), (45, 20), (32, 25), (44, 17), (40, 2), (24, 24), (45, 4), (27, 37), (3, 32), (18, 35), (2, 23), (19, 22), (17, 33), (19, 1), (34, 7), (35, 40), (3, 30), (45, 34), (36, 17), (3, 13), (19, 39), (17, 30), (34, 32), (41, 1), (3, 22), (29, 30), (20, 37), (28, 29), (26, 26), (25, 17), (30, 29), (20, 11), (28, 34), (43, 38), (1, 32), (36, 25), (0, 26), (4, 12), (25, 15), (45, 25), (20, 33), (2, 17), (25, 33), (6, 27), (38, 34), (35, 16), (15, 0), (3, 12), (31, 31), (35, 6), (7, 3), (12, 36), (26, 11), (27, 32), (6, 7), (11, 20), (8, 33), (39, 31), (7, 22), (30, 28), (8, 10), (33, 23), (43, 1), (40, 35), (46, 20), (43, 5), (18, 1), (46, 34), (22, 28), (47, 7), (39, 2), (36, 31), (27, 22), (9, 19), (6, 10), (22, 34), (37, 2), (25, 21), (29, 31), (9, 33), (19, 38), (8, 38), (6, 22), (27, 19), (7, 8), (5, 30), (2, 15), (26, 35), (32, 5), (11, 33), (41, 7), (0, 16), (43, 23), (15, 17), (26, 27), (18, 26), (25, 19), (21, 35), (42, 29), (32, 36), (18, 16), (24, 8), (15, 39), (23, 19), (24, 1), (18, 31), (22, 1), (13, 19), (12, 21), (2, 20), (3, 0), (45, 28), (18, 13), (12, 32), (33, 38), (16, 25), (0, 18), (41, 33), (46, 17), (18, 36), (10, 21), (2, 32), (37, 35), (15, 18), (47, 4), (36, 10), (16, 29), (22, 5), (34, 37), (13, 30), (18, 21), (6, 1), (24, 9), (16, 12), (12, 11), (43, 22), (21, 6), (28, 0), (44, 7), (11, 38), (0, 27), (4, 16), (10, 17), (17, 10), (40, 12), (46, 22), (7, 31), (41, 39), (23, 17), (2, 11), (0, 13), (33, 6), (38, 23), (47, 35), (43, 15), (45, 7), (21, 27), (21, 16), (46, 13), (14, 30), (3, 4), (29, 12), (31, 2), (29, 4), (33, 20), (27, 4), (22, 13), (36, 24), (21, 3), (38, 25), (22, 14), (16, 17), (38, 11), (35, 36), (0, 40), (41, 38), (12, 1), (30, 6), (22, 26), (45, 37), (37, 37), (37, 39), (26, 14), (11, 40), (5, 8), (46, 37), (6, 5), (31, 22), (35, 18), (43, 31), (16, 14), (47, 19), (10, 6), (8, 36), (11, 31), (9, 12), (37, 22), (16, 8), (8, 31), (32, 21), (29, 8), (27, 0), (42, 34), (8, 0), (19, 33), (43, 29), (40, 4), (38, 39), (27, 34), (30, 35), (1, 31), (45, 16), (37, 10), (11, 28), (20, 25), (33, 35), (15, 34), (40, 10), (11, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 29), (1, 4), (26, 15), (32, 40), (7, 40), (2, 13), (12, 10), (19, 35), (26, 22), (22, 28), (19, 33), (2, 15), (4, 24), (20, 33), (24, 23), (23, 37), (33, 39), (26, 11), (1, 27), (2, 31), (14, 27), (26, 4), (37, 32), (25, 35), (10, 29), (33, 20), (16, 2), (14, 26), (33, 13), (26, 30), (40, 30), (7, 13), (36, 37), (42, 27), (35, 7), (31, 6), (34, 12), (17, 29), (34, 31), (3, 30), (6, 25), (34, 34), (44, 33), (10, 9), (10, 6), (41, 34), (36, 5), (30, 27), (17, 14), (16, 21), (14, 22), (38, 28), (1, 10), (8, 34), (37, 36), (24, 27), (37, 30), (32, 31), (36, 19), (11, 17), (14, 35), (28, 10), (36, 32), (24, 20), (17, 5), (23, 12), (2, 6), (20, 29), (20, 36), (43, 18), (23, 18), (36, 2), (33, 14), (28, 29), (11, 13), (40, 34), (17, 12), (37, 20), (18, 13), (3, 21), (32, 17), (3, 36), (43, 24), (4, 12), (42, 35), (1, 9), (38, 21), (39, 17), (30, 1), (33, 40), (25, 34), (38, 10), (17, 28), (10, 33), (41, 18), (22, 34), (24, 18), (23, 11), (17, 16), (4, 4), (31, 25), (41, 22), (10, 12), (14, 37), (40, 31), (16, 17), (12, 19), (19, 20), (14, 32), (26, 33), (1, 18), (20, 13), (25, 3), (30, 40), (4, 6), (24, 17), (33, 22), (11, 32), (12, 31), (8, 7), (41, 9), (43, 38), (33, 11), (19, 36), (6, 26), (12, 40), (7, 9), (25, 1), (34, 28), (13, 39), (2, 27), (22, 26), (30, 29), (19, 30), (17, 25), (1, 26), (33, 21), (40, 15), (35, 24), (42, 0), (36, 15), (4, 11), (29, 14), (12, 6), (44, 2), (12, 29), (36, 28), (37, 39), (8, 15), (38, 34), (31, 33), (7, 23), (21, 13), (3, 22), (11, 19), (0, 34), (42, 39), (14, 0), (23, 39), (35, 35), (14, 10), (4, 27), (26, 10), (32, 35), (42, 12), (35, 5), (12, 21), (11, 39), (17, 30), (3, 11), (4, 29), (26, 40), (7, 20), (2, 14), (21, 31), (39, 4), (41, 4), (19, 15), (21, 10), (0, 15), (30, 33), (18, 23), (33, 19), (26, 0), (29, 19), (18, 19), (15, 6), (3, 8), (31, 12), (32, 25), (3, 26), (5, 5), (44, 9), (7, 11), (22, 6), (36, 33), (19, 2), (3, 40), (30, 17), (27, 29), (27, 36), (6, 19), (35, 0), (30, 6), (18, 26), (4, 22), (30, 38), (0, 30), (31, 9), (5, 36), (38, 30), (20, 26), (12, 2), (35, 3), (7, 1), (43, 16), (29, 5), (40, 13), (22, 10), (39, 27), (39, 35), (24, 32), (22, 36), (24, 0), (13, 7), (42, 20), (32, 12), (30, 25), (1, 40), (24, 8), (28, 36), (11, 28), (20, 9), (5, 40), (36, 20), (28, 35), (12, 27), (40, 18), (25, 5), (3, 33), (19, 23), (44, 0), (10, 28), (16, 38), (0, 27), (31, 2), (36, 30), (7, 26), (32, 21), (34, 37), (14, 38), (28, 15), (16, 26), (14, 20), (1, 1), (43, 33), (2, 37), (38, 25), (37, 28), (28, 27), (33, 31), (27, 4), (27, 1), (35, 38), (42, 22), (8, 26), (38, 31), (38, 14), (19, 5), (0, 18), (1, 19), (33, 28), (29, 29), (18, 5), (19, 29), (5, 18), (32, 22), (41, 24), (34, 2), (34, 38), (9, 40), (16, 1), (13, 30), (21, 23), (25, 29), (10, 36), (5, 13), (25, 18), (1, 5), (27, 15), (42, 9), (43, 32), (11, 8), (4, 9), (13, 11), (34, 15), (13, 38), (15, 32), (4, 34), (8, 32), (30, 37), (15, 2), (13, 40), (20, 20), (26, 23), (23, 35), (18, 15), (37, 8), (38, 35), (17, 32), (20, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 3), (29, 17), (24, 24), (5, 27), (16, 8), (32, 44), (8, 31), (18, 0), (15, 17), (39, 42), (37, 26), (12, 16), (35, 18), (9, 35), (24, 18), (0, 15), (12, 1), (40, 42), (20, 29), (12, 23), (43, 3), (5, 21), (16, 16), (26, 5), (2, 16), (20, 32), (33, 2), (10, 36), (27, 14), (14, 2), (45, 24), (22, 23), (3, 10), (24, 26), (13, 14), (45, 0), (23, 7), (0, 43), (6, 33), (17, 11), (1, 10), (3, 25), (45, 39), (40, 6), (38, 9), (35, 8), (22, 3), (6, 20), (47, 23), (34, 9), (6, 28), (15, 10), (6, 36), (11, 0), (13, 23), (29, 1), (19, 14), (24, 28), (10, 26), (48, 32), (34, 6), (26, 10), (2, 40), (33, 13), (25, 6), (4, 25), (36, 20), (42, 37), (15, 7), (15, 9), (19, 43), (10, 21), (22, 8), (16, 17), (19, 25), (13, 40), (41, 41), (16, 22), (21, 26), (48, 23), (15, 40), (4, 27), (45, 32), (23, 5), (37, 8), (17, 23), (13, 7), (3, 11), (46, 35), (47, 38), (28, 13), (29, 9), (23, 19), (33, 0), (8, 8), (36, 9), (12, 31), (42, 10), (39, 8), (23, 40), (19, 15), (6, 25), (40, 19), (0, 30), (47, 22), (21, 40), (4, 18), (28, 9), (38, 31), (19, 5), (17, 35), (14, 36), (7, 16), (23, 36), (0, 26), (30, 39), (48, 12), (8, 10), (7, 37), (5, 30), (6, 10), (34, 15), (12, 43), (27, 18), (14, 29), (10, 31), (12, 22), (31, 24), (29, 41), (13, 44), (23, 30), (23, 27), (48, 22), (33, 39), (31, 44), (34, 12), (13, 34), (44, 13), (17, 0), (24, 1), (11, 26), (32, 2), (35, 11), (34, 22), (36, 24), (48, 17), (3, 32), (38, 19), (32, 31), (41, 3), (26, 27), (7, 11), (46, 24), (33, 32), (12, 15), (4, 12), (27, 12), (27, 31), (16, 13), (26, 21), (21, 4), (5, 26), (31, 31), (13, 19), (45, 2), (44, 20), (18, 20), (24, 20), (0, 33), (20, 19), (26, 22), (8, 40), (23, 14), (37, 9), (10, 11), (4, 0), (40, 21), (28, 30), (0, 34), (40, 44), (46, 41), (16, 39), (36, 1), (10, 20), (20, 23), (24, 21), (34, 10), (20, 40), (42, 35), (35, 29), (2, 20), (27, 16), (12, 13), (26, 11), (36, 14), (17, 6), (33, 43), (39, 9), (18, 12), (15, 44), (24, 0), (44, 23), (0, 22), (33, 27), (16, 7), (34, 7), (19, 33), (0, 23), (18, 40), (47, 9), (10, 39), (2, 10), (18, 14), (7, 31), (0, 14), (48, 11), (23, 15), (9, 18), (38, 5), (10, 37), (41, 43), (8, 23), (37, 44), (19, 41), (2, 28), (41, 23), (36, 41), (15, 24), (29, 13), (38, 3), (45, 15), (22, 31), (33, 22), (43, 1), (10, 13), (45, 27), (32, 21), (44, 18), (37, 34), (42, 28), (18, 33), (48, 5), (42, 5), (45, 3), (43, 7), (3, 40), (33, 18), (37, 7), (10, 32), (33, 12), (11, 32), (33, 20), (2, 7), (45, 16), (21, 27), (44, 12), (7, 15), (39, 11), (38, 22), (21, 33), (6, 24), (30, 10), (2, 29), (15, 6), (3, 29), (1, 5), (44, 9), (39, 22), (12, 6), (25, 28), (2, 44), (39, 10), (40, 40), (8, 25), (5, 23), (24, 29), (30, 23), (46, 23), (18, 22), (20, 2), (6, 17), (0, 32), (41, 18), (35, 7), (39, 38), (2, 15), (30, 30), (19, 0), (22, 5), (43, 29), (9, 21), (35, 17), (19, 17), (2, 43), (14, 23), (48, 24), (40, 23), (6, 12), (41, 39), (11, 37), (12, 42), (14, 18), (41, 31), (22, 30), (34, 30), (22, 14), (14, 9), (42, 18), (43, 2), (18, 13), (1, 12), (34, 0), (20, 31), (32, 11), (19, 4), (9, 16), (26, 31), (25, 7), (5, 44), (41, 14), (33, 4), (47, 33), (14, 26), (9, 12), (38, 32), (11, 29), (5, 3), (1, 39), (30, 20), (17, 14), (35, 26), (10, 42), (33, 37), (10, 19), (31, 37), (35, 9), (7, 19), (23, 22), (35, 13), (31, 18), (42, 15), (39, 17), (9, 6), (41, 0), (10, 4), (3, 24), (46, 18), (37, 19), (10, 22), (14, 14), (26, 6), (14, 40), (11, 28), (37, 23), (30, 15), (18, 9), (24, 9), (12, 20), (28, 2), (17, 9), (43, 26), (20, 18), (47, 8), (31, 4), (14, 42), (25, 27), (38, 39), (34, 39), (39, 41), (22, 40), (13, 13), (28, 6), (43, 8), (35, 28), (6, 4), (21, 22), (8, 42), (38, 14), (47, 29), (39, 24), (0, 10), (0, 5), (44, 37), (29, 16), (48, 43), (36, 31), (43, 28), (14, 22), (42, 43), (16, 4), (12, 38), (20, 36), (30, 33), (24, 25), (22, 25), (25, 40), (35, 14), (24, 43), (12, 7), (3, 1), (16, 33), (3, 6), (28, 38), (9, 31), (27, 9), (17, 39), (30, 6), (47, 16), (14, 17), (0, 42), (15, 34), (19, 19), (47, 11), (36, 4), (36, 10), (31, 21), (13, 25), (21, 28), (39, 44), (4, 32), (21, 39), (48, 36), (30, 27), (2, 30), (42, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 4), (19, 22), (17, 21), (9, 13), (3, 33), (37, 23), (39, 27), (29, 18), (3, 40), (12, 24), (45, 37), (11, 33), (45, 20), (37, 30), (32, 40), (2, 42), (46, 8), (20, 37), (33, 3), (2, 22), (9, 24), (43, 22), (8, 2), (38, 25), (5, 24), (9, 9), (16, 18), (16, 30), (32, 9), (15, 18), (48, 3), (38, 42), (26, 14), (32, 26), (46, 16), (17, 31), (18, 11), (41, 9), (18, 25), (38, 16), (14, 7), (6, 7), (14, 36), (41, 3), (6, 10), (18, 12), (31, 9), (34, 10), (16, 13), (37, 25), (39, 4), (0, 33), (17, 38), (13, 33), (37, 9), (13, 34), (22, 1), (48, 14), (5, 7), (34, 25), (42, 9), (10, 4), (0, 23), (4, 18), (18, 31), (24, 24), (17, 11), (36, 11), (40, 38), (22, 22), (9, 26), (20, 2), (19, 33), (46, 9), (26, 10), (28, 9), (40, 24), (45, 5), (39, 30), (35, 38), (40, 7), (0, 24), (25, 7), (28, 12), (32, 11), (14, 11), (26, 4), (25, 13), (46, 3), (40, 33), (9, 12), (12, 20), (14, 6), (30, 22), (27, 16), (44, 29), (39, 32), (14, 4), (11, 5), (22, 17), (29, 21), (30, 39), (8, 22), (34, 40), (5, 28), (42, 5), (3, 8), (22, 9), (22, 4), (4, 28), (28, 15), (17, 19), (19, 2), (13, 3), (14, 39), (2, 14), (5, 11), (40, 37), (2, 13), (18, 1), (10, 28), (8, 14), (13, 6), (15, 7), (28, 7), (22, 37), (0, 1), (16, 6), (36, 30), (17, 23), (45, 26), (12, 37), (3, 0), (47, 41), (41, 16), (42, 22), (10, 31), (13, 9), (22, 27), (36, 20), (7, 17), (16, 11), (20, 19), (47, 27), (33, 7), (6, 0), (7, 14), (16, 34), (27, 28), (14, 38), (3, 27), (22, 30), (32, 28), (47, 21), (25, 0), (29, 22), (38, 27), (7, 19), (29, 29), (5, 35), (20, 27), (43, 5), (3, 2), (24, 38), (41, 27), (37, 21), (24, 36), (44, 39), (9, 11), (40, 21), (16, 8), (32, 13), (0, 10), (46, 33), (23, 12), (26, 40), (0, 19), (3, 25), (3, 9), (41, 7), (43, 30), (20, 36), (26, 7), (40, 16), (14, 32), (19, 30), (11, 29), (31, 27), (12, 28), (13, 26), (5, 15), (15, 38), (46, 5), (16, 39), (1, 24), (21, 33), (19, 13), (26, 13), (11, 14), (20, 16), (3, 36), (31, 0), (40, 25), (41, 1), (31, 25), (19, 42), (17, 27), (46, 39), (37, 33), (19, 24), (39, 18), (35, 1), (18, 35), (44, 41), (37, 2), (11, 11), (2, 26), (24, 37), (9, 0), (21, 27), (32, 22), (13, 12), (11, 3), (19, 21), (6, 16), (36, 29), (14, 28), (2, 17), (35, 5), (11, 35), (28, 39), (28, 28), (4, 25), (20, 34), (31, 34), (5, 41), (48, 20), (35, 13), (36, 28), (25, 18), (26, 35), (26, 17), (44, 22), (1, 4), (9, 3), (48, 17), (16, 38), (22, 13), (22, 42), (12, 41), (2, 41), (10, 9), (22, 15), (2, 0), (40, 42), (7, 32), (12, 31), (34, 6), (8, 39), (12, 27), (35, 23), (38, 4), (45, 2), (11, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 7), (20, 18), (10, 5), (30, 15), (41, 47), (45, 12), (15, 41), (8, 45), (35, 0), (28, 38), (7, 1), (44, 11), (29, 27), (35, 11), (4, 35), (6, 13), (12, 43), (36, 10), (16, 27), (29, 10), (22, 38), (35, 21), (28, 13), (38, 7), (32, 16), (18, 40), (26, 42), (20, 40), (3, 38), (14, 10), (1, 34), (5, 16), (1, 47), (17, 6), (23, 43), (8, 16), (36, 14), (23, 41), (11, 10), (23, 14), (47, 35), (42, 21), (25, 45), (4, 32), (21, 18), (23, 2), (20, 13), (16, 17), (31, 18), (42, 34), (13, 20), (44, 26), (5, 8), (10, 31), (34, 2), (8, 17), (12, 27), (34, 1), (2, 34), (1, 3), (13, 43), (39, 25), (14, 33), (42, 36), (13, 28), (32, 34), (39, 24), (42, 33), (30, 7), (5, 25), (43, 33), (40, 33), (9, 44), (4, 3), (9, 43), (10, 34), (21, 34), (23, 44), (43, 24), (46, 47), (13, 5), (34, 26), (33, 10), (1, 21), (27, 44), (46, 31), (27, 34), (15, 17), (25, 41), (32, 27), (33, 1), (43, 27), (21, 29), (18, 28), (8, 25), (36, 15), (18, 4), (5, 5), (24, 5), (29, 31), (30, 19), (22, 4), (5, 0), (30, 35), (15, 16), (44, 13), (21, 8), (35, 28), (27, 3), (0, 34), (44, 40), (33, 7), (19, 1), (29, 40), (15, 39), (47, 32), (26, 13), (39, 9), (39, 29), (4, 41), (7, 41), (45, 17), (47, 36), (46, 0), (11, 39), (42, 22), (47, 17), (33, 23), (14, 36), (1, 33), (35, 23), (1, 14), (8, 2), (40, 42), (9, 41), (5, 21), (20, 43), (41, 32), (27, 24), (43, 20), (1, 24), (8, 7), (3, 47), (11, 8), (26, 33), (4, 27), (6, 35), (36, 22), (33, 3), (17, 13), (15, 12), (14, 3), (11, 26), (45, 32), (30, 40), (39, 40), (20, 23), (29, 25), (16, 9), (15, 34), (27, 7), (43, 46), (34, 33), (17, 44), (13, 34), (36, 30), (4, 30), (30, 45), (39, 21), (42, 15), (35, 19), (44, 30), (30, 38), (45, 33), (12, 26), (11, 42), (0, 44), (39, 15), (35, 45), (36, 25), (17, 47), (28, 10), (46, 43), (19, 4), (26, 30), (3, 37), (2, 25), (0, 20), (31, 30), (31, 32), (1, 25), (25, 17), (32, 31), (10, 8), (8, 0), (1, 36), (41, 36), (17, 33), (36, 42), (15, 47), (20, 41), (33, 39), (4, 8), (37, 42), (22, 27), (45, 5), (26, 17), (38, 18), (37, 3), (28, 21), (16, 24), (42, 41), (21, 36), (8, 42), (30, 0), (34, 39), (47, 3), (12, 33), (28, 14), (10, 46), (28, 5), (17, 38), (37, 34), (6, 40), (23, 7), (37, 32), (36, 36), (16, 19), (10, 19), (36, 0), (30, 37), (27, 17), (21, 4), (39, 17), (31, 10), (21, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 37), (41, 1), (17, 23), (37, 10), (30, 14), (18, 15), (27, 2), (12, 24), (9, 41), (19, 5), (18, 40), (37, 2), (15, 42), (2, 41), (2, 24), (14, 9), (12, 10), (19, 40), (26, 18), (4, 36), (38, 16), (34, 19), (14, 8), (24, 20), (16, 10), (16, 1), (43, 32), (9, 14), (38, 4), (16, 24), (9, 5), (37, 24), (30, 2), (28, 23), (16, 25), (28, 10), (41, 7), (8, 39), (21, 16), (18, 3), (13, 35), (25, 20), (32, 27), (19, 26), (0, 34), (15, 29), (21, 15), (6, 40), (30, 17), (23, 25), (27, 7), (8, 22), (10, 40), (12, 5), (22, 14), (9, 39), (7, 9), (43, 22), (40, 3), (18, 18), (28, 1), (44, 29), (39, 2), (4, 2), (19, 33), (28, 7), (13, 21), (31, 40), (37, 22), (44, 40), (9, 9), (9, 19), (22, 10), (43, 1), (33, 20), (9, 16), (35, 12), (32, 1), (11, 27), (8, 34), (39, 14), (3, 20), (39, 9), (16, 29), (4, 17), (29, 7), (38, 6), (21, 7), (35, 8), (20, 40), (1, 11), (30, 34), (13, 10), (22, 31), (20, 17), (34, 40), (14, 23), (36, 11), (41, 41), (8, 16), (23, 13), (0, 17), (20, 14), (20, 18), (32, 20), (19, 17), (10, 14), (43, 5), (3, 15), (6, 42), (0, 13), (32, 31), (23, 34), (33, 15), (20, 26), (0, 39), (31, 7), (23, 31), (2, 22), (1, 27), (12, 6), (21, 24), (26, 29), (1, 6), (11, 0), (16, 39), (38, 33), (43, 41), (7, 36), (26, 27), (44, 9), (44, 20), (33, 21), (42, 5), (5, 41), (0, 38), (3, 28), (12, 4), (14, 32), (10, 6), (20, 7), (2, 42), (35, 10), (15, 24), (0, 30), (20, 30), (13, 33), (33, 12), (14, 20), (20, 31), (14, 41), (35, 20), (10, 1), (0, 16), (9, 17), (3, 36), (35, 32), (37, 32), (12, 3), (1, 16), (37, 11), (24, 23), (19, 21), (42, 21), (13, 28), (6, 24), (31, 12), (33, 16), (0, 5), (16, 19), (23, 6), (40, 33), (29, 27), (12, 9), (37, 26), (30, 25), (36, 17), (12, 18), (31, 10), (43, 17), (20, 32), (32, 26), (26, 28), (22, 13), (24, 35), (35, 22), (1, 10), (22, 32), (44, 8), (25, 17), (32, 0), (43, 30), (1, 25), (32, 15), (15, 23), (23, 12), (5, 42), (3, 31), (44, 13), (10, 13), (40, 1), (40, 18), (17, 27), (28, 3), (4, 31), (40, 10), (37, 40), (34, 38), (30, 7), (31, 42), (18, 17), (11, 1), (6, 38), (30, 30), (29, 16), (31, 41), (11, 26), (38, 34), (7, 17), (39, 26), (0, 23), (31, 15), (28, 12), (31, 8), (20, 6), (7, 15), (22, 4), (15, 35), (6, 39), (25, 21), (8, 10), (26, 11), (18, 23), (20, 35), (40, 30), (13, 9), (2, 31), (22, 24), (16, 42), (33, 11), (10, 42), (7, 31), (39, 28), (15, 40), (35, 25), (22, 23), (2, 2), (18, 1), (11, 40), (36, 29), (29, 40), (21, 32), (43, 14), (25, 24), (35, 2), (35, 11), (2, 14), (22, 42), (3, 0), (9, 4), (42, 26), (3, 41), (2, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 33), (38, 29), (41, 45), (13, 19), (14, 42), (19, 41), (26, 16), (26, 2), (2, 43), (38, 23), (26, 41), (21, 13), (31, 28), (26, 37), (4, 1), (5, 3), (42, 45), (15, 15), (20, 46), (34, 20), (6, 21), (21, 39), (32, 34), (18, 10), (20, 39), (37, 7), (29, 26), (3, 42), (23, 5), (3, 11), (2, 14), (29, 4), (11, 29), (22, 35), (29, 37), (13, 4), (26, 27), (5, 24), (36, 1), (20, 7), (6, 23), (21, 36), (17, 23), (44, 37), (39, 3), (2, 18), (43, 31), (6, 13), (26, 7), (33, 9), (34, 37), (35, 13), (15, 32), (6, 30), (22, 2), (19, 14), (30, 27), (22, 7), (25, 29), (35, 7), (15, 20), (18, 3), (4, 25), (23, 22), (37, 46), (11, 32), (20, 2), (38, 25), (35, 11), (37, 30), (16, 1), (16, 30), (5, 2), (27, 10), (24, 30), (43, 12), (5, 40), (33, 47), (37, 41), (41, 18), (26, 31), (27, 18), (22, 25), (22, 16), (2, 38), (13, 30), (26, 18), (10, 25), (0, 9), (14, 34), (32, 38), (12, 18), (10, 13), (25, 4), (37, 43), (40, 43), (22, 15), (44, 15), (33, 5), (42, 11), (19, 20), (8, 21), (12, 29), (38, 13), (0, 14), (3, 28), (28, 18), (23, 30), (22, 22), (44, 12), (3, 40), (37, 0), (8, 36), (9, 1), (11, 31), (21, 6), (1, 14), (9, 15), (21, 10), (18, 16), (17, 8), (0, 24), (21, 43), (8, 45), (15, 8), (14, 31), (0, 30), (31, 40), (19, 21), (7, 14), (26, 15), (3, 27), (9, 6), (38, 46), (42, 38), (39, 10), (28, 6), (1, 35), (9, 34), (20, 22), (11, 36), (20, 25), (40, 40), (41, 30), (34, 29), (24, 33), (26, 25), (15, 26), (28, 37), (15, 47), (1, 0), (25, 0), (40, 4), (19, 7), (43, 10), (27, 20), (29, 8), (32, 33), (0, 3), (28, 11), (26, 40), (30, 32), (18, 42), (9, 2), (26, 13), (35, 41), (14, 1), (26, 8), (39, 20), (33, 39), (19, 1), (42, 36), (25, 10), (40, 17), (4, 24), (16, 4), (39, 35), (44, 21), (14, 0), (28, 38), (15, 33), (41, 22), (42, 24), (4, 11), (21, 47), (32, 39), (20, 10), (43, 36), (7, 44), (44, 42), (14, 8), (2, 30), (8, 31), (31, 8), (39, 25), (42, 44), (27, 6), (35, 23), (5, 19), (37, 15), (21, 11), (28, 27), (5, 15), (13, 47), (4, 41), (32, 17), (28, 8), (37, 1), (36, 40), (1, 33), (1, 30), (36, 16), (39, 2), (39, 24), (10, 21), (44, 2), (33, 29), (5, 36), (8, 10), (19, 4), (11, 28), (30, 26), (31, 20), (24, 36), (13, 8), (41, 43), (6, 22), (27, 24), (31, 45), (15, 21), (7, 29), (31, 25), (5, 33), (3, 31), (12, 36), (5, 44), (41, 42), (44, 18), (44, 26), (6, 32), (11, 17), (28, 41), (15, 17), (29, 17), (39, 8), (39, 15), (29, 13), (22, 31), (6, 42), (38, 30), (14, 12), (36, 18), (40, 47), (11, 3), (40, 5), (43, 5), (36, 43), (14, 44), (20, 29), (33, 44), (32, 28), (34, 2), (31, 16), (44, 40), (7, 36), (24, 38), (27, 8), (6, 16), (9, 22), (44, 27), (37, 38), (18, 33), (2, 34), (41, 34), (1, 31), (30, 10), (9, 43), (14, 4), (3, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 10), (15, 1), (17, 17), (26, 22), (13, 1), (21, 12), (27, 26), (22, 34), (25, 27), (27, 1), (12, 16), (34, 15), (17, 21), (2, 21), (40, 26), (4, 8), (28, 18), (11, 17), (6, 36), (17, 14), (28, 31), (24, 22), (10, 4), (20, 42), (16, 44), (20, 27), (10, 18), (5, 27), (32, 18), (20, 11), (26, 15), (15, 46), (15, 30), (8, 40), (35, 42), (35, 26), (2, 7), (15, 25), (18, 14), (12, 42), (33, 12), (21, 17), (7, 6), (0, 10), (4, 45), (8, 37), (38, 32), (13, 17), (15, 33), (12, 0), (27, 48), (36, 46), (20, 43), (11, 16), (18, 38), (4, 15), (25, 10), (36, 26), (28, 14), (20, 40), (12, 5), (18, 30), (35, 17), (38, 4), (36, 38), (35, 18), (32, 23), (8, 12), (5, 11), (35, 41), (33, 33), (26, 10), (24, 39), (20, 6), (39, 31), (26, 16), (3, 20), (6, 32), (16, 36), (30, 38), (32, 25), (8, 21), (27, 4), (26, 27), (29, 7), (31, 22), (23, 29), (36, 10), (32, 19), (20, 41), (19, 17), (12, 40), (14, 30), (11, 29), (37, 0), (37, 32), (16, 29), (12, 11), (10, 29), (21, 34), (21, 28), (0, 19), (21, 8), (23, 43), (6, 39), (28, 22), (15, 13), (38, 42), (30, 26), (39, 18), (0, 43), (35, 27), (14, 13), (2, 34), (19, 26), (22, 13), (6, 27), (21, 37), (13, 7), (21, 2), (27, 7), (13, 35), (16, 28), (36, 14), (28, 1), (32, 28), (38, 43), (21, 27), (0, 39), (18, 27), (24, 28), (16, 6), (14, 46), (13, 47), (13, 43), (33, 23), (13, 18), (17, 27), (27, 11), (37, 29), (9, 0), (5, 14), (38, 31), (0, 48), (18, 11), (40, 36), (0, 5), (6, 14), (19, 2), (34, 4), (13, 45), (21, 5), (33, 29), (11, 38), (39, 17), (38, 7), (35, 5), (2, 45), (14, 0), (8, 9), (29, 18), (10, 3), (7, 0), (23, 48), (5, 6), (9, 48), (12, 25), (26, 21), (23, 0), (15, 20), (1, 42), (30, 25), (7, 5), (30, 40), (30, 47), (31, 47), (18, 35), (1, 18), (4, 47), (18, 16), (25, 44), (14, 29), (0, 33), (36, 7), (23, 46), (13, 32), (29, 0), (31, 20), (34, 24), (27, 45), (19, 4), (37, 12), (18, 46), (25, 13), (9, 20), (35, 36), (31, 1), (26, 41), (2, 28), (27, 8), (40, 6), (11, 3), (18, 6), (35, 47), (7, 9), (19, 47), (11, 28), (8, 31), (15, 6), (25, 48), (3, 14), (39, 4), (31, 40), (10, 28), (25, 29), (35, 31), (6, 1), (32, 32), (32, 37), (9, 46), (17, 39), (5, 33), (12, 45), (24, 37), (38, 37), (6, 7), (17, 31), (11, 36), (12, 24), (11, 37), (5, 43), (17, 34), (11, 44), (39, 8), (26, 9), (40, 0), (34, 12), (14, 9), (10, 27), (17, 12), (22, 25), (18, 4), (18, 44), (37, 43), (29, 14), (8, 36), (40, 13), (37, 47), (16, 8), (13, 0), (34, 10), (19, 1), (9, 44), (28, 17), (37, 28), (39, 46), (35, 30), (6, 33), (6, 23), (21, 18), (32, 1), (35, 11), (30, 10), (10, 11), (4, 43), (31, 38), (12, 21), (38, 11), (30, 39), (10, 2), (39, 27), (9, 28), (40, 29), (3, 35), (17, 43), (16, 46), (18, 20), (20, 0), (7, 34), (28, 24), (30, 6), (9, 9), (10, 37), (13, 24), (33, 26), (7, 45), (1, 35), (8, 15), (12, 47), (24, 35), (22, 21), (16, 25), (8, 48), (11, 10), (0, 14), (23, 38), (4, 16), (10, 47), (19, 27), (9, 42), (16, 30), (11, 34), (33, 30), (25, 5), (31, 28), (0, 46), (13, 21), (3, 22), (4, 31), (3, 39), (0, 1), (10, 46), (24, 25), (30, 13), (26, 44), (27, 39), (3, 18), (25, 31), (26, 40), (11, 7), (21, 24), (28, 30), (22, 3), (8, 0), (34, 9), (26, 39), (30, 34), (1, 14), (16, 17), (24, 32), (31, 19), (4, 38), (28, 20), (5, 2), (36, 4), (5, 38), (9, 25), (4, 32), (4, 7), (2, 3), (2, 31), (16, 18), (12, 31), (10, 42), (7, 4), (23, 37), (19, 43), (32, 9), (27, 44), (20, 20), (21, 20), (30, 22), (9, 26), (18, 34), (39, 20), (21, 14), (21, 22), (14, 24), (8, 6), (29, 24), (40, 17), (30, 2), (27, 40), (38, 1), (39, 5), (34, 39), (2, 48), (16, 34), (8, 20), (32, 12), (40, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 44), (36, 42), (33, 43), (23, 37), (10, 22), (25, 40), (23, 32), (26, 9), (5, 0), (6, 36), (5, 32), (37, 0), (17, 33), (44, 20), (34, 45), (11, 27), (2, 43), (19, 35), (40, 2), (35, 9), (14, 17), (18, 7), (31, 24), (10, 11), (3, 9), (7, 24), (10, 27), (7, 13), (29, 20), (45, 35), (41, 4), (4, 6), (18, 23), (31, 45), (24, 43), (0, 44), (5, 43), (22, 31), (20, 41), (26, 1), (28, 40), (21, 15), (25, 1), (33, 5), (14, 35), (8, 45), (3, 19), (0, 19), (36, 33), (44, 45), (4, 23), (44, 16), (0, 15), (16, 4), (33, 1), (38, 15), (18, 3), (41, 9), (7, 17), (42, 32), (16, 22), (40, 44), (41, 12), (43, 2), (17, 26), (8, 0), (22, 8), (21, 8), (28, 36), (44, 12), (29, 30), (32, 41), (2, 15), (5, 14), (11, 31), (45, 5), (14, 29), (15, 45), (8, 34), (30, 40), (1, 12), (35, 14), (2, 39), (24, 2), (19, 4), (29, 45), (7, 15), (3, 12), (10, 32), (33, 8), (30, 45), (19, 13), (1, 21), (15, 38), (45, 29), (0, 42), (23, 0), (3, 24), (37, 8), (34, 15), (21, 20), (33, 28), (20, 24), (37, 10), (31, 16), (18, 15), (15, 33), (14, 33), (10, 10), (36, 9), (16, 27), (33, 3), (4, 34), (9, 39), (1, 39), (28, 34), (13, 19), (43, 33), (8, 42), (21, 7), (25, 4), (0, 13), (7, 23), (44, 41), (22, 41), (0, 34), (3, 40), (8, 4), (43, 6), (19, 15), (36, 8), (5, 21), (15, 32), (13, 3), (32, 16), (10, 19), (1, 26), (28, 25), (37, 22), (43, 35), (32, 27), (15, 23), (6, 23), (12, 43), (13, 37), (13, 40), (39, 5), (24, 6), (36, 28), (12, 11), (23, 33), (22, 22), (40, 40), (41, 30), (12, 18), (43, 3), (45, 6), (26, 27), (29, 39), (1, 9), (5, 28), (45, 16), (2, 29), (19, 45), (38, 0), (20, 10), (22, 2), (30, 0), (30, 39), (5, 3), (22, 29), (45, 31), (23, 45), (3, 39), (13, 43), (37, 32), (8, 36), (37, 18), (38, 1), (20, 11), (7, 43), (21, 38), (28, 9), (28, 26), (40, 43), (44, 38), (21, 9), (1, 1), (38, 33), (19, 39), (39, 7), (39, 30), (43, 39), (34, 13), (35, 41), (10, 33), (13, 33), (44, 44), (20, 2), (12, 33), (29, 22), (15, 40), (9, 40), (26, 4), (20, 27), (44, 18), (27, 27), (2, 30), (8, 12), (35, 19), (29, 28), (28, 22), (7, 44), (11, 44), (37, 45), (38, 37), (13, 4), (21, 28), (18, 26), (3, 18), (39, 22), (32, 35), (21, 3), (19, 34), (18, 33), (45, 34), (44, 32), (6, 41), (39, 24), (33, 9), (16, 43), (26, 15), (19, 19), (39, 12), (34, 17), (16, 6), (20, 45)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 4), (41, 4), (45, 39), (9, 35), (2, 29), (38, 36), (8, 38), (16, 10), (35, 42), (23, 44), (39, 6), (3, 1), (30, 39), (18, 44), (15, 20), (42, 33), (15, 18), (31, 30), (38, 19), (26, 41), (18, 22), (17, 32), (10, 18), (23, 16), (24, 38), (20, 0), (15, 44), (16, 19), (42, 24), (35, 16), (29, 23), (39, 15), (31, 25), (16, 15), (27, 22), (8, 28), (34, 22), (18, 24), (40, 44), (38, 18), (17, 28), (4, 20), (45, 25), (5, 1), (21, 23), (23, 7), (33, 2), (23, 29), (20, 18), (28, 10), (10, 42), (29, 33), (30, 15), (11, 23), (11, 3), (24, 37), (14, 17), (32, 16), (19, 26), (12, 15), (31, 2), (5, 5), (17, 5), (25, 27), (28, 12), (34, 19), (31, 26), (34, 6), (13, 35), (29, 0), (25, 7), (37, 4), (17, 22), (5, 12), (36, 33), (23, 27), (16, 23), (33, 6), (27, 32), (41, 36), (28, 23), (35, 8), (10, 10), (42, 13), (37, 3), (26, 43), (39, 24), (44, 19), (9, 39), (21, 40), (0, 4), (40, 13), (40, 27), (14, 24), (19, 20), (32, 32), (41, 13), (40, 28), (8, 9), (17, 41), (26, 11), (29, 42), (5, 42), (45, 31), (32, 15), (39, 18), (32, 33), (26, 25), (14, 3), (21, 10), (21, 8), (8, 31), (8, 13), (21, 42), (34, 28), (45, 1), (13, 38), (41, 23), (11, 38), (14, 7), (20, 7), (31, 41), (30, 33), (19, 16), (36, 40), (12, 5), (8, 33), (17, 19), (42, 35), (21, 15), (8, 36), (14, 10), (30, 1), (7, 33), (44, 22), (42, 6), (30, 30), (8, 40), (1, 0), (43, 4), (40, 39), (31, 14), (40, 21), (38, 8), (15, 38), (24, 19), (5, 13), (1, 29), (26, 29), (8, 39), (35, 40), (4, 13), (33, 15), (8, 24), (26, 36), (30, 25), (42, 7), (22, 19), (1, 35), (37, 10), (13, 34), (37, 13), (37, 19), (16, 13), (27, 27), (35, 30), (43, 28), (30, 41), (8, 22), (33, 23), (40, 42), (30, 10), (0, 5), (28, 39), (21, 11), (36, 19), (43, 16), (25, 23), (11, 31), (34, 1), (11, 12), (5, 18), (31, 6), (15, 26), (38, 11), (40, 9), (29, 19), (3, 25), (23, 24), (16, 38), (32, 5), (4, 38), (26, 20), (15, 37), (8, 21), (20, 41), (38, 3), (10, 36), (28, 15), (29, 43), (22, 20), (34, 31), (38, 6), (32, 40), (6, 39), (26, 19), (32, 19), (19, 15), (11, 29), (28, 32), (1, 30), (11, 27), (41, 14), (32, 34), (12, 10), (44, 35), (7, 39), (14, 18), (33, 0), (4, 9), (3, 32), (0, 6), (2, 3), (38, 12), (13, 30), (16, 40), (29, 6), (29, 2), (1, 9), (37, 20), (20, 12), (19, 17), (21, 25), (34, 34), (42, 36), (14, 43), (24, 20), (44, 42), (11, 13), (10, 30), (42, 17), (5, 35), (34, 9), (10, 12), (26, 4), (19, 43), (10, 40), (45, 26), (5, 30), (27, 17), (19, 19), (45, 43), (19, 22), (19, 3), (19, 24), (14, 20), (9, 6), (2, 17), (40, 19), (32, 7), (13, 1), (24, 42), (24, 22), (25, 35), (20, 4), (42, 16), (18, 14), (30, 5), (36, 35), (36, 13), (41, 11), (14, 42), (20, 20), (44, 7), (25, 40), (18, 18), (7, 25), (35, 12), (45, 30), (14, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 19), (18, 30), (26, 4), (0, 24), (41, 29), (11, 30), (30, 17), (33, 38), (11, 15), (13, 18), (21, 14), (35, 40), (36, 18), (32, 2), (36, 6), (39, 41), (17, 41), (15, 5), (26, 26), (36, 8), (10, 16), (34, 34), (11, 21), (1, 3), (8, 0), (36, 11), (22, 11), (5, 5), (8, 28), (38, 17), (12, 7), (5, 19), (18, 28), (37, 36), (9, 18), (16, 5), (5, 24), (34, 16), (14, 35), (13, 25), (40, 0), (2, 28), (8, 40), (32, 34), (24, 7), (27, 23), (23, 1), (27, 41), (34, 4), (19, 3), (2, 10), (4, 5), (7, 22), (20, 13), (34, 41), (36, 35), (0, 3), (33, 25), (12, 12), (30, 13), (12, 26), (12, 17), (24, 15), (41, 17), (26, 8), (12, 30), (32, 36), (30, 4), (33, 3), (26, 6), (44, 36), (12, 9), (38, 35), (29, 38), (18, 31), (22, 41), (40, 39), (39, 34), (40, 13), (8, 32), (19, 6), (3, 7), (41, 18), (32, 35), (27, 24), (25, 41), (7, 27), (11, 40), (14, 13), (4, 39), (18, 19), (10, 22), (13, 31), (38, 18), (38, 27), (33, 7), (19, 7), (27, 1), (23, 11), (14, 1), (25, 38), (1, 20), (27, 15), (10, 2), (4, 7), (41, 9), (22, 10), (6, 37), (23, 20), (18, 2), (42, 26), (13, 29), (26, 7), (30, 34), (9, 29), (23, 26), (3, 2), (13, 17), (25, 31), (22, 33), (39, 21), (0, 4), (28, 10), (26, 38), (14, 38), (24, 11), (10, 26), (7, 33), (27, 4), (1, 37), (32, 30), (6, 28), (28, 4), (33, 1), (30, 0), (6, 24), (17, 9), (9, 39), (1, 27), (20, 9), (40, 2), (41, 13), (22, 9), (1, 5), (17, 15), (42, 6), (27, 8), (29, 20), (24, 13), (34, 19), (31, 27), (29, 8), (16, 18), (24, 34), (30, 2), (2, 14), (25, 28), (4, 8), (41, 4), (44, 2), (9, 7), (2, 31), (5, 18), (44, 39), (26, 3), (32, 13), (12, 10), (35, 16), (30, 32), (30, 38), (8, 10), (10, 38), (0, 30), (30, 19), (30, 16), (18, 16), (43, 33), (21, 13), (5, 39), (10, 18), (34, 7), (0, 11), (23, 23), (40, 27), (37, 25), (31, 1), (42, 24), (20, 10), (28, 2), (25, 20), (14, 26), (24, 3), (27, 14), (24, 40), (38, 6), (27, 7), (40, 7), (37, 32), (14, 11), (0, 32), (7, 40), (25, 36), (1, 36), (30, 30), (18, 29), (0, 33), (27, 16), (13, 35), (40, 15), (4, 31), (41, 39), (22, 21), (11, 22), (26, 41), (32, 16), (32, 1), (37, 16), (33, 10), (11, 32), (37, 0), (2, 16), (19, 9), (14, 21), (22, 35), (39, 19), (13, 39), (44, 15), (17, 28), (12, 16), (37, 13), (20, 15), (38, 4), (1, 8), (16, 39), (40, 38), (28, 37), (21, 22), (38, 8), (28, 27), (43, 13), (9, 13), (19, 16), (33, 13), (5, 30), (23, 6), (3, 27), (22, 19), (16, 28), (17, 12), (17, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 9), (31, 19), (30, 12), (7, 7), (37, 34), (4, 18), (30, 1), (18, 0), (20, 15), (17, 3), (37, 4), (8, 25), (1, 30), (29, 32), (24, 36), (10, 1), (10, 37), (8, 36), (11, 34), (37, 16), (29, 12), (29, 11), (17, 17), (38, 0), (4, 0), (31, 39), (9, 18), (4, 10), (36, 8), (12, 5), (34, 8), (20, 4), (35, 27), (38, 16), (35, 24), (44, 15), (34, 16), (24, 15), (10, 11), (18, 19), (36, 24), (14, 21), (18, 28), (24, 0), (22, 11), (9, 36), (7, 31), (25, 33), (22, 13), (24, 28), (11, 28), (32, 8), (21, 7), (17, 12), (19, 26), (28, 19), (18, 16), (31, 1), (10, 17), (18, 20), (9, 20), (36, 12), (1, 10), (4, 20), (31, 34), (42, 38), (7, 32), (22, 36), (32, 35), (1, 1), (24, 4), (38, 27), (39, 36), (22, 1), (6, 19), (39, 1), (39, 12), (38, 26), (14, 27), (39, 16), (39, 31), (36, 13), (24, 7), (14, 18), (12, 9), (24, 13), (30, 26), (2, 38), (21, 24), (10, 5), (29, 6), (42, 12), (31, 11), (13, 25), (26, 0), (3, 38), (25, 8), (39, 20), (23, 25), (27, 35), (25, 4), (18, 10), (3, 17), (41, 4), (36, 34), (13, 28), (18, 22), (23, 10), (16, 37), (39, 22), (10, 30), (25, 11), (0, 26), (43, 39), (21, 2), (41, 39), (39, 3), (11, 9), (29, 5), (34, 35), (21, 10), (42, 28), (12, 2), (18, 27), (39, 11), (4, 1), (23, 37), (10, 20), (23, 33), (7, 9), (43, 32), (35, 7), (16, 3), (40, 34), (20, 31), (38, 19), (27, 19), (44, 18), (37, 9), (45, 16), (40, 1), (13, 23), (17, 31), (3, 33), (29, 2), (37, 7), (19, 25), (23, 22), (43, 11), (42, 36), (20, 3), (19, 6), (3, 39), (42, 39), (15, 8), (12, 16), (5, 15), (3, 4), (19, 27), (25, 37), (8, 24), (40, 2), (15, 32), (31, 15), (9, 15), (23, 14), (36, 18), (38, 8), (19, 7), (15, 3), (11, 23), (12, 20), (22, 4), (34, 34), (12, 12), (15, 10), (1, 36), (0, 16), (22, 8), (27, 23), (37, 5), (24, 3), (19, 4), (2, 9), (9, 17), (11, 38), (16, 25), (3, 28), (21, 14), (14, 3), (2, 39), (24, 19), (30, 11), (16, 36), (41, 36), (20, 5), (24, 8), (32, 10), (38, 12), (17, 16), (7, 17), (17, 39), (26, 11), (9, 33), (20, 28), (9, 11), (29, 16), (4, 28), (21, 8), (0, 4), (4, 15), (34, 19), (30, 31), (38, 31), (20, 0), (44, 32), (20, 14), (11, 16), (13, 35), (27, 10), (19, 11), (8, 34), (5, 16), (5, 20), (30, 4), (37, 6), (35, 17), (6, 0), (44, 4), (8, 3), (3, 27), (42, 13), (39, 21), (3, 36), (3, 9), (14, 22), (12, 23), (22, 37), (28, 37), (5, 3), (18, 18), (13, 15), (19, 24), (43, 27), (39, 34), (15, 15), (37, 27), (36, 22), (10, 14), (38, 5), (41, 5), (18, 30), (3, 6), (28, 0), (14, 15), (9, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 30), (12, 25), (0, 23), (24, 24), (30, 33), (22, 39), (13, 38), (17, 12), (42, 2), (40, 17), (2, 27), (1, 27), (26, 9), (38, 28), (27, 25), (20, 21), (9, 4), (7, 13), (10, 13), (32, 36), (1, 33), (21, 31), (21, 22), (40, 20), (11, 13), (22, 4), (31, 24), (0, 22), (33, 24), (29, 8), (32, 31), (15, 24), (40, 26), (14, 38), (10, 5), (38, 33), (2, 37), (20, 32), (15, 0), (2, 23), (17, 2), (19, 1), (25, 21), (23, 25), (15, 22), (35, 39), (27, 6), (33, 2), (8, 12), (33, 22), (30, 30), (39, 37), (39, 14), (36, 27), (33, 34), (1, 9), (21, 11), (31, 16), (2, 17), (5, 38), (38, 3), (42, 1), (40, 1), (1, 40), (30, 40), (38, 10), (25, 37), (22, 31), (9, 37), (17, 3), (12, 15), (33, 3), (25, 9), (8, 16), (28, 26), (33, 15), (7, 21), (13, 13), (12, 35), (28, 2), (27, 1), (14, 6), (2, 31), (14, 10), (39, 41), (30, 7), (14, 22), (0, 26), (26, 7), (30, 34), (25, 15), (26, 15), (31, 34), (26, 38), (4, 10), (5, 19), (39, 22), (37, 2), (18, 20), (37, 39), (27, 10), (12, 32), (21, 16), (8, 14), (4, 35), (12, 24), (35, 23), (14, 30), (30, 18), (26, 0), (40, 36), (34, 15), (24, 12), (41, 2), (20, 7), (11, 12), (19, 22), (16, 35), (26, 39), (1, 14), (8, 18), (39, 34), (42, 7), (23, 21), (6, 22), (30, 22), (20, 19), (11, 18), (20, 37), (12, 2), (7, 6), (9, 32), (12, 34), (5, 32), (10, 27), (33, 39), (27, 33), (3, 29), (32, 20), (12, 28), (0, 5), (16, 4), (22, 32), (19, 0), (29, 27), (32, 0), (35, 18), (16, 13), (0, 9), (16, 24), (29, 38), (15, 37), (29, 26), (11, 10), (0, 32), (27, 22), (37, 7), (15, 39), (10, 32), (5, 3), (35, 21), (28, 11), (17, 11), (39, 12), (21, 20), (22, 14), (40, 4), (11, 41), (41, 5), (31, 10), (19, 15), (15, 16), (17, 29), (42, 6), (13, 40), (40, 25), (0, 18), (9, 15), (16, 30), (27, 38), (2, 34), (19, 11), (19, 18), (0, 3), (15, 21), (30, 36), (24, 41), (2, 22), (31, 31), (4, 29), (42, 5), (15, 40), (8, 10), (17, 7), (20, 12), (5, 33), (19, 34), (28, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 15), (16, 41), (44, 6), (26, 29), (17, 37), (42, 2), (4, 22), (45, 4), (13, 31), (10, 32), (28, 5), (5, 39), (11, 11), (25, 39), (43, 29), (21, 33), (1, 40), (45, 10), (3, 28), (33, 23), (5, 18), (17, 0), (22, 1), (31, 11), (39, 8), (46, 40), (9, 1), (13, 13), (16, 6), (10, 30), (26, 39), (4, 18), (44, 32), (2, 7), (9, 34), (37, 42), (20, 9), (8, 28), (27, 15), (45, 43), (47, 36), (17, 39), (37, 5), (17, 29), (30, 20), (37, 43), (37, 35), (4, 8), (41, 16), (24, 42), (25, 27), (17, 13), (8, 9), (41, 20), (16, 36), (45, 42), (1, 30), (38, 15), (40, 20), (46, 18), (15, 16), (33, 11), (45, 37), (10, 34), (6, 12), (32, 32), (32, 1), (32, 23), (30, 43), (11, 27), (25, 38), (10, 25), (0, 34), (14, 36), (6, 41), (37, 16), (27, 16), (3, 11), (33, 19), (46, 28), (22, 28), (10, 36), (16, 37), (7, 27), (8, 35), (27, 27), (11, 22), (9, 2), (44, 36), (24, 5), (30, 0), (12, 34), (31, 18), (23, 31), (18, 20), (27, 21), (4, 43), (33, 17), (47, 34), (5, 10), (26, 14), (18, 33), (20, 31), (6, 24), (41, 11), (30, 19), (11, 37), (7, 39), (25, 37), (13, 1), (43, 35), (37, 14), (36, 1), (27, 9), (4, 2), (5, 3), (13, 18), (4, 33), (21, 7), (42, 12), (3, 27), (26, 10), (13, 6), (40, 14), (6, 32), (24, 38), (12, 21), (35, 40), (40, 10), (4, 5), (18, 13), (36, 25), (24, 21), (31, 10), (16, 9), (27, 30), (34, 2), (27, 11), (16, 25), (33, 40), (14, 5), (3, 7), (8, 34), (3, 40), (12, 32), (17, 20), (40, 34), (1, 6), (46, 17), (14, 31), (11, 8), (9, 10), (32, 7), (47, 26), (11, 7), (37, 7), (16, 26), (27, 42), (24, 16), (23, 34), (44, 3), (38, 14), (15, 28), (43, 42), (15, 39), (43, 33), (15, 42), (31, 20), (34, 9), (33, 4), (38, 12), (1, 9), (22, 43), (30, 29), (3, 4), (21, 12), (36, 27), (26, 2), (14, 17), (10, 9), (5, 8), (43, 5), (25, 42), (7, 10), (31, 26), (42, 39), (32, 2), (22, 24), (28, 15), (47, 3), (16, 42), (20, 36), (6, 1), (29, 40), (1, 7), (30, 35), (10, 26), (0, 35), (7, 36), (24, 6), (0, 10), (28, 7), (9, 14), (46, 30), (8, 30), (18, 10), (7, 1), (8, 37), (19, 29), (43, 0), (16, 20), (18, 12), (20, 8), (31, 24), (38, 21), (36, 15), (44, 12), (41, 2), (6, 10), (43, 16), (43, 43), (32, 39), (17, 12), (1, 20), (27, 23), (2, 41), (34, 37), (5, 31), (42, 35), (43, 17), (12, 39), (25, 20), (39, 42), (17, 6), (16, 5), (34, 6), (21, 20), (25, 7), (27, 6), (15, 11), (23, 10), (7, 6), (46, 22), (38, 27), (28, 12), (38, 19), (14, 20), (39, 18), (43, 38), (40, 6), (13, 24), (38, 34), (13, 26), (46, 11), (10, 8), (28, 40), (28, 0), (45, 36), (42, 41), (39, 28), (19, 19), (46, 41), (2, 31), (34, 33), (36, 13), (26, 6), (7, 31), (12, 3), (41, 39), (3, 39), (21, 13), (12, 31), (35, 18), (28, 24), (41, 3), (36, 17), (35, 4), (8, 0), (30, 32), (0, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (44, 8), (29, 3), (41, 29), (24, 0), (14, 40), (15, 27), (11, 7), (29, 27), (10, 31), (27, 29), (8, 37), (43, 32), (43, 0), (5, 31), (24, 28), (1, 5), (35, 39), (25, 4), (35, 36), (34, 20), (33, 19), (10, 42), (42, 18), (20, 15), (10, 39), (21, 43), (14, 34), (0, 7), (17, 37), (4, 27), (0, 39), (44, 27), (23, 18), (2, 1), (30, 2), (41, 44), (0, 24), (0, 46), (10, 1), (35, 41), (14, 31), (36, 35), (3, 23), (23, 32), (22, 38), (24, 31), (19, 45), (15, 14), (23, 2), (32, 41), (32, 42), (42, 10), (29, 25), (10, 40), (34, 2), (1, 38), (40, 8), (35, 29), (20, 21), (4, 26), (28, 11), (11, 8), (1, 13), (34, 26), (35, 8), (46, 33), (29, 14), (32, 19), (29, 45), (21, 5), (19, 3), (6, 46), (31, 37), (2, 24), (39, 2), (32, 5), (15, 10), (2, 36), (17, 39), (28, 40), (0, 33), (46, 42), (24, 15), (46, 1), (18, 11), (11, 18), (22, 11), (14, 11), (26, 41), (26, 28), (0, 44), (42, 13), (47, 21), (26, 43), (41, 23), (8, 19), (16, 30), (40, 27), (27, 2), (43, 4), (39, 8), (36, 0), (46, 7), (31, 39), (5, 21), (37, 45), (7, 41), (46, 32), (31, 41), (19, 42), (28, 20), (0, 30), (31, 33), (1, 36), (20, 17), (41, 5), (7, 22), (22, 4), (35, 43), (25, 45), (29, 29), (0, 11), (46, 35), (46, 16), (35, 22), (46, 43), (16, 17), (27, 18), (21, 20), (7, 18), (27, 32), (20, 2), (40, 39), (44, 36), (25, 30), (31, 30), (3, 36), (24, 33), (39, 9), (23, 37), (45, 17), (34, 10), (21, 21), (36, 42), (21, 3), (26, 30), (25, 42), (37, 16), (9, 34), (44, 35), (39, 16), (12, 15), (20, 39), (1, 28), (38, 9), (1, 4), (46, 25), (16, 16), (23, 5), (17, 24), (11, 28), (8, 14), (22, 19), (4, 14), (17, 22), (27, 3), (46, 21), (42, 32), (35, 2), (7, 28), (11, 15), (33, 23), (11, 45), (1, 39), (2, 23), (41, 0), (21, 23), (46, 18), (19, 30), (26, 25), (19, 11), (45, 44), (2, 3), (12, 28), (1, 35), (32, 12), (47, 0), (33, 24), (3, 37), (12, 35), (9, 43), (30, 41), (7, 43), (21, 14), (41, 15), (21, 40), (44, 13), (33, 35), (44, 6), (44, 25), (37, 9), (37, 14), (23, 3), (1, 24), (32, 34), (26, 4), (9, 31), (8, 23), (32, 13), (28, 2), (35, 1), (13, 14), (37, 41), (33, 18), (10, 30), (5, 42), (2, 43), (40, 7), (25, 25), (1, 44), (10, 36), (10, 20), (47, 44), (26, 8), (13, 36), (30, 18), (29, 32), (27, 40), (14, 21), (28, 27), (2, 17), (24, 46), (20, 0), (15, 20), (19, 21), (24, 24), (3, 5), (26, 21), (5, 20), (13, 10), (9, 23), (7, 25), (30, 24), (5, 13), (15, 36), (27, 19), (17, 25), (7, 31), (30, 15), (38, 7), (45, 41), (43, 42), (12, 5), (47, 32), (36, 22), (34, 38), (7, 44), (39, 21), (16, 9), (16, 28), (33, 30), (19, 34), (5, 44), (37, 31), (0, 27), (46, 9), (47, 40), (17, 0), (11, 22), (46, 46), (32, 20), (7, 32), (2, 32), (39, 12), (17, 20), (34, 9), (26, 40), (29, 13), (29, 36), (40, 33), (11, 16), (24, 20), (9, 8), (17, 26), (32, 37), (16, 18), (22, 32), (13, 40), (19, 29), (47, 5), (12, 11), (9, 25), (41, 9), (12, 33), (2, 46), (12, 44), (16, 26), (4, 44), (39, 29), (33, 0), (16, 14), (16, 8), (30, 8), (21, 22), (12, 13), (11, 10), (19, 41), (29, 0), (1, 32), (3, 39), (28, 17), (37, 18), (25, 5), (16, 35), (33, 45), (4, 12), (6, 12), (47, 27), (20, 24), (11, 9), (21, 17), (4, 15), (40, 32), (10, 38), (22, 41), (40, 46), (5, 5), (37, 5), (4, 1), (39, 17), (1, 18), (44, 39), (35, 27), (20, 36), (7, 10), (21, 25), (38, 28), (38, 42), (38, 16), (39, 37), (39, 41), (8, 25), (42, 11), (45, 2), (23, 34), (30, 19), (45, 5), (34, 45), (0, 1), (41, 22), (36, 14), (42, 35), (47, 24), (38, 20), (39, 33), (24, 2), (7, 9), (14, 19), (16, 24), (43, 25), (13, 46), (8, 18), (40, 20), (8, 29), (15, 38), (45, 18), (6, 45), (22, 9), (20, 1), (11, 29), (13, 0), (18, 27), (8, 38), (34, 44), (5, 40), (13, 45), (14, 23), (10, 27), (41, 16), (6, 6), (33, 15), (42, 40), (21, 29), (35, 11), (43, 18), (45, 42), (15, 34), (32, 15), (30, 10), (8, 31), (10, 0), (18, 18), (2, 27), (4, 32), (37, 38), (43, 40), (25, 46), (35, 17), (38, 29), (32, 1), (22, 22), (39, 44), (27, 42), (23, 25), (1, 15), (33, 16), (9, 15), (29, 21), (35, 21), (18, 2), (13, 29), (1, 23), (4, 45), (35, 37), (17, 34), (4, 2), (12, 2), (9, 30), (5, 34), (17, 21), (22, 26), (26, 42), (8, 34), (22, 37), (12, 12), (9, 7), (0, 12), (9, 9), (33, 32), (25, 2), (35, 45), (29, 42), (26, 36), (25, 23), (14, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 24), (35, 48), (43, 2), (2, 45), (15, 14), (11, 19), (42, 16), (20, 10), (35, 21), (17, 32), (30, 6), (19, 14), (1, 23), (6, 27), (36, 11), (5, 7), (35, 12), (13, 12), (27, 44), (30, 47), (27, 26), (36, 28), (17, 33), (44, 31), (42, 28), (17, 23), (25, 33), (39, 39), (20, 43), (23, 42), (40, 39), (9, 0), (32, 31), (21, 20), (33, 28), (35, 23), (24, 42), (25, 31), (24, 27), (34, 28), (34, 3), (38, 38), (0, 41), (42, 19), (13, 37), (7, 1), (15, 31), (40, 27), (15, 22), (23, 38), (31, 23), (24, 31), (0, 48), (33, 24), (29, 20), (31, 26), (38, 35), (33, 20), (26, 8), (45, 17), (23, 17), (1, 25), (38, 11), (27, 3), (25, 12), (31, 17), (30, 8), (9, 13), (4, 29), (22, 42), (36, 42), (22, 40), (3, 10), (4, 9), (5, 33), (37, 9), (16, 32), (38, 41), (28, 18), (21, 41), (28, 22), (17, 41), (26, 30), (42, 18), (40, 9), (26, 20), (16, 4), (20, 24), (0, 12), (41, 20), (7, 37), (37, 44), (13, 35), (27, 6), (1, 0), (27, 45), (12, 19), (28, 20), (14, 35), (27, 22), (26, 17), (30, 34), (9, 36), (11, 37), (27, 40), (0, 14), (3, 18), (8, 15), (21, 42), (26, 2), (39, 46), (33, 48), (1, 46), (33, 0), (25, 15), (18, 41), (16, 48), (33, 10), (30, 7), (3, 29), (5, 12), (22, 21), (23, 20), (27, 28), (19, 21), (30, 11), (9, 35), (29, 47), (41, 42), (21, 2), (29, 23), (23, 39), (42, 7), (12, 12), (20, 28), (41, 36), (24, 37), (20, 11), (22, 45), (5, 18), (38, 23), (15, 27), (28, 0), (2, 18), (0, 39), (21, 21), (45, 39), (15, 48), (18, 31), (17, 25), (28, 36), (30, 18), (6, 35), (28, 15), (35, 0), (27, 48), (29, 15), (40, 41), (3, 16), (28, 44), (28, 24), (26, 44), (7, 12), (23, 13), (4, 23), (12, 30), (9, 17), (33, 15), (5, 38), (6, 36), (32, 13), (19, 48), (25, 17), (19, 11), (39, 47), (31, 8), (4, 28), (36, 5), (3, 31), (18, 32), (1, 45), (2, 1), (35, 11), (13, 45), (27, 8), (40, 24), (40, 25), (13, 43), (15, 6), (42, 35), (30, 41), (32, 46), (41, 48), (34, 0), (18, 22), (14, 18), (37, 23), (21, 28), (7, 18), (38, 6), (18, 45), (6, 21), (18, 5), (26, 19), (1, 26), (10, 21), (5, 25), (9, 12), (4, 15), (14, 33), (33, 22), (9, 20), (18, 1), (27, 24), (5, 36), (16, 3), (36, 4), (34, 2), (6, 3), (40, 31), (39, 30), (3, 1), (44, 6), (21, 17), (4, 47), (14, 34), (20, 33), (11, 17), (41, 35), (41, 10), (7, 40), (6, 28), (23, 15), (22, 28), (31, 16), (45, 29), (24, 33), (11, 1), (28, 40), (1, 7), (35, 7), (22, 14), (0, 3), (7, 11), (29, 16), (11, 36), (7, 17), (37, 1), (4, 18), (16, 12), (41, 6), (4, 21), (5, 15), (36, 0), (23, 12), (5, 32), (7, 25), (31, 28), (39, 34), (39, 44), (26, 1), (34, 48), (14, 13), (32, 17), (0, 45), (6, 18), (16, 42), (1, 33), (19, 27), (31, 43), (37, 21), (8, 8), (44, 27), (28, 19), (21, 30), (0, 42), (38, 30), (17, 3), (1, 12), (43, 47), (10, 4), (27, 34), (34, 37), (24, 40), (27, 31), (22, 48), (26, 5), (18, 7), (18, 10), (15, 17), (37, 30), (27, 30), (41, 18), (19, 7), (25, 46), (30, 40), (37, 38), (36, 26), (35, 45), (44, 32), (27, 18), (31, 34), (24, 13), (15, 23), (13, 16), (35, 30), (5, 9), (45, 26), (32, 11), (39, 20), (30, 1), (33, 7), (34, 12), (13, 29), (16, 36), (24, 15), (3, 25), (27, 35), (32, 27), (10, 24), (38, 39), (45, 10), (13, 5), (38, 18), (15, 42), (33, 44), (5, 26), (2, 2), (34, 7), (23, 24), (5, 34), (24, 0), (30, 26), (43, 19), (3, 36), (13, 32), (4, 45), (24, 23), (24, 28), (8, 33), (2, 12), (29, 48), (43, 6), (15, 36), (21, 11), (20, 8), (41, 45), (5, 44), (13, 21), (27, 32), (14, 44), (43, 11), (42, 43), (7, 6), (43, 25), (33, 33), (2, 26), (4, 6), (36, 33), (21, 46), (9, 8), (8, 21), (33, 31), (11, 47), (2, 21), (26, 6), (0, 8), (5, 42), (12, 27), (35, 5), (31, 4), (22, 15), (40, 35), (23, 47), (4, 25), (1, 22), (45, 30), (12, 7), (35, 17), (3, 40), (14, 45), (35, 2), (32, 48), (38, 46), (41, 2), (41, 32), (18, 23), (5, 10), (22, 25), (8, 1), (33, 4), (6, 11), (14, 2), (1, 42), (18, 8), (29, 29), (32, 39), (18, 25), (22, 46), (19, 22), (31, 39), (12, 11), (34, 44), (29, 40), (30, 24), (12, 44), (28, 23), (16, 27), (38, 0), (39, 24), (37, 40), (31, 46), (41, 39), (25, 45), (27, 29), (34, 16), (3, 19), (39, 42), (29, 3), (8, 37), (12, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 48x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 3), (4, 3), (37, 35), (20, 21), (30, 3), (19, 38), (18, 5), (43, 18), (43, 27), (45, 30), (34, 8), (42, 31), (5, 37), (47, 4), (23, 22), (33, 7), (23, 33), (13, 14), (13, 12), (46, 14), (36, 5), (44, 20), (18, 3), (12, 2), (1, 9), (24, 26), (37, 31), (39, 12), (36, 23), (16, 12), (40, 10), (45, 31), (11, 41), (24, 32), (15, 19), (46, 12), (13, 31), (37, 10), (36, 33), (2, 42), (44, 39), (10, 29), (8, 28), (23, 24), (0, 19), (47, 0), (8, 25), (4, 27), (24, 10), (42, 41), (28, 23), (40, 27), (43, 42), (38, 39), (46, 36), (5, 16), (6, 28), (11, 11), (28, 25), (26, 9), (6, 42), (13, 37), (39, 10), (39, 22), (5, 27), (4, 25), (5, 13), (30, 36), (33, 41), (10, 12), (9, 19), (0, 18), (21, 29), (18, 19), (11, 5), (29, 29), (20, 13), (46, 37), (9, 20), (9, 33), (0, 5), (16, 5), (7, 3), (34, 24), (22, 15), (44, 40), (6, 3), (14, 14), (43, 1), (27, 22), (27, 13), (45, 36), (37, 13), (37, 1), (10, 28), (4, 14), (5, 36), (37, 5), (42, 37), (33, 2), (15, 25), (47, 30), (31, 38), (31, 25), (45, 26), (23, 10), (6, 16), (11, 32), (22, 18), (18, 0), (14, 31), (0, 40), (6, 6), (35, 28), (25, 17), (20, 17), (46, 17), (1, 28), (38, 12), (13, 0), (46, 3), (13, 10), (44, 36), (38, 22), (7, 38), (21, 20), (44, 8), (5, 11), (44, 21), (14, 42), (13, 39), (34, 34), (17, 21), (7, 1), (22, 32), (4, 24), (45, 27), (43, 2), (9, 40), (12, 4), (2, 2), (45, 8), (34, 7), (25, 12), (28, 28), (17, 42), (8, 29), (27, 4), (37, 40), (23, 5), (28, 37), (34, 38), (35, 20), (19, 5), (44, 24), (0, 11), (38, 28), (27, 18), (16, 21), (19, 9), (17, 5), (17, 23), (19, 39), (32, 33), (33, 4), (47, 15), (32, 0), (12, 15), (30, 7), (41, 4), (7, 28), (14, 28), (32, 2), (46, 15), (24, 1), (2, 18), (40, 13), (25, 41), (29, 22), (9, 6), (32, 22), (3, 4), (21, 21), (1, 4), (11, 18), (35, 27), (32, 31), (18, 17), (47, 34), (22, 21), (18, 1), (23, 13), (31, 29), (42, 38), (46, 1), (0, 7), (3, 20), (42, 18), (24, 40), (18, 41), (41, 37), (26, 1), (23, 27), (4, 11), (2, 17), (35, 19), (34, 42), (42, 14), (10, 3), (32, 17), (6, 22), (38, 26), (23, 8), (20, 16), (10, 37), (6, 13), (29, 13), (32, 38), (39, 21), (2, 31), (10, 32), (4, 15), (7, 17), (23, 31), (33, 6), (7, 10), (28, 41), (46, 20), (7, 5), (19, 12), (32, 26), (38, 20), (5, 12), (34, 16), (8, 5), (24, 19), (20, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 11), (39, 3), (22, 27), (27, 2), (34, 24), (34, 4), (23, 23), (5, 35), (14, 19), (26, 31), (22, 1), (43, 25), (12, 12), (18, 0), (25, 32), (5, 21), (9, 29), (7, 21), (29, 23), (23, 16), (6, 4), (9, 9), (34, 27), (24, 36), (33, 29), (6, 23), (33, 37), (16, 29), (22, 32), (31, 5), (20, 29), (38, 17), (38, 21), (27, 23), (16, 10), (26, 23), (9, 31), (39, 38), (5, 27), (6, 30), (6, 27), (25, 9), (19, 3), (30, 24), (9, 32), (41, 31), (13, 28), (12, 31), (8, 27), (24, 16), (42, 31), (20, 22), (21, 13), (36, 35), (10, 24), (19, 25), (6, 39), (27, 32), (11, 14), (21, 37), (35, 25), (14, 0), (34, 32), (12, 21), (23, 36), (19, 28), (4, 18), (14, 22), (36, 15), (27, 27), (7, 39), (6, 2), (35, 9), (18, 10), (32, 15), (0, 26), (14, 28), (23, 28), (7, 20), (3, 9), (40, 34), (9, 8), (17, 37), (22, 34), (24, 27), (36, 23), (23, 4), (32, 13), (39, 29), (12, 29), (27, 12), (35, 19), (24, 20), (10, 4), (39, 14), (15, 34), (7, 24), (35, 35), (1, 24), (29, 8), (30, 25), (20, 17), (3, 23), (13, 35), (34, 36), (33, 23), (5, 2), (40, 15), (4, 38), (13, 23), (16, 30), (7, 19), (12, 1), (6, 13), (29, 9), (28, 7), (26, 36), (21, 14), (8, 9), (41, 21), (33, 8), (27, 0), (7, 38), (0, 5), (31, 4), (33, 6), (16, 11), (31, 18), (8, 19), (14, 32), (27, 4), (36, 19), (7, 13), (21, 26), (38, 10), (32, 16), (23, 27), (2, 25), (36, 33), (2, 5), (23, 39), (26, 38), (14, 11), (17, 29), (28, 20), (32, 7), (2, 15), (2, 33), (22, 20), (11, 3), (39, 37), (25, 2), (43, 32), (38, 26), (3, 29), (13, 32), (15, 11), (19, 10), (31, 25), (28, 25), (43, 22), (2, 31), (26, 25), (22, 26), (4, 24), (25, 12), (6, 11), (24, 35), (43, 9), (25, 26), (39, 6), (43, 21), (9, 24), (26, 22), (13, 2), (15, 31), (26, 10), (34, 9), (9, 3), (32, 1), (6, 14), (35, 5), (21, 8), (33, 25), (35, 34), (0, 18), (24, 21), (36, 9), (35, 11), (22, 16), (26, 13), (7, 29), (6, 5), (1, 22), (16, 26), (35, 20), (34, 28), (39, 20), (0, 2), (0, 31), (12, 22), (6, 20), (21, 10), (17, 24), (10, 1), (3, 24), (15, 36), (35, 16), (40, 1), (35, 29), (24, 19), (17, 10), (15, 10), (25, 16), (37, 13), (38, 35), (40, 29), (26, 3), (33, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 46), (24, 44), (21, 36), (25, 27), (37, 32), (14, 28), (21, 38), (26, 43), (12, 30), (4, 43), (47, 5), (5, 16), (37, 38), (27, 47), (43, 44), (42, 29), (46, 48), (35, 12), (30, 39), (20, 7), (45, 7), (2, 44), (33, 16), (23, 9), (39, 14), (7, 11), (26, 25), (28, 40), (18, 12), (12, 11), (37, 2), (17, 23), (35, 40), (40, 7), (8, 18), (9, 25), (15, 40), (20, 31), (7, 13), (32, 2), (36, 23), (31, 20), (12, 38), (9, 2), (42, 4), (19, 24), (17, 26), (30, 27), (8, 43), (41, 43), (30, 43), (21, 43), (24, 23), (10, 16), (1, 38), (0, 47), (21, 30), (6, 0), (6, 13), (27, 22), (1, 15), (19, 8), (7, 26), (44, 9), (33, 14), (38, 44), (7, 46), (26, 4), (18, 23), (23, 0), (32, 21), (43, 10), (15, 42), (37, 19), (9, 1), (4, 19), (16, 2), (23, 41), (47, 25), (38, 2), (5, 15), (24, 10), (15, 6), (43, 14), (35, 1), (42, 40), (28, 35), (28, 17), (35, 13), (19, 41), (25, 25), (11, 12), (21, 27), (27, 18), (43, 34), (5, 22), (31, 8), (38, 37), (34, 43), (22, 5), (26, 1), (26, 2), (15, 18), (24, 18), (44, 31), (29, 38), (46, 28), (29, 27), (4, 24), (45, 21), (10, 18), (34, 27), (41, 11), (28, 21), (19, 13), (17, 10), (24, 11), (30, 36), (17, 39), (2, 12), (3, 13), (44, 32), (25, 40), (8, 13), (6, 32), (0, 9), (8, 12), (45, 25), (29, 3), (28, 45), (15, 4), (16, 27), (40, 11), (33, 24), (26, 33), (22, 45), (47, 3), (16, 29), (16, 10), (16, 30), (8, 21), (25, 7), (39, 40), (25, 33), (20, 25), (27, 1), (19, 4), (3, 28), (4, 30), (46, 37), (5, 38), (7, 41), (2, 15), (10, 30), (40, 0), (32, 13), (27, 38), (20, 21), (1, 23), (6, 19), (44, 46), (42, 11), (33, 1), (18, 1), (24, 14), (0, 32), (47, 38), (47, 20), (19, 19), (20, 26), (32, 19), (38, 29), (25, 4), (39, 17), (42, 24), (36, 46), (21, 4), (36, 27), (43, 8), (36, 15), (20, 8), (5, 21), (41, 34), (10, 33), (14, 0), (33, 44), (21, 2), (17, 38), (45, 46), (35, 7), (6, 8), (3, 3), (46, 2), (31, 42), (40, 37), (35, 16), (11, 16), (10, 26), (31, 46), (35, 11), (13, 42), (47, 23), (47, 36), (31, 16), (41, 5), (23, 27), (29, 31), (1, 20), (3, 23), (11, 20), (45, 10), (28, 31), (34, 45), (46, 0), (33, 36), (4, 48), (0, 42), (21, 23), (28, 16), (33, 41), (28, 19), (38, 47), (6, 14), (41, 0), (14, 16), (2, 27), (21, 12), (27, 31), (24, 43), (36, 47), (35, 23), (13, 0), (18, 15), (34, 0), (3, 22), (2, 3), (16, 39), (34, 9), (25, 20), (41, 16), (21, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 21), (29, 25), (20, 22), (37, 30), (6, 22), (18, 8), (29, 33), (23, 41), (0, 19), (0, 29), (28, 20), (28, 13), (15, 36), (39, 36), (30, 17), (45, 17), (40, 14), (14, 3), (13, 18), (24, 2), (30, 2), (39, 7), (1, 28), (25, 24), (18, 14), (39, 11), (46, 1), (15, 4), (38, 13), (38, 19), (4, 8), (18, 13), (21, 38), (13, 27), (25, 33), (20, 32), (46, 0), (42, 8), (33, 14), (21, 25), (15, 15), (20, 9), (43, 28), (31, 29), (38, 11), (31, 35), (26, 3), (7, 34), (0, 20), (32, 33), (9, 39), (20, 29), (0, 27), (32, 11), (15, 5), (20, 7), (42, 33), (26, 7), (20, 16), (37, 11), (33, 21), (45, 14), (16, 39), (33, 5), (42, 13), (24, 36), (5, 8), (4, 31), (46, 4), (21, 23), (14, 29), (36, 0), (26, 36), (10, 1), (34, 35), (9, 33), (7, 32), (2, 36), (37, 13), (1, 36), (25, 38), (33, 4), (2, 5), (27, 33), (29, 20), (38, 31), (11, 10), (24, 29), (42, 28), (33, 16), (11, 28), (37, 22), (28, 10), (0, 39), (34, 7), (39, 16), (25, 17), (18, 42), (40, 31), (40, 1), (7, 11), (27, 25), (19, 11), (14, 33), (17, 32), (45, 6), (33, 18), (3, 15), (29, 3), (15, 35), (32, 19), (42, 37), (40, 7), (35, 3), (18, 25), (30, 23), (38, 25), (27, 23), (32, 13), (44, 35), (30, 8), (9, 36), (41, 31), (12, 22), (14, 19), (41, 32), (39, 8), (7, 3), (10, 27), (0, 6), (29, 39), (30, 26), (6, 31), (21, 14), (15, 19), (29, 21), (0, 28), (30, 0), (7, 17), (23, 10), (34, 25), (19, 10), (13, 35), (41, 25), (15, 18), (11, 13), (21, 16), (46, 28), (9, 11), (21, 33), (17, 35), (12, 32), (33, 36), (24, 23), (31, 31), (1, 30), (21, 26), (0, 23), (26, 19), (28, 32), (12, 5), (27, 28), (34, 33), (29, 38), (2, 27), (44, 8), (21, 40), (12, 20), (2, 8), (18, 32), (18, 12), (8, 7), (32, 40), (43, 0), (28, 39), (38, 18), (13, 29), (41, 6), (46, 25), (0, 8), (36, 10), (19, 7), (20, 30), (10, 2), (11, 29), (18, 27), (17, 27), (5, 36), (35, 32), (32, 29), (31, 37), (39, 2), (24, 6), (13, 4), (32, 6), (24, 20), (8, 17), (3, 6), (28, 7), (20, 18), (17, 19), (8, 0), (17, 0), (19, 39), (38, 14), (17, 25), (31, 12), (30, 30), (46, 13), (32, 22), (33, 23), (17, 26), (19, 29), (43, 15), (45, 16), (33, 9), (44, 1), (8, 32), (24, 1), (12, 35), (40, 42), (32, 37), (40, 22), (6, 4), (21, 9), (19, 18), (36, 1), (14, 20), (25, 0), (34, 36), (40, 2), (46, 7), (11, 6), (9, 2), (30, 10), (0, 31), (46, 33), (5, 21), (45, 28), (5, 34), (8, 42), (34, 16), (27, 14), (34, 4), (4, 39), (27, 9), (40, 12), (35, 15), (40, 13), (8, 23), (11, 31), (20, 42), (3, 36), (40, 5), (33, 15), (46, 3), (36, 21), (12, 38), (37, 28), (4, 38), (42, 39), (37, 19), (24, 21), (36, 33), (6, 26), (37, 23), (44, 16), (0, 33), (26, 8), (5, 7), (4, 14), (20, 23), (39, 5), (11, 23), (29, 19), (36, 9), (18, 7), (34, 21), (1, 2), (34, 27), (41, 10), (30, 36), (34, 15), (26, 34), (6, 16), (23, 33), (29, 18), (32, 34), (18, 17), (45, 29), (5, 25), (35, 25), (24, 39), (6, 40), (11, 25), (10, 21), (29, 37), (4, 7), (17, 6), (45, 30), (5, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 27), (13, 17), (15, 34), (19, 0), (30, 35), (31, 11), (10, 36), (38, 34), (34, 42), (3, 2), (29, 32), (16, 24), (19, 1), (31, 7), (16, 22), (29, 8), (22, 43), (21, 40), (9, 7), (27, 11), (28, 17), (2, 16), (23, 4), (8, 27), (9, 9), (37, 14), (35, 40), (11, 12), (40, 14), (17, 41), (39, 6), (34, 7), (0, 35), (5, 6), (21, 27), (31, 4), (5, 22), (26, 12), (22, 27), (31, 37), (6, 36), (7, 36), (32, 17), (15, 19), (11, 21), (33, 39), (2, 21), (17, 23), (28, 13), (18, 28), (3, 31), (5, 13), (26, 7), (36, 21), (19, 17), (20, 0), (34, 41), (31, 13), (10, 37), (6, 15), (3, 27), (5, 24), (26, 10), (17, 10), (39, 10), (37, 36), (3, 39), (33, 13), (12, 42), (22, 29), (13, 23), (12, 20), (5, 43), (13, 6), (0, 14), (26, 17), (12, 33), (21, 1), (1, 34), (2, 13), (25, 15), (5, 34), (3, 6), (34, 35), (14, 29), (7, 28), (30, 4), (32, 6), (2, 15), (27, 15), (36, 26), (36, 40), (28, 16), (27, 43), (27, 32), (5, 16), (3, 3), (20, 6), (9, 25), (17, 21), (19, 22), (10, 25), (1, 43), (17, 39), (4, 2), (23, 34), (1, 26), (8, 6), (0, 31), (9, 26), (11, 29), (2, 0), (2, 26), (32, 37), (32, 31), (27, 5), (33, 4), (37, 3), (12, 3), (29, 21), (36, 31), (36, 33), (16, 27), (34, 11), (1, 2), (16, 7), (39, 26), (34, 8), (28, 15), (14, 26), (31, 24), (14, 22), (9, 3), (26, 1), (19, 8), (2, 30), (5, 18), (23, 41), (27, 33), (4, 21), (8, 18), (21, 38), (6, 24), (7, 12), (40, 25), (38, 42), (2, 12), (17, 43), (29, 4), (19, 6), (40, 4), (9, 24), (7, 9), (4, 36), (33, 33), (10, 24), (28, 3), (28, 6), (32, 7), (37, 26), (24, 39), (18, 40), (13, 24), (33, 32), (3, 8), (15, 8), (33, 20), (32, 20), (40, 16), (18, 43), (38, 40), (5, 30), (34, 18), (39, 22), (7, 2), (5, 3), (36, 24), (39, 40), (9, 21), (34, 10), (25, 16), (18, 16), (28, 12), (9, 14), (15, 12), (8, 26), (21, 25), (23, 33), (3, 16), (17, 8), (29, 7), (19, 18), (10, 14), (3, 26), (2, 39), (40, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (32, 4), (15, 38), (38, 40), (31, 17), (15, 10), (37, 29), (5, 35), (33, 31), (8, 27), (3, 41), (25, 26), (34, 41), (27, 34), (30, 21), (0, 30), (1, 6), (33, 19), (20, 16), (4, 40), (4, 19), (14, 21), (9, 7), (14, 0), (40, 36), (19, 34), (13, 23), (18, 27), (5, 28), (31, 3), (27, 6), (31, 12), (9, 31), (11, 8), (33, 29), (10, 14), (3, 8), (10, 40), (3, 39), (19, 14), (16, 6), (14, 5), (27, 35), (26, 22), (0, 29), (32, 19), (7, 7), (23, 19), (31, 40), (28, 4), (29, 10), (5, 22), (14, 33), (39, 22), (9, 24), (41, 36), (13, 4), (42, 6), (35, 37), (12, 24), (21, 23), (4, 34), (21, 37), (33, 35), (27, 28), (5, 25), (23, 33), (35, 19), (17, 2), (33, 20), (32, 0), (20, 29), (24, 32), (0, 6), (8, 14), (38, 25), (39, 0), (36, 3), (35, 11), (35, 39), (41, 32), (11, 40), (21, 10), (5, 9), (26, 18), (12, 19), (16, 5), (9, 6), (16, 28), (5, 11), (34, 26), (32, 38), (27, 21), (27, 0), (12, 0), (3, 12), (37, 12), (6, 28), (39, 21), (10, 21), (19, 2), (41, 12), (10, 36), (6, 24), (39, 39), (3, 25), (7, 15), (36, 17), (24, 11), (39, 1), (12, 18), (9, 15), (30, 15), (7, 1), (0, 21), (12, 30), (17, 8), (16, 29), (34, 29), (28, 34), (31, 28), (14, 35), (30, 17), (22, 24), (29, 9), (27, 26), (22, 37), (5, 12), (33, 34), (11, 14), (42, 1), (6, 17), (35, 5), (25, 4), (17, 32), (34, 16), (3, 2), (26, 35), (37, 26), (16, 14), (6, 35), (25, 3), (29, 3), (30, 40), (30, 0), (11, 2), (13, 24), (28, 16), (19, 16), (0, 9), (5, 24), (3, 28), (23, 31), (34, 12), (0, 7), (8, 32), (14, 38), (41, 19), (19, 37), (7, 24), (38, 2), (22, 11), (24, 14), (23, 37), (4, 17), (33, 39), (14, 2), (2, 9), (5, 3), (1, 1), (17, 23), (27, 14), (39, 31), (24, 5), (25, 31), (9, 34), (41, 41), (29, 6), (6, 3), (41, 31), (39, 18), (35, 16), (24, 21), (26, 0), (34, 33), (17, 4), (40, 17), (0, 36), (37, 23), (19, 10), (0, 23), (12, 23), (16, 7), (5, 30), (18, 9), (42, 36), (12, 5), (17, 33), (5, 15), (26, 21), (42, 9), (8, 37), (10, 20), (23, 23), (35, 4), (29, 23), (20, 41), (37, 39), (38, 38), (0, 4), (27, 29), (36, 25), (25, 9), (41, 2), (28, 2), (5, 6), (24, 16), (37, 5), (10, 7), (17, 17), (24, 10), (31, 37), (20, 0), (11, 25), (26, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 18), (18, 40), (38, 17), (32, 3), (29, 26), (12, 21), (16, 33), (6, 11), (15, 11), (27, 36), (16, 26), (33, 28), (28, 17), (31, 29), (36, 19), (40, 20), (2, 16), (11, 13), (8, 45), (17, 3), (2, 29), (41, 27), (20, 3), (9, 16), (34, 36), (39, 18), (39, 20), (35, 24), (29, 6), (30, 9), (35, 4), (14, 6), (21, 22), (35, 43), (17, 28), (32, 25), (9, 32), (20, 4), (0, 2), (35, 36), (34, 42), (14, 14), (24, 6), (3, 4), (17, 41), (0, 31), (11, 36), (9, 29), (25, 39), (28, 32), (41, 26), (16, 36), (23, 18), (40, 1), (24, 12), (19, 7), (16, 30), (0, 33), (37, 33), (39, 13), (10, 4), (1, 39), (38, 1), (33, 27), (6, 6), (17, 39), (23, 19), (5, 4), (38, 22), (24, 8), (11, 6), (3, 19), (39, 7), (27, 5), (18, 43), (29, 18), (40, 29), (40, 23), (10, 0), (0, 20), (40, 5), (39, 27), (36, 6), (31, 35), (22, 38), (11, 2), (39, 15), (4, 39), (33, 30), (25, 6), (41, 3), (19, 15), (26, 21), (33, 31), (18, 27), (6, 38), (27, 10), (35, 20), (1, 35), (3, 20), (12, 7), (38, 15), (35, 15), (16, 23), (36, 41), (18, 3), (11, 14), (25, 3), (20, 24), (33, 7), (38, 24), (36, 24), (16, 38), (19, 9), (33, 43), (5, 18), (32, 24), (12, 45), (7, 6), (3, 30), (28, 9), (34, 32), (34, 31), (6, 31), (35, 34), (20, 43), (21, 5), (21, 4), (29, 1), (15, 9), (41, 38), (29, 4), (1, 8), (35, 7), (6, 39), (12, 0), (33, 12), (41, 17), (30, 37), (25, 12), (0, 37), (12, 35), (26, 42), (29, 32), (3, 6), (1, 20), (25, 0), (29, 7), (27, 30), (8, 13), (36, 27), (27, 12), (7, 39), (12, 11), (32, 12), (34, 9), (22, 20), (29, 15), (24, 35), (29, 0), (7, 2), (16, 42), (12, 29), (13, 11), (34, 40), (32, 17), (35, 32), (36, 32), (25, 16), (34, 20), (26, 38), (25, 14), (29, 45), (30, 39), (29, 5), (18, 32), (0, 28), (16, 24), (33, 6), (0, 15), (5, 9), (22, 43), (31, 22), (33, 37), (36, 0), (41, 30), (31, 36), (30, 7), (30, 42), (0, 13), (22, 28), (30, 6), (3, 23), (26, 6), (9, 36), (22, 37), (7, 18), (18, 35), (19, 10), (7, 20), (16, 15), (11, 5), (37, 16), (5, 2), (18, 4), (1, 40), (19, 22), (34, 43), (41, 16), (15, 43), (29, 35), (15, 20), (21, 6), (8, 39), (23, 32), (12, 24), (25, 33), (10, 5), (4, 1), (9, 21), (12, 15), (5, 40), (1, 45), (28, 1), (2, 28), (19, 19), (41, 35), (4, 10), (24, 21), (39, 24), (37, 36), (29, 17), (16, 29), (16, 17), (28, 5), (26, 31), (1, 15), (37, 20), (30, 30), (15, 3), (17, 0), (6, 12), (13, 12), (21, 16), (33, 33), (21, 12), (22, 11), (18, 31), (1, 32), (4, 8), (19, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 20), (9, 26), (0, 2), (34, 19), (35, 39), (41, 19), (10, 41), (26, 12), (40, 26), (16, 38), (36, 23), (0, 26), (26, 29), (12, 24), (22, 44), (38, 18), (13, 15), (30, 38), (36, 25), (24, 13), (14, 11), (27, 19), (11, 35), (28, 8), (35, 15), (13, 17), (17, 45), (12, 23), (3, 28), (17, 4), (6, 40), (23, 43), (19, 37), (39, 35), (25, 21), (26, 30), (15, 35), (20, 8), (36, 44), (9, 18), (12, 27), (5, 42), (21, 27), (6, 5), (13, 37), (19, 15), (15, 43), (18, 22), (35, 16), (29, 21), (33, 30), (5, 25), (9, 23), (11, 38), (0, 37), (24, 44), (16, 32), (40, 0), (1, 22), (13, 7), (34, 27), (30, 33), (33, 12), (32, 41), (37, 12), (30, 12), (31, 11), (23, 28), (14, 20), (40, 43), (38, 37), (30, 7), (11, 27), (18, 6), (1, 37), (24, 43), (13, 20), (0, 21), (11, 15), (1, 28), (35, 10), (38, 24), (24, 5), (14, 35), (20, 16), (36, 29), (30, 32), (4, 23), (36, 13), (33, 41), (6, 10), (34, 3), (2, 13), (38, 44), (32, 20), (3, 42), (7, 4), (12, 9), (6, 8), (8, 6), (25, 29), (1, 4), (23, 17), (35, 9), (35, 23), (40, 34), (1, 35), (31, 18), (4, 33), (37, 27), (10, 45), (14, 12), (36, 15), (25, 6), (7, 15), (36, 28), (13, 24), (29, 15), (39, 36), (8, 4), (17, 15), (8, 44), (35, 4), (2, 34), (38, 31), (12, 44), (41, 3), (36, 31), (34, 13), (18, 2), (18, 45), (1, 20), (12, 29), (31, 31), (29, 45), (33, 5), (32, 5), (7, 30), (3, 38), (12, 28), (31, 30), (32, 27), (34, 28), (28, 38), (34, 32), (10, 44), (23, 19), (38, 9), (19, 7), (40, 20), (38, 10), (3, 6), (21, 29), (17, 30), (38, 16), (26, 22), (41, 28), (39, 2), (30, 4), (41, 44), (39, 14), (31, 43), (3, 14), (29, 22), (20, 5), (2, 8), (7, 28), (28, 22), (35, 36), (26, 44), (21, 7), (39, 31), (1, 9), (17, 19), (16, 11), (12, 2), (38, 20), (16, 2), (9, 16), (31, 6), (15, 23), (8, 26), (17, 21), (5, 35), (33, 34), (12, 18), (3, 29), (20, 25), (27, 25), (9, 8), (19, 43), (1, 16), (24, 0), (27, 44), (18, 15), (37, 18), (39, 38), (30, 15), (6, 43), (16, 45), (25, 16), (15, 28), (6, 12), (22, 2), (17, 33), (11, 10), (11, 18), (39, 7), (37, 31), (4, 12), (13, 22), (7, 10), (8, 28), (5, 0), (28, 4), (33, 44), (38, 14), (10, 38), (1, 2), (12, 30), (11, 30), (38, 4), (33, 21), (24, 19), (41, 4), (26, 14), (33, 24), (41, 26), (29, 6), (17, 42), (28, 16), (9, 21), (9, 32), (6, 30), (22, 19), (31, 5), (39, 37), (41, 41), (34, 40), (6, 2), (13, 43), (24, 1), (9, 17), (14, 1), (36, 41), (28, 21), (4, 1), (27, 24), (17, 11), (39, 28), (16, 44), (5, 1), (13, 41), (10, 11), (2, 26), (19, 31), (38, 39), (40, 29), (32, 16), (30, 44), (17, 23), (38, 21), (22, 39), (12, 19), (34, 6), (39, 41), (31, 32), (5, 24), (27, 35), (39, 5), (36, 45), (9, 14), (40, 10), (39, 27), (9, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 29), (35, 34), (24, 8), (12, 20), (28, 6), (16, 45), (37, 26), (21, 47), (12, 2), (27, 2), (40, 36), (32, 3), (18, 20), (25, 30), (18, 43), (36, 4), (12, 5), (6, 5), (37, 3), (27, 9), (32, 19), (5, 18), (2, 21), (11, 44), (40, 21), (17, 19), (40, 10), (40, 29), (13, 45), (9, 17), (36, 20), (40, 18), (0, 2), (1, 30), (40, 16), (27, 25), (38, 31), (40, 13), (24, 20), (39, 16), (1, 29), (2, 18), (30, 34), (5, 34), (0, 26), (4, 11), (23, 32), (6, 34), (7, 14), (15, 41), (36, 32), (1, 37), (20, 33), (31, 12), (36, 31), (10, 27), (8, 33), (8, 27), (27, 37), (33, 20), (23, 12), (28, 42), (21, 4), (10, 6), (4, 23), (16, 11), (15, 29), (21, 2), (32, 7), (4, 8), (37, 37), (39, 24), (35, 42), (31, 25), (24, 23), (12, 26), (32, 25), (30, 18), (36, 11), (2, 2), (11, 20), (25, 27), (13, 5), (37, 40), (34, 12), (5, 33), (21, 27), (38, 28), (23, 19), (28, 31), (12, 6), (22, 23), (7, 43), (12, 38), (6, 31), (17, 5), (12, 36), (22, 41), (34, 2), (30, 8), (20, 0), (6, 9), (20, 26), (20, 12), (30, 31), (30, 47), (9, 24), (24, 16), (40, 40), (40, 6), (7, 9), (31, 5), (40, 43), (17, 2), (15, 43), (17, 29), (17, 32), (6, 7), (38, 42), (33, 9), (5, 32), (34, 32), (39, 23), (7, 45), (11, 39), (21, 29), (4, 33), (13, 2), (35, 30), (4, 40), (30, 27), (27, 30), (22, 47), (23, 30), (28, 47), (0, 23), (8, 45), (33, 34), (2, 44), (32, 9), (21, 38), (1, 12), (16, 31), (33, 8), (24, 30), (7, 47), (35, 44), (38, 43), (27, 3), (11, 38), (11, 1), (19, 14), (37, 10), (23, 24), (0, 21), (39, 37), (35, 40), (39, 42), (19, 41), (22, 10), (40, 12), (30, 21), (31, 0), (37, 42), (38, 4), (33, 41), (26, 4), (34, 19), (3, 3), (25, 18), (6, 26), (28, 27), (25, 5), (36, 3), (29, 1), (11, 29), (15, 4), (23, 42), (17, 33), (13, 6), (14, 14), (22, 16), (33, 32), (25, 16), (7, 29), (9, 6), (16, 18), (17, 1), (12, 7), (5, 8), (3, 33), (12, 3), (8, 44), (13, 16), (2, 36), (29, 42), (19, 18), (4, 1), (23, 11), (0, 43), (11, 6), (20, 25), (30, 5), (7, 23), (13, 9), (35, 25), (25, 2), (3, 22), (11, 31), (23, 13), (36, 1), (33, 24), (34, 47), (6, 14), (36, 40), (14, 47), (29, 10), (22, 34), (6, 0), (30, 1), (8, 37), (35, 39), (38, 14), (32, 31), (3, 28), (33, 43), (0, 44), (34, 40), (36, 26), (21, 26), (28, 5), (23, 40), (16, 12), (1, 32), (16, 14), (29, 40), (10, 5), (28, 4), (15, 9), (30, 43), (9, 7), (1, 15), (1, 1), (9, 13), (16, 24), (14, 33), (2, 27), (22, 31), (26, 11), (35, 3), (14, 44), (12, 42), (29, 2), (21, 46), (40, 41), (3, 25), (5, 29), (17, 24), (37, 21), (4, 3), (36, 14), (30, 15), (2, 17), (22, 43), (27, 31), (31, 11), (28, 44), (1, 46), (9, 30), (22, 26), (35, 9), (15, 21), (9, 46), (1, 18), (20, 13), (17, 26), (4, 13), (34, 31), (11, 43), (19, 12), (26, 33), (38, 3), (25, 47), (20, 17), (23, 26), (5, 22), (39, 38), (18, 41), (14, 17), (24, 43), (18, 17), (11, 25), (18, 24), (8, 2), (34, 41), (10, 8), (4, 39), (36, 17), (5, 28), (14, 29), (3, 46), (36, 38), (36, 2), (1, 27), (18, 47), (6, 21), (4, 42), (29, 15), (6, 45), (24, 22), (2, 23), (15, 28), (10, 7), (27, 29), (9, 27), (10, 10), (11, 0), (39, 0), (10, 42), (21, 39), (38, 15), (23, 45), (16, 10), (35, 11), (26, 17), (25, 23), (19, 42), (19, 0), (27, 39), (27, 44), (14, 4), (12, 0), (36, 15), (31, 40), (0, 7), (21, 12), (10, 15), (19, 39), (13, 34), (11, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 27), (20, 0), (43, 21), (37, 6), (12, 22), (5, 19), (40, 2), (16, 31), (36, 6), (9, 8), (45, 4), (29, 9), (14, 20), (12, 26), (26, 4), (25, 8), (20, 35), (13, 12), (44, 15), (25, 32), (0, 16), (23, 20), (8, 20), (32, 21), (5, 9), (30, 27), (10, 14), (7, 18), (10, 4), (25, 14), (7, 38), (35, 40), (37, 30), (9, 26), (14, 6), (12, 34), (45, 39), (6, 30), (22, 18), (30, 35), (19, 19), (36, 29), (27, 11), (9, 40), (31, 18), (27, 21), (46, 19), (3, 28), (3, 0), (41, 30), (12, 10), (32, 6), (18, 3), (31, 28), (9, 33), (34, 7), (19, 23), (4, 38), (25, 13), (9, 16), (18, 12), (29, 36), (7, 16), (31, 14), (43, 1), (39, 7), (45, 23), (24, 37), (3, 35), (22, 10), (17, 23), (28, 28), (36, 2), (40, 29), (29, 7), (16, 23), (37, 22), (23, 35), (9, 38), (22, 22), (10, 24), (36, 34), (34, 17), (7, 23), (44, 28), (1, 15), (12, 1), (11, 15), (32, 15), (41, 22), (4, 19), (26, 12), (33, 20), (18, 23), (45, 40), (4, 36), (14, 18), (2, 26), (19, 26), (14, 0), (21, 27), (28, 23), (25, 36), (42, 22), (5, 38), (11, 25), (38, 19), (30, 40), (33, 35), (17, 39), (13, 0), (16, 8), (24, 17), (8, 11), (43, 39), (38, 9), (19, 40), (43, 10), (6, 35), (0, 3), (16, 34), (19, 14), (46, 15), (41, 35), (21, 17), (8, 24), (1, 4), (4, 16), (31, 33), (44, 14), (1, 6), (43, 38), (40, 0), (4, 27), (12, 12), (8, 0), (29, 10), (17, 25), (45, 34), (24, 1), (28, 3), (30, 25), (37, 16), (43, 17), (2, 11), (22, 5), (30, 11), (19, 31), (39, 14), (38, 11), (40, 11), (6, 26), (34, 10), (9, 34), (45, 24), (26, 20), (26, 28), (0, 25), (17, 11), (34, 16), (24, 39), (29, 33), (14, 19), (4, 33), (33, 0), (13, 30), (30, 16), (26, 14), (6, 13), (18, 29), (20, 15), (37, 13), (14, 10), (30, 19), (21, 34), (9, 3), (32, 35), (4, 40), (22, 9), (23, 16), (40, 22), (23, 1), (0, 31), (12, 14), (25, 19), (20, 11), (22, 12), (30, 0), (26, 19), (4, 2), (21, 4), (7, 17), (21, 15), (36, 38), (1, 0), (25, 5), (36, 19), (31, 30), (46, 28), (0, 27), (43, 19), (40, 37), (18, 4), (24, 8), (38, 2), (16, 12), (0, 10), (20, 10), (4, 11), (19, 30), (10, 23), (1, 14), (0, 2), (37, 28), (33, 26), (16, 21), (0, 7), (11, 5), (13, 3), (37, 23), (16, 16), (15, 5), (34, 28), (40, 19), (34, 0), (5, 23), (35, 33), (13, 31), (40, 24), (29, 19), (7, 32), (1, 19), (45, 30), (30, 17), (13, 19), (15, 10), (46, 22), (14, 21), (42, 32), (34, 30), (4, 1), (32, 38), (24, 0), (32, 14), (15, 32), (9, 10), (26, 17), (20, 1), (42, 39), (32, 22), (28, 27), (37, 1), (15, 11), (3, 4), (8, 25), (6, 4), (29, 21), (22, 28), (23, 22), (43, 31), (34, 40), (1, 31), (26, 3), (4, 5), (43, 2), (29, 29), (7, 13), (37, 12), (3, 31), (41, 16), (23, 38), (39, 28), (4, 0), (36, 15), (23, 21), (13, 7), (1, 37), (18, 9), (36, 22), (29, 26), (24, 31), (8, 39), (11, 39), (15, 4), (3, 16), (39, 20), (43, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 25), (21, 44), (8, 13), (3, 31), (41, 39), (14, 25), (14, 19), (29, 32), (33, 9), (23, 9), (14, 45), (27, 22), (35, 23), (6, 6), (27, 26), (7, 43), (14, 27), (15, 17), (24, 23), (24, 42), (14, 16), (36, 6), (43, 35), (7, 39), (18, 1), (27, 30), (18, 34), (19, 32), (9, 12), (16, 35), (38, 34), (7, 22), (18, 43), (2, 29), (42, 12), (22, 6), (23, 19), (21, 2), (35, 2), (5, 0), (32, 41), (9, 6), (23, 26), (43, 27), (35, 4), (41, 6), (17, 36), (0, 17), (23, 30), (28, 6), (38, 23), (10, 31), (38, 38), (3, 14), (25, 35), (26, 20), (33, 3), (0, 43), (28, 30), (35, 33), (37, 2), (15, 43), (17, 9), (6, 14), (3, 45), (8, 19), (25, 10), (17, 28), (20, 26), (31, 30), (13, 23), (29, 36), (38, 4), (31, 9), (4, 31), (35, 21), (33, 25), (8, 39), (24, 17), (25, 3), (38, 33), (3, 29), (32, 11), (12, 26), (41, 1), (37, 33), (16, 31), (18, 3), (32, 40), (13, 2), (5, 33), (39, 23), (4, 2), (32, 1), (17, 19), (37, 38), (12, 38), (40, 38), (5, 15), (35, 34), (4, 1), (18, 4), (20, 15), (37, 8), (41, 21), (19, 0), (22, 31), (9, 20), (16, 45), (40, 32), (0, 44), (37, 43), (1, 41), (43, 43), (12, 27), (14, 36), (27, 1), (10, 11), (18, 14), (34, 29), (29, 14), (7, 18), (16, 7), (41, 37), (18, 44), (1, 3), (2, 33), (36, 30), (27, 20), (0, 24), (15, 4), (17, 8), (26, 10), (36, 8), (43, 20), (18, 39), (11, 18), (39, 44), (25, 37), (11, 28), (41, 4), (30, 29), (28, 21), (42, 20), (14, 32), (11, 38), (15, 44), (13, 11), (39, 38), (31, 42), (27, 43), (32, 16), (25, 6), (10, 1), (0, 42), (38, 10), (12, 33), (15, 21), (32, 5), (23, 22), (11, 35), (28, 2), (43, 32), (36, 19), (16, 24), (39, 35), (8, 5), (4, 17), (6, 2), (33, 19), (13, 39), (38, 26), (18, 5), (25, 25), (31, 26), (20, 34), (30, 13), (12, 34), (3, 41), (3, 26), (8, 20), (31, 18), (9, 18), (4, 22), (40, 14), (7, 17), (15, 1), (26, 18), (31, 45), (17, 14), (7, 44), (26, 29), (8, 15), (13, 0), (3, 25), (31, 3), (34, 0), (7, 23), (11, 24), (23, 17), (27, 10), (30, 32), (5, 14), (20, 31), (29, 4), (42, 41), (13, 36), (20, 39), (10, 25), (9, 11), (8, 8), (22, 8), (24, 15), (13, 24), (40, 45), (26, 11), (35, 9), (35, 38), (18, 28), (11, 23), (31, 40), (18, 24), (9, 35), (4, 39), (14, 8), (39, 37), (15, 42), (0, 38), (25, 12), (15, 35), (34, 42), (12, 30), (21, 21), (36, 7), (43, 30), (28, 11), (40, 3), (31, 34), (24, 31), (41, 36), (15, 20), (24, 14), (19, 1), (34, 43), (17, 38), (30, 27), (22, 13), (11, 12), (32, 33), (39, 20), (18, 12), (5, 18), (1, 5), (6, 10), (32, 13), (39, 8), (13, 28), (34, 26), (41, 22), (24, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (32, 34), (38, 31), (6, 12), (16, 17), (27, 37), (32, 39), (26, 0), (31, 30), (29, 31), (16, 37), (13, 28), (0, 19), (2, 8), (17, 0), (32, 20), (26, 39), (9, 1), (34, 30), (7, 11), (4, 33), (22, 25), (40, 24), (7, 10), (21, 18), (5, 26), (7, 30), (3, 36), (32, 30), (10, 15), (40, 22), (40, 23), (36, 18), (38, 16), (25, 33), (3, 24), (7, 22), (8, 23), (12, 24), (1, 31), (20, 30), (14, 7), (0, 30), (37, 19), (8, 32), (8, 18), (32, 35), (25, 17), (20, 3), (20, 5), (29, 40), (29, 20), (16, 35), (1, 25), (13, 17), (31, 5), (27, 2), (22, 18), (28, 24), (13, 15), (2, 5), (10, 27), (39, 35), (36, 38), (21, 35), (35, 33), (28, 28), (26, 37), (40, 19), (28, 7), (13, 11), (36, 25), (17, 36), (7, 14), (31, 12), (1, 7), (18, 7), (18, 38), (34, 35), (6, 6), (7, 36), (20, 14), (24, 34), (9, 18), (23, 0), (16, 7), (6, 39), (31, 39), (8, 16), (16, 3), (4, 6), (29, 36), (35, 18), (19, 16), (31, 18), (34, 36), (1, 29), (19, 17), (2, 32), (23, 39), (14, 32), (16, 13), (25, 39), (23, 4), (35, 10), (26, 11), (4, 18), (18, 20), (23, 5), (3, 20), (1, 24), (39, 38), (14, 17), (20, 9), (9, 6), (11, 0), (11, 37), (35, 1), (38, 3), (38, 21), (33, 12), (9, 39), (16, 34), (35, 8), (37, 31), (0, 5), (1, 14), (32, 27), (7, 17), (25, 8), (38, 18), (15, 3), (2, 33), (28, 25), (41, 26), (7, 2), (29, 11), (1, 4), (0, 3), (15, 18), (36, 35), (4, 22), (29, 26), (16, 10), (32, 0), (27, 16), (20, 18), (4, 40), (23, 24), (12, 34), (33, 39), (24, 31), (22, 13), (39, 31), (24, 5), (1, 36), (9, 24), (37, 39), (34, 0), (0, 27), (6, 3), (26, 15), (35, 25), (24, 1), (26, 9), (22, 2), (9, 33), (39, 1), (29, 24), (29, 5), (23, 19), (31, 2), (11, 39), (10, 9), (23, 26), (24, 37), (9, 16), (0, 17), (41, 2), (40, 32), (40, 34), (18, 29), (10, 39), (3, 29), (32, 16), (30, 12), (23, 36), (28, 5), (15, 12), (8, 4), (27, 5), (30, 11), (16, 32), (37, 6), (28, 30), (12, 23), (9, 40), (26, 36), (12, 16), (8, 31), (16, 20), (19, 15), (36, 13), (20, 26), (6, 7), (0, 37), (32, 40), (27, 11), (24, 23), (26, 3), (20, 19), (9, 2), (40, 14), (20, 27), (33, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 26), (35, 16), (38, 29), (25, 5), (37, 20), (0, 4), (18, 16), (33, 4), (16, 11), (23, 0), (21, 25), (35, 5), (31, 15), (38, 34), (29, 32), (35, 26), (40, 4), (10, 11), (10, 26), (29, 24), (31, 7), (6, 32), (20, 14), (43, 37), (0, 13), (34, 4), (30, 25), (4, 37), (16, 16), (32, 23), (36, 21), (27, 7), (22, 29), (4, 19), (34, 11), (23, 2), (32, 0), (19, 16), (6, 28), (15, 10), (41, 22), (0, 24), (40, 2), (41, 17), (42, 20), (7, 39), (5, 3), (13, 32), (34, 8), (35, 27), (29, 22), (8, 17), (18, 37), (6, 36), (41, 14), (5, 22), (19, 31), (0, 2), (14, 14), (42, 35), (33, 15), (16, 2), (3, 40), (4, 26), (26, 40), (44, 29), (3, 35), (39, 27), (21, 17), (1, 26), (22, 12), (37, 26), (43, 16), (13, 10), (15, 40), (5, 27), (33, 3), (21, 11), (12, 22), (33, 22), (42, 30), (14, 24), (2, 14), (1, 39), (29, 8), (31, 17), (5, 38), (9, 4), (45, 30), (36, 27), (6, 40), (31, 39), (45, 29), (40, 17), (5, 35), (5, 34), (15, 27), (37, 0), (20, 23), (2, 2), (1, 17), (44, 23), (42, 33), (18, 14), (30, 38), (44, 36), (3, 30), (35, 15), (14, 5), (38, 31), (24, 4), (43, 21), (44, 12), (13, 9), (22, 3), (6, 16), (26, 34), (21, 16), (42, 4), (22, 5), (29, 36), (24, 37), (25, 3), (35, 4), (9, 34), (40, 36), (30, 15), (42, 9), (16, 23), (9, 3), (6, 4), (40, 39), (45, 35), (32, 22), (1, 3), (37, 23), (15, 33), (6, 35), (45, 39), (9, 11), (40, 27), (10, 29), (36, 30), (28, 6), (26, 26), (0, 32), (42, 11), (9, 13), (39, 23), (8, 7), (31, 32), (28, 12), (30, 22), (0, 20), (35, 23), (41, 34), (37, 37), (1, 25), (40, 34), (26, 38), (33, 20), (35, 24), (8, 8), (21, 39), (10, 6), (13, 4), (28, 24), (8, 11), (14, 18), (16, 29), (42, 39), (15, 4), (23, 19), (28, 30), (10, 27), (10, 28), (23, 16), (26, 25), (34, 29), (27, 22), (26, 24), (38, 7), (21, 10), (5, 5), (43, 24), (7, 36), (39, 29), (17, 16), (34, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 27), (44, 26), (46, 37), (0, 5), (45, 19), (15, 34), (6, 40), (2, 33), (13, 26), (14, 30), (17, 41), (5, 37), (1, 29), (30, 13), (27, 34), (43, 11), (21, 20), (14, 26), (29, 35), (17, 29), (36, 5), (26, 39), (18, 37), (14, 42), (33, 35), (30, 42), (0, 18), (32, 30), (40, 19), (7, 17), (33, 39), (38, 15), (43, 23), (19, 35), (8, 43), (30, 11), (20, 24), (23, 24), (25, 10), (17, 27), (5, 41), (17, 3), (4, 26), (28, 5), (3, 23), (14, 24), (11, 21), (16, 35), (4, 23), (46, 39), (31, 11), (20, 35), (7, 42), (13, 7), (23, 9), (28, 38), (37, 43), (21, 12), (23, 39), (35, 7), (36, 28), (34, 2), (13, 13), (14, 12), (38, 24), (11, 30), (10, 0), (25, 25), (9, 18), (26, 4), (2, 28), (16, 12), (32, 36), (9, 25), (38, 20), (31, 9), (10, 15), (43, 13), (3, 15), (43, 39), (33, 31), (20, 40), (32, 21), (17, 5), (36, 17), (23, 43), (29, 22), (2, 25), (0, 11), (26, 32), (20, 16), (44, 25), (30, 14), (14, 13), (17, 19), (2, 11), (27, 9), (39, 12), (16, 0), (37, 14), (39, 13), (41, 27), (40, 23), (21, 33), (36, 10), (39, 32), (27, 40), (3, 4), (21, 3), (19, 22), (22, 1), (14, 0), (23, 21), (2, 9), (24, 40), (46, 35), (37, 27), (7, 0), (41, 17), (28, 13), (23, 3), (11, 15), (1, 13), (29, 31), (43, 35), (31, 25), (37, 8), (18, 5), (38, 29), (24, 34), (43, 5), (44, 31), (23, 32), (20, 34), (5, 1), (30, 38), (25, 43), (46, 3), (37, 12), (11, 38), (29, 42), (6, 0), (20, 6), (18, 33), (7, 10), (8, 15), (31, 7), (20, 21), (22, 30), (21, 30), (16, 20), (5, 35), (6, 19), (3, 42), (22, 2), (46, 14), (24, 44), (5, 42), (10, 2), (30, 44), (3, 8), (27, 44), (22, 16), (4, 16), (44, 24), (9, 14), (26, 0), (16, 26), (34, 27), (39, 1), (21, 4), (6, 2), (27, 22), (7, 34), (14, 20), (0, 12), (38, 19), (13, 6), (7, 30), (32, 42), (15, 36), (6, 36), (11, 27), (40, 17), (32, 14), (42, 11), (17, 24), (7, 21), (31, 3), (11, 8), (36, 0), (31, 18), (43, 36), (44, 43), (27, 17), (11, 23), (31, 39), (28, 18), (25, 7), (4, 7), (27, 16), (25, 13), (30, 8), (11, 42), (7, 25), (0, 24), (10, 17), (21, 15), (34, 40), (34, 20), (39, 17), (3, 2), (42, 4), (10, 3), (7, 14), (29, 2), (31, 1), (0, 33), (27, 28), (39, 44), (16, 14), (43, 40), (13, 9), (16, 4), (30, 31), (3, 37), (8, 34), (38, 34), (4, 22), (9, 2), (27, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 25), (32, 6), (2, 13), (6, 16), (34, 24), (30, 30), (3, 13), (9, 37), (5, 5), (26, 34), (6, 11), (9, 3), (35, 23), (13, 37), (9, 41), (39, 2), (33, 19), (24, 3), (27, 3), (2, 30), (21, 38), (4, 10), (8, 26), (10, 26), (34, 5), (2, 2), (17, 12), (33, 33), (16, 34), (16, 30), (9, 26), (39, 19), (22, 24), (2, 9), (20, 41), (0, 6), (32, 44), (24, 39), (14, 43), (15, 10), (8, 33), (1, 39), (7, 20), (26, 43), (37, 16), (24, 22), (16, 8), (30, 18), (38, 37), (35, 24), (22, 35), (34, 41), (38, 40), (24, 27), (22, 16), (15, 38), (1, 25), (37, 35), (12, 25), (0, 23), (15, 40), (14, 22), (29, 16), (32, 18), (24, 18), (21, 44), (8, 11), (22, 20), (29, 34), (18, 10), (10, 10), (10, 0), (33, 24), (36, 40), (37, 14), (0, 43), (28, 30), (3, 37), (0, 29), (28, 29), (29, 30), (38, 35), (10, 32), (38, 41), (37, 21), (10, 35), (19, 3), (38, 31), (34, 21), (21, 5), (38, 7), (0, 21), (14, 40), (7, 36), (7, 14), (36, 5), (19, 31), (37, 22), (19, 25), (34, 15), (14, 3), (19, 19), (36, 33), (39, 12), (33, 3), (23, 23), (15, 25), (15, 19), (27, 38), (21, 25), (23, 30), (21, 3), (10, 6), (25, 34), (26, 12), (19, 15), (30, 13), (11, 7), (9, 30), (32, 34), (21, 33), (2, 7), (14, 6), (2, 14), (17, 33), (11, 32), (27, 33), (21, 13), (1, 22), (19, 39), (15, 16), (3, 1), (15, 9), (22, 38), (17, 36), (8, 19), (13, 0), (36, 37), (9, 1), (20, 0), (29, 27), (34, 9), (24, 6), (26, 36), (15, 4), (35, 13), (39, 35), (31, 7), (17, 21), (18, 36), (25, 19), (9, 40), (35, 0), (7, 33), (4, 34), (4, 18), (38, 15), (0, 2), (37, 26), (36, 22), (32, 42), (15, 24), (25, 31), (26, 20), (7, 15), (13, 41), (6, 21), (39, 29), (19, 43), (18, 18), (38, 44), (27, 35), (38, 10), (34, 18), (37, 24), (34, 22), (23, 2), (28, 25), (22, 3), (35, 2), (21, 28), (1, 40), (27, 41), (12, 34), (28, 40), (21, 10), (10, 11), (26, 23), (14, 34), (27, 11), (36, 17), (34, 19), (34, 27), (2, 39), (33, 12), (38, 18), (9, 21), (5, 41), (15, 43), (17, 24), (39, 1), (16, 7), (5, 6), (5, 13), (31, 20), (2, 36), (31, 33), (6, 25), (25, 5), (13, 38), (26, 39), (29, 19), (38, 27), (39, 22), (29, 39), (30, 17), (19, 26), (8, 44), (21, 32), (11, 22), (6, 1), (12, 28), (14, 19), (13, 15), (22, 40), (37, 27), (37, 30), (14, 36), (14, 17), (13, 3), (6, 2), (20, 22), (38, 21), (9, 2), (29, 29), (26, 3), (39, 4), (5, 18), (34, 13), (26, 44), (1, 24), (5, 12), (23, 37), (36, 41), (26, 29), (11, 13), (5, 27), (21, 22), (0, 14), (5, 14), (1, 9), (19, 9), (9, 35), (25, 4), (22, 9), (36, 0), (5, 31), (7, 34), (30, 25), (1, 1), (29, 36), (9, 32), (15, 26), (0, 26), (33, 23), (18, 14), (34, 0), (24, 34), (25, 16), (23, 41), (20, 43), (16, 39), (28, 38), (4, 17), (37, 42), (21, 39), (35, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 10), (17, 9), (35, 32), (11, 29), (24, 37), (25, 5), (11, 24), (11, 6), (11, 41), (19, 22), (2, 20), (19, 24), (29, 10), (23, 19), (27, 38), (37, 28), (38, 27), (21, 11), (0, 9), (27, 20), (4, 19), (32, 41), (0, 16), (19, 31), (32, 29), (1, 45), (3, 27), (36, 32), (9, 35), (32, 42), (33, 34), (31, 18), (34, 38), (27, 28), (16, 0), (25, 29), (36, 10), (6, 30), (18, 4), (31, 40), (38, 16), (20, 19), (25, 13), (29, 13), (33, 1), (38, 7), (14, 1), (11, 32), (13, 44), (34, 36), (31, 39), (7, 23), (25, 8), (33, 15), (37, 34), (29, 38), (7, 31), (1, 42), (7, 25), (12, 22), (37, 1), (29, 20), (4, 45), (15, 6), (16, 29), (22, 18), (19, 21), (27, 29), (28, 8), (15, 17), (28, 25), (2, 44), (29, 29), (36, 41), (6, 14), (27, 6), (12, 23), (16, 38), (35, 41), (28, 38), (2, 1), (1, 27), (14, 31), (14, 19), (39, 44), (34, 6), (11, 30), (29, 23), (24, 33), (37, 33), (34, 37), (31, 44), (33, 28), (1, 41), (36, 15), (38, 38), (33, 45), (24, 22), (26, 11), (24, 24), (22, 30), (35, 19), (29, 5), (37, 32), (21, 20), (9, 26), (22, 31), (28, 3), (19, 2), (15, 28), (11, 34), (12, 6), (36, 39), (11, 40), (31, 7), (31, 8), (4, 32), (2, 36), (12, 35), (15, 42), (10, 40), (9, 13), (38, 24), (29, 26), (36, 11), (0, 19), (27, 2), (26, 38), (6, 17), (30, 45), (10, 26), (5, 18), (21, 17), (37, 17), (25, 11), (38, 21), (27, 23), (22, 20), (30, 7), (23, 31), (20, 39), (38, 11), (4, 39), (5, 1), (32, 43), (0, 29), (33, 18), (15, 40), (35, 13), (31, 17), (31, 21), (23, 37), (15, 7), (9, 21), (9, 3), (6, 10), (5, 43), (20, 4), (15, 19), (8, 7), (29, 40), (26, 10), (27, 14), (29, 31), (20, 16), (21, 29), (31, 28), (16, 32), (30, 10), (19, 34), (15, 15), (22, 12), (14, 12), (3, 23), (31, 37), (6, 12), (17, 4), (26, 32), (27, 26), (16, 11), (8, 38), (5, 24), (21, 36), (9, 8), (10, 0), (29, 43), (8, 32), (11, 16), (6, 40), (30, 20), (24, 25), (33, 41), (3, 35), (13, 24), (26, 31), (9, 1), (28, 26), (26, 35), (27, 36), (2, 16), (25, 32), (10, 15), (36, 34), (21, 35), (11, 7), (5, 35), (10, 21), (15, 44), (6, 25), (18, 14), (2, 25), (19, 44), (28, 31), (24, 41), (1, 6), (23, 7), (33, 11), (37, 0), (7, 46), (13, 34), (26, 15), (4, 9), (12, 17), (2, 7), (12, 27), (3, 9), (23, 2), (33, 43), (39, 33), (2, 0), (27, 1), (22, 15), (30, 22), (8, 21), (28, 24), (35, 40), (12, 39), (12, 30), (24, 18), (20, 20), (20, 35), (9, 44), (7, 20), (32, 10), (24, 16), (6, 43), (12, 29), (7, 1), (24, 46), (6, 45), (7, 19), (30, 8), (16, 7), (28, 35), (3, 4), (37, 18), (39, 18), (0, 7), (18, 13), (31, 19), (3, 16), (25, 26), (32, 35), (37, 19), (18, 0), (23, 6), (0, 13), (26, 39), (22, 19), (36, 16), (21, 7), (18, 9), (11, 44), (25, 35), (38, 17), (12, 45), (37, 46), (13, 5), (8, 46), (8, 23), (2, 31), (25, 37), (13, 28), (15, 30), (3, 45), (19, 28), (29, 32), (11, 10), (39, 34), (17, 41), (35, 4), (26, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 41), (39, 35), (34, 23), (34, 3), (0, 8), (29, 9), (16, 15), (33, 0), (5, 16), (18, 35), (35, 8), (0, 4), (18, 34), (5, 17), (8, 13), (25, 5), (11, 31), (26, 0), (9, 32), (24, 38), (34, 6), (36, 9), (33, 10), (9, 24), (28, 11), (17, 34), (7, 38), (14, 15), (39, 31), (2, 2), (16, 0), (2, 39), (38, 3), (34, 43), (2, 38), (28, 19), (13, 4), (5, 36), (31, 37), (25, 27), (22, 24), (6, 34), (17, 23), (17, 35), (26, 1), (16, 40), (18, 1), (29, 18), (18, 2), (3, 12), (24, 13), (0, 22), (10, 17), (6, 4), (23, 4), (30, 30), (18, 24), (8, 25), (27, 19), (31, 42), (16, 27), (27, 4), (22, 37), (38, 13), (29, 32), (31, 31), (9, 23), (33, 13), (20, 15), (25, 18), (3, 21), (12, 39), (5, 33), (31, 0), (25, 16), (24, 12), (33, 14), (32, 34), (17, 20), (37, 5), (3, 40), (33, 38), (22, 30), (28, 30), (6, 19), (12, 21), (39, 21), (39, 16), (6, 20), (12, 28), (22, 33), (22, 29), (20, 10), (28, 0), (13, 24), (24, 32), (5, 14), (36, 34), (24, 27), (6, 2), (8, 4), (12, 18), (8, 10), (3, 14), (24, 23), (13, 22), (7, 3), (15, 7), (2, 3), (1, 9), (19, 33), (14, 2), (31, 15), (15, 28), (13, 37), (7, 34), (9, 7), (22, 1), (10, 20), (32, 18), (4, 13), (22, 4), (24, 18), (11, 35), (32, 25), (34, 9), (17, 10), (25, 42), (19, 30), (21, 42), (9, 41), (18, 15), (38, 19), (16, 41), (27, 33), (21, 41), (20, 18), (38, 8), (12, 2), (27, 43), (4, 14), (7, 36), (3, 10), (29, 19), (16, 9), (33, 34), (38, 1), (17, 42), (15, 31), (39, 8), (34, 22), (11, 21), (35, 33), (10, 10), (7, 37), (10, 14), (25, 28), (1, 23), (15, 22), (1, 15), (1, 26), (7, 33), (4, 21), (36, 38), (7, 22), (15, 14), (23, 10), (39, 34), (10, 15), (30, 14), (34, 11), (19, 42), (19, 6), (29, 14), (34, 42), (35, 4), (11, 9), (24, 36), (35, 5), (32, 35), (15, 1), (15, 43), (1, 25), (39, 42), (26, 36), (14, 3), (18, 14), (30, 27), (11, 15), (30, 7), (39, 24), (2, 26), (29, 36), (9, 35), (1, 41), (5, 0), (34, 25), (20, 16), (8, 29), (32, 17), (20, 37), (3, 35), (11, 0), (3, 26), (13, 20), (4, 43), (22, 38), (6, 9), (20, 35), (23, 43), (33, 8), (8, 41), (15, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 34), (10, 34), (20, 23), (42, 10), (11, 8), (42, 22), (26, 11), (31, 16), (17, 33), (29, 13), (4, 26), (43, 6), (38, 13), (18, 28), (8, 26), (25, 1), (16, 40), (43, 36), (1, 30), (12, 20), (39, 8), (34, 23), (14, 41), (5, 18), (0, 14), (22, 13), (20, 2), (16, 2), (38, 39), (2, 28), (13, 10), (4, 24), (19, 5), (25, 36), (32, 21), (42, 8), (7, 38), (19, 45), (13, 21), (34, 21), (35, 32), (2, 29), (17, 18), (1, 37), (0, 18), (36, 21), (10, 4), (18, 24), (5, 29), (17, 12), (6, 1), (25, 8), (17, 24), (8, 29), (18, 34), (26, 17), (18, 21), (0, 37), (29, 35), (40, 14), (33, 44), (3, 4), (21, 21), (28, 24), (20, 14), (23, 2), (7, 14), (44, 12), (41, 26), (33, 29), (22, 9), (15, 45), (19, 33), (16, 35), (12, 43), (32, 36), (3, 11), (2, 37), (22, 28), (33, 31), (30, 6), (29, 1), (9, 31), (16, 4), (18, 23), (37, 1), (9, 16), (26, 45), (15, 0), (16, 8), (8, 33), (6, 25), (26, 18), (8, 34), (20, 37), (44, 44), (42, 5), (2, 17), (5, 7), (21, 17), (31, 30), (22, 16), (14, 13), (24, 24), (19, 26), (5, 41), (42, 38), (4, 40), (9, 20), (21, 27), (0, 20), (24, 5), (40, 25), (17, 3), (22, 24), (35, 16), (40, 6), (10, 32), (15, 14), (43, 38), (20, 19), (30, 5), (34, 22), (4, 31), (40, 3), (3, 25), (24, 2), (39, 2), (13, 31), (41, 22), (29, 5), (38, 45), (12, 19), (28, 36), (15, 6), (4, 8), (11, 42), (16, 42), (37, 0), (34, 29), (13, 40), (9, 26), (36, 31), (1, 5), (19, 10), (27, 31), (1, 43), (42, 4), (37, 5), (40, 5), (40, 30), (21, 33), (21, 30), (25, 27), (14, 25), (3, 5), (2, 15), (16, 38), (22, 0), (26, 1), (21, 42), (10, 0), (35, 3), (0, 38), (38, 36), (11, 0), (17, 0), (35, 43), (22, 32), (2, 8), (22, 35), (28, 27), (12, 28), (24, 45), (15, 39), (2, 33), (10, 37), (39, 7), (42, 18), (5, 32), (7, 17), (33, 17), (37, 30), (27, 29), (1, 12), (11, 12), (5, 23), (36, 29), (27, 35), (38, 15), (29, 22), (4, 0), (27, 0), (21, 28), (22, 14), (1, 9), (31, 6), (13, 3), (11, 22), (3, 1), (37, 38), (8, 31), (27, 32), (8, 0), (43, 14), (12, 37), (31, 41), (5, 34), (9, 28), (19, 38), (19, 18), (38, 14), (16, 10), (13, 15), (37, 34), (27, 28), (16, 14), (41, 24), (27, 3), (4, 28), (27, 37), (28, 42), (36, 30), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 8), (8, 8), (46, 7), (24, 30), (33, 14), (5, 36), (15, 5), (16, 12), (45, 2), (29, 35), (13, 34), (22, 34), (44, 0), (1, 7), (43, 25), (37, 22), (30, 3), (20, 5), (18, 0), (39, 12), (37, 8), (4, 35), (12, 12), (11, 27), (37, 15), (22, 21), (17, 8), (9, 10), (21, 3), (21, 21), (14, 25), (45, 31), (14, 10), (24, 32), (22, 4), (45, 24), (28, 1), (8, 43), (9, 25), (38, 16), (35, 8), (2, 16), (29, 36), (41, 15), (47, 35), (38, 1), (25, 21), (7, 15), (16, 1), (2, 4), (45, 29), (30, 4), (27, 3), (0, 35), (37, 28), (14, 26), (20, 29), (1, 2), (31, 25), (22, 29), (1, 29), (30, 5), (26, 11), (7, 27), (11, 6), (30, 44), (6, 23), (45, 7), (2, 3), (0, 43), (30, 27), (24, 40), (7, 19), (28, 40), (30, 40), (23, 34), (44, 38), (12, 10), (15, 27), (5, 33), (39, 38), (3, 39), (21, 5), (37, 9), (30, 23), (15, 12), (31, 12), (1, 40), (19, 14), (9, 44), (11, 38), (18, 37), (0, 17), (10, 32), (37, 18), (25, 42), (33, 6), (44, 5), (42, 4), (5, 14), (34, 23), (10, 43), (36, 9), (38, 9), (20, 42), (30, 25), (8, 18), (42, 33), (9, 29), (15, 44), (35, 11), (28, 25), (31, 31), (4, 39), (9, 39), (23, 13), (5, 9), (20, 10), (47, 31), (42, 24), (19, 4), (1, 44), (29, 0), (37, 0), (27, 32), (17, 27), (39, 6), (2, 37), (0, 19), (17, 15), (36, 33), (24, 0), (27, 43), (13, 42), (17, 37), (9, 12), (32, 42), (42, 30), (8, 32), (23, 15), (23, 14), (22, 38), (28, 0), (22, 42), (41, 17), (17, 1), (40, 24), (37, 14), (8, 13), (13, 35), (22, 1), (8, 31), (4, 43), (24, 21), (35, 22), (7, 23), (3, 36), (7, 30), (29, 12), (17, 26), (40, 38), (37, 10), (18, 28), (9, 13), (43, 27), (24, 4), (26, 30), (3, 0), (11, 31), (45, 44), (23, 11), (24, 2), (11, 16), (47, 24), (44, 18), (9, 16), (39, 17), (15, 37), (31, 15), (37, 39), (37, 6), (41, 28), (44, 12), (31, 27), (3, 35), (34, 33), (28, 14), (9, 21), (36, 6), (8, 33), (25, 39), (24, 29), (40, 37), (28, 11), (41, 24), (39, 26), (31, 36), (28, 5), (23, 25), (26, 15), (34, 16), (20, 37), (4, 9), (41, 40), (9, 31), (4, 38), (18, 13), (16, 29), (32, 41), (39, 39), (32, 0), (30, 1), (20, 8), (41, 12), (6, 25), (42, 19), (41, 5), (32, 34), (28, 6), (40, 42), (28, 22), (35, 2), (29, 31), (28, 20), (5, 3), (26, 7), (13, 5), (7, 5), (47, 20), (17, 5), (40, 8), (31, 26), (14, 39), (39, 16), (41, 11), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 40), (37, 3), (38, 48), (46, 17), (33, 17), (11, 36), (34, 31), (3, 23), (22, 44), (36, 38), (29, 0), (35, 29), (27, 1), (24, 48), (7, 44), (25, 10), (1, 23), (22, 28), (40, 42), (34, 25), (5, 24), (3, 3), (33, 36), (28, 28), (6, 36), (45, 31), (35, 4), (32, 48), (40, 31), (39, 21), (14, 43), (8, 16), (24, 8), (19, 15), (33, 45), (6, 48), (28, 37), (16, 16), (35, 16), (18, 42), (29, 25), (7, 12), (7, 46), (25, 23), (42, 16), (41, 25), (39, 30), (17, 13), (28, 11), (18, 6), (43, 7), (3, 45), (9, 2), (25, 37), (9, 34), (6, 24), (39, 27), (41, 37), (25, 1), (19, 18), (15, 8), (17, 26), (47, 11), (34, 46), (32, 32), (33, 8), (8, 9), (20, 39), (7, 19), (15, 41), (6, 6), (44, 18), (40, 28), (15, 46), (21, 24), (13, 11), (16, 21), (7, 13), (6, 46), (34, 33), (37, 30), (29, 42), (25, 36), (9, 27), (22, 25), (26, 19), (22, 18), (20, 1), (39, 12), (9, 48), (7, 35), (21, 21), (48, 34), (26, 17), (12, 12), (44, 21), (30, 20), (38, 16), (18, 33), (14, 48), (21, 41), (1, 7), (15, 14), (19, 14), (17, 44), (12, 0), (44, 14), (15, 47), (1, 27), (4, 22), (8, 38), (21, 48), (7, 1), (30, 8), (32, 33), (17, 2), (23, 8), (40, 41), (6, 0), (31, 10), (26, 6), (39, 22), (39, 37), (6, 14), (45, 3), (11, 35), (9, 41), (24, 11), (18, 16), (20, 48), (26, 41), (9, 3), (13, 12), (44, 41), (14, 38), (14, 10), (28, 4), (38, 47), (47, 3), (23, 24), (4, 23), (26, 40), (15, 36), (19, 4), (23, 26), (38, 8), (5, 33), (42, 23), (13, 8), (25, 35), (7, 3), (25, 15), (24, 2), (35, 17), (46, 30), (7, 34), (34, 30), (15, 44), (35, 21), (9, 6), (30, 38), (14, 42), (30, 35), (46, 19), (18, 15), (34, 4), (35, 41), (35, 34), (8, 36), (47, 25), (5, 32), (10, 20), (44, 36), (0, 43), (18, 10), (16, 34), (13, 47), (5, 5), (19, 10), (4, 0), (23, 27), (3, 33), (32, 14), (41, 34), (17, 1), (48, 6), (29, 34), (23, 13), (23, 34), (33, 18), (16, 26), (37, 21), (38, 19), (21, 0), (44, 35), (34, 38), (37, 26), (4, 38), (37, 4), (18, 0), (16, 27), (28, 7), (1, 37), (0, 19), (1, 1), (30, 40), (39, 43), (34, 16), (38, 24), (41, 16), (23, 4), (12, 9), (18, 19), (19, 40), (36, 10), (9, 47), (44, 9), (23, 47), (33, 13), (24, 20), (47, 12), (3, 13), (34, 42), (40, 19), (12, 29), (35, 6), (14, 9), (30, 22), (14, 13), (5, 38), (46, 41), (6, 20), (40, 37), (2, 28), (29, 48), (20, 15), (26, 42), (31, 9), (44, 22), (42, 26), (41, 5), (7, 8), (4, 19), (22, 7), (12, 20), (6, 47), (16, 14), (20, 0), (14, 4), (32, 10), (31, 47), (13, 23), (16, 40), (22, 21), (46, 10), (30, 25), (24, 5), (10, 2), (0, 42), (30, 37), (7, 18), (11, 6), (4, 47), (28, 48), (29, 8), (4, 26), (7, 45), (28, 9), (17, 19), (33, 39), (2, 3), (1, 33), (2, 35), (13, 39), (39, 3), (22, 15), (9, 25), (0, 14), (32, 4), (1, 6), (18, 28), (22, 5), (8, 33), (13, 41), (5, 47), (26, 28), (39, 24), (38, 10), (5, 27), (18, 11), (45, 35), (29, 4), (45, 33), (28, 1), (9, 39), (29, 30), (26, 44), (41, 43), (45, 10), (43, 18), (46, 36), (17, 42), (43, 38), (4, 4), (30, 23), (41, 29), (23, 28), (4, 40), (14, 26), (40, 22), (23, 33), (33, 27), (36, 8), (30, 27), (44, 29), (39, 14), (19, 23), (20, 43), (21, 30), (41, 36), (46, 5), (31, 27), (15, 3), (8, 39), (9, 26), (37, 33), (33, 2), (9, 22), (25, 48), (20, 13), (6, 3), (12, 48), (10, 13), (43, 34), (42, 12), (0, 5), (27, 12), (27, 47), (23, 32), (26, 18), (13, 29), (25, 29), (8, 18), (0, 6), (36, 13), (46, 37), (11, 22), (41, 32), (34, 12), (7, 25), (5, 8), (12, 34), (7, 10), (24, 7), (4, 10), (1, 44), (20, 4), (16, 39), (13, 42), (28, 21), (32, 35), (45, 19), (45, 17), (11, 27), (13, 34), (16, 12), (27, 38), (17, 33), (21, 39), (42, 13), (41, 15), (5, 43), (23, 40), (9, 37), (35, 26), (11, 2), (7, 31), (15, 10), (43, 43), (45, 40), (27, 6), (2, 38), (21, 31), (3, 14), (35, 32), (6, 31), (16, 41), (31, 42), (40, 43), (38, 9), (13, 22), (42, 36), (33, 30), (8, 25), (48, 15), (43, 14), (47, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 16), (12, 8), (23, 18), (10, 11), (23, 1), (8, 18), (44, 14), (7, 16), (16, 16), (32, 21), (25, 10), (30, 29), (4, 14), (32, 9), (18, 3), (24, 14), (6, 19), (18, 40), (20, 11), (42, 23), (37, 37), (15, 37), (29, 23), (1, 14), (11, 30), (16, 32), (18, 34), (7, 1), (9, 1), (37, 19), (33, 7), (28, 0), (21, 12), (43, 37), (34, 23), (35, 39), (36, 20), (16, 2), (12, 31), (26, 29), (38, 2), (33, 25), (40, 34), (0, 30), (28, 9), (35, 28), (25, 32), (13, 21), (35, 27), (26, 35), (0, 38), (41, 9), (0, 6), (23, 31), (20, 14), (11, 39), (36, 18), (14, 26), (0, 2), (25, 34), (24, 6), (21, 33), (1, 10), (25, 38), (42, 33), (14, 30), (34, 19), (3, 40), (0, 33), (37, 17), (36, 41), (25, 15), (32, 3), (24, 24), (42, 19), (16, 27), (30, 7), (40, 23), (13, 18), (18, 38), (24, 1), (21, 31), (33, 12), (23, 16), (18, 14), (11, 6), (8, 9), (37, 0), (17, 3), (37, 12), (24, 28), (1, 16), (30, 22), (31, 13), (40, 8), (10, 37), (9, 25), (10, 25), (27, 7), (21, 25), (26, 19), (24, 8), (34, 1), (32, 26), (16, 18), (22, 32), (40, 38), (35, 1), (16, 31), (42, 29), (30, 18), (21, 28), (13, 22), (11, 0), (37, 25), (30, 40), (13, 16), (5, 15), (22, 16), (18, 32), (4, 25), (10, 13), (36, 24), (19, 33), (33, 19), (3, 37), (31, 40), (41, 34), (15, 30), (13, 11), (31, 3), (33, 24), (29, 33), (17, 4), (36, 4), (26, 12), (3, 3), (19, 24), (33, 33), (31, 10), (33, 26), (37, 8), (21, 22), (21, 27), (30, 31), (32, 16), (31, 19), (27, 26), (15, 39), (7, 22), (38, 24), (10, 17), (30, 5), (4, 2), (0, 15), (4, 1), (13, 20), (17, 9), (18, 12), (25, 30), (25, 31), (28, 41), (37, 23), (19, 1), (14, 35), (4, 22), (6, 36), (20, 17), (0, 29), (18, 37), (7, 2), (7, 15), (43, 35), (11, 32), (34, 41), (39, 37), (17, 22), (7, 18), (19, 32), (36, 30), (10, 2), (1, 13), (18, 1), (14, 22), (13, 9), (27, 39), (39, 30), (41, 36), (37, 7), (28, 6), (14, 2), (16, 9), (42, 16), (19, 28), (24, 0), (17, 7), (35, 30), (28, 24), (22, 14), (13, 14), (27, 22), (19, 38), (9, 41), (15, 27), (26, 21), (7, 9), (10, 16), (42, 32), (31, 5), (2, 7), (5, 16), (24, 25), (22, 37), (7, 24), (42, 27), (39, 0), (14, 38), (9, 38), (33, 35), (36, 13), (6, 13), (31, 41), (43, 24), (20, 27), (0, 34), (41, 32), (32, 7), (29, 9), (40, 0), (19, 36), (31, 23), (25, 25), (0, 10), (10, 40), (21, 17), (31, 0), (2, 13), (36, 33), (25, 41), (40, 41), (7, 6), (34, 17), (21, 36), (42, 28), (9, 14), (3, 30), (3, 20), (22, 30), (10, 14), (20, 32), (29, 26), (33, 11), (44, 17), (2, 11), (41, 12), (43, 28), (43, 17), (11, 22), (15, 12), (3, 10), (12, 28), (20, 29), (27, 21), (22, 23), (1, 26), (16, 13), (1, 30), (28, 4), (13, 17), (8, 14), (40, 14), (31, 9), (6, 38), (9, 37), (31, 21), (34, 37), (34, 12), (17, 2), (6, 35), (22, 15), (36, 10), (38, 19), (33, 0), (38, 23), (7, 4), (6, 33), (22, 20), (10, 12), (29, 24), (28, 34), (21, 30), (41, 35), (23, 23), (33, 32), (37, 39), (40, 17), (43, 32), (7, 31), (2, 37), (1, 32), (18, 8), (35, 16), (23, 19), (37, 5), (14, 27), (7, 38), (35, 34), (39, 25), (22, 13), (33, 23), (5, 30), (23, 22), (21, 26), (22, 12), (27, 30), (41, 33), (34, 3), (44, 12), (20, 21), (12, 15), (31, 38), (35, 8), (30, 36), (25, 23), (3, 36), (39, 27), (21, 18), (28, 1), (19, 31), (34, 34), (28, 39), (40, 2), (5, 25), (26, 20), (34, 16), (43, 39), (29, 35), (28, 40), (2, 19), (21, 37), (9, 8), (35, 5), (12, 11), (37, 29), (7, 20), (36, 34), (35, 22), (31, 22), (29, 0), (10, 35), (3, 39), (14, 7), (44, 37), (14, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 32), (6, 19), (26, 29), (10, 6), (19, 9), (20, 4), (9, 3), (4, 40), (25, 35), (40, 34), (43, 39), (13, 11), (40, 24), (7, 16), (18, 17), (17, 6), (44, 12), (32, 42), (7, 38), (35, 37), (35, 42), (31, 39), (6, 3), (34, 42), (0, 24), (36, 23), (28, 7), (40, 15), (39, 18), (4, 7), (25, 5), (31, 25), (40, 20), (1, 17), (18, 28), (3, 20), (43, 17), (21, 29), (2, 24), (40, 12), (10, 34), (12, 23), (3, 14), (23, 21), (42, 0), (41, 39), (1, 41), (10, 42), (43, 4), (41, 14), (22, 15), (38, 32), (2, 22), (22, 13), (30, 39), (17, 15), (1, 19), (5, 21), (43, 35), (1, 35), (2, 18), (45, 32), (24, 11), (11, 11), (8, 29), (15, 18), (24, 12), (7, 33), (0, 16), (6, 2), (33, 1), (9, 6), (24, 30), (22, 24), (37, 10), (45, 31), (36, 38), (3, 40), (33, 9), (38, 24), (16, 31), (36, 0), (23, 22), (4, 37), (17, 42), (18, 25), (21, 33), (13, 20), (25, 17), (32, 19), (36, 30), (42, 31), (5, 19), (44, 27), (2, 25), (26, 38), (44, 19), (10, 22), (35, 21), (9, 31), (5, 6), (43, 33), (2, 15), (22, 38), (20, 13), (44, 17), (22, 39), (19, 5), (43, 38), (3, 27), (1, 16), (41, 18), (37, 39), (29, 15), (41, 24), (29, 32), (25, 31), (45, 39), (7, 14), (12, 28), (14, 13), (41, 1), (39, 1), (44, 30), (26, 17), (29, 9), (40, 0), (25, 32), (34, 41), (42, 12), (15, 16), (4, 3), (35, 26), (4, 10), (29, 26), (8, 37), (4, 19), (1, 7), (38, 37), (35, 23), (14, 6), (28, 13), (13, 31), (15, 1), (15, 33), (0, 34), (10, 15), (19, 17), (23, 12), (31, 27), (41, 10), (0, 23), (12, 5), (6, 37), (44, 15), (31, 18), (28, 25), (19, 28), (2, 7), (18, 15), (7, 41), (30, 42), (32, 15), (30, 27), (33, 0), (45, 18), (16, 41), (4, 0), (18, 0), (38, 2), (35, 8), (43, 8), (0, 37), (12, 2), (36, 9), (12, 11), (39, 26), (5, 18), (13, 16), (4, 9), (22, 8), (32, 31), (43, 14), (18, 10), (40, 30), (3, 4), (30, 1), (16, 28), (37, 23), (16, 9), (43, 3), (32, 23), (32, 14), (42, 3), (37, 37), (4, 13), (34, 2), (26, 6), (1, 34), (36, 17), (28, 9), (13, 19), (14, 40), (42, 16), (7, 32), (23, 17), (8, 36), (0, 2), (20, 26), (16, 25), (40, 37), (10, 26), (6, 9), (24, 33), (10, 12), (30, 14), (3, 39), (19, 27), (32, 12), (29, 14), (6, 15), (42, 27), (24, 25), (4, 15), (9, 32), (35, 31), (9, 34), (39, 20), (8, 5), (17, 1), (27, 30), (28, 39), (4, 20), (7, 18), (44, 24), (28, 29), (33, 21), (16, 1), (22, 10), (36, 24), (29, 4), (41, 9), (11, 1), (23, 30), (1, 10), (32, 10), (30, 38), (12, 3), (23, 37), (6, 6), (29, 27), (40, 6), (33, 13), (9, 40), (17, 23), (28, 35), (8, 40), (23, 26), (2, 26), (9, 16), (19, 35), (19, 10), (37, 40), (21, 5), (27, 24), (17, 31), (32, 18), (19, 22), (35, 40), (19, 26), (36, 14), (35, 9), (21, 40), (21, 36), (14, 3), (33, 39), (42, 23), (21, 9), (40, 19), (0, 7), (28, 22), (40, 25), (35, 7), (37, 36), (33, 14), (26, 9), (40, 41), (1, 37), (29, 42), (22, 5), (10, 0), (0, 4), (37, 5), (4, 23), (17, 30), (39, 34), (35, 19), (37, 25), (30, 23), (11, 10), (30, 11), (2, 12), (24, 34), (17, 17), (14, 30), (38, 19), (14, 26), (19, 21), (20, 18), (26, 30), (31, 36), (43, 29), (35, 13), (25, 23), (31, 33), (24, 23), (24, 3), (25, 26), (31, 42), (12, 8), (32, 2), (30, 6), (32, 26), (27, 38), (34, 10), (36, 4), (28, 36), (36, 19), (36, 13), (33, 26), (10, 39), (20, 11), (29, 29), (42, 39), (5, 9), (28, 24), (8, 19), (35, 30), (32, 36), (22, 4), (9, 14), (21, 11), (22, 11), (10, 8), (12, 32), (29, 33), (27, 33), (2, 34), (21, 27), (7, 39), (20, 37), (5, 29), (2, 20), (6, 40), (41, 38), (17, 18), (8, 10), (1, 42), (7, 26), (14, 9), (0, 11), (13, 27), (29, 21), (34, 18), (10, 40), (19, 1), (26, 13), (32, 39), (6, 27), (26, 42), (23, 15), (11, 0), (33, 4), (8, 28), (45, 22), (21, 16), (33, 3), (10, 14), (34, 26), (31, 13), (23, 14), (43, 18), (39, 24), (42, 34), (26, 26), (1, 32), (8, 0), (1, 24), (8, 24), (2, 42), (30, 7), (12, 9), (3, 3), (6, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 7), (5, 28), (36, 33), (20, 13), (3, 20), (20, 4), (28, 9), (34, 1), (46, 23), (12, 42), (36, 30), (12, 23), (34, 38), (41, 42), (39, 46), (1, 45), (41, 28), (2, 9), (22, 25), (47, 35), (43, 11), (17, 25), (29, 13), (7, 41), (4, 35), (36, 42), (6, 39), (31, 34), (25, 32), (9, 41), (41, 2), (19, 5), (34, 0), (10, 41), (12, 45), (23, 40), (30, 39), (36, 1), (11, 0), (35, 31), (18, 15), (38, 40), (41, 23), (3, 2), (48, 22), (11, 21), (1, 30), (42, 5), (33, 48), (21, 4), (5, 0), (38, 15), (16, 35), (34, 6), (36, 7), (48, 39), (34, 37), (44, 45), (20, 1), (7, 34), (47, 6), (8, 1), (22, 30), (40, 21), (29, 0), (44, 17), (23, 6), (14, 48), (18, 33), (14, 36), (27, 15), (42, 13), (39, 11), (41, 6), (20, 26), (23, 3), (47, 19), (25, 37), (38, 8), (46, 2), (42, 9), (9, 31), (22, 47), (25, 11), (4, 46), (4, 20), (2, 44), (31, 46), (30, 19), (27, 27), (33, 44), (36, 38), (2, 13), (31, 7), (17, 19), (24, 27), (12, 14), (38, 25), (48, 9), (27, 46), (10, 47), (24, 0), (19, 10), (33, 46), (35, 10), (20, 7), (25, 24), (29, 47), (26, 0), (44, 41), (39, 43), (13, 7), (23, 32), (21, 38), (9, 18), (40, 41), (3, 28), (33, 11), (27, 28), (40, 44), (5, 29), (10, 38), (5, 14), (26, 42), (34, 43), (40, 28), (6, 28), (47, 12), (32, 46), (13, 18), (15, 46), (6, 14), (43, 15), (16, 26), (48, 28), (26, 15), (39, 41), (28, 12), (34, 3), (42, 26), (8, 32), (25, 14), (27, 40), (37, 19), (28, 16), (4, 26), (28, 17), (15, 23), (27, 37), (3, 26), (46, 35), (1, 28), (3, 23), (5, 18), (29, 14), (17, 13), (34, 45), (31, 11), (45, 44), (37, 41), (43, 36), (37, 27), (16, 37), (18, 20), (17, 4), (20, 20), (11, 46), (7, 4), (5, 11), (16, 7), (46, 40), (4, 41), (11, 38), (19, 48), (25, 31), (9, 3), (48, 40), (30, 15), (21, 9), (14, 5), (44, 31), (19, 47), (9, 9), (33, 30), (35, 5), (13, 45), (25, 42), (24, 4), (26, 16), (2, 32), (29, 5), (48, 30), (28, 39), (46, 24), (12, 24), (2, 35), (46, 20), (1, 44), (29, 31), (42, 38), (12, 25), (30, 6), (47, 7), (10, 19), (4, 0), (31, 8), (42, 44), (8, 46), (21, 3), (36, 20), (14, 15), (12, 12), (30, 41), (28, 19), (47, 22), (45, 14), (10, 37), (10, 6), (11, 4), (10, 1), (3, 25), (24, 15), (36, 21), (20, 12), (12, 26), (4, 28), (4, 7), (35, 43), (39, 22), (18, 3), (41, 13), (9, 45), (6, 4), (45, 29), (29, 18), (9, 1), (42, 16), (47, 40), (4, 24), (41, 44), (28, 29), (36, 29), (4, 19), (48, 13), (43, 13), (44, 21), (17, 17), (6, 2), (8, 15), (31, 25), (25, 6), (33, 38), (5, 10), (40, 14), (33, 5), (17, 7), (47, 3), (21, 45), (3, 19), (24, 10), (16, 45), (2, 30), (29, 6), (16, 0), (43, 7), (23, 47), (46, 14), (6, 18), (17, 24), (11, 22), (11, 29), (31, 44), (23, 16), (6, 46), (15, 4), (48, 19), (36, 12), (19, 39), (42, 29), (43, 25), (37, 22), (31, 15), (39, 36), (35, 1), (4, 5), (14, 39), (23, 39), (10, 15), (30, 13), (42, 43), (11, 26), (11, 6), (39, 20), (5, 46), (28, 13), (47, 4), (1, 24), (19, 45), (28, 45), (41, 29), (11, 12), (24, 14), (45, 26), (10, 3), (5, 31), (27, 48), (30, 48), (39, 31), (22, 38), (33, 2), (3, 32), (22, 13), (20, 3), (44, 39), (11, 1), (4, 30), (31, 3), (2, 45), (33, 0), (32, 44), (14, 25), (32, 38), (7, 3), (31, 32), (14, 47), (9, 33), (40, 38), (38, 12), (22, 8), (31, 27), (27, 12), (12, 0), (47, 16), (44, 3), (36, 35), (33, 8), (7, 26), (43, 38), (23, 38), (15, 13), (31, 26), (30, 33), (39, 30), (15, 12), (21, 22), (18, 18), (37, 29), (21, 46), (39, 40), (11, 11), (6, 43), (23, 1), (18, 2), (33, 25), (34, 30), (24, 32), (9, 43), (2, 34), (5, 22), (7, 9), (16, 42), (9, 38), (43, 47), (0, 27), (34, 41), (22, 27), (30, 0), (25, 27), (44, 9), (26, 23), (22, 32), (20, 43), (11, 45), (28, 36), (28, 41), (16, 30), (7, 11), (42, 3), (41, 36), (22, 33), (21, 26), (11, 8), (8, 47), (5, 20), (9, 46), (18, 11), (32, 14), (35, 26), (43, 46), (37, 24), (28, 40), (2, 33), (28, 43), (6, 6), (13, 30), (22, 28), (43, 3), (32, 5), (12, 21), (7, 28), (38, 13), (19, 46), (33, 24), (20, 11), (37, 15), (48, 8), (12, 44), (44, 32), (35, 37), (43, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 28), (7, 7), (3, 23), (22, 39), (29, 27), (2, 15), (34, 8), (36, 25), (16, 2), (35, 20), (6, 27), (27, 18), (33, 29), (42, 9), (15, 6), (38, 9), (38, 2), (19, 35), (40, 31), (41, 36), (11, 18), (0, 14), (32, 20), (22, 22), (20, 32), (41, 24), (22, 2), (18, 41), (28, 37), (21, 20), (1, 20), (40, 25), (15, 25), (19, 36), (2, 2), (37, 26), (0, 36), (17, 20), (12, 3), (25, 23), (9, 29), (4, 21), (38, 20), (26, 11), (42, 12), (30, 19), (16, 30), (18, 12), (15, 18), (41, 35), (41, 15), (0, 37), (35, 12), (31, 25), (5, 30), (5, 17), (28, 0), (39, 23), (17, 4), (29, 20), (33, 14), (19, 42), (11, 1), (39, 34), (11, 28), (1, 33), (14, 12), (23, 37), (20, 41), (32, 12), (12, 9), (21, 18), (35, 34), (28, 11), (32, 6), (7, 17), (39, 12), (8, 8), (41, 39), (6, 29), (11, 41), (38, 40), (38, 28), (25, 2), (1, 12), (2, 31), (35, 30), (27, 22), (21, 9), (26, 9), (2, 13), (3, 25), (39, 17), (33, 11), (32, 30), (5, 3), (5, 25), (1, 25), (18, 25), (1, 0), (20, 20), (11, 37), (28, 39), (11, 2), (8, 28), (0, 29), (34, 39), (38, 30), (39, 9), (27, 10), (28, 1), (27, 23), (2, 42), (33, 23), (17, 19), (42, 4), (38, 25), (9, 13), (37, 0), (12, 12), (3, 18), (24, 5), (9, 37), (5, 35), (27, 16), (17, 23), (15, 14), (15, 40), (38, 15), (7, 8), (40, 40), (11, 33), (10, 21), (11, 0), (9, 36), (38, 23), (2, 40), (26, 5), (15, 23), (3, 14), (18, 17), (10, 20), (0, 23), (19, 34), (18, 23), (16, 42), (25, 28), (37, 11), (27, 28), (42, 22), (24, 13), (39, 35), (27, 32), (40, 26), (16, 4), (38, 21), (8, 29), (35, 37), (22, 20), (7, 38), (28, 19), (16, 39), (12, 8), (31, 6), (15, 8), (30, 36), (16, 15), (37, 34), (7, 36), (23, 38), (21, 40), (22, 26), (18, 26), (29, 26), (41, 14), (19, 30), (1, 2), (38, 11), (16, 8), (31, 22), (14, 17), (16, 7), (14, 39), (7, 9), (39, 0), (0, 17), (35, 35), (38, 16), (0, 16), (28, 17), (32, 11), (32, 5), (29, 42), (9, 5), (17, 11), (8, 27), (19, 15), (35, 5), (7, 11), (37, 5), (21, 6), (21, 4), (2, 3), (3, 4), (32, 41), (21, 14), (21, 34), (33, 9), (3, 11), (41, 18), (36, 21), (15, 30), (41, 0), (21, 41), (13, 8), (38, 39), (20, 21), (36, 1), (25, 16), (21, 13), (33, 25), (5, 36), (15, 16), (28, 30), (29, 24), (5, 7), (10, 27), (31, 14), (32, 10), (4, 28), (7, 28), (26, 40), (23, 29), (3, 29), (29, 30), (2, 32), (37, 13), (36, 15), (16, 40), (19, 26), (11, 15), (0, 32), (27, 26), (25, 33), (10, 33), (6, 38), (12, 10), (38, 37), (5, 28), (35, 33), (32, 15), (5, 15), (14, 21), (9, 11), (2, 5), (27, 40), (39, 2), (36, 16), (13, 29), (1, 36), (31, 30), (11, 19), (7, 1), (31, 0), (23, 41), (2, 19), (18, 19), (36, 39), (26, 30), (18, 34), (19, 40), (39, 33), (8, 33), (2, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 17), (25, 2), (13, 32), (32, 35), (2, 2), (20, 19), (24, 29), (11, 22), (3, 23), (26, 37), (41, 22), (14, 36), (40, 6), (4, 5), (28, 29), (26, 2), (30, 2), (12, 3), (30, 18), (15, 15), (15, 2), (1, 9), (38, 11), (30, 6), (34, 21), (25, 37), (15, 39), (34, 1), (33, 9), (2, 26), (24, 20), (30, 1), (20, 38), (2, 5), (8, 15), (35, 37), (31, 34), (17, 11), (11, 38), (1, 26), (9, 7), (13, 7), (40, 20), (28, 25), (39, 8), (23, 20), (41, 3), (25, 26), (10, 38), (23, 5), (34, 28), (4, 37), (26, 16), (26, 25), (6, 10), (34, 2), (17, 8), (4, 22), (14, 8), (8, 11), (16, 29), (30, 10), (24, 4), (6, 2), (32, 20), (23, 14), (36, 23), (15, 14), (13, 23), (23, 12), (30, 13), (6, 24), (7, 40), (24, 1), (26, 12), (11, 15), (7, 17), (16, 40), (5, 38), (33, 21), (12, 25), (5, 5), (38, 29), (22, 33), (38, 36), (39, 23), (37, 24), (2, 18), (5, 22), (0, 27), (38, 16), (11, 32), (1, 11), (31, 33), (18, 3), (22, 16), (10, 20), (13, 39), (37, 19), (26, 24), (19, 23), (10, 37), (24, 10), (25, 29), (7, 5), (18, 6), (13, 6), (28, 18), (31, 17), (32, 30), (10, 15), (36, 31), (5, 18), (29, 17), (19, 25), (8, 38), (41, 30), (3, 10), (42, 25), (1, 38), (12, 13), (15, 27), (16, 1), (38, 20), (25, 14), (27, 34), (2, 27), (39, 29), (14, 34), (31, 12), (39, 34), (39, 19), (18, 37), (37, 39), (19, 11), (20, 24), (6, 26), (32, 14), (42, 18), (26, 5), (29, 39), (36, 1), (9, 33), (30, 12), (25, 27), (23, 26), (28, 39), (26, 26), (28, 35), (26, 23), (13, 0), (4, 23), (16, 25), (35, 15), (8, 0), (30, 9), (40, 29), (40, 27), (4, 13), (15, 37), (39, 18), (21, 14), (13, 22), (28, 8), (42, 19), (22, 20), (25, 6), (19, 21), (11, 11), (22, 6), (3, 15), (0, 40), (33, 8), (37, 14), (31, 22), (7, 9), (30, 28), (19, 5), (10, 3), (7, 33), (12, 11), (11, 36), (28, 31), (16, 18), (23, 4), (8, 17), (41, 26), (42, 27), (37, 5), (6, 25), (30, 16), (16, 17), (6, 6), (25, 23), (20, 25), (19, 8), (38, 39), (7, 28), (2, 28), (40, 24), (17, 27), (5, 21), (8, 21), (31, 8), (3, 13), (42, 1), (22, 11), (15, 40), (15, 30), (26, 10), (8, 9), (25, 13), (40, 23), (36, 5), (27, 41), (15, 32), (9, 25), (4, 19), (29, 1), (28, 17), (21, 35), (27, 6), (12, 12), (3, 1), (28, 1), (8, 39), (24, 25), (16, 36), (34, 27), (14, 39), (4, 11), (34, 13), (10, 2), (39, 31), (36, 26), (5, 27), (26, 40), (19, 12), (14, 17), (42, 36), (36, 24), (5, 37), (34, 7), (40, 33), (23, 23), (7, 8), (27, 11), (5, 4), (8, 32), (14, 9), (4, 8), (39, 32), (23, 1), (22, 17), (23, 39), (1, 18), (37, 37), (20, 28), (7, 23), (22, 21), (22, 31), (28, 22), (18, 30), (3, 20), (7, 24), (5, 15), (41, 5), (3, 14), (22, 9), (38, 21), (33, 4), (4, 15), (19, 0), (14, 21), (39, 26), (30, 7), (26, 9), (24, 16), (9, 9), (18, 36), (27, 9), (10, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 9), (14, 28), (2, 39), (35, 32), (12, 35), (35, 29), (2, 46), (9, 13), (0, 45), (27, 30), (4, 6), (23, 22), (34, 38), (12, 24), (13, 28), (38, 36), (4, 31), (21, 34), (29, 1), (11, 2), (30, 40), (35, 24), (1, 12), (25, 13), (15, 19), (5, 21), (11, 0), (23, 32), (9, 39), (5, 38), (34, 13), (9, 38), (6, 41), (14, 5), (2, 15), (42, 37), (0, 35), (23, 43), (23, 23), (25, 5), (32, 0), (32, 20), (29, 22), (42, 18), (0, 14), (28, 32), (18, 40), (23, 13), (14, 45), (32, 26), (35, 13), (7, 2), (40, 16), (35, 12), (28, 16), (23, 7), (18, 27), (30, 28), (34, 30), (29, 42), (2, 1), (22, 3), (7, 7), (0, 9), (6, 0), (14, 4), (28, 28), (42, 19), (8, 34), (2, 4), (2, 10), (19, 24), (6, 11), (4, 24), (18, 32), (9, 25), (41, 38), (41, 37), (15, 1), (31, 0), (31, 44), (37, 43), (37, 44), (8, 25), (19, 6), (15, 4), (29, 32), (30, 25), (26, 33), (28, 34), (29, 27), (22, 39), (33, 0), (30, 10), (32, 27), (39, 28), (37, 5), (19, 19), (8, 0), (1, 24), (26, 14), (15, 33), (18, 39), (39, 20), (15, 20), (37, 7), (40, 23), (8, 11), (27, 10), (15, 44), (20, 41), (19, 9), (19, 4), (25, 25), (36, 6), (14, 0), (24, 35), (7, 1), (20, 13), (5, 2), (41, 16), (2, 18), (31, 35), (34, 41), (37, 1), (8, 8), (19, 28), (1, 44), (33, 34), (24, 46), (13, 46), (17, 15), (34, 40), (39, 31), (19, 11), (17, 14), (11, 3), (18, 46), (34, 11), (3, 16), (26, 16), (34, 27), (15, 18), (23, 20), (36, 20), (19, 43), (1, 18), (10, 29), (10, 40), (3, 25), (34, 3), (26, 3), (36, 19), (20, 21), (30, 41), (7, 16), (34, 31), (32, 9), (6, 38), (7, 35), (5, 5), (28, 37), (0, 24), (10, 32), (10, 9), (23, 6), (3, 39), (19, 15), (20, 39), (37, 0), (10, 19), (33, 17), (29, 31), (3, 27), (10, 15), (23, 33), (20, 8), (35, 0), (9, 24), (39, 33), (14, 10), (0, 40), (2, 41), (2, 28), (24, 41), (37, 29), (34, 20), (19, 37), (27, 7), (14, 18), (17, 30), (12, 41), (21, 20), (41, 35), (13, 33), (14, 19), (12, 34), (0, 2), (29, 30), (34, 17), (33, 43), (4, 33), (23, 18), (6, 4), (15, 13), (38, 37), (23, 42), (17, 19), (24, 32), (28, 29), (3, 29), (21, 39), (33, 12), (38, 15), (41, 41), (32, 28), (39, 38), (7, 26), (17, 24), (42, 16), (13, 43), (3, 24), (4, 38), (12, 23), (13, 31), (31, 38), (3, 13), (30, 36), (32, 16), (29, 34), (25, 40), (13, 24), (22, 14), (29, 16), (17, 21), (13, 41), (30, 24), (42, 22), (1, 20), (35, 40), (16, 9), (25, 8), (36, 8), (15, 42), (34, 36), (14, 3), (39, 41), (29, 0), (34, 2), (18, 35), (35, 20), (30, 5), (40, 28), (30, 6), (31, 31), (23, 0), (31, 27), (17, 5), (25, 27), (40, 18), (16, 8), (3, 15), (27, 38), (23, 45), (5, 30), (2, 38), (35, 5), (6, 34), (4, 26), (33, 32), (29, 36), (26, 24), (20, 1), (22, 15), (28, 17), (28, 18), (10, 21), (12, 31), (7, 36), (19, 1), (27, 44), (21, 38), (29, 15), (21, 0), (19, 16), (13, 44), (3, 23), (38, 26), (31, 6), (3, 40), (19, 23), (2, 35), (34, 7), (0, 34), (16, 6), (12, 18), (21, 18), (24, 24), (2, 29), (6, 12), (12, 36), (26, 21), (42, 3), (31, 18), (25, 10), (36, 21), (24, 15), (20, 38), (17, 33), (6, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 39), (4, 3), (31, 23), (13, 8), (22, 36), (37, 35), (14, 34), (29, 27), (11, 42), (39, 27), (25, 9), (16, 19), (38, 38), (16, 6), (13, 0), (14, 42), (31, 12), (31, 34), (18, 25), (32, 10), (35, 6), (17, 27), (21, 36), (38, 39), (11, 5), (31, 42), (6, 3), (5, 8), (30, 1), (11, 8), (3, 39), (42, 40), (9, 15), (9, 23), (22, 39), (11, 2), (13, 15), (14, 2), (5, 19), (29, 21), (12, 45), (17, 39), (9, 10), (22, 20), (11, 16), (42, 38), (8, 22), (44, 34), (32, 1), (36, 22), (34, 10), (40, 6), (21, 17), (3, 29), (30, 4), (19, 40), (20, 30), (31, 39), (21, 42), (23, 42), (19, 34), (2, 24), (34, 12), (22, 33), (7, 14), (43, 17), (40, 10), (4, 20), (35, 37), (25, 32), (6, 21), (8, 5), (44, 21), (34, 17), (38, 43), (0, 28), (30, 34), (20, 2), (6, 4), (44, 38), (3, 32), (7, 10), (27, 5), (21, 13), (6, 16), (39, 43), (8, 6), (0, 30), (17, 9), (6, 31), (16, 23), (41, 38), (17, 43), (43, 44), (30, 17), (31, 16), (4, 28), (28, 11), (41, 10), (20, 23), (20, 38), (26, 29), (37, 43), (26, 6), (16, 30), (34, 46), (5, 5), (24, 19), (0, 14), (10, 13), (30, 12), (42, 9), (13, 23), (8, 39), (34, 19), (20, 32), (23, 1), (20, 25), (43, 34), (22, 23), (37, 19), (24, 18), (43, 3), (22, 42), (42, 31), (30, 46), (33, 17), (12, 37), (30, 28), (22, 35), (30, 26), (21, 43), (9, 4), (5, 35), (44, 11), (43, 7), (24, 25), (28, 19), (25, 20), (28, 45), (38, 22), (14, 6), (7, 23), (44, 7), (40, 1), (2, 33), (40, 38), (32, 42), (31, 27), (27, 33), (0, 9), (40, 15), (20, 27), (20, 8), (23, 11), (36, 35), (30, 40), (28, 41), (26, 45), (0, 12), (34, 2), (14, 26), (39, 14), (18, 40), (40, 17), (13, 21), (30, 37), (44, 37), (28, 39), (17, 32), (41, 13), (21, 22), (14, 32), (36, 25), (32, 2), (29, 1), (33, 40), (26, 43), (8, 2), (36, 41), (13, 3), (13, 11), (18, 28), (3, 14), (22, 6), (18, 44), (19, 19), (27, 43), (29, 33), (34, 1), (14, 0), (8, 1), (30, 13), (12, 24), (2, 17), (38, 37), (7, 35), (20, 22), (43, 46), (8, 9), (29, 32), (41, 11), (35, 14), (17, 45), (44, 39), (41, 23), (44, 41), (16, 27), (8, 30), (10, 29), (0, 26), (10, 20), (21, 30), (30, 11), (15, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 15), (42, 0), (3, 16), (16, 9), (42, 13), (37, 31), (38, 0), (0, 18), (2, 23), (25, 3), (14, 34), (1, 11), (6, 37), (12, 1), (37, 40), (23, 28), (11, 10), (29, 41), (25, 11), (6, 6), (10, 3), (15, 19), (28, 29), (6, 19), (0, 33), (42, 28), (7, 17), (23, 2), (12, 13), (8, 7), (34, 5), (5, 8), (43, 8), (36, 4), (21, 41), (15, 30), (11, 11), (41, 33), (43, 1), (26, 9), (27, 42), (18, 22), (31, 38), (9, 16), (16, 15), (41, 34), (23, 21), (41, 41), (10, 16), (31, 17), (12, 18), (26, 11), (25, 31), (44, 3), (30, 17), (24, 23), (9, 34), (36, 18), (37, 1), (14, 31), (34, 27), (38, 19), (7, 25), (7, 5), (43, 23), (24, 36), (7, 41), (35, 19), (20, 11), (4, 10), (5, 38), (16, 13), (1, 35), (24, 29), (8, 18), (1, 30), (2, 9), (38, 7), (43, 14), (10, 42), (13, 27), (44, 21), (3, 26), (35, 34), (12, 10), (36, 38), (8, 9), (4, 31), (30, 21), (22, 1), (23, 15), (26, 31), (33, 10), (20, 33), (43, 26), (31, 1), (9, 17), (17, 20), (30, 27), (38, 24), (7, 42), (10, 33), (30, 36), (2, 18), (21, 8), (5, 33), (38, 34), (0, 6), (32, 13), (33, 36), (10, 32), (7, 16), (38, 21), (11, 25), (37, 5), (31, 22), (11, 2), (9, 3), (0, 16), (12, 23), (16, 38), (36, 3), (19, 18), (23, 29), (30, 24), (1, 16), (38, 31), (4, 32), (25, 42), (11, 20), (21, 9), (20, 26), (22, 16), (2, 39), (15, 26), (24, 33), (9, 2), (24, 20), (19, 20), (9, 19), (2, 4), (40, 14), (5, 31), (23, 5), (8, 35), (23, 35), (7, 9), (16, 16), (25, 36), (24, 30), (8, 4), (30, 5), (39, 41), (31, 40), (19, 4), (3, 20), (28, 35), (37, 34), (43, 33), (33, 17), (35, 13), (1, 26), (6, 34), (21, 3), (22, 26), (40, 19), (7, 20), (5, 11), (15, 38), (25, 40), (3, 18), (4, 15), (12, 14), (22, 18), (24, 37), (25, 22), (36, 30), (20, 24), (29, 0), (3, 42), (41, 21), (13, 40), (34, 23), (40, 30), (27, 3), (32, 22), (27, 17), (1, 39), (26, 12), (4, 37), (11, 34), (7, 6), (19, 25), (23, 9), (42, 20), (31, 41), (37, 18), (42, 29), (14, 19), (10, 12), (1, 25), (33, 13), (2, 10), (5, 26), (19, 17), (14, 0), (19, 2), (6, 23), (35, 22), (10, 29), (6, 30), (14, 42), (34, 4), (36, 31), (5, 34), (11, 33), (32, 23), (16, 21), (34, 28), (2, 6), (20, 4), (12, 35), (15, 7), (34, 13), (16, 2), (41, 14), (40, 27), (7, 19), (16, 42), (21, 19), (27, 31), (1, 2), (32, 0), (36, 25), (37, 22), (11, 4), (28, 13), (9, 39), (26, 20), (24, 2), (29, 7), (27, 25), (39, 32), (2, 27), (37, 11), (8, 38), (6, 25), (15, 22), (33, 34), (18, 21), (13, 32), (4, 29), (4, 0), (13, 37), (39, 42), (30, 16), (6, 22), (28, 38), (17, 10), (33, 29), (8, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 25), (5, 21), (41, 25), (30, 23), (23, 37), (5, 34), (1, 5), (0, 39), (22, 25), (17, 10), (18, 13), (7, 38), (4, 37), (0, 4), (36, 31), (2, 3), (7, 30), (13, 28), (4, 16), (9, 18), (27, 38), (14, 20), (39, 30), (15, 18), (3, 22), (33, 7), (36, 1), (21, 25), (28, 30), (23, 9), (1, 28), (26, 31), (2, 20), (14, 34), (7, 25), (6, 16), (31, 2), (12, 17), (0, 35), (5, 20), (24, 19), (4, 0), (34, 31), (35, 18), (31, 39), (31, 18), (1, 9), (18, 32), (4, 35), (3, 8), (29, 14), (15, 39), (15, 0), (5, 15), (1, 19), (1, 30), (13, 38), (7, 15), (3, 34), (5, 39), (11, 7), (9, 4), (32, 29), (15, 31), (13, 10), (32, 37), (35, 34), (23, 10), (12, 5), (4, 18), (11, 38), (37, 28), (8, 29), (37, 36), (21, 4), (5, 32), (15, 16), (29, 19), (18, 19), (40, 15), (1, 25), (28, 20), (36, 15), (19, 15), (33, 16), (8, 38), (5, 31), (5, 27), (10, 11), (0, 33), (28, 39), (21, 16), (31, 7), (27, 29), (2, 21), (29, 17), (18, 4), (6, 1), (24, 10), (37, 18), (13, 6), (9, 39), (23, 4), (3, 33), (10, 30), (32, 16), (19, 19), (29, 6), (40, 13), (40, 8), (41, 9), (31, 3), (30, 3), (17, 36), (19, 12), (31, 22), (4, 9), (22, 36), (10, 10), (27, 30), (38, 29), (41, 3), (32, 14), (26, 16), (5, 6), (23, 1), (39, 5), (25, 30), (36, 23), (39, 10), (4, 15), (12, 34), (26, 22), (20, 6), (32, 7), (28, 21), (6, 17), (11, 10), (38, 28), (25, 3), (4, 28), (40, 20), (4, 25), (38, 7), (2, 5), (34, 25), (28, 24), (16, 2), (21, 30), (23, 12), (20, 11), (38, 24), (7, 34), (12, 16), (11, 28), (25, 27), (6, 22), (26, 29), (5, 36), (11, 3), (22, 11), (29, 30), (33, 27), (26, 39), (11, 5), (11, 13), (13, 29), (34, 28), (23, 24), (16, 15), (29, 31), (20, 10), (20, 5), (19, 38), (28, 10), (30, 24), (31, 11), (8, 30), (28, 37), (0, 25), (9, 30), (0, 31), (21, 20), (34, 35), (18, 30), (7, 7), (13, 27), (37, 22), (12, 25), (1, 10), (8, 26), (7, 0), (19, 16), (9, 7), (30, 21), (37, 5), (23, 32), (32, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 1), (21, 38), (12, 5), (30, 18), (4, 23), (10, 32), (5, 6), (19, 23), (29, 46), (11, 23), (35, 18), (23, 23), (5, 22), (12, 35), (4, 12), (14, 6), (11, 13), (24, 10), (14, 10), (22, 37), (25, 27), (24, 20), (29, 38), (29, 6), (16, 47), (36, 23), (3, 0), (16, 28), (17, 9), (15, 45), (4, 19), (30, 39), (24, 21), (1, 48), (39, 30), (37, 27), (14, 16), (11, 44), (36, 12), (32, 39), (9, 24), (4, 37), (7, 17), (14, 47), (35, 6), (8, 4), (34, 32), (10, 21), (32, 8), (21, 11), (11, 30), (28, 41), (1, 20), (37, 40), (30, 3), (13, 17), (4, 1), (27, 7), (6, 6), (15, 31), (15, 16), (10, 31), (8, 47), (38, 43), (9, 41), (8, 10), (7, 20), (2, 17), (21, 44), (6, 14), (18, 34), (37, 20), (14, 27), (24, 27), (19, 27), (22, 17), (13, 40), (23, 37), (1, 10), (8, 30), (18, 18), (32, 10), (1, 12), (28, 3), (31, 31), (6, 30), (9, 19), (27, 19), (20, 44), (4, 10), (27, 31), (18, 7), (36, 5), (11, 35), (18, 0), (6, 9), (35, 27), (6, 42), (13, 42), (2, 21), (34, 5), (18, 8), (38, 32), (4, 5), (16, 16), (11, 17), (17, 22), (0, 13), (4, 30), (24, 32), (29, 36), (17, 32), (32, 6), (10, 34), (15, 43), (24, 6), (3, 40), (9, 47), (23, 40), (29, 29), (28, 34), (20, 2), (18, 39), (7, 42), (15, 36), (39, 20), (3, 48), (17, 37), (33, 35), (26, 40), (26, 20), (12, 6), (13, 21), (8, 8), (21, 33), (34, 39), (36, 27), (32, 46), (15, 8), (14, 30), (26, 0), (5, 15), (3, 32), (1, 22), (34, 38), (39, 39), (20, 13), (38, 38), (20, 26), (14, 37), (27, 20), (19, 34), (29, 12), (32, 38), (0, 2), (13, 7), (37, 6), (31, 27), (0, 12), (24, 37), (11, 41), (35, 13), (17, 41), (31, 2), (3, 16), (9, 26), (13, 41), (39, 25), (31, 32), (14, 11), (29, 30), (6, 26), (28, 5), (8, 21), (12, 11), (20, 5), (30, 42), (13, 18), (13, 3), (32, 5), (3, 5), (32, 4), (39, 23), (16, 41), (17, 24), (14, 23), (34, 24), (19, 47), (21, 45), (30, 11), (28, 25), (16, 30), (31, 36), (39, 2), (15, 20), (35, 29), (26, 30), (28, 46), (25, 32), (1, 35), (10, 41), (33, 6), (34, 22), (39, 13), (12, 4), (12, 28), (9, 46), (17, 30), (22, 21), (30, 41), (10, 25), (23, 10), (8, 15), (22, 26), (26, 7), (2, 19), (7, 0), (14, 20), (36, 9), (8, 7), (2, 47), (34, 36), (23, 39), (11, 27), (1, 18), (27, 17), (38, 9), (22, 12), (22, 1), (5, 46), (38, 18), (16, 12), (35, 41), (1, 43), (25, 43), (36, 48), (32, 2), (28, 47), (12, 47), (6, 32), (37, 7), (22, 29), (8, 20), (29, 10), (18, 25), (0, 4), (15, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 48), (7, 37), (4, 21), (9, 24), (8, 18), (17, 44), (17, 9), (44, 48), (34, 23), (40, 13), (46, 19), (13, 14), (9, 39), (6, 3), (18, 48), (25, 15), (43, 27), (30, 45), (35, 18), (39, 34), (27, 42), (5, 5), (39, 10), (38, 47), (22, 41), (5, 15), (2, 44), (15, 17), (14, 33), (10, 22), (28, 27), (18, 12), (22, 34), (37, 1), (23, 42), (46, 1), (30, 23), (37, 21), (45, 2), (30, 5), (40, 44), (29, 39), (0, 45), (9, 30), (40, 10), (9, 21), (10, 16), (32, 35), (44, 7), (16, 35), (21, 4), (23, 4), (26, 28), (29, 15), (35, 28), (16, 25), (13, 13), (25, 19), (23, 0), (16, 0), (36, 26), (6, 36), (25, 36), (31, 15), (45, 18), (39, 5), (44, 25), (30, 34), (32, 21), (28, 8), (3, 39), (37, 46), (40, 8), (21, 47), (15, 18), (34, 15), (27, 26), (38, 40), (25, 42), (13, 4), (18, 0), (29, 35), (18, 27), (41, 48), (24, 28), (33, 29), (8, 33), (6, 0), (17, 47), (42, 0), (15, 41), (26, 24), (46, 30), (41, 8), (40, 33), (3, 48), (41, 44), (19, 4), (20, 47), (10, 23), (4, 39), (45, 14), (29, 41), (20, 34), (19, 45), (0, 13), (14, 32), (7, 36), (34, 40), (19, 34), (19, 28), (16, 23), (30, 18), (15, 9), (11, 44), (43, 7), (1, 35), (18, 38), (24, 42), (21, 23), (0, 2), (2, 19), (20, 12), (18, 32), (46, 47), (8, 23), (6, 30), (9, 40), (38, 23), (15, 19), (18, 14), (4, 37), (17, 26), (20, 42), (34, 19), (45, 29), (3, 28), (20, 30), (14, 12), (27, 15), (16, 42), (38, 31), (4, 44), (15, 22), (45, 17), (33, 3), (31, 39), (26, 48), (34, 28), (7, 15), (32, 19), (36, 29), (30, 27), (21, 41), (44, 36), (25, 29), (19, 47), (41, 18), (2, 25), (43, 39), (39, 1), (13, 47), (1, 31), (42, 36), (4, 8), (16, 22), (28, 38), (36, 4), (11, 6), (33, 26), (38, 9), (17, 33), (1, 46), (0, 35), (22, 21), (42, 24), (31, 30), (44, 8), (30, 25), (12, 35), (37, 38), (8, 20), (38, 21), (12, 43), (14, 15), (36, 38), (30, 16), (31, 16), (10, 45), (43, 12), (12, 42), (21, 37), (14, 47), (33, 12), (33, 39), (1, 45), (8, 27), (2, 30), (18, 6), (6, 15), (44, 39), (38, 39), (29, 10), (1, 4), (40, 31), (43, 41), (41, 4), (4, 7), (8, 24), (29, 34), (23, 7), (28, 23), (20, 46), (3, 38), (25, 47), (30, 48), (1, 48), (7, 27), (10, 34), (15, 32), (18, 5), (37, 28), (4, 33), (3, 32), (25, 35), (30, 30), (23, 9), (17, 35), (30, 4), (26, 38), (41, 20), (5, 16), (3, 40), (13, 29), (35, 30), (43, 38), (28, 3), (4, 22), (11, 18), (32, 0), (20, 2), (41, 30), (18, 2), (4, 25), (35, 12), (33, 40), (3, 47), (0, 3), (32, 42), (40, 22), (17, 25), (2, 40), (42, 44), (6, 25), (19, 38), (15, 45), (25, 13), (33, 45), (31, 5), (10, 9), (35, 38), (34, 45), (30, 2), (24, 19), (30, 11), (32, 39), (11, 47), (29, 1), (26, 3), (18, 23), (10, 13), (16, 16), (39, 7), (26, 25), (4, 45), (37, 35), (14, 36), (37, 16), (2, 16), (1, 21), (1, 29), (39, 41), (1, 34), (40, 9), (38, 41), (24, 10), (21, 28), (2, 26), (26, 10), (26, 33), (31, 22), (24, 16), (4, 40), (36, 32), (40, 28), (15, 15), (24, 1), (2, 32), (7, 23), (8, 21), (39, 30), (26, 4), (30, 38), (43, 16), (36, 5), (24, 6), (36, 24), (0, 1), (14, 19), (32, 18), (14, 4), (0, 30), (3, 26), (20, 19), (3, 16), (14, 9), (39, 45), (13, 19), (4, 10), (33, 28), (44, 16), (27, 4), (32, 40), (12, 21), (46, 36), (2, 6), (20, 32), (10, 4), (25, 33), (14, 22), (5, 32), (36, 2), (8, 16), (14, 37), (44, 24), (11, 19), (30, 33), (36, 28), (13, 34), (35, 46), (25, 38), (31, 40), (23, 22), (12, 14), (35, 34), (13, 44), (24, 44), (7, 40), (46, 10), (39, 17), (0, 22), (32, 9), (27, 16), (21, 19), (5, 0), (29, 13), (8, 19), (14, 43), (27, 37), (34, 16), (17, 5), (23, 43), (27, 17), (43, 4), (23, 28), (28, 26), (27, 2), (41, 41), (0, 26), (27, 18), (45, 32), (3, 27), (42, 37), (27, 32), (6, 17), (22, 25), (23, 3), (25, 1), (46, 11), (25, 20), (6, 40), (27, 10), (42, 28), (14, 16), (9, 4), (3, 21), (22, 38), (20, 5), (5, 25), (11, 5), (45, 45), (34, 35), (8, 14), (25, 41), (2, 42), (28, 17), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 41), (31, 5), (8, 35), (7, 37), (30, 15), (13, 36), (36, 5), (45, 36), (41, 12), (2, 10), (10, 11), (30, 2), (45, 11), (10, 39), (12, 29), (44, 13), (3, 7), (4, 8), (44, 5), (1, 8), (14, 16), (7, 26), (31, 20), (0, 24), (42, 41), (5, 23), (15, 29), (15, 19), (32, 13), (30, 40), (45, 19), (2, 0), (24, 9), (5, 9), (39, 6), (41, 1), (28, 30), (36, 40), (23, 39), (47, 32), (10, 37), (13, 20), (26, 42), (29, 4), (46, 33), (16, 13), (36, 11), (34, 16), (28, 4), (12, 41), (21, 16), (25, 18), (43, 2), (13, 32), (22, 40), (1, 5), (18, 6), (10, 14), (4, 18), (10, 35), (10, 21), (22, 6), (22, 23), (3, 2), (34, 14), (7, 16), (17, 12), (14, 37), (45, 39), (39, 39), (24, 43), (33, 9), (36, 25), (30, 41), (9, 29), (35, 8), (46, 42), (22, 38), (41, 28), (39, 14), (1, 22), (41, 8), (25, 0), (41, 37), (5, 34), (17, 23), (14, 10), (4, 36), (10, 18), (42, 7), (0, 25), (39, 43), (32, 4), (20, 1), (33, 8), (34, 5), (14, 33), (34, 37), (40, 26), (15, 7), (1, 3), (13, 13), (42, 27), (33, 18), (29, 36), (21, 1), (33, 17), (11, 21), (2, 36), (20, 6), (6, 40), (35, 22), (27, 43), (27, 25), (31, 42), (10, 36), (39, 32), (10, 25), (43, 23), (7, 2), (43, 37), (0, 5), (14, 26), (39, 4), (13, 42), (9, 11), (21, 31), (27, 32), (1, 43), (45, 35), (5, 26), (22, 29), (11, 5), (46, 16), (6, 22), (40, 39), (47, 16), (44, 23), (35, 25), (7, 43), (22, 37), (23, 16), (29, 42), (44, 8), (45, 18), (9, 17), (26, 31), (42, 4), (44, 35), (34, 29), (25, 33), (22, 30), (6, 13), (8, 22), (34, 17), (15, 38), (23, 29), (9, 41), (28, 3), (19, 28), (2, 14), (24, 28), (9, 26), (12, 6), (16, 0), (28, 34), (27, 1), (3, 30), (37, 8), (31, 38), (8, 11), (34, 30), (28, 1), (27, 16), (1, 17), (21, 8), (36, 18), (4, 39), (31, 40), (38, 43), (46, 14), (15, 24), (29, 34), (45, 27), (19, 22), (9, 22), (32, 33), (21, 27), (47, 40), (18, 32), (22, 9), (25, 2), (32, 35), (21, 24), (41, 29), (11, 27), (18, 24), (44, 21), (27, 8), (32, 40), (12, 1), (19, 16), (34, 0), (10, 19), (0, 17), (41, 13), (28, 41), (38, 36), (22, 13), (34, 42), (5, 32), (7, 17), (29, 28), (23, 33), (44, 7), (11, 38), (19, 27), (33, 29), (28, 6), (32, 36), (6, 9), (8, 26), (13, 34), (4, 42), (31, 25), (34, 1), (41, 6), (44, 11), (1, 20), (2, 20), (27, 21), (18, 4), (26, 29), (26, 24), (41, 24), (14, 15), (8, 23), (42, 25), (23, 30), (46, 36), (23, 25), (24, 18), (14, 32), (28, 37), (36, 2), (42, 9), (8, 3), (15, 42), (39, 40), (3, 4), (4, 31), (36, 19), (0, 8), (5, 37), (41, 2), (13, 6), (11, 22), (17, 40), (3, 6), (44, 40), (24, 12), (2, 37), (25, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 38), (13, 0), (15, 17), (39, 32), (18, 5), (7, 7), (28, 31), (35, 29), (39, 30), (0, 27), (22, 8), (39, 3), (18, 4), (19, 20), (11, 28), (34, 11), (22, 15), (42, 27), (4, 33), (38, 29), (42, 9), (19, 15), (18, 17), (2, 5), (29, 39), (30, 15), (24, 15), (10, 8), (14, 24), (25, 17), (44, 33), (11, 27), (10, 10), (28, 30), (45, 38), (45, 6), (20, 10), (15, 31), (3, 22), (6, 32), (10, 12), (31, 40), (9, 5), (2, 10), (10, 27), (45, 1), (10, 32), (27, 32), (32, 22), (42, 21), (30, 20), (25, 30), (2, 20), (36, 20), (3, 14), (34, 32), (37, 20), (35, 25), (26, 15), (32, 20), (24, 35), (17, 27), (29, 15), (20, 12), (17, 12), (39, 27), (31, 29), (34, 21), (1, 17), (33, 24), (0, 6), (11, 16), (17, 33), (12, 35), (13, 20), (38, 34), (5, 11), (35, 41), (46, 24), (0, 5), (0, 33), (34, 1), (5, 5), (42, 28), (27, 34), (6, 4), (29, 23), (27, 4), (16, 10), (33, 16), (43, 35), (15, 18), (17, 28), (17, 6), (13, 35), (42, 22), (33, 21), (41, 32), (0, 34), (37, 36), (8, 3), (27, 11), (24, 19), (3, 6), (8, 39), (1, 21), (30, 33), (17, 38), (17, 36), (12, 36), (8, 26), (2, 19), (30, 14), (25, 23), (30, 8), (28, 26), (36, 34), (19, 30), (18, 33), (27, 25), (41, 16), (2, 9), (18, 36), (32, 24), (46, 33), (37, 26), (20, 34), (32, 6), (2, 22), (28, 4), (30, 4), (26, 8), (30, 11), (28, 18), (31, 41), (6, 14), (42, 31), (39, 28), (18, 3), (6, 10), (42, 36), (45, 16), (38, 7), (5, 2), (37, 28), (23, 21), (36, 0), (39, 38), (11, 5), (3, 4), (38, 1), (31, 1), (35, 6), (13, 32), (16, 15), (41, 41), (17, 16), (35, 30), (8, 37), (19, 25), (2, 16), (25, 4), (19, 19), (19, 2), (42, 15), (15, 24), (34, 15), (2, 21), (29, 37), (4, 7), (31, 31), (35, 27), (13, 17), (29, 1), (0, 13), (26, 23), (38, 27), (39, 34), (3, 26), (21, 8), (29, 24), (35, 39), (38, 35), (33, 8), (33, 11), (9, 8), (44, 16), (32, 11), (4, 28), (36, 18), (7, 26), (14, 37), (20, 35), (42, 18), (38, 16), (45, 32), (17, 22), (13, 16), (30, 24), (24, 14), (13, 27), (25, 32), (40, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 15), (25, 40), (21, 8), (6, 26), (24, 37), (23, 20), (25, 36), (3, 40), (29, 17), (8, 6), (44, 33), (18, 27), (14, 14), (10, 20), (15, 11), (22, 29), (38, 24), (31, 26), (4, 0), (20, 39), (13, 0), (22, 28), (26, 17), (43, 40), (32, 37), (15, 5), (10, 6), (5, 12), (12, 11), (0, 25), (3, 16), (14, 35), (36, 35), (19, 43), (39, 22), (11, 40), (28, 38), (22, 32), (8, 12), (4, 8), (5, 28), (41, 40), (45, 17), (21, 41), (36, 1), (42, 28), (18, 15), (1, 18), (42, 22), (27, 38), (1, 33), (20, 43), (20, 24), (29, 12), (3, 22), (2, 27), (30, 20), (24, 5), (33, 42), (5, 35), (7, 35), (11, 25), (31, 34), (14, 27), (44, 24), (33, 9), (20, 26), (18, 12), (33, 22), (35, 3), (28, 10), (17, 8), (40, 41), (42, 42), (1, 0), (4, 25), (20, 40), (32, 41), (14, 30), (13, 10), (28, 18), (4, 9), (28, 5), (39, 21), (32, 23), (41, 35), (20, 38), (43, 6), (42, 16), (35, 24), (1, 31), (33, 16), (0, 2), (9, 27), (0, 6), (3, 41), (41, 12), (21, 19), (14, 19), (28, 21), (10, 26), (24, 3), (25, 32), (28, 1), (0, 20), (6, 40), (21, 29), (4, 5), (9, 5), (4, 38), (3, 3), (5, 19), (25, 29), (22, 22), (10, 16), (39, 4), (37, 34), (9, 20), (27, 8), (28, 13), (16, 39), (41, 24), (4, 34), (8, 5), (29, 27), (8, 37), (7, 31), (32, 5), (6, 37), (33, 19), (1, 41), (44, 8), (22, 43), (16, 1), (26, 1), (31, 25), (7, 33), (22, 8), (17, 41), (16, 24), (1, 26), (26, 37), (35, 10), (43, 31), (30, 14), (44, 34), (23, 22), (7, 3), (32, 36), (4, 26), (40, 8), (22, 42), (38, 5), (14, 5), (42, 35), (3, 33), (22, 4), (0, 14), (8, 10), (26, 15), (18, 18), (15, 23), (38, 12), (41, 6), (41, 38), (4, 30), (27, 19), (24, 18), (17, 3), (44, 7), (38, 20), (5, 36), (8, 8), (36, 25), (26, 28), (3, 37), (36, 3), (14, 18), (3, 13), (29, 32), (43, 24), (40, 5), (21, 1), (36, 4), (40, 15), (13, 25), (44, 28), (31, 23), (30, 8), (31, 15), (27, 42), (18, 16), (11, 5), (23, 23), (19, 22), (1, 5), (45, 2), (42, 21), (36, 29), (24, 1), (6, 33), (10, 24), (38, 21), (7, 11), (0, 3), (40, 13), (45, 18), (45, 1), (41, 0), (24, 8), (30, 38), (17, 43), (14, 7), (34, 13), (24, 15), (38, 9), (45, 5), (14, 34), (16, 10), (31, 17), (11, 23), (35, 30), (6, 29), (12, 5), (45, 36), (5, 13), (2, 2), (36, 27), (15, 33), (25, 0), (36, 23), (10, 8), (22, 21), (32, 26), (39, 30), (26, 11), (25, 27), (24, 24), (19, 29), (43, 18), (12, 41), (5, 23), (30, 1), (30, 25), (39, 14), (24, 12), (27, 7), (40, 6), (43, 9), (42, 34), (15, 4), (15, 37), (22, 2), (33, 13), (34, 19), (36, 41), (3, 28), (12, 31), (38, 17), (28, 15), (16, 18), (35, 25), (37, 28), (39, 17), (10, 13), (9, 35), (29, 16), (38, 22), (15, 17), (20, 14), (8, 35), (26, 39), (5, 16), (26, 22), (28, 40), (9, 6), (8, 2), (21, 6), (14, 2), (35, 26), (2, 13), (33, 0), (34, 4), (19, 36), (30, 3), (24, 13), (30, 26), (17, 20), (7, 8), (23, 32), (27, 33), (24, 4), (35, 17), (38, 42), (33, 1), (37, 24), (10, 35), (15, 0), (2, 23), (12, 10), (28, 12), (44, 12), (32, 40), (39, 5), (11, 32), (40, 32), (9, 24), (45, 19), (22, 3), (29, 21), (16, 23), (28, 42), (11, 22), (20, 36), (43, 4), (36, 11), (31, 22), (5, 37), (37, 27), (19, 34), (39, 24), (20, 8), (5, 41), (12, 30), (19, 3), (44, 23), (11, 17), (45, 41), (12, 27), (38, 32), (18, 41), (33, 18), (30, 33), (10, 4), (14, 29), (39, 20), (35, 7), (33, 27), (3, 34), (11, 41), (23, 1), (9, 18), (11, 19), (32, 33), (43, 13), (40, 14), (21, 13), (16, 12), (11, 8), (1, 43), (39, 41), (29, 28), (36, 15), (14, 36), (21, 2), (38, 7), (2, 32), (41, 27), (45, 39), (19, 4), (9, 43), (30, 11), (22, 5), (24, 41), (21, 16), (9, 37), (22, 25), (33, 2), (39, 7), (11, 21), (19, 28), (44, 25), (36, 2), (34, 6), (22, 9), (34, 15), (30, 21), (30, 42), (2, 25), (43, 7), (27, 9), (17, 15), (19, 15), (29, 37), (12, 20), (2, 41), (6, 25), (13, 3), (16, 36), (26, 4), (27, 41), (8, 22), (2, 0), (22, 39), (36, 19), (37, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (45, 29), (26, 5), (35, 29), (38, 38), (36, 42), (21, 4), (26, 0), (33, 5), (15, 28), (39, 12), (17, 19), (31, 13), (29, 12), (9, 11), (14, 34), (25, 2), (23, 34), (21, 32), (46, 0), (33, 12), (39, 18), (7, 40), (42, 40), (8, 29), (29, 6), (27, 21), (39, 15), (23, 16), (4, 7), (10, 45), (36, 5), (9, 16), (1, 7), (24, 44), (25, 1), (19, 19), (35, 9), (38, 3), (16, 20), (25, 15), (16, 42), (9, 35), (40, 45), (36, 3), (33, 22), (32, 43), (27, 13), (37, 37), (8, 4), (32, 26), (2, 29), (1, 2), (40, 44), (34, 23), (34, 15), (5, 17), (39, 1), (45, 24), (22, 2), (22, 13), (5, 28), (6, 18), (43, 38), (32, 31), (37, 20), (23, 24), (41, 5), (21, 10), (0, 28), (4, 19), (2, 10), (28, 44), (1, 1), (18, 45), (35, 18), (43, 17), (27, 29), (46, 41), (21, 21), (11, 8), (47, 39), (24, 26), (17, 39), (12, 22), (40, 9), (6, 29), (43, 6), (40, 23), (3, 25), (16, 17), (5, 12), (45, 31), (41, 2), (36, 28), (2, 17), (9, 30), (37, 28), (6, 20), (40, 10), (2, 21), (33, 21), (26, 42), (7, 29), (28, 13), (0, 42), (11, 20), (5, 22), (30, 45), (3, 41), (11, 41), (0, 12), (37, 39), (3, 11), (31, 14), (45, 38), (22, 31), (18, 7), (46, 3), (40, 35), (2, 22), (47, 11), (18, 44), (14, 23), (4, 5), (6, 17), (28, 5), (4, 1), (1, 20), (39, 30), (1, 26), (35, 22), (20, 0), (42, 35), (16, 7), (32, 27), (10, 5), (45, 1), (12, 37), (21, 0), (39, 37), (31, 44), (47, 36), (17, 36), (1, 43), (10, 42), (15, 18), (29, 26), (20, 4), (20, 41), (39, 8), (28, 35), (22, 4), (24, 42), (46, 4), (1, 14), (17, 12), (44, 14), (4, 28), (46, 9), (9, 22), (46, 21), (26, 2), (32, 6), (15, 10), (4, 11), (1, 32), (7, 36), (32, 16), (9, 8), (29, 32), (31, 37), (22, 33), (42, 19), (25, 27), (14, 45), (46, 22), (37, 11), (13, 25), (22, 25), (5, 32), (45, 26), (2, 27), (13, 44), (25, 45), (39, 39), (16, 25), (44, 38), (3, 36), (19, 22), (3, 28), (6, 28), (36, 7), (35, 16), (24, 28), (42, 36), (0, 31), (46, 13), (25, 18), (17, 31), (46, 33), (29, 4), (44, 44), (23, 15), (34, 2), (7, 18), (41, 39), (43, 8), (2, 43), (34, 41), (36, 30), (20, 25), (33, 0), (30, 31), (42, 26), (34, 34), (15, 30), (9, 4), (33, 17), (11, 10), (17, 25), (1, 23), (9, 43), (10, 20), (17, 24), (22, 42), (23, 30), (43, 27), (19, 10), (39, 23), (20, 15), (41, 16), (19, 6), (28, 28), (16, 45), (9, 34), (8, 7), (40, 43), (20, 35), (8, 18), (34, 28), (7, 16), (47, 17), (16, 31), (27, 28), (19, 34), (36, 45), (47, 40), (21, 33), (7, 22), (27, 4), (7, 23), (34, 14), (33, 15), (3, 26), (46, 1), (42, 10), (4, 14), (27, 17), (46, 27), (14, 7), (44, 35), (22, 16), (28, 30), (41, 40), (29, 10), (32, 15), (27, 15), (38, 10), (33, 16), (38, 18), (13, 5), (24, 34), (16, 11), (8, 1), (17, 34), (24, 4), (11, 2), (40, 28), (39, 35), (20, 39), (14, 2), (15, 1), (0, 9), (26, 25), (36, 35), (15, 21), (15, 29), (30, 5), (33, 33), (27, 23), (32, 9), (10, 36), (16, 18), (25, 0), (45, 8), (27, 0), (4, 23), (7, 38), (29, 27), (17, 32), (2, 37), (11, 33), (13, 39), (40, 18), (33, 43), (35, 20), (23, 11), (13, 2), (18, 1), (6, 40), (15, 17), (29, 8), (5, 20), (19, 2), (13, 12), (23, 7), (42, 39), (10, 33), (35, 12), (23, 17), (30, 35), (9, 7), (3, 12), (2, 26), (37, 7), (36, 8), (41, 34), (18, 34), (34, 40), (45, 19), (41, 11), (2, 45), (5, 9), (13, 13), (39, 36), (1, 37), (11, 39), (27, 12), (24, 39), (12, 3), (15, 13), (29, 16), (40, 37), (14, 28), (7, 34), (26, 35), (10, 35), (22, 40), (24, 11), (31, 17), (3, 23), (23, 26), (44, 21), (33, 37), (21, 16), (21, 1), (15, 22), (10, 38), (45, 20), (41, 18), (2, 20), (3, 44), (26, 27), (26, 43), (45, 15), (44, 32), (8, 34), (16, 16), (33, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 9), (11, 22), (11, 20), (30, 5), (0, 9), (31, 31), (24, 13), (23, 27), (43, 3), (41, 34), (13, 22), (35, 14), (10, 3), (15, 10), (25, 34), (25, 36), (12, 0), (4, 16), (22, 34), (7, 38), (7, 5), (43, 12), (42, 33), (34, 14), (5, 19), (16, 31), (22, 25), (4, 20), (29, 32), (6, 14), (3, 6), (34, 7), (38, 20), (0, 37), (22, 20), (26, 21), (28, 0), (3, 10), (43, 2), (35, 33), (29, 39), (44, 10), (23, 32), (6, 39), (28, 15), (24, 31), (29, 11), (39, 21), (15, 35), (40, 3), (31, 5), (14, 36), (15, 2), (18, 30), (26, 24), (14, 25), (19, 19), (22, 12), (1, 12), (36, 23), (25, 21), (32, 4), (40, 18), (1, 19), (21, 37), (30, 35), (21, 34), (32, 8), (21, 32), (18, 5), (18, 29), (38, 28), (26, 39), (11, 21), (35, 10), (7, 11), (35, 4), (34, 18), (40, 20), (37, 4), (44, 15), (31, 33), (13, 25), (27, 36), (1, 29), (1, 0), (28, 18), (36, 7), (2, 21), (0, 28), (21, 16), (10, 9), (10, 1), (3, 27), (6, 9), (28, 23), (37, 20), (4, 9), (23, 1), (3, 14), (24, 21), (10, 39), (13, 27), (42, 22), (31, 16), (30, 23), (25, 4), (17, 29), (25, 29), (31, 22), (17, 20), (18, 24), (11, 12), (12, 7), (8, 32), (27, 33), (41, 11), (38, 31), (30, 16), (37, 18), (36, 13), (15, 16), (15, 23), (12, 21), (43, 16), (37, 7), (29, 17), (32, 25), (21, 17), (42, 26), (36, 18), (29, 26), (42, 21), (14, 19), (40, 15), (20, 10), (30, 12), (17, 22), (25, 13), (43, 19), (25, 3), (27, 8), (27, 2), (26, 33), (4, 29), (2, 22), (32, 6), (30, 24), (31, 13), (0, 18), (17, 13), (15, 34), (19, 25), (4, 11), (2, 39), (31, 39), (37, 23), (18, 15), (2, 33), (21, 13), (0, 30), (17, 11), (32, 35), (9, 23), (6, 24), (2, 31), (31, 25), (40, 12), (40, 31), (15, 5), (20, 16), (33, 19), (23, 25), (30, 27), (22, 29), (37, 8), (11, 0), (15, 7), (6, 15), (4, 21), (2, 5), (24, 4), (25, 2), (39, 37), (31, 17), (30, 11), (15, 36), (28, 1), (26, 29), (16, 14), (5, 11), (23, 16), (43, 11), (12, 34), (38, 34), (43, 36), (20, 15), (37, 17), (13, 19), (38, 15), (12, 5), (18, 18), (29, 20), (31, 27), (5, 31), (23, 39), (18, 37), (10, 10), (44, 9), (16, 1), (3, 36), (36, 4), (11, 38), (41, 4), (31, 2), (27, 30), (14, 12), (42, 36), (41, 27), (12, 29), (16, 22), (10, 7), (20, 21), (15, 31), (5, 30), (3, 2), (5, 13), (34, 39), (26, 7), (24, 9), (36, 26), (20, 38), (29, 8), (27, 38), (5, 18), (7, 27), (20, 33), (13, 5), (15, 37), (34, 19), (15, 12), (38, 35), (43, 7), (40, 14), (23, 33), (41, 1), (20, 17), (29, 15), (2, 3), (28, 2), (37, 12), (35, 16), (32, 20), (16, 19), (20, 37), (35, 32), (37, 27), (13, 20), (8, 27), (7, 7), (14, 14), (44, 21), (9, 39), (30, 21), (16, 11), (30, 28), (36, 15), (42, 5), (10, 31), (19, 23), (39, 39), (40, 32), (7, 10), (29, 27), (33, 32), (13, 6), (11, 19), (25, 31), (21, 4), (0, 12), (34, 5), (4, 0), (27, 14), (41, 15), (21, 19), (39, 23), (19, 8), (6, 28), (9, 8), (34, 2), (3, 18), (25, 10), (5, 29), (30, 4), (23, 28), (44, 17), (23, 17), (19, 20), (27, 26), (1, 33), (10, 30), (25, 18), (12, 12), (8, 14), (3, 25), (10, 23), (27, 7), (29, 33), (39, 10), (4, 2), (20, 23), (33, 24), (39, 1), (8, 4), (34, 37), (7, 25), (20, 29), (12, 26), (38, 8), (36, 0), (23, 31), (26, 25), (18, 20), (9, 18), (35, 34), (43, 38), (41, 20), (9, 24), (1, 22), (35, 23), (33, 15), (31, 11), (10, 32), (27, 18), (44, 22), (44, 33), (41, 3), (41, 36), (19, 15), (3, 29), (7, 28), (22, 21), (30, 13), (39, 13), (39, 34), (21, 10), (4, 28), (0, 38), (38, 26), (7, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 31), (30, 14), (25, 32), (0, 13), (33, 12), (20, 28), (10, 19), (35, 13), (33, 7), (43, 26), (31, 35), (29, 10), (27, 35), (36, 34), (6, 22), (36, 3), (35, 30), (29, 30), (26, 31), (16, 7), (40, 22), (13, 7), (20, 10), (35, 38), (21, 18), (3, 20), (13, 20), (19, 11), (6, 4), (35, 15), (16, 28), (30, 26), (31, 19), (38, 36), (2, 7), (28, 12), (37, 0), (40, 8), (43, 8), (16, 19), (4, 28), (15, 13), (40, 0), (10, 38), (0, 29), (39, 24), (27, 18), (20, 2), (16, 9), (35, 12), (31, 14), (5, 34), (18, 33), (13, 26), (38, 28), (42, 36), (14, 40), (6, 13), (10, 21), (36, 21), (43, 19), (14, 0), (20, 6), (27, 15), (18, 31), (21, 22), (4, 3), (17, 7), (22, 4), (42, 31), (31, 40), (7, 1), (28, 17), (40, 1), (1, 28), (2, 29), (3, 15), (26, 39), (44, 38), (28, 13), (14, 11), (4, 8), (16, 1), (17, 25), (33, 0), (31, 26), (34, 29), (14, 16), (7, 24), (44, 7), (41, 32), (31, 38), (25, 35), (37, 23), (35, 37), (30, 32), (14, 2), (18, 34), (10, 26), (44, 9), (37, 15), (21, 14), (28, 25), (29, 35), (8, 15), (39, 29), (42, 24), (42, 11), (27, 4), (16, 33), (23, 2), (32, 37), (44, 8), (39, 27), (14, 4), (21, 38), (34, 31), (6, 24), (22, 5), (28, 35), (21, 23), (39, 25), (11, 27), (44, 35), (21, 2), (40, 26), (33, 29), (29, 31), (13, 21), (37, 35), (35, 26), (0, 36), (12, 21), (20, 20), (42, 18), (32, 20), (41, 9), (22, 31), (26, 28), (30, 13), (3, 14), (13, 12), (30, 36), (18, 29), (3, 22), (42, 6), (41, 26), (20, 35), (29, 7), (19, 29), (39, 32), (43, 2), (45, 15), (13, 30), (29, 40), (31, 31), (30, 27), (24, 8), (33, 2), (3, 21), (38, 4), (43, 39), (34, 35), (31, 4), (39, 33), (43, 18), (43, 30), (39, 10), (44, 6), (23, 27), (34, 1), (23, 17), (2, 19), (25, 2), (6, 0), (27, 17), (31, 15), (33, 14), (3, 16), (9, 15), (2, 16), (36, 25), (11, 1), (23, 38), (6, 8), (37, 19), (41, 10), (23, 33), (41, 5), (21, 15), (34, 27), (8, 2), (2, 18), (9, 24), (9, 35), (28, 29), (3, 36), (19, 37), (4, 11), (11, 18), (41, 4), (28, 38), (21, 26), (25, 11), (23, 20), (43, 40), (37, 38), (2, 17), (14, 32), (25, 28), (12, 5), (23, 37), (10, 28), (3, 24), (8, 3), (41, 27), (14, 10), (5, 17), (14, 34), (26, 4), (2, 9), (34, 11), (18, 26), (19, 19), (13, 39), (21, 20), (13, 35), (22, 3), (2, 14), (45, 25), (17, 4), (21, 32), (29, 19), (45, 13), (8, 21), (19, 25), (10, 5), (2, 37), (1, 37), (9, 1), (15, 19), (45, 35), (30, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 23), (12, 5), (27, 44), (35, 44), (38, 4), (13, 9), (44, 37), (5, 0), (43, 33), (11, 6), (20, 26), (43, 42), (48, 9), (35, 12), (34, 25), (47, 36), (21, 19), (19, 13), (15, 20), (28, 30), (48, 39), (14, 22), (20, 11), (22, 38), (27, 0), (35, 29), (14, 30), (38, 33), (21, 40), (43, 31), (39, 43), (31, 36), (46, 48), (39, 20), (35, 33), (10, 45), (20, 4), (2, 32), (28, 4), (6, 35), (32, 31), (33, 16), (26, 38), (21, 29), (22, 31), (26, 2), (5, 14), (35, 31), (31, 35), (29, 23), (1, 33), (2, 37), (35, 39), (18, 38), (39, 35), (37, 29), (31, 29), (14, 20), (30, 0), (21, 37), (38, 34), (36, 28), (5, 32), (25, 9), (11, 1), (45, 10), (12, 11), (33, 44), (29, 13), (5, 13), (10, 40), (5, 10), (0, 39), (18, 34), (11, 26), (47, 11), (36, 42), (35, 22), (14, 19), (3, 30), (5, 17), (42, 48), (26, 1), (22, 41), (43, 11), (33, 17), (14, 26), (8, 41), (14, 14), (0, 4), (21, 11), (25, 30), (17, 20), (13, 24), (2, 24), (15, 41), (25, 34), (36, 13), (44, 11), (1, 43), (10, 0), (16, 3), (33, 48), (2, 31), (28, 2), (30, 10), (22, 45), (38, 9), (37, 5), (16, 46), (11, 10), (42, 43), (40, 33), (21, 3), (24, 40), (24, 1), (36, 11), (32, 42), (37, 3), (23, 16), (39, 32), (22, 16), (2, 9), (40, 31), (4, 20), (32, 47), (30, 24), (42, 27), (40, 47), (22, 7), (16, 48), (44, 1), (24, 30), (46, 46), (39, 48), (21, 32), (30, 20), (33, 28), (20, 7), (41, 22), (25, 26), (8, 6), (39, 34), (37, 18), (28, 39), (29, 4), (45, 37), (40, 44), (42, 38), (28, 33), (22, 17), (26, 40), (40, 28), (45, 30), (38, 10), (44, 39), (17, 25), (14, 38), (12, 35), (21, 14), (40, 3), (35, 6), (48, 34), (27, 7), (29, 24), (11, 14), (40, 9), (32, 15), (31, 12), (12, 6), (2, 2), (29, 47), (44, 19), (6, 27), (8, 24), (4, 47), (9, 10), (48, 0), (30, 43), (14, 33), (33, 43), (2, 12), (6, 25), (14, 36), (48, 14), (16, 29), (43, 37), (43, 14), (20, 27), (47, 44), (41, 27), (35, 42), (12, 41), (19, 47), (23, 13), (41, 13), (2, 13), (9, 38), (40, 40), (46, 34), (42, 21), (42, 7), (47, 39), (9, 24), (10, 38), (10, 3), (13, 15), (12, 46), (16, 24), (44, 5), (23, 34), (12, 39), (11, 43), (30, 3), (34, 19), (18, 41), (16, 33), (29, 41), (17, 45), (2, 36), (1, 0), (40, 46), (46, 41), (16, 26), (2, 47), (5, 44), (41, 46), (39, 8), (17, 15), (1, 32), (4, 8), (39, 2), (14, 47), (28, 15), (2, 3), (40, 1), (37, 7), (48, 17), (6, 16), (41, 30), (9, 8), (8, 22), (21, 31), (42, 30), (19, 15), (24, 2), (21, 13), (8, 37), (1, 48), (28, 13), (13, 36), (1, 13), (28, 48), (43, 30), (2, 20), (22, 33), (12, 8), (7, 45), (22, 27), (26, 17), (10, 46), (35, 40), (27, 47), (45, 45), (18, 36), (46, 10), (0, 48), (36, 1), (11, 36), (9, 16), (38, 12), (26, 25), (7, 11), (41, 34), (21, 27), (38, 37), (12, 16), (18, 25), (35, 46), (1, 22), (3, 14), (8, 40), (0, 37), (14, 29), (45, 48), (9, 19), (24, 13), (10, 36), (41, 8), (18, 18), (47, 42), (15, 17), (3, 18), (45, 1), (13, 2), (12, 48), (4, 24), (25, 8), (32, 24), (30, 40), (26, 44), (28, 8), (7, 1), (14, 46), (34, 41), (9, 6), (41, 19), (19, 5), (47, 18), (44, 47), (42, 1), (16, 22), (5, 29), (27, 22), (22, 36), (42, 9), (26, 20), (34, 1), (2, 33), (42, 35), (18, 32), (38, 35), (26, 4), (44, 12), (35, 8), (42, 37), (13, 5), (16, 28), (16, 6), (34, 3), (31, 1), (26, 21), (0, 41), (3, 43), (41, 35), (15, 8), (45, 21), (4, 32), (45, 22), (18, 42), (24, 48), (23, 38), (5, 23), (31, 18), (32, 29), (9, 20), (13, 6), (32, 17), (18, 43), (43, 44), (14, 35), (6, 4), (12, 21), (13, 7), (23, 37), (9, 48), (18, 7), (24, 28), (28, 34), (38, 48), (32, 37), (13, 43), (33, 9), (4, 38), (24, 5), (46, 29), (15, 21), (5, 4), (11, 45), (13, 45), (12, 2), (32, 1), (27, 26), (44, 42), (23, 28), (37, 12), (18, 17), (33, 33), (8, 3), (5, 25), (14, 25), (44, 0), (8, 39), (32, 44), (26, 43), (15, 2), (32, 40), (27, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 10), (12, 21), (42, 3), (45, 40), (25, 10), (18, 2), (46, 34), (34, 3), (25, 20), (47, 36), (7, 1), (30, 7), (26, 19), (36, 28), (15, 33), (36, 39), (35, 5), (29, 32), (20, 35), (6, 17), (12, 24), (46, 5), (3, 11), (21, 32), (39, 0), (1, 23), (23, 38), (23, 33), (0, 15), (0, 27), (3, 22), (47, 39), (38, 26), (39, 38), (30, 24), (15, 32), (20, 5), (1, 13), (40, 3), (20, 20), (9, 31), (27, 35), (9, 1), (9, 29), (16, 25), (46, 41), (41, 9), (24, 6), (39, 30), (35, 14), (8, 11), (10, 37), (13, 41), (30, 40), (29, 40), (37, 37), (41, 26), (5, 4), (20, 40), (41, 5), (12, 31), (7, 23), (28, 23), (17, 25), (4, 29), (27, 0), (28, 31), (45, 15), (3, 4), (1, 22), (31, 16), (38, 20), (28, 4), (9, 38), (15, 39), (41, 32), (28, 1), (24, 36), (14, 22), (7, 12), (11, 0), (1, 6), (3, 32), (4, 18), (8, 7), (0, 9), (15, 15), (41, 39), (4, 32), (39, 8), (32, 9), (34, 25), (36, 23), (12, 33), (42, 37), (36, 35), (11, 16), (23, 5), (0, 30), (22, 7), (44, 37), (16, 27), (30, 11), (36, 21), (18, 34), (1, 17), (1, 34), (12, 15), (22, 17), (8, 3), (9, 6), (16, 7), (46, 21), (3, 27), (44, 41), (4, 14), (5, 13), (13, 1), (20, 10), (44, 22), (4, 33), (16, 34), (24, 9), (0, 24), (13, 27), (47, 35), (9, 10), (0, 7), (10, 10), (17, 8), (23, 26), (14, 19), (10, 31), (33, 32), (14, 26), (3, 18), (31, 8), (5, 34), (9, 20), (28, 30), (47, 28), (46, 15), (47, 23), (3, 15), (7, 24), (39, 28), (26, 11), (46, 11), (41, 1), (47, 5), (31, 3), (26, 35), (13, 14), (25, 17), (44, 10), (8, 9), (34, 38), (0, 31), (9, 16), (27, 32), (33, 40), (45, 16), (29, 21), (6, 34), (37, 23), (37, 31), (18, 41), (16, 39), (6, 31), (10, 26), (26, 26), (4, 10), (26, 25), (1, 25), (6, 37), (46, 32), (13, 10), (37, 24), (31, 21), (8, 35), (10, 29), (0, 8), (22, 3), (14, 21), (24, 37), (24, 24), (4, 17), (13, 19), (41, 19), (43, 29), (44, 25), (37, 5), (6, 36), (27, 4), (41, 31), (12, 10), (45, 29), (16, 29), (16, 41), (13, 12), (17, 41), (1, 26), (21, 24), (45, 18), (29, 39), (21, 21), (15, 23), (3, 5), (5, 15), (13, 24), (25, 37), (9, 37), (39, 40), (21, 25), (19, 10), (42, 29), (19, 8), (1, 14), (28, 38), (46, 16), (38, 13), (29, 23), (32, 24), (26, 8), (8, 10), (1, 15), (15, 28), (47, 26), (6, 33), (18, 33), (30, 35), (41, 41), (0, 6), (11, 29), (1, 1), (0, 3), (8, 12), (37, 7), (8, 17), (17, 10), (27, 3), (19, 13), (24, 27), (15, 20), (16, 15), (25, 24), (44, 3), (39, 27), (13, 17), (29, 4), (36, 22), (47, 4), (0, 21), (13, 25), (28, 32), (13, 9), (31, 35), (12, 36), (42, 16), (34, 7), (38, 35), (28, 39), (27, 28), (9, 4), (6, 26), (30, 25), (1, 3), (0, 26), (3, 23), (22, 15), (33, 30), (9, 30), (41, 15), (30, 12), (28, 24), (38, 6), (22, 39), (41, 24), (2, 11), (26, 40), (1, 9), (18, 6), (2, 2), (19, 21), (12, 1), (29, 27), (29, 18), (37, 17), (43, 12), (17, 29), (45, 22), (37, 12), (8, 32), (43, 37), (46, 27), (2, 5), (33, 11), (42, 11), (41, 27), (10, 19), (8, 38), (18, 32), (25, 11), (0, 4), (13, 34), (36, 6), (30, 32), (0, 11), (8, 20), (23, 22), (22, 18), (26, 16), (9, 33), (33, 24), (5, 28), (43, 25), (43, 20), (45, 3), (47, 25), (24, 35), (8, 39), (37, 9), (18, 25), (1, 37), (25, 39), (16, 38), (17, 23), (16, 22), (3, 29), (35, 0), (29, 24), (15, 40), (9, 40), (13, 38), (22, 2), (8, 14), (31, 19), (11, 20), (46, 1), (0, 5), (28, 13), (39, 23), (35, 1), (40, 4), (37, 32), (47, 22), (12, 5), (29, 12), (34, 4), (26, 31), (28, 0), (19, 35), (0, 33), (35, 9), (27, 39), (47, 11), (30, 10), (12, 8), (40, 12), (17, 4), (4, 25), (19, 11), (45, 13), (41, 22), (46, 0), (45, 21), (45, 32), (20, 24), (32, 11), (0, 39), (26, 37), (24, 39), (9, 2), (22, 23), (11, 35), (24, 15), (2, 37), (12, 0), (34, 11), (42, 27), (6, 32), (18, 7), (20, 3), (32, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 20), (0, 24), (9, 27), (18, 11), (42, 22), (33, 34), (1, 29), (33, 36), (8, 14), (34, 15), (44, 40), (22, 32), (26, 4), (10, 35), (42, 16), (8, 26), (5, 4), (32, 12), (35, 9), (3, 20), (3, 27), (31, 0), (11, 33), (24, 33), (16, 3), (28, 19), (25, 38), (43, 31), (29, 2), (35, 3), (30, 31), (14, 8), (32, 39), (21, 15), (29, 7), (29, 5), (7, 15), (28, 34), (44, 29), (19, 25), (22, 16), (19, 5), (11, 25), (37, 6), (8, 39), (21, 10), (27, 25), (19, 14), (33, 23), (13, 33), (2, 3), (4, 30), (14, 11), (27, 26), (31, 21), (35, 37), (17, 37), (7, 27), (35, 10), (31, 7), (13, 12), (26, 23), (31, 4), (26, 31), (7, 35), (28, 6), (40, 14), (42, 18), (24, 27), (13, 22), (32, 10), (44, 27), (2, 5), (32, 14), (10, 33), (39, 2), (13, 31), (11, 34), (34, 22), (24, 26), (26, 13), (28, 8), (3, 17), (18, 3), (34, 26), (25, 21), (24, 34), (16, 20), (2, 2), (25, 33), (41, 15), (30, 4), (18, 39), (33, 31), (33, 26), (21, 2), (15, 22), (3, 40), (18, 5), (24, 31), (28, 18), (34, 20), (35, 38), (14, 42), (21, 39), (40, 23), (0, 37), (42, 17), (27, 1), (8, 3), (26, 41), (12, 3), (33, 3), (41, 16), (30, 0), (7, 42), (4, 13), (24, 25), (4, 22), (30, 5), (8, 40), (15, 13), (42, 25), (21, 27), (10, 15), (44, 30), (22, 21), (11, 28), (10, 38), (33, 11), (18, 32), (1, 14), (27, 41), (26, 22), (23, 16), (12, 21), (25, 35), (33, 5), (0, 42), (19, 32), (1, 37), (4, 39), (35, 32), (36, 24), (17, 8), (37, 4), (27, 30), (41, 37), (30, 36), (21, 11), (12, 33), (1, 0), (33, 2), (42, 7), (40, 42), (7, 23), (14, 18), (10, 21), (31, 26), (24, 20), (10, 36), (43, 36), (0, 32), (36, 5), (25, 4), (17, 10), (7, 28), (17, 23), (25, 1), (3, 19), (44, 13), (31, 32), (14, 21), (33, 13), (34, 30), (12, 31), (29, 9), (1, 16), (18, 20), (4, 33), (43, 41), (22, 33), (40, 10), (20, 23), (28, 17), (13, 42), (11, 24), (10, 4), (44, 7), (30, 15), (28, 12), (34, 42), (17, 32), (13, 16), (22, 15), (18, 9), (3, 2), (36, 17), (15, 36), (18, 13), (41, 42), (21, 16), (39, 35), (8, 35), (37, 25), (1, 20), (38, 36), (43, 25), (44, 28), (8, 1), (0, 19), (4, 36), (16, 36), (31, 41), (25, 11), (12, 37), (39, 22), (15, 29), (18, 41), (1, 31), (33, 4), (11, 4), (9, 40), (33, 38), (11, 39), (7, 11), (42, 20), (36, 14), (23, 22), (38, 34), (16, 30), (17, 28), (23, 42), (12, 39), (43, 32), (4, 4), (2, 38), (17, 5), (36, 25), (36, 3), (34, 25), (14, 39), (41, 5), (37, 21), (6, 2), (14, 26), (40, 22), (21, 19), (4, 16), (38, 5), (28, 13), (7, 31), (2, 9), (37, 30), (0, 20), (31, 18), (22, 24), (26, 2), (5, 31), (21, 8), (0, 17), (12, 41), (19, 6), (34, 41), (23, 25), (40, 11), (18, 38), (15, 6), (39, 42), (30, 24), (20, 12), (4, 25), (23, 4), (26, 5), (11, 22), (32, 23), (35, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 28), (39, 10), (41, 22), (28, 11), (8, 38), (22, 13), (8, 8), (18, 22), (36, 18), (1, 10), (23, 13), (17, 38), (35, 1), (7, 38), (20, 32), (3, 33), (6, 42), (38, 11), (3, 0), (26, 17), (35, 25), (8, 21), (19, 9), (8, 26), (42, 33), (5, 9), (18, 16), (17, 1), (21, 35), (11, 21), (39, 0), (42, 13), (18, 6), (41, 5), (34, 1), (5, 0), (16, 35), (35, 42), (40, 20), (36, 30), (34, 24), (31, 30), (18, 2), (37, 35), (20, 2), (6, 25), (10, 2), (31, 31), (14, 39), (25, 5), (36, 13), (28, 39), (41, 24), (36, 40), (41, 33), (12, 22), (13, 39), (8, 18), (6, 19), (15, 30), (27, 21), (40, 38), (42, 20), (19, 11), (34, 7), (42, 32), (39, 33), (39, 19), (15, 21), (1, 18), (37, 32), (17, 12), (10, 37), (3, 19), (12, 29), (25, 4), (12, 16), (5, 31), (37, 34), (30, 10), (0, 26), (12, 40), (8, 11), (19, 3), (9, 22), (40, 8), (14, 7), (41, 36), (19, 41), (40, 5), (2, 40), (36, 33), (29, 30), (15, 37), (16, 14), (24, 29), (42, 11), (25, 37), (31, 42), (19, 27), (28, 42), (21, 1), (11, 38), (43, 7), (16, 39), (13, 35), (4, 38), (5, 28), (29, 21), (36, 1), (10, 10), (32, 21), (19, 29), (3, 3), (43, 24), (26, 2), (38, 38), (23, 14), (38, 42), (0, 13), (42, 16), (35, 7), (4, 34), (3, 34), (17, 11), (36, 7), (2, 35), (41, 26), (0, 25), (26, 20), (40, 33), (32, 15), (10, 31), (40, 28), (35, 32), (34, 20), (7, 16), (4, 28), (25, 18), (17, 16), (10, 8), (28, 20), (39, 25), (0, 32), (25, 20), (27, 39), (41, 37), (10, 35), (20, 23), (1, 2), (8, 32), (5, 15), (8, 16), (9, 9), (19, 31), (13, 5), (43, 14), (39, 36), (26, 26), (11, 22), (30, 16), (17, 29), (0, 7), (26, 40), (9, 38), (1, 27), (34, 34), (40, 25), (24, 9), (16, 34), (28, 8), (20, 28), (5, 7), (20, 5), (4, 39), (2, 32), (13, 27), (20, 3), (0, 10), (37, 15), (0, 1), (22, 6), (15, 26), (27, 35), (8, 19), (18, 3), (18, 0), (27, 36), (12, 42), (5, 4), (42, 28), (42, 31), (29, 40), (10, 33), (7, 31), (26, 28), (2, 34), (27, 24), (9, 32), (2, 20), (39, 7), (21, 7), (1, 34), (11, 33), (2, 22), (28, 17), (18, 7), (4, 7), (16, 5), (36, 12), (30, 13), (15, 22), (33, 24), (2, 42), (6, 35), (37, 3), (29, 32), (3, 28), (9, 14), (2, 24), (1, 33), (24, 33), (14, 1), (7, 12), (30, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 23), (6, 17), (39, 13), (13, 21), (1, 42), (35, 17), (1, 1), (27, 14), (30, 38), (9, 44), (12, 1), (30, 20), (41, 9), (20, 9), (36, 2), (39, 39), (43, 8), (38, 41), (21, 5), (42, 31), (38, 29), (44, 15), (29, 43), (37, 14), (25, 43), (42, 0), (29, 31), (13, 19), (45, 29), (8, 8), (29, 23), (24, 12), (17, 28), (34, 16), (14, 14), (34, 23), (5, 36), (4, 11), (39, 26), (28, 11), (45, 28), (1, 21), (43, 11), (30, 31), (36, 11), (27, 18), (42, 16), (8, 35), (28, 0), (42, 8), (4, 6), (38, 12), (40, 12), (27, 38), (3, 11), (3, 33), (41, 22), (14, 12), (42, 5), (34, 31), (24, 5), (4, 16), (16, 5), (13, 38), (30, 4), (2, 6), (7, 4), (29, 37), (29, 4), (26, 14), (36, 8), (34, 42), (43, 16), (13, 22), (35, 6), (36, 4), (46, 25), (43, 38), (2, 7), (26, 43), (22, 42), (25, 15), (8, 41), (11, 17), (39, 25), (39, 19), (1, 15), (15, 21), (25, 33), (4, 40), (9, 11), (16, 44), (9, 23), (31, 14), (43, 36), (46, 38), (1, 0), (29, 11), (18, 18), (29, 40), (35, 9), (14, 40), (21, 33), (2, 39), (34, 5), (42, 13), (43, 32), (36, 19), (21, 7), (12, 10), (37, 24), (38, 26), (38, 24), (4, 37), (40, 7), (6, 35), (0, 36), (20, 37), (20, 34), (34, 32), (37, 16), (25, 16), (36, 18), (30, 39), (7, 17), (6, 34), (7, 7), (9, 33), (12, 31), (37, 4), (18, 26), (44, 38), (31, 15), (43, 24), (4, 0), (34, 1), (42, 25), (45, 22), (10, 27), (19, 5), (7, 34), (33, 39), (16, 16), (12, 23), (19, 3), (39, 32), (41, 6), (5, 7), (25, 27), (9, 8), (41, 28), (24, 10), (22, 30), (18, 10), (11, 11), (38, 36), (39, 4), (38, 15), (34, 10), (36, 30), (14, 30), (20, 15), (46, 2), (34, 26), (18, 30), (6, 4), (19, 16), (35, 43), (40, 29), (1, 24), (6, 22), (3, 6), (31, 16), (32, 0), (18, 3), (20, 21), (0, 43), (32, 11), (7, 26), (13, 33), (1, 31), (36, 28), (35, 26), (13, 3), (0, 40), (24, 25), (30, 42), (19, 25), (34, 29), (31, 40), (14, 5), (26, 17), (15, 39), (40, 42), (19, 8), (40, 15), (0, 33), (40, 37), (14, 21), (41, 36), (19, 34), (3, 21), (43, 13), (35, 2), (40, 3), (8, 24), (9, 18), (22, 11), (20, 40), (4, 42), (29, 5), (28, 33), (25, 24), (23, 33), (11, 27), (12, 33), (5, 9), (35, 3), (37, 44), (39, 16), (18, 38), (6, 20), (12, 18), (5, 6), (14, 28), (34, 37), (8, 44), (35, 0), (6, 14), (7, 24), (32, 18), (40, 28), (30, 5), (24, 13), (38, 4), (36, 34), (39, 35), (30, 22), (17, 22), (34, 22), (17, 24), (43, 25), (9, 10), (21, 20), (37, 22), (6, 38), (24, 28), (29, 8), (14, 34), (37, 36), (9, 43), (8, 13), (38, 2), (15, 24), (23, 32), (32, 13), (3, 10), (21, 22), (46, 42), (20, 17), (46, 18), (5, 34), (5, 16), (30, 36), (15, 43), (12, 4), (41, 40), (18, 1), (17, 2), (6, 13), (30, 26), (33, 35), (41, 2), (43, 14), (22, 19), (24, 39), (5, 39), (11, 19), (22, 9), (23, 38), (27, 23), (35, 21), (41, 35), (46, 12), (39, 44), (43, 9), (45, 5), (12, 30), (1, 5), (32, 40), (2, 30), (28, 18), (5, 19), (16, 14), (17, 40), (2, 28), (10, 19), (36, 0), (42, 15), (4, 7), (10, 38), (1, 38), (6, 32), (28, 17), (37, 33), (31, 34), (1, 19), (9, 0), (45, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 25), (7, 3), (17, 19), (13, 17), (11, 7), (9, 34), (15, 7), (38, 6), (40, 18), (13, 18), (23, 41), (18, 36), (13, 5), (17, 24), (1, 4), (37, 5), (12, 15), (25, 7), (38, 1), (20, 32), (37, 26), (6, 35), (34, 1), (9, 38), (7, 22), (22, 22), (16, 24), (27, 37), (21, 13), (17, 39), (15, 8), (2, 41), (27, 35), (20, 29), (4, 32), (0, 11), (3, 1), (27, 17), (19, 18), (2, 0), (14, 8), (27, 31), (36, 3), (8, 16), (0, 7), (19, 6), (21, 35), (26, 21), (35, 42), (35, 35), (24, 32), (22, 35), (7, 33), (34, 10), (31, 6), (25, 30), (33, 6), (5, 1), (33, 42), (8, 3), (40, 25), (35, 32), (9, 27), (31, 13), (30, 32), (0, 13), (32, 22), (13, 6), (20, 41), (12, 34), (23, 6), (24, 13), (18, 30), (19, 21), (34, 36), (24, 37), (12, 12), (18, 16), (30, 18), (40, 32), (19, 19), (19, 26), (15, 29), (40, 12), (13, 24), (19, 32), (21, 23), (13, 39), (1, 19), (24, 14), (14, 11), (40, 1), (6, 16), (14, 33), (13, 2), (6, 26), (7, 38), (23, 22), (1, 35), (18, 15), (39, 33), (7, 9), (4, 18), (28, 2), (40, 22), (32, 24), (38, 21), (21, 7), (28, 12), (19, 9), (20, 1), (24, 21), (17, 9), (22, 7), (29, 41), (7, 0), (40, 0), (40, 34), (19, 17), (1, 28), (10, 28), (3, 27), (0, 17), (14, 5), (31, 31), (10, 30), (10, 2), (34, 35), (15, 28), (24, 29), (39, 13), (23, 29), (32, 12), (17, 37), (25, 32), (2, 7), (27, 36), (36, 10), (36, 27), (32, 40), (21, 27), (19, 37), (12, 30), (9, 7), (5, 16), (2, 30), (20, 9), (10, 41), (29, 13), (22, 13), (0, 36), (19, 30), (40, 19), (29, 15), (33, 15), (17, 3), (31, 28), (2, 2), (10, 11), (13, 34), (6, 5), (35, 40), (7, 2), (28, 4), (28, 13), (18, 9), (23, 5), (20, 38), (37, 30), (18, 21), (18, 24), (6, 8), (24, 5), (19, 0), (3, 5), (19, 23), (28, 24), (2, 24), (39, 16), (37, 40), (36, 42), (24, 26), (29, 24), (18, 25), (11, 39), (22, 31), (32, 14), (17, 40), (38, 5), (3, 4), (38, 7), (22, 23), (7, 24), (39, 7), (7, 14), (32, 20), (23, 10), (28, 33), (19, 34), (22, 15), (12, 22), (28, 20), (11, 10), (28, 3), (37, 41), (5, 5), (1, 38), (12, 41), (30, 22), (9, 19), (31, 16), (1, 10), (29, 35), (1, 2), (21, 19), (12, 5), (7, 19), (39, 9), (29, 12), (39, 24), (25, 26), (9, 14), (29, 36), (1, 24), (29, 20), (17, 28), (28, 10), (34, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 22), (44, 31), (10, 12), (16, 44), (17, 26), (35, 7), (17, 16), (5, 28), (1, 32), (33, 11), (28, 9), (37, 27), (19, 44), (7, 37), (23, 35), (15, 38), (30, 45), (41, 3), (6, 45), (36, 35), (8, 16), (27, 21), (42, 34), (47, 39), (16, 37), (5, 10), (13, 44), (21, 42), (22, 41), (42, 12), (29, 21), (16, 25), (34, 44), (15, 27), (13, 31), (39, 40), (32, 17), (28, 34), (5, 30), (41, 32), (16, 43), (30, 22), (22, 5), (19, 41), (20, 44), (16, 14), (11, 25), (28, 45), (0, 27), (39, 14), (0, 7), (11, 31), (41, 45), (0, 3), (33, 45), (33, 25), (27, 4), (15, 26), (26, 17), (7, 23), (16, 19), (24, 45), (1, 19), (2, 37), (24, 38), (41, 38), (19, 37), (1, 14), (21, 19), (32, 37), (27, 7), (30, 14), (35, 21), (33, 5), (13, 17), (40, 18), (9, 41), (1, 33), (16, 0), (1, 4), (34, 34), (18, 26), (34, 31), (24, 43), (42, 46), (39, 12), (12, 35), (38, 19), (10, 39), (0, 37), (24, 9), (36, 12), (21, 29), (9, 11), (34, 21), (0, 21), (38, 4), (10, 26), (37, 12), (22, 8), (14, 5), (13, 36), (21, 25), (31, 0), (21, 2), (10, 15), (23, 14), (34, 41), (17, 43), (48, 29), (1, 27), (40, 45), (32, 24), (0, 35), (42, 17), (36, 46), (26, 39), (29, 11), (46, 40), (27, 0), (41, 22), (28, 6), (44, 40), (29, 4), (37, 11), (20, 31), (32, 20), (31, 31), (18, 1), (24, 6), (16, 21), (48, 27), (22, 40), (41, 40), (19, 20), (26, 22), (46, 32), (22, 17), (3, 41), (6, 17), (47, 19), (9, 0), (13, 32), (21, 27), (3, 8), (0, 33), (32, 38), (47, 36), (42, 0), (22, 13), (36, 8), (36, 18), (40, 10), (4, 34), (8, 7), (2, 30), (28, 13), (15, 6), (19, 8), (43, 17), (35, 28), (32, 39), (36, 24), (28, 20), (39, 39), (34, 25), (23, 20), (3, 38), (11, 15), (37, 43), (45, 29), (44, 33), (45, 8), (17, 29), (33, 34), (44, 24), (16, 5), (2, 31), (40, 44), (9, 10), (27, 12), (1, 21), (4, 18), (6, 36), (3, 31), (45, 23), (3, 10), (43, 21), (4, 1), (44, 39), (7, 33), (40, 36), (5, 40), (10, 2), (7, 34), (10, 23), (48, 4), (1, 38), (45, 17), (0, 25), (28, 27), (26, 25), (13, 43), (29, 26), (42, 28), (32, 13), (25, 3), (46, 31), (45, 16), (2, 0), (15, 13), (32, 27), (35, 8), (17, 40), (10, 11), (48, 5), (9, 46), (45, 36), (2, 1), (35, 29), (15, 44), (39, 43), (31, 2), (38, 2), (40, 43), (26, 42), (48, 6), (46, 8), (25, 27), (16, 7), (30, 2), (44, 26), (35, 38), (47, 17), (36, 13), (8, 41), (43, 42), (18, 44), (35, 20), (15, 30), (9, 6), (35, 36), (18, 23), (2, 27), (11, 36), (9, 14), (29, 30), (19, 36), (2, 15), (27, 37), (13, 35), (40, 14), (20, 1), (17, 46), (12, 29), (32, 44), (23, 30), (16, 39), (12, 30), (47, 43), (0, 42), (34, 14), (25, 20), (37, 17), (28, 19), (3, 13), (5, 36), (0, 17), (38, 41), (26, 31), (3, 23), (1, 45), (32, 21), (40, 9), (47, 45), (8, 0), (12, 19), (15, 24), (24, 26), (5, 6), (17, 4), (9, 34), (44, 14), (21, 4), (14, 2), (41, 41), (32, 8), (32, 2), (15, 5), (18, 38), (18, 22), (47, 18), (1, 34), (20, 2), (28, 26), (44, 35), (9, 29), (15, 42), (43, 4), (9, 2), (4, 46), (47, 6), (7, 32), (25, 1), (48, 42), (20, 14), (6, 46), (24, 29), (47, 21), (30, 25), (7, 41), (44, 17), (30, 17), (36, 21), (40, 11), (20, 32), (30, 12), (3, 22), (43, 25), (32, 18), (34, 37), (41, 10), (23, 0), (6, 26), (9, 28), (39, 36), (27, 19), (7, 38), (18, 8), (42, 37), (21, 31), (23, 27), (11, 40), (32, 6), (19, 34), (8, 38), (38, 17), (38, 14), (32, 34), (45, 15), (0, 23), (39, 17), (30, 19), (40, 17), (35, 15), (48, 7), (5, 29), (44, 11), (13, 42), (22, 36), (14, 33), (12, 45), (5, 12), (43, 16), (46, 25), (4, 31), (27, 35), (19, 21), (48, 24), (47, 23), (25, 11), (36, 2), (20, 36), (33, 17), (23, 22), (37, 18), (25, 44), (42, 14), (27, 43), (31, 8), (41, 1), (8, 40), (23, 39), (45, 34), (29, 36), (39, 38), (31, 36), (14, 7), (28, 10), (46, 37), (20, 24), (7, 18), (47, 11), (37, 15), (16, 12), (5, 0), (34, 45), (9, 43), (40, 3), (41, 36), (27, 18), (42, 5), (43, 37), (40, 38), (34, 26), (29, 18), (35, 43), (2, 6), (1, 0), (39, 5), (25, 35), (15, 37), (33, 18), (40, 35), (12, 12), (6, 19), (7, 11), (44, 8), (42, 38), (1, 39), (31, 11), (27, 36), (42, 26), (10, 38), (14, 15), (1, 8), (11, 12), (44, 10), (17, 17), (26, 15), (8, 24), (40, 22), (11, 26), (37, 4), (47, 30), (46, 41), (22, 14), (17, 18), (1, 46), (34, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 39), (38, 39), (39, 6), (1, 2), (21, 25), (39, 9), (20, 17), (35, 18), (10, 21), (18, 41), (16, 22), (33, 33), (11, 42), (25, 36), (37, 9), (40, 24), (6, 13), (8, 32), (35, 39), (7, 11), (40, 19), (40, 3), (22, 10), (14, 22), (13, 32), (12, 3), (35, 28), (15, 36), (36, 25), (18, 39), (34, 25), (0, 14), (39, 22), (39, 14), (40, 33), (6, 19), (0, 23), (21, 39), (15, 7), (0, 7), (40, 18), (35, 11), (39, 32), (17, 32), (39, 1), (37, 29), (16, 8), (4, 25), (14, 2), (29, 19), (38, 20), (17, 36), (15, 42), (33, 4), (38, 9), (23, 41), (8, 25), (23, 12), (13, 26), (3, 4), (24, 19), (32, 7), (37, 26), (19, 39), (23, 40), (32, 8), (6, 14), (32, 40), (1, 23), (15, 33), (17, 38), (0, 11), (5, 16), (6, 5), (27, 4), (4, 39), (4, 13), (8, 34), (10, 11), (1, 22), (32, 31), (3, 18), (36, 33), (17, 12), (1, 38), (30, 23), (24, 42), (32, 37), (4, 6), (24, 10), (18, 17), (15, 37), (37, 23), (37, 28), (30, 41), (33, 12), (32, 28), (20, 20), (5, 36), (7, 19), (18, 40), (24, 31), (7, 16), (27, 9), (18, 31), (18, 21), (4, 0), (9, 17), (5, 40), (21, 38), (16, 14), (5, 12), (15, 1), (10, 20), (3, 14), (28, 36), (28, 0), (22, 9), (2, 12), (4, 15), (19, 35), (35, 37), (13, 28), (31, 29), (40, 34), (36, 15), (14, 31), (36, 23), (12, 17), (33, 41), (25, 33), (9, 6), (14, 5), (35, 19), (28, 14), (30, 42), (7, 6), (19, 31), (14, 9), (30, 9), (9, 40), (17, 1), (32, 5), (16, 39), (12, 15), (28, 12), (35, 5), (0, 33), (20, 30), (26, 7), (21, 27), (14, 39), (24, 41), (4, 3), (14, 16), (6, 4), (29, 40), (18, 3), (38, 14), (7, 7), (7, 42), (17, 25), (29, 7), (29, 32), (1, 12), (31, 11), (1, 14), (1, 34), (10, 13), (20, 10), (15, 30), (6, 22), (15, 21), (7, 12), (25, 22), (29, 18), (17, 14), (25, 32), (17, 13), (9, 22), (20, 25), (25, 29), (5, 2), (5, 23), (17, 20), (12, 31), (11, 32), (39, 12), (9, 34), (12, 13), (0, 6), (8, 1), (3, 0), (24, 23), (22, 33), (21, 10), (40, 15), (10, 16), (29, 36), (23, 34), (4, 30), (23, 26), (21, 13), (38, 7), (20, 3), (9, 37), (0, 26), (20, 11), (30, 13), (7, 28), (28, 5), (27, 35), (8, 27), (2, 11), (13, 24), (2, 41), (8, 10), (21, 40), (22, 13), (15, 16), (18, 32), (5, 39), (28, 10), (16, 19), (32, 23), (35, 35), (13, 1), (1, 31), (29, 10), (33, 31), (21, 6), (30, 8), (24, 8), (27, 25), (39, 36), (13, 14), (24, 4), (34, 13), (14, 19), (28, 27), (13, 16), (2, 32), (10, 2), (1, 18), (19, 21), (22, 25), (39, 7), (35, 21), (28, 15), (31, 26), (39, 37), (17, 30), (23, 32), (11, 21), (25, 0), (14, 3), (7, 3), (3, 39), (16, 35), (17, 34), (22, 18), (22, 1), (24, 24), (12, 7), (34, 11), (19, 24), (24, 30), (5, 41), (29, 37), (29, 27), (31, 20), (8, 26), (32, 20), (10, 25), (13, 35), (16, 27), (12, 22), (1, 3), (30, 29), (3, 38), (12, 18), (10, 23), (20, 15), (3, 29), (26, 17), (36, 32), (36, 5), (37, 24), (15, 25), (7, 37), (20, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 21), (42, 22), (41, 9), (20, 6), (37, 39), (45, 26), (44, 34), (8, 5), (0, 18), (19, 33), (37, 3), (28, 12), (31, 20), (33, 26), (3, 25), (1, 3), (45, 10), (16, 8), (25, 39), (41, 15), (20, 18), (13, 12), (45, 23), (22, 35), (33, 34), (35, 6), (35, 31), (5, 10), (29, 27), (6, 26), (6, 33), (32, 19), (24, 10), (1, 42), (7, 35), (12, 36), (8, 19), (32, 26), (18, 31), (5, 18), (14, 30), (13, 13), (26, 10), (45, 9), (6, 16), (27, 9), (25, 22), (32, 3), (8, 4), (6, 6), (0, 41), (27, 17), (11, 41), (1, 22), (43, 23), (23, 21), (42, 30), (24, 33), (31, 16), (6, 7), (17, 40), (38, 1), (26, 17), (5, 11), (38, 6), (7, 4), (12, 15), (43, 30), (3, 3), (13, 38), (43, 28), (6, 1), (9, 3), (24, 34), (44, 9), (17, 20), (34, 18), (23, 7), (33, 8), (21, 15), (43, 20), (32, 33), (32, 8), (39, 38), (1, 10), (36, 17), (27, 1), (22, 29), (20, 5), (38, 10), (0, 13), (16, 3), (9, 11), (7, 26), (36, 5), (13, 9), (9, 34), (40, 10), (44, 36), (8, 6), (8, 14), (32, 30), (15, 19), (9, 31), (44, 19), (18, 12), (29, 42), (33, 23), (45, 4), (17, 27), (2, 19), (43, 12), (13, 40), (38, 16), (27, 42), (4, 20), (0, 35), (8, 31), (16, 13), (15, 33), (23, 33), (44, 37), (34, 17), (6, 2), (22, 12), (32, 10), (10, 13), (38, 31), (19, 13), (37, 22), (9, 37), (14, 6), (42, 39), (34, 1), (10, 20), (32, 24), (25, 16), (19, 38), (14, 25), (9, 2), (5, 15), (5, 25), (15, 20), (32, 36), (42, 0), (23, 38), (44, 27), (30, 35), (41, 7), (17, 25), (6, 22), (45, 13), (36, 16), (7, 3), (33, 27), (31, 19), (33, 14), (26, 19), (32, 41), (34, 24), (14, 37), (45, 36), (4, 32), (16, 7), (40, 40), (30, 22), (35, 34), (33, 13), (11, 42), (9, 6), (19, 11), (26, 12), (34, 37), (12, 6), (37, 34), (9, 12), (2, 16), (40, 32), (34, 40), (24, 15), (44, 8), (35, 20), (17, 24), (28, 21), (25, 11), (44, 5), (19, 39), (35, 33), (6, 20), (10, 11), (19, 40), (15, 4), (33, 32), (30, 27), (37, 17), (42, 16), (19, 10), (45, 16), (6, 38), (23, 39), (11, 23), (5, 9), (37, 7), (34, 19), (45, 5), (20, 26), (1, 29), (27, 38), (25, 25), (24, 20), (0, 20), (21, 3), (29, 6), (42, 38), (22, 4), (36, 4), (43, 25), (27, 19), (36, 23), (27, 8), (24, 31), (37, 26), (18, 36), (7, 36), (45, 30), (4, 36), (20, 2), (26, 5), (32, 25), (31, 27), (29, 11), (29, 3), (34, 9), (38, 25), (3, 37), (26, 25), (28, 13), (34, 26), (39, 23), (29, 26), (14, 24), (10, 17), (4, 31), (31, 30), (2, 27), (34, 4), (35, 8), (5, 21), (39, 4), (20, 27), (45, 1), (23, 3), (43, 9), (25, 35), (25, 4), (3, 10), (21, 26), (12, 41), (3, 20), (37, 18), (29, 4), (8, 29), (32, 4), (24, 14), (27, 13), (3, 39), (7, 25), (39, 2), (19, 16), (30, 41), (31, 41), (11, 18), (37, 14), (39, 32), (30, 39), (31, 9), (31, 26), (38, 0), (17, 13), (18, 7), (41, 34), (25, 38), (18, 1), (40, 7), (11, 19), (12, 22), (40, 1), (29, 5), (23, 31), (35, 38), (3, 19), (11, 33), (2, 2), (43, 13), (23, 20), (17, 2), (43, 4), (28, 15), (20, 9), (16, 16), (2, 3), (21, 12), (42, 2), (29, 24), (38, 42), (12, 25), (24, 24), (41, 25), (14, 38), (42, 10), (30, 11), (28, 14), (5, 41), (14, 29), (45, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 11), (30, 20), (17, 15), (2, 26), (35, 40), (4, 3), (28, 40), (41, 24), (19, 10), (34, 37), (12, 39), (17, 43), (36, 14), (29, 6), (5, 12), (41, 43), (11, 31), (37, 1), (40, 24), (29, 37), (20, 23), (23, 20), (6, 2), (1, 38), (44, 28), (5, 36), (46, 38), (17, 25), (18, 26), (0, 7), (0, 21), (7, 5), (40, 34), (28, 14), (4, 19), (7, 30), (39, 25), (4, 6), (2, 35), (27, 22), (10, 36), (22, 17), (37, 23), (18, 16), (14, 16), (46, 10), (21, 26), (41, 27), (36, 13), (26, 27), (17, 19), (13, 17), (18, 9), (35, 2), (44, 42), (34, 6), (13, 36), (40, 7), (14, 14), (42, 39), (11, 34), (30, 12), (18, 1), (12, 3), (16, 25), (10, 15), (31, 19), (24, 35), (22, 2), (31, 18), (27, 5), (0, 26), (13, 41), (10, 0), (38, 5), (40, 8), (11, 26), (43, 13), (6, 15), (25, 15), (40, 40), (41, 12), (38, 41), (14, 26), (35, 34), (22, 25), (2, 2), (20, 33), (38, 36), (3, 15), (31, 25), (20, 3), (34, 40), (23, 26), (8, 23), (32, 40), (1, 9), (7, 13), (6, 21), (7, 34), (5, 25), (42, 21), (3, 3), (27, 8), (19, 9), (7, 11), (14, 6), (28, 9), (20, 5), (1, 2), (3, 43), (12, 34), (10, 20), (45, 16), (15, 5), (46, 27), (32, 5), (20, 32), (28, 7), (10, 4), (31, 2), (34, 23), (32, 38), (40, 6), (12, 5), (36, 23), (17, 14), (43, 39), (21, 9), (12, 26), (8, 43), (14, 34), (19, 21), (19, 29), (23, 19), (13, 34), (22, 24), (2, 4), (23, 2), (32, 13), (32, 32), (29, 33), (11, 0), (36, 10), (18, 6), (10, 10), (5, 37), (36, 19), (8, 18), (4, 41), (7, 1), (19, 26), (17, 41), (30, 17), (6, 12), (32, 41), (33, 17), (28, 36), (35, 8), (45, 34), (13, 37), (33, 16), (42, 20), (3, 35), (8, 13), (17, 33), (8, 27), (2, 31), (45, 27), (29, 34), (29, 43), (30, 32), (7, 38), (10, 37), (0, 23), (17, 21), (14, 2), (4, 26), (20, 14), (28, 2), (5, 41), (22, 21), (34, 13), (6, 16), (30, 38), (37, 21), (6, 22), (7, 20), (17, 26), (37, 0), (28, 3), (13, 8), (31, 17), (26, 36), (43, 22), (32, 4), (6, 20), (20, 29), (11, 17), (5, 8), (9, 43), (4, 23), (15, 17), (44, 10), (31, 43), (26, 15), (33, 10), (8, 24), (4, 1), (39, 24), (38, 23), (27, 26), (11, 14), (4, 36), (29, 16), (9, 21), (20, 7), (28, 10), (23, 43), (12, 11), (36, 15), (32, 21), (30, 8), (25, 9), (45, 4), (3, 37), (6, 28), (42, 7), (16, 9), (43, 6), (32, 1), (15, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 28), (14, 5), (17, 36), (12, 27), (27, 4), (28, 8), (28, 25), (24, 30), (29, 23), (39, 38), (14, 22), (27, 24), (19, 2), (27, 32), (42, 20), (16, 34), (31, 29), (33, 0), (41, 39), (12, 4), (9, 25), (38, 2), (40, 5), (39, 36), (9, 27), (30, 16), (29, 38), (42, 32), (34, 30), (25, 19), (10, 29), (42, 12), (1, 38), (10, 8), (19, 16), (22, 24), (31, 0), (35, 26), (35, 18), (42, 14), (28, 15), (31, 30), (38, 3), (12, 6), (9, 32), (36, 36), (3, 19), (15, 6), (32, 18), (25, 36), (20, 15), (5, 25), (20, 2), (23, 25), (12, 16), (12, 37), (38, 14), (2, 9), (4, 11), (11, 23), (25, 37), (14, 2), (25, 16), (12, 30), (13, 9), (7, 14), (31, 9), (32, 28), (33, 11), (9, 4), (27, 40), (21, 22), (8, 3), (0, 16), (37, 1), (28, 16), (5, 28), (40, 8), (7, 5), (2, 27), (19, 40), (0, 22), (0, 6), (1, 29), (21, 31), (33, 29), (14, 3), (29, 16), (42, 33), (19, 6), (39, 2), (35, 25), (3, 15), (17, 2), (36, 8), (30, 18), (24, 28), (31, 10), (6, 26), (16, 18), (15, 1), (27, 28), (17, 34), (32, 10), (26, 30), (5, 5), (6, 5), (14, 39), (32, 20), (9, 33), (8, 15), (12, 26), (19, 38), (5, 2), (31, 22), (16, 28), (38, 36), (24, 31), (38, 33), (19, 27), (5, 21), (2, 22), (41, 15), (12, 24), (35, 8), (39, 4), (16, 12), (29, 26), (37, 12), (23, 12), (42, 16), (20, 27), (36, 4), (41, 35), (33, 35), (10, 25), (18, 26), (34, 9), (39, 1), (32, 15), (7, 2), (34, 31), (40, 35), (15, 0), (18, 19), (20, 34), (13, 19), (18, 32), (11, 34), (16, 40), (25, 0), (27, 25), (6, 7), (0, 4), (25, 28), (17, 11), (15, 30), (13, 0), (3, 21), (31, 34), (33, 17), (20, 16), (7, 13), (11, 19), (6, 4), (38, 1), (10, 5), (13, 34), (20, 17), (22, 1), (34, 11), (26, 28), (9, 7), (20, 7), (35, 29), (23, 39), (39, 33), (17, 7), (15, 32), (6, 32), (15, 13), (14, 8), (0, 2), (3, 0), (21, 6), (4, 3), (10, 40), (35, 30), (24, 8), (37, 6), (31, 36), (16, 4), (39, 23), (38, 28), (32, 29), (29, 37), (0, 28), (27, 16), (14, 23), (40, 36), (2, 29), (32, 22), (31, 20), (13, 33), (11, 25), (7, 18), (33, 28), (7, 6), (12, 38), (5, 31), (37, 30), (1, 14), (34, 29), (22, 19), (29, 30), (39, 39), (1, 10), (17, 20), (26, 40), (34, 20), (15, 14), (1, 26), (30, 21), (39, 34), (6, 29), (20, 24), (40, 6), (21, 9), (3, 18), (40, 0), (41, 40), (39, 3), (31, 12), (29, 9), (7, 23), (2, 35), (7, 29), (11, 17), (6, 28), (27, 27), (5, 26), (23, 36), (37, 16), (15, 22), (14, 30), (13, 6), (5, 34), (2, 26), (36, 22), (22, 40), (3, 4), (11, 0), (6, 35), (42, 10), (40, 20), (26, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 23), (14, 38), (38, 17), (9, 15), (26, 35), (32, 42), (29, 10), (42, 20), (5, 39), (24, 29), (15, 11), (20, 23), (15, 31), (17, 5), (38, 30), (40, 22), (4, 4), (43, 15), (18, 44), (30, 12), (24, 34), (3, 14), (18, 28), (7, 7), (1, 39), (4, 35), (42, 39), (17, 26), (41, 32), (42, 22), (41, 2), (4, 10), (8, 41), (2, 26), (18, 2), (4, 2), (12, 16), (23, 4), (14, 9), (17, 7), (10, 11), (36, 6), (16, 35), (28, 37), (46, 42), (37, 20), (44, 34), (42, 5), (35, 43), (21, 10), (43, 27), (43, 23), (19, 8), (6, 31), (32, 13), (47, 39), (22, 18), (22, 10), (5, 23), (34, 27), (31, 11), (1, 43), (9, 26), (36, 3), (24, 5), (0, 6), (35, 37), (28, 15), (30, 37), (41, 37), (21, 26), (28, 25), (28, 29), (14, 23), (46, 7), (40, 33), (13, 38), (30, 43), (31, 10), (31, 2), (37, 36), (35, 38), (17, 4), (27, 36), (14, 42), (7, 15), (28, 38), (26, 44), (24, 15), (32, 38), (41, 10), (11, 13), (37, 27), (7, 39), (30, 11), (15, 33), (2, 15), (10, 40), (32, 7), (9, 28), (43, 14), (36, 42), (13, 34), (43, 24), (2, 22), (30, 9), (3, 35), (35, 34), (20, 12), (5, 6), (42, 25), (3, 20), (33, 27), (11, 39), (24, 30), (32, 41), (31, 21), (17, 17), (9, 24), (40, 31), (8, 3), (44, 5), (39, 30), (46, 18), (33, 15), (37, 13), (37, 12), (13, 23), (42, 41), (19, 10), (12, 19), (9, 1), (23, 9), (1, 1), (19, 39), (12, 6), (8, 14), (28, 12), (6, 38), (41, 19), (1, 23), (10, 2), (42, 6), (41, 23), (11, 11), (11, 32), (4, 25), (24, 0), (42, 7), (12, 25), (46, 38), (22, 9), (14, 12), (34, 18), (28, 9), (32, 9), (29, 31), (12, 15), (31, 15), (1, 35), (23, 30), (2, 3), (17, 22), (4, 27), (11, 14), (45, 44), (25, 35), (34, 22), (29, 0), (3, 24), (7, 32), (3, 32), (33, 8), (30, 26), (32, 12), (14, 11), (36, 24), (22, 42), (36, 30), (25, 6), (23, 12), (21, 8), (23, 37), (12, 43), (29, 6), (26, 36), (22, 22), (24, 36), (19, 15), (36, 2), (27, 8), (38, 33), (36, 19), (0, 5), (23, 42), (23, 1), (30, 6), (44, 12), (25, 13), (35, 21), (28, 24), (15, 30), (15, 37), (7, 25), (1, 20), (8, 17), (28, 14), (41, 34), (7, 19), (10, 22), (25, 36), (11, 17), (41, 39), (18, 36), (21, 24), (1, 33), (26, 12), (28, 42), (19, 6), (46, 24), (4, 28), (21, 5), (42, 34), (7, 9), (28, 22), (26, 13), (37, 42), (46, 35), (4, 29), (20, 7), (45, 35), (39, 9), (36, 29), (28, 34), (3, 38), (34, 40), (42, 28), (43, 21), (11, 36), (2, 19), (18, 38), (0, 26), (8, 39), (1, 16), (44, 21), (35, 32), (35, 26), (32, 30), (6, 18), (40, 12), (16, 38), (23, 15), (13, 13), (15, 21), (47, 25), (10, 28), (19, 33), (27, 11), (10, 16), (9, 40), (6, 30), (47, 27), (12, 13), (34, 8), (10, 32), (4, 8), (26, 39), (46, 29), (27, 43), (10, 21), (23, 21), (38, 10), (9, 9), (8, 27), (27, 10), (39, 25), (41, 17), (41, 43), (44, 33), (7, 31), (17, 16), (24, 26), (20, 30), (36, 38), (37, 17), (39, 21), (25, 23), (20, 44), (5, 26), (18, 6), (45, 17), (10, 34), (2, 38), (22, 6), (0, 4), (0, 29), (25, 5), (29, 34), (14, 43), (29, 32), (18, 40), (26, 0), (31, 17), (1, 27), (18, 32), (38, 23), (43, 7), (18, 3), (22, 2), (21, 3), (47, 33), (41, 44), (17, 23), (33, 18), (8, 9), (26, 30), (31, 18), (26, 23), (11, 41), (4, 19), (40, 34), (42, 32), (28, 5), (10, 43), (20, 8), (37, 38), (3, 29), (35, 1), (37, 40), (43, 26), (43, 43), (41, 0), (22, 35), (5, 22), (40, 39), (40, 43), (24, 31), (8, 10), (7, 36), (46, 39), (43, 31), (44, 17), (13, 4), (30, 0), (47, 26), (23, 28), (37, 32), (44, 10), (5, 28), (34, 17), (37, 44), (22, 28), (32, 5), (5, 20), (2, 2), (8, 12), (15, 17), (18, 43), (22, 14), (29, 37), (17, 43), (27, 0), (12, 26), (14, 32), (45, 9), (0, 42), (16, 26), (38, 21), (7, 1), (32, 39), (36, 8), (33, 31), (43, 40), (32, 3), (31, 1), (30, 39), (36, 9), (27, 41), (22, 41), (29, 17), (14, 44), (3, 26), (15, 29), (13, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 3), (26, 35), (17, 38), (29, 6), (14, 2), (5, 35), (3, 42), (27, 0), (7, 4), (38, 10), (38, 41), (34, 39), (4, 18), (23, 48), (37, 2), (30, 6), (18, 38), (19, 26), (10, 47), (20, 37), (14, 24), (8, 47), (27, 16), (39, 42), (15, 17), (9, 9), (40, 32), (6, 47), (30, 29), (13, 48), (33, 31), (29, 35), (35, 4), (16, 14), (11, 8), (7, 20), (31, 1), (27, 29), (40, 7), (19, 3), (34, 42), (6, 36), (19, 45), (33, 24), (0, 37), (24, 26), (31, 24), (14, 8), (24, 20), (6, 28), (26, 32), (24, 38), (0, 18), (4, 39), (34, 12), (16, 3), (37, 24), (4, 45), (8, 40), (4, 41), (2, 31), (17, 39), (24, 42), (6, 40), (34, 29), (23, 21), (34, 44), (16, 28), (6, 35), (30, 15), (7, 8), (30, 22), (16, 5), (28, 45), (16, 22), (37, 44), (31, 46), (11, 25), (21, 17), (26, 33), (24, 24), (40, 10), (32, 15), (0, 14), (19, 24), (37, 34), (33, 34), (10, 1), (3, 17), (4, 48), (9, 3), (34, 27), (11, 26), (21, 33), (31, 9), (24, 1), (6, 42), (29, 33), (25, 28), (17, 6), (13, 35), (29, 46), (16, 29), (15, 26), (6, 45), (5, 2), (16, 25), (33, 44), (0, 4), (33, 14), (40, 25), (22, 0), (34, 19), (1, 1), (25, 19), (27, 28), (34, 25), (14, 23), (38, 35), (22, 24), (32, 30), (21, 27), (37, 6), (20, 17), (14, 28), (31, 31), (25, 36), (1, 32), (0, 46), (34, 11), (15, 25), (0, 39), (24, 27), (30, 32), (7, 22), (10, 11), (40, 14), (10, 37), (14, 18), (29, 34), (8, 12), (15, 34), (21, 31), (25, 22), (9, 41), (1, 33), (39, 1), (23, 4), (2, 36), (7, 47), (27, 1), (13, 11), (36, 35), (36, 36), (9, 17), (36, 33), (8, 1), (39, 20), (17, 8), (16, 41), (29, 19), (2, 9), (32, 33), (32, 28), (32, 21), (26, 1), (10, 25), (17, 24), (20, 7), (28, 26), (16, 45), (9, 32), (2, 26), (33, 13), (36, 34), (1, 45), (40, 24), (12, 0), (20, 36), (33, 10), (15, 11), (25, 11), (5, 48), (24, 37), (4, 35), (29, 7), (38, 23), (8, 3), (37, 37), (29, 15), (25, 4), (5, 47), (1, 10), (23, 43), (32, 1), (39, 45), (24, 4), (26, 36), (27, 35), (22, 37), (9, 23), (0, 22), (15, 20), (5, 0), (36, 27), (18, 30), (37, 21), (40, 26), (4, 3), (8, 21), (35, 37), (0, 8), (16, 4), (4, 42), (6, 39), (39, 46), (21, 1), (32, 26), (28, 21), (8, 34), (19, 44), (7, 32), (1, 48), (21, 39), (35, 15), (31, 47), (33, 3), (34, 9), (6, 41), (13, 32), (39, 41), (9, 10), (6, 2), (13, 9), (17, 11), (14, 16), (27, 11), (30, 4), (18, 41), (2, 18), (34, 26), (4, 27), (38, 40), (32, 39), (28, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (47, 21), (43, 3), (36, 22), (15, 16), (15, 4), (10, 16), (48, 19), (40, 34), (22, 32), (31, 9), (5, 15), (47, 12), (46, 28), (21, 5), (17, 3), (19, 4), (15, 10), (33, 5), (21, 32), (36, 11), (34, 21), (20, 1), (44, 1), (31, 16), (16, 26), (7, 7), (1, 30), (22, 24), (26, 7), (4, 8), (16, 32), (38, 8), (3, 33), (24, 32), (17, 19), (10, 38), (9, 16), (16, 5), (28, 10), (7, 19), (33, 36), (44, 25), (21, 36), (39, 37), (9, 34), (42, 16), (1, 32), (35, 10), (21, 31), (5, 19), (1, 17), (13, 27), (20, 13), (37, 0), (32, 32), (17, 22), (42, 23), (4, 33), (11, 6), (0, 9), (16, 21), (11, 3), (33, 26), (7, 22), (3, 0), (12, 28), (29, 43), (4, 41), (39, 42), (0, 12), (17, 20), (32, 5), (0, 14), (20, 38), (2, 24), (29, 14), (42, 38), (15, 12), (14, 27), (17, 10), (28, 13), (37, 19), (13, 42), (11, 9), (9, 20), (31, 11), (15, 7), (45, 11), (43, 9), (30, 24), (25, 27), (21, 1), (10, 25), (45, 20), (27, 23), (22, 36), (24, 34), (32, 40), (14, 8), (13, 33), (2, 15), (29, 37), (26, 31), (12, 9), (27, 33), (13, 13), (4, 32), (38, 15), (18, 26), (14, 12), (6, 22), (0, 24), (17, 31), (21, 35), (6, 36), (25, 37), (8, 25), (37, 12), (25, 7), (46, 7), (1, 29), (16, 2), (40, 38), (42, 26), (1, 27), (40, 15), (2, 9), (34, 9), (17, 34), (23, 2), (15, 21), (6, 42), (30, 19), (13, 41), (33, 31), (38, 30), (4, 5), (11, 39), (17, 0), (11, 24), (12, 30), (0, 35), (29, 9), (28, 34), (11, 16), (33, 15), (24, 42), (46, 18), (46, 2), (18, 19), (31, 26), (34, 30), (44, 13), (19, 22), (13, 7), (47, 27), (36, 3), (39, 10), (23, 43), (31, 0), (14, 30), (4, 31), (34, 36), (2, 6), (23, 39), (39, 9), (22, 3), (24, 15), (33, 22), (17, 14), (16, 20), (39, 0), (22, 15), (43, 19), (23, 27), (4, 23), (14, 5), (16, 7), (15, 37), (48, 15), (37, 1), (41, 35), (40, 5), (9, 43), (41, 8), (45, 13), (40, 22), (41, 20), (20, 19), (32, 17), (18, 3), (37, 41), (29, 10), (6, 34), (3, 24), (36, 21), (0, 28), (39, 43), (1, 35), (28, 23), (1, 9), (26, 16), (33, 23), (36, 14), (19, 34), (41, 13), (21, 0), (37, 13), (33, 19), (26, 3), (0, 15), (27, 19), (3, 26), (11, 27), (8, 28), (8, 1), (45, 30), (7, 5), (38, 19), (29, 15), (42, 6), (41, 6), (3, 9), (22, 28), (38, 21), (28, 31), (24, 41), (6, 0), (47, 25), (35, 17), (39, 36), (41, 23), (8, 14), (27, 42), (20, 8), (36, 38), (43, 8), (17, 12), (47, 29), (29, 32), (21, 23), (37, 8), (30, 40), (37, 35), (35, 25), (27, 16), (44, 12), (10, 2), (6, 30), (1, 41), (24, 4), (31, 1), (1, 37), (36, 26), (9, 33), (47, 39), (42, 40), (7, 4), (12, 40), (6, 24), (39, 24), (37, 36), (26, 0), (39, 30), (27, 21), (48, 41), (22, 23), (25, 20), (24, 40), (35, 34), (9, 10), (37, 15), (30, 7), (27, 17), (35, 11), (23, 15), (36, 43), (40, 2), (46, 14), (14, 0), (13, 24), (7, 34), (36, 25), (21, 25), (29, 39), (2, 41), (13, 3), (44, 36), (42, 14), (19, 25), (40, 7), (45, 19), (1, 4), (36, 0), (23, 21), (13, 0), (21, 15), (22, 4), (24, 7), (44, 27), (29, 41), (45, 12), (46, 23), (25, 2), (4, 43), (42, 4), (15, 31), (9, 15), (45, 18), (39, 26), (39, 25), (43, 27), (19, 10), (10, 10), (47, 19), (3, 7), (3, 30), (48, 3), (26, 38), (8, 8), (40, 36), (36, 6), (6, 14), (42, 28), (29, 27), (20, 18), (32, 4), (44, 28), (37, 9), (26, 22), (14, 32), (33, 20), (2, 12), (25, 43), (21, 34), (40, 1), (2, 37), (32, 26), (40, 26), (36, 12), (18, 40), (42, 12), (15, 19), (37, 43), (44, 35), (30, 30), (9, 41), (25, 30), (9, 40), (36, 42), (41, 27), (5, 8), (8, 15), (21, 16), (8, 21), (30, 32), (29, 11), (25, 41), (18, 4), (33, 10), (17, 6), (25, 31), (23, 8), (5, 25), (28, 22), (46, 37), (43, 18), (40, 30), (21, 39), (29, 5), (31, 35), (0, 39), (4, 3), (42, 29), (11, 17), (15, 20), (0, 21), (10, 5), (11, 37), (24, 8), (8, 6), (39, 18), (0, 1), (36, 20), (34, 18), (42, 25), (27, 7), (36, 30), (47, 3), (4, 10), (14, 36), (47, 14), (32, 30), (15, 13), (31, 14), (46, 25), (4, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 45), (5, 1), (21, 7), (47, 30), (34, 44), (17, 27), (38, 27), (37, 47), (17, 20), (4, 24), (19, 12), (11, 19), (13, 12), (46, 5), (24, 3), (47, 20), (41, 30), (14, 28), (46, 34), (8, 40), (12, 36), (2, 33), (15, 41), (27, 2), (10, 0), (12, 22), (9, 42), (5, 14), (30, 27), (18, 2), (18, 22), (11, 29), (28, 46), (25, 38), (25, 13), (10, 17), (11, 6), (19, 28), (14, 45), (8, 28), (48, 18), (30, 16), (30, 30), (43, 35), (43, 21), (40, 0), (30, 33), (38, 44), (29, 3), (37, 5), (30, 22), (23, 8), (28, 5), (5, 8), (9, 28), (42, 6), (21, 29), (46, 47), (3, 23), (44, 25), (9, 12), (21, 30), (41, 29), (27, 31), (42, 13), (10, 7), (20, 38), (47, 0), (42, 43), (18, 35), (16, 33), (9, 8), (31, 28), (0, 27), (9, 6), (33, 1), (41, 21), (7, 8), (25, 40), (17, 11), (27, 33), (33, 25), (18, 1), (1, 8), (16, 18), (20, 3), (25, 25), (39, 12), (40, 9), (33, 39), (2, 47), (44, 15), (37, 45), (23, 7), (43, 18), (23, 13), (36, 32), (4, 12), (39, 37), (46, 9), (42, 33), (45, 17), (25, 32), (14, 21), (48, 24), (46, 3), (39, 1), (27, 12), (7, 28), (46, 1), (29, 5), (43, 26), (20, 2), (29, 16), (31, 35), (37, 39), (18, 6), (38, 14), (36, 36), (7, 31), (9, 18), (7, 46), (24, 32), (43, 31), (7, 32), (30, 39), (31, 47), (24, 40), (14, 30), (8, 2), (14, 35), (42, 25), (48, 7), (41, 14), (26, 42), (42, 28), (8, 22), (6, 36), (42, 22), (31, 15), (38, 8), (5, 25), (43, 9), (7, 3), (28, 32), (34, 27), (29, 8), (7, 47), (3, 12), (35, 10), (15, 12), (19, 35), (27, 38), (2, 3), (44, 18), (19, 6), (25, 35), (13, 11), (4, 39), (12, 44), (24, 45), (42, 30), (35, 11), (3, 47), (39, 5), (6, 24), (8, 8), (5, 29), (1, 28), (32, 27), (20, 23), (31, 37), (26, 33), (42, 19), (48, 46), (25, 21), (32, 44), (14, 33), (11, 27), (0, 43), (12, 27), (17, 0), (15, 23), (38, 23), (1, 6), (3, 15), (36, 28), (12, 38), (3, 41), (7, 37), (29, 32), (35, 14), (17, 13), (23, 22), (14, 24), (47, 29), (22, 1), (37, 43), (23, 44), (46, 35), (27, 35), (5, 44), (15, 10), (36, 22), (41, 26), (28, 21), (22, 4), (5, 41), (34, 7), (29, 35), (29, 0), (44, 17), (26, 5), (16, 13), (21, 18), (41, 24), (5, 32), (29, 18), (9, 38), (31, 31), (6, 14), (13, 17), (18, 20), (41, 7), (39, 33), (9, 29), (0, 19), (44, 37), (39, 20), (27, 25), (10, 11), (15, 22), (33, 10), (13, 46), (20, 19), (9, 14), (27, 47), (39, 17), (39, 9), (19, 19), (43, 11), (8, 26), (32, 43), (15, 7), (27, 17), (22, 9), (44, 34), (18, 34), (2, 35), (34, 21), (37, 1), (15, 13), (28, 23), (29, 1), (23, 17), (34, 43), (36, 6), (22, 39), (10, 34), (38, 0), (47, 32), (15, 17), (2, 0), (42, 35), (40, 28), (41, 13), (45, 1), (35, 23), (44, 10), (43, 8), (11, 12), (1, 23), (28, 15), (44, 2), (47, 42), (45, 30), (21, 46), (47, 27), (38, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 24), (13, 32), (36, 1), (16, 4), (18, 30), (8, 21), (19, 14), (41, 0), (30, 33), (10, 28), (18, 13), (12, 41), (4, 39), (24, 20), (36, 13), (29, 36), (22, 27), (32, 40), (27, 29), (6, 24), (23, 34), (32, 9), (26, 22), (21, 26), (4, 25), (3, 23), (23, 33), (17, 5), (4, 12), (17, 16), (36, 11), (40, 16), (18, 34), (4, 16), (33, 15), (32, 12), (26, 33), (18, 1), (11, 24), (25, 1), (24, 33), (16, 22), (3, 32), (33, 3), (33, 4), (9, 10), (35, 24), (5, 41), (26, 6), (9, 7), (11, 18), (12, 31), (14, 26), (21, 40), (20, 38), (31, 0), (32, 34), (40, 17), (8, 9), (29, 28), (16, 28), (2, 3), (1, 7), (27, 21), (28, 3), (36, 22), (25, 26), (24, 5), (6, 5), (12, 9), (0, 24), (8, 36), (8, 3), (25, 3), (11, 2), (29, 18), (27, 18), (35, 22), (38, 9), (20, 25), (23, 5), (2, 6), (19, 19), (9, 31), (27, 30), (19, 1), (0, 40), (41, 25), (28, 17), (11, 34), (19, 7), (35, 36), (15, 23), (31, 32), (10, 41), (39, 11), (18, 33), (9, 37), (16, 7), (5, 3), (15, 32), (8, 29), (9, 1), (29, 14), (8, 38), (19, 38), (28, 0), (23, 9), (37, 12), (40, 27), (39, 20), (26, 3), (40, 23), (36, 0), (40, 37), (17, 3), (33, 21), (38, 1), (41, 32), (6, 31), (33, 5), (27, 37), (25, 30), (27, 24), (33, 9), (7, 20), (10, 37), (36, 32), (34, 5), (26, 17), (20, 5), (27, 31), (23, 37), (8, 26), (15, 24), (5, 38), (34, 10), (20, 19), (7, 4), (0, 10), (37, 23), (21, 25), (17, 21), (36, 39), (33, 40), (4, 29), (0, 12), (6, 8), (30, 18), (32, 16), (30, 10), (17, 41), (5, 33), (32, 14), (3, 28), (40, 11), (39, 36), (25, 36), (25, 27), (15, 28), (34, 8), (13, 30), (12, 22), (4, 22), (25, 9), (24, 37), (33, 39), (40, 18), (19, 10), (17, 31), (23, 35), (24, 14), (2, 15), (4, 10), (30, 24), (33, 1), (24, 19), (36, 15), (12, 1), (18, 3), (32, 11), (23, 12), (11, 4), (2, 20), (36, 30), (38, 29), (14, 34), (14, 35), (21, 36), (33, 6), (30, 5), (29, 35), (6, 0), (18, 38), (13, 17), (22, 28), (30, 23), (20, 20), (41, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 34), (8, 20), (12, 38), (31, 1), (21, 2), (8, 30), (4, 27), (14, 19), (22, 2), (32, 6), (12, 2), (8, 48), (18, 8), (32, 10), (24, 5), (14, 0), (31, 0), (9, 38), (7, 47), (10, 20), (2, 16), (18, 33), (35, 44), (37, 36), (3, 7), (9, 48), (36, 0), (4, 38), (22, 48), (6, 11), (10, 16), (29, 9), (19, 25), (37, 24), (36, 37), (4, 36), (21, 46), (22, 33), (28, 14), (3, 26), (9, 0), (23, 12), (27, 31), (22, 19), (13, 27), (29, 26), (36, 9), (33, 6), (24, 13), (29, 24), (34, 6), (35, 25), (11, 9), (37, 30), (18, 14), (11, 1), (2, 33), (34, 1), (5, 31), (9, 42), (33, 23), (20, 38), (0, 45), (24, 46), (10, 1), (36, 38), (13, 33), (11, 46), (11, 25), (19, 48), (19, 24), (30, 3), (26, 43), (9, 7), (7, 42), (36, 22), (17, 8), (13, 7), (32, 11), (3, 48), (1, 3), (15, 28), (14, 48), (29, 22), (25, 42), (10, 21), (31, 37), (22, 27), (24, 20), (19, 8), (31, 29), (34, 35), (13, 26), (30, 18), (4, 8), (38, 5), (15, 45), (33, 25), (0, 25), (6, 38), (19, 15), (3, 43), (13, 46), (8, 33), (30, 14), (15, 9), (14, 31), (12, 0), (29, 44), (23, 10), (21, 41), (7, 21), (36, 17), (20, 46), (27, 46), (11, 5), (3, 14), (26, 39), (25, 0), (4, 44), (26, 5), (31, 21), (4, 28), (24, 24), (1, 19), (10, 3), (11, 33), (27, 5), (29, 47), (3, 44), (19, 22), (36, 11), (17, 15), (19, 16), (18, 21), (34, 15), (14, 38), (30, 39), (8, 6), (20, 11), (36, 25), (20, 28), (0, 3), (17, 40), (14, 37), (16, 30), (19, 45), (34, 47), (34, 13), (26, 2), (19, 35), (6, 10), (3, 11), (28, 36), (10, 9), (14, 7), (31, 7), (28, 19), (7, 5), (23, 34), (25, 18), (29, 37), (16, 17), (29, 28), (33, 32), (18, 9), (33, 27), (17, 37), (35, 39), (36, 19), (15, 38), (23, 15), (15, 33), (8, 12), (0, 34), (14, 29), (20, 39), (22, 6), (26, 20), (15, 44), (38, 10), (10, 34), (21, 26), (13, 44), (18, 44), (16, 46), (3, 8), (8, 42), (4, 10), (11, 31), (11, 12), (26, 17), (29, 5), (5, 15), (0, 15), (7, 28), (17, 18), (23, 48), (18, 45), (33, 7), (36, 27), (20, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 9), (8, 20), (7, 33), (8, 31), (16, 27), (19, 9), (16, 21), (4, 15), (7, 2), (6, 29), (37, 30), (36, 23), (1, 23), (14, 21), (26, 42), (7, 21), (23, 17), (8, 42), (29, 11), (39, 10), (35, 3), (34, 41), (12, 17), (25, 8), (28, 12), (0, 43), (16, 24), (29, 43), (12, 10), (31, 14), (21, 15), (0, 5), (1, 10), (31, 17), (25, 44), (7, 20), (35, 44), (28, 5), (13, 15), (19, 41), (41, 22), (15, 24), (8, 22), (8, 14), (12, 21), (38, 32), (17, 31), (35, 30), (0, 2), (10, 30), (36, 34), (32, 1), (18, 17), (41, 12), (27, 0), (33, 20), (26, 4), (3, 41), (9, 40), (4, 44), (10, 38), (1, 33), (41, 17), (24, 3), (6, 35), (31, 24), (2, 17), (24, 33), (26, 5), (1, 7), (4, 33), (27, 19), (11, 37), (41, 0), (1, 38), (15, 4), (10, 43), (14, 41), (1, 2), (17, 5), (37, 40), (33, 44), (36, 22), (40, 36), (33, 24), (29, 7), (5, 35), (27, 27), (38, 3), (15, 44), (8, 17), (9, 3), (0, 17), (17, 36), (35, 28), (38, 34), (34, 29), (28, 29), (23, 41), (32, 35), (39, 43), (36, 41), (36, 8), (13, 42), (24, 25), (19, 39), (17, 34), (24, 26), (23, 16), (36, 38), (5, 9), (13, 4), (6, 18), (27, 3), (13, 28), (20, 39), (10, 20), (8, 8), (19, 38), (20, 5), (33, 43), (2, 14), (24, 31), (22, 31), (13, 39), (27, 35), (2, 38), (37, 34), (2, 20), (5, 33), (38, 38), (36, 19), (38, 10), (39, 37), (26, 38), (16, 25), (25, 36), (18, 24), (20, 18), (32, 13), (26, 21), (17, 44), (18, 35), (33, 40), (20, 42), (13, 34), (39, 16), (2, 21), (18, 38), (31, 5), (14, 20), (13, 41), (14, 0), (41, 26), (28, 10), (1, 18), (14, 14), (14, 43), (28, 9), (25, 11), (26, 0), (33, 9), (1, 1), (41, 23), (19, 26), (29, 0), (40, 6), (25, 39), (5, 40), (32, 27), (6, 24), (34, 10), (19, 16), (23, 15), (27, 10), (6, 25), (11, 32), (16, 10), (27, 37), (33, 38), (6, 5), (38, 30), (3, 16), (27, 24), (12, 39), (2, 42), (33, 17), (25, 20), (32, 5), (2, 2), (1, 17), (2, 18), (15, 22), (22, 28), (31, 34), (22, 16), (25, 0), (22, 12), (11, 28), (3, 36), (12, 44), (9, 29), (22, 2), (18, 15), (16, 40), (0, 13), (13, 31), (28, 4), (40, 40), (2, 23), (28, 41), (15, 36), (39, 14), (10, 5), (7, 7), (15, 42), (37, 27), (21, 11), (18, 43), (38, 31), (21, 19), (23, 13), (29, 33), (22, 32), (3, 13), (32, 24), (26, 28), (27, 38), (8, 25), (24, 2), (37, 20), (36, 1), (34, 4), (0, 36), (8, 9), (23, 33), (21, 25), (24, 41), (6, 9), (18, 6), (9, 28), (35, 36), (22, 33), (18, 34), (21, 35), (5, 43), (12, 32), (2, 11), (22, 43), (32, 38), (38, 25), (30, 35), (29, 28), (29, 31), (20, 25), (12, 15), (38, 43), (6, 43), (28, 25), (35, 5), (22, 26), (11, 35), (20, 41), (2, 22), (8, 21), (26, 6), (1, 11), (5, 32), (39, 27), (9, 42), (11, 2), (1, 26), (10, 10), (0, 31), (31, 4), (28, 11), (2, 31), (30, 32), (34, 21), (20, 44), (31, 2), (20, 7), (33, 32), (16, 19), (22, 18), (15, 21), (10, 1), (30, 24), (30, 6), (24, 19), (39, 35), (28, 14), (37, 17), (16, 44), (33, 14), (2, 29), (25, 7), (35, 43), (5, 28), (40, 8), (4, 35), (19, 12), (16, 38), (17, 35), (13, 17), (8, 19), (1, 32), (28, 34), (15, 5), (39, 17), (20, 23), (12, 41), (40, 14), (29, 34), (34, 32), (20, 20), (1, 6), (38, 44), (5, 19), (16, 42), (20, 15), (1, 9), (31, 29), (14, 4), (10, 24), (11, 39), (41, 11), (17, 6), (41, 2), (24, 20), (41, 16), (41, 38), (17, 21), (10, 6), (37, 14), (21, 17), (20, 32), (11, 38), (37, 21), (0, 40), (3, 35), (21, 3), (10, 31), (19, 40), (21, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 27), (29, 32), (22, 9), (27, 21), (6, 6), (17, 22), (5, 13), (31, 8), (9, 21), (4, 15), (44, 21), (39, 37), (42, 36), (27, 25), (3, 31), (14, 4), (35, 7), (14, 10), (3, 19), (43, 9), (9, 14), (24, 33), (26, 6), (15, 17), (30, 4), (25, 31), (12, 34), (33, 36), (17, 0), (13, 6), (39, 9), (32, 12), (28, 7), (8, 26), (22, 12), (1, 25), (32, 25), (36, 21), (21, 39), (6, 17), (41, 3), (27, 5), (34, 15), (12, 16), (22, 39), (31, 6), (38, 2), (2, 34), (27, 20), (31, 34), (3, 16), (13, 34), (5, 38), (19, 20), (12, 20), (3, 9), (2, 39), (26, 30), (18, 39), (20, 23), (34, 4), (7, 11), (38, 31), (25, 6), (31, 9), (24, 26), (1, 37), (43, 12), (29, 36), (32, 21), (24, 3), (40, 24), (23, 1), (25, 17), (9, 20), (34, 10), (23, 38), (25, 36), (27, 17), (1, 21), (34, 36), (34, 27), (31, 32), (24, 0), (21, 27), (20, 38), (9, 5), (24, 8), (3, 0), (43, 29), (39, 7), (7, 22), (43, 23), (5, 29), (2, 29), (40, 27), (22, 5), (42, 15), (40, 0), (27, 26), (5, 35), (41, 11), (0, 35), (23, 16), (2, 33), (44, 7), (8, 30), (24, 13), (33, 20), (14, 37), (14, 36), (12, 24), (38, 15), (40, 33), (1, 14), (14, 16), (23, 2), (33, 34), (9, 2), (0, 29), (23, 3), (5, 31), (25, 38), (17, 30), (33, 26), (25, 32), (23, 0), (16, 37), (7, 16), (15, 2), (13, 30), (2, 37), (0, 3), (7, 35), (2, 21), (35, 19), (5, 16), (2, 14), (42, 37), (20, 17), (24, 29), (8, 0), (3, 8), (0, 13), (43, 17), (43, 24), (15, 11), (9, 31), (10, 21), (39, 33), (8, 4), (1, 29), (26, 29), (24, 35), (44, 18), (1, 27), (37, 13), (9, 23), (12, 25), (28, 32), (43, 36), (2, 23), (6, 35), (38, 9), (15, 7), (4, 7), (34, 32), (24, 39), (10, 37), (43, 3), (4, 26), (27, 7), (7, 10), (10, 13), (40, 32), (22, 19), (7, 21), (22, 15), (30, 19), (43, 19), (22, 17), (42, 20), (40, 7), (1, 5), (10, 32), (21, 35), (40, 2), (5, 37), (37, 23), (6, 31), (18, 22), (37, 19), (28, 35), (12, 27), (27, 14), (36, 17), (40, 38), (42, 26), (38, 16), (14, 1), (12, 29), (40, 39), (4, 2), (17, 19), (10, 30), (21, 37), (21, 14), (32, 39), (43, 18), (23, 32), (44, 13), (23, 19), (43, 8), (6, 4), (21, 6), (31, 22), (10, 36), (17, 33), (19, 32), (39, 39), (14, 33), (35, 39), (34, 20), (12, 35), (28, 39), (24, 28), (9, 10), (38, 8), (22, 33), (7, 25), (2, 2), (38, 7), (10, 24), (42, 21), (6, 18), (40, 36), (22, 25), (23, 7), (26, 21), (19, 35), (23, 12), (22, 29), (10, 14), (12, 8), (10, 1), (25, 39), (38, 11), (27, 29), (26, 25), (40, 22), (17, 10), (9, 27), (14, 2), (33, 17), (23, 17), (28, 9), (44, 36), (12, 0), (26, 17), (40, 9), (43, 15), (3, 36), (34, 39), (10, 23), (13, 36), (44, 15), (5, 21), (23, 18), (26, 14), (23, 21), (28, 34), (7, 31), (29, 8), (26, 9), (6, 37), (15, 32), (21, 23), (30, 10), (4, 18), (44, 37), (16, 1), (30, 0), (39, 8), (19, 2), (30, 22), (28, 18), (15, 18), (17, 39), (1, 6), (42, 8), (16, 15), (30, 33), (15, 39), (8, 8), (39, 18), (41, 26), (16, 26), (26, 37), (41, 27), (8, 10), (2, 24), (31, 5), (6, 8), (3, 13), (23, 27), (11, 22), (16, 28), (42, 38), (12, 6), (29, 33), (28, 31), (34, 38), (34, 37), (26, 18), (21, 19), (17, 7), (25, 33), (16, 20), (14, 11), (13, 39), (31, 4), (41, 25), (16, 34), (4, 34), (36, 32), (36, 28), (24, 36), (33, 22), (42, 33), (7, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 30), (34, 21), (21, 35), (43, 22), (26, 37), (20, 6), (24, 2), (40, 12), (28, 17), (31, 24), (25, 9), (28, 20), (4, 10), (28, 31), (28, 25), (32, 37), (14, 37), (2, 15), (15, 36), (13, 39), (11, 29), (31, 40), (36, 40), (0, 37), (28, 13), (33, 21), (35, 5), (28, 10), (0, 21), (4, 24), (12, 20), (4, 0), (25, 37), (30, 7), (30, 8), (43, 3), (10, 3), (31, 22), (13, 21), (24, 19), (32, 24), (13, 3), (2, 30), (7, 37), (24, 7), (25, 13), (28, 4), (34, 0), (12, 33), (21, 8), (10, 1), (13, 32), (18, 20), (14, 7), (2, 29), (26, 36), (17, 9), (21, 37), (1, 23), (29, 35), (21, 25), (22, 20), (34, 28), (39, 28), (3, 33), (32, 4), (33, 28), (18, 11), (41, 28), (40, 32), (33, 30), (28, 32), (33, 33), (22, 24), (43, 13), (35, 23), (38, 35), (43, 26), (35, 40), (8, 14), (16, 9), (27, 23), (40, 31), (41, 4), (22, 5), (32, 38), (33, 11), (18, 27), (26, 6), (19, 11), (9, 30), (31, 2), (35, 3), (24, 25), (43, 10), (9, 14), (32, 19), (33, 36), (38, 28), (32, 36), (37, 31), (7, 3), (12, 7), (9, 25), (18, 22), (8, 34), (34, 9), (29, 39), (1, 16), (27, 21), (42, 20), (5, 30), (23, 1), (1, 11), (38, 10), (37, 33), (38, 9), (7, 31), (38, 4), (19, 39), (17, 28), (16, 37), (19, 7), (14, 12), (38, 18), (38, 19), (1, 24), (36, 1), (10, 32), (30, 39), (11, 6), (10, 31), (14, 3), (23, 19), (19, 33), (36, 2), (17, 30), (26, 34), (26, 39), (41, 31), (20, 14), (37, 3), (22, 28), (37, 10), (29, 30), (30, 19), (19, 24), (1, 3), (14, 38), (35, 26), (39, 9), (8, 2), (23, 3), (12, 17), (9, 32), (22, 40), (0, 11), (34, 10), (43, 21), (4, 35), (8, 38), (11, 23), (11, 5), (35, 9), (3, 9), (14, 35), (21, 7), (16, 0), (41, 24), (17, 39), (5, 28), (8, 39), (9, 17), (25, 39), (37, 28), (35, 16), (29, 20), (34, 32), (20, 29), (7, 39), (35, 36), (13, 34), (2, 23), (37, 14), (25, 8), (20, 9), (41, 14), (41, 22), (19, 3), (5, 17), (40, 19), (8, 28), (39, 19), (15, 6), (42, 25), (30, 26), (29, 13), (21, 39), (16, 23), (39, 24), (15, 19), (5, 29), (32, 14), (3, 17), (15, 31), (30, 18), (6, 17), (23, 40), (3, 34), (6, 29), (26, 25), (18, 36), (25, 32), (10, 33), (39, 10), (1, 8), (3, 21), (35, 0), (17, 37), (1, 6), (8, 1), (18, 26), (2, 7), (16, 18), (14, 2), (1, 31), (16, 13), (12, 22), (42, 37), (26, 13), (5, 19), (9, 16), (15, 34), (24, 21), (31, 35), (7, 38), (7, 1), (25, 26), (6, 18), (28, 11), (15, 8), (26, 20), (24, 28), (36, 27), (37, 12), (22, 31), (22, 23), (19, 36), (36, 6), (21, 2), (20, 24), (39, 7), (15, 22), (16, 14), (23, 24), (17, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 13), (40, 22), (1, 14), (5, 43), (42, 31), (4, 15), (20, 20), (11, 27), (16, 21), (31, 3), (39, 29), (3, 43), (25, 20), (43, 5), (32, 11), (43, 14), (32, 28), (25, 3), (6, 37), (25, 44), (30, 21), (38, 11), (21, 23), (16, 7), (42, 13), (30, 22), (39, 18), (35, 23), (35, 1), (27, 5), (36, 33), (15, 19), (8, 17), (29, 8), (44, 37), (39, 33), (1, 38), (14, 31), (21, 13), (38, 34), (6, 35), (18, 23), (29, 24), (20, 6), (31, 35), (35, 18), (41, 33), (28, 6), (29, 17), (1, 37), (32, 22), (26, 3), (28, 0), (15, 3), (26, 43), (0, 19), (14, 34), (10, 35), (28, 29), (27, 10), (16, 22), (23, 14), (18, 36), (19, 20), (28, 32), (6, 18), (44, 1), (21, 28), (20, 36), (7, 30), (1, 18), (2, 18), (34, 29), (36, 35), (35, 4), (29, 30), (0, 34), (35, 11), (41, 45), (43, 19), (31, 20), (23, 39), (2, 42), (27, 35), (35, 30), (30, 3), (28, 7), (20, 44), (38, 32), (21, 44), (28, 34), (2, 38), (14, 36), (21, 10), (36, 45), (23, 0), (13, 28), (25, 42), (26, 12), (23, 19), (17, 34), (31, 36), (8, 34), (30, 25), (40, 4), (12, 35), (27, 44), (9, 22), (9, 21), (15, 4), (5, 13), (1, 35), (25, 21), (25, 1), (7, 29), (1, 29), (3, 28), (5, 10), (21, 3), (35, 10), (38, 23), (44, 7), (3, 18), (40, 38), (17, 36), (0, 13), (23, 18), (22, 8), (20, 12), (11, 7), (5, 27), (34, 2), (9, 44), (36, 6), (15, 18), (13, 3), (13, 39), (39, 17), (1, 5), (21, 1), (31, 38), (34, 33), (4, 9), (2, 40), (25, 2), (11, 26), (38, 7), (4, 19), (43, 0), (41, 15), (23, 13), (14, 15), (7, 8), (12, 19), (14, 16), (0, 27), (32, 42), (36, 25), (33, 35), (16, 42), (19, 39), (36, 43), (12, 6), (10, 33), (40, 21), (9, 33), (11, 18), (0, 37), (4, 3), (11, 45), (19, 34), (28, 22), (17, 19), (42, 28), (25, 14), (22, 27), (12, 3), (4, 8), (33, 33), (44, 12), (3, 7), (39, 42), (0, 33), (21, 20), (19, 22), (34, 4), (43, 13), (25, 13), (32, 38), (25, 45), (44, 11), (3, 33), (29, 13), (36, 37), (37, 29), (31, 34), (16, 28), (34, 1), (14, 37), (10, 20), (24, 22), (19, 28), (26, 36), (0, 1), (39, 10), (34, 45), (4, 26), (24, 33), (25, 4), (35, 22), (8, 33), (0, 28), (39, 39), (34, 3), (26, 34), (0, 36), (31, 25), (8, 40), (38, 22), (30, 41), (18, 44), (8, 30), (19, 24), (1, 42), (12, 30), (14, 23), (30, 45), (1, 3), (21, 43), (36, 17), (8, 16), (41, 12), (2, 2), (12, 12), (30, 44), (34, 9), (7, 31), (28, 33), (20, 26), (41, 11), (24, 25), (26, 21), (21, 31), (12, 32), (25, 43), (16, 12), (41, 44), (10, 6), (12, 21), (25, 10), (16, 31), (29, 11), (32, 13), (4, 13), (17, 4), (19, 25), (6, 14), (2, 14), (11, 11), (34, 25), (9, 24), (36, 11), (39, 25), (37, 43), (22, 19), (19, 21), (37, 26), (40, 16), (26, 37), (20, 41), (6, 5), (20, 43), (11, 28), (42, 0), (36, 26), (43, 44), (15, 38), (36, 3), (11, 3), (40, 42), (7, 37), (3, 13), (6, 38), (41, 30), (6, 2), (26, 4), (37, 37), (8, 36), (14, 28), (41, 9), (10, 8), (28, 3), (7, 21), (2, 10), (40, 0), (26, 40), (0, 3), (30, 34), (44, 15), (21, 27), (10, 18), (24, 13), (19, 42), (11, 40), (36, 7), (11, 2), (23, 38), (36, 40), (11, 1), (22, 21), (34, 41), (19, 38), (41, 27), (26, 7), (13, 27), (28, 2), (33, 1), (36, 27), (20, 37), (29, 1), (3, 45), (3, 36), (40, 12), (21, 45), (16, 15), (2, 13), (21, 32), (35, 16), (18, 17), (15, 10), (33, 6), (37, 20), (36, 30), (21, 26), (5, 24), (31, 22), (10, 11), (7, 39), (14, 41), (23, 16), (1, 24), (44, 14), (31, 4), (0, 41), (15, 43), (36, 22), (6, 7), (24, 27), (0, 15), (42, 38), (31, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 43), (33, 40), (23, 37), (14, 48), (13, 18), (0, 35), (21, 2), (15, 8), (22, 34), (31, 45), (5, 39), (25, 48), (22, 44), (29, 38), (7, 33), (11, 28), (32, 1), (7, 21), (42, 1), (1, 25), (40, 42), (30, 11), (26, 15), (1, 16), (32, 13), (10, 40), (13, 43), (21, 7), (1, 12), (1, 45), (9, 15), (24, 44), (34, 39), (41, 21), (16, 33), (40, 8), (20, 9), (12, 6), (37, 28), (0, 48), (12, 36), (16, 1), (24, 35), (6, 38), (18, 3), (29, 8), (39, 3), (27, 32), (17, 10), (18, 48), (32, 47), (28, 4), (29, 3), (19, 37), (40, 36), (14, 10), (11, 43), (37, 20), (1, 47), (23, 20), (5, 8), (3, 28), (39, 7), (29, 46), (3, 30), (23, 27), (25, 19), (12, 0), (13, 6), (3, 21), (31, 43), (28, 20), (28, 37), (1, 32), (27, 29), (20, 18), (12, 26), (19, 0), (33, 18), (27, 48), (11, 42), (27, 0), (26, 43), (40, 22), (30, 14), (9, 42), (27, 43), (23, 43), (10, 1), (16, 6), (24, 38), (8, 6), (29, 19), (38, 30), (5, 35), (4, 12), (23, 47), (38, 27), (28, 12), (35, 2), (25, 46), (6, 26), (20, 0), (35, 16), (14, 3), (2, 23), (37, 31), (36, 11), (35, 25), (15, 10), (39, 34), (7, 44), (31, 17), (26, 3), (3, 17), (12, 29), (41, 24), (38, 39), (29, 30), (21, 46), (19, 14), (16, 17), (40, 14), (18, 16), (11, 17), (36, 47), (7, 24), (10, 48), (4, 46), (20, 40), (35, 32), (34, 40), (21, 30), (15, 28), (36, 28), (1, 43), (0, 19), (22, 27), (21, 9), (26, 30), (23, 8), (26, 24), (19, 42), (2, 15), (36, 38), (16, 0), (21, 39), (20, 29), (24, 39), (5, 9), (40, 33), (23, 15), (18, 39), (34, 10), (40, 25), (7, 30), (25, 13), (25, 38), (16, 31), (7, 12), (34, 27), (3, 34), (32, 46), (12, 2), (7, 43), (42, 5), (36, 8), (28, 47), (25, 24), (22, 28), (21, 36), (29, 40), (10, 26), (37, 2), (3, 36), (0, 47), (2, 19), (3, 5), (34, 38), (28, 46), (18, 24), (21, 21), (4, 37), (29, 10), (41, 46), (30, 34), (29, 35), (15, 20), (23, 26), (16, 44), (15, 41), (39, 46), (19, 26), (15, 48), (1, 41), (17, 7), (13, 0), (12, 27), (29, 9), (14, 15), (17, 32), (13, 3), (3, 45), (5, 1), (32, 18), (22, 2), (0, 21), (30, 39), (19, 40), (17, 12), (26, 26), (22, 4), (14, 27), (33, 16), (35, 1), (37, 37), (29, 22), (1, 29), (3, 25), (26, 45), (17, 11), (33, 21), (36, 18), (35, 20), (19, 32), (12, 10), (8, 0), (38, 28), (10, 45), (15, 18), (39, 2), (14, 40), (37, 46), (16, 12), (9, 13), (33, 24), (24, 11), (9, 9), (12, 33), (25, 27), (20, 48), (40, 1), (42, 46), (16, 8), (3, 35), (21, 48), (8, 29), (34, 37), (6, 19), (30, 46), (29, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 29), (37, 10), (26, 0), (21, 25), (22, 35), (4, 3), (26, 14), (39, 14), (23, 32), (9, 20), (25, 2), (35, 30), (4, 30), (30, 21), (32, 37), (2, 19), (37, 39), (12, 11), (2, 29), (37, 13), (39, 6), (25, 1), (15, 33), (23, 36), (7, 24), (9, 10), (15, 38), (36, 3), (11, 4), (32, 2), (6, 35), (16, 2), (9, 12), (9, 25), (40, 19), (42, 34), (5, 27), (9, 31), (12, 15), (3, 9), (37, 28), (13, 12), (18, 17), (17, 12), (16, 18), (38, 18), (9, 37), (37, 27), (34, 33), (16, 8), (28, 5), (29, 7), (12, 37), (17, 16), (21, 9), (1, 30), (0, 24), (11, 38), (3, 27), (10, 15), (4, 25), (6, 14), (23, 23), (42, 22), (21, 8), (19, 14), (42, 19), (27, 15), (20, 1), (41, 13), (13, 22), (24, 10), (7, 4), (26, 11), (22, 8), (7, 38), (11, 20), (28, 8), (34, 4), (29, 23), (0, 33), (31, 5), (18, 13), (29, 20), (30, 3), (1, 0), (33, 28), (39, 15), (20, 18), (23, 28), (38, 23), (8, 14), (11, 35), (20, 13), (41, 22), (12, 17), (20, 36), (26, 17), (42, 16), (6, 13), (41, 7), (12, 12), (0, 2), (5, 36), (2, 4), (39, 21), (22, 32), (8, 18), (14, 4), (37, 34), (32, 28), (16, 14), (35, 13), (4, 22), (16, 22), (6, 26), (35, 20), (1, 34), (40, 39), (1, 14), (15, 24), (6, 4), (10, 3), (24, 9), (34, 27), (15, 7), (1, 6), (1, 35), (25, 30), (25, 16), (14, 24), (26, 31), (17, 18), (34, 24), (8, 24), (13, 18), (34, 38), (40, 29), (30, 14), (13, 37), (23, 22), (5, 4), (29, 14), (41, 1), (39, 16), (26, 10), (29, 22), (26, 20), (42, 5), (2, 16), (12, 24), (11, 32), (38, 2), (26, 9), (33, 29), (33, 2), (3, 7), (32, 18), (3, 33), (22, 20), (24, 26), (16, 35), (0, 22), (33, 12), (6, 2), (28, 13), (38, 30), (38, 21), (1, 28), (12, 28), (36, 7), (13, 28), (20, 37), (13, 10), (16, 31), (1, 23), (1, 19), (27, 38), (22, 10), (18, 38), (16, 10), (29, 0), (26, 27), (42, 15), (13, 17), (19, 31), (28, 22), (2, 18), (23, 18), (31, 3), (7, 23), (26, 3), (11, 39), (38, 24), (10, 36), (27, 20), (34, 5), (42, 0), (5, 33), (10, 26), (12, 32), (22, 13), (1, 2), (30, 9), (40, 7), (9, 2), (34, 10), (24, 25), (7, 37), (18, 10), (29, 35), (2, 35), (17, 26), (5, 2), (30, 4), (4, 28), (17, 30), (7, 36), (12, 25), (13, 23), (39, 36), (4, 31), (42, 30), (25, 31), (36, 16), (28, 0), (13, 39), (5, 11), (28, 7), (1, 18), (16, 29), (29, 27), (20, 19), (3, 8), (12, 23), (3, 35), (33, 7), (12, 0), (36, 33), (22, 23), (29, 12), (7, 29), (20, 4), (1, 29), (3, 0), (24, 6), (36, 11), (24, 15), (8, 19), (7, 32), (31, 18), (30, 6), (17, 2), (12, 6), (36, 6), (11, 33), (39, 23), (33, 21), (36, 27), (24, 23), (7, 17), (15, 26), (25, 10), (6, 22), (35, 28), (5, 15), (35, 17), (9, 26), (33, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (39, 14), (2, 40), (26, 29), (17, 8), (14, 6), (25, 39), (7, 24), (33, 29), (29, 18), (30, 39), (19, 1), (12, 13), (11, 40), (8, 20), (24, 19), (41, 28), (28, 17), (38, 2), (18, 43), (6, 41), (10, 10), (19, 35), (33, 40), (23, 24), (39, 41), (3, 16), (11, 4), (0, 15), (0, 23), (8, 25), (14, 26), (6, 39), (14, 4), (28, 23), (37, 30), (9, 44), (1, 11), (2, 37), (9, 10), (11, 20), (1, 41), (21, 42), (8, 10), (2, 3), (15, 19), (32, 27), (37, 21), (7, 15), (33, 39), (13, 26), (26, 4), (5, 5), (31, 9), (22, 7), (18, 34), (35, 1), (1, 6), (12, 16), (33, 20), (31, 11), (9, 41), (2, 7), (39, 18), (12, 36), (1, 28), (37, 38), (33, 28), (12, 32), (3, 18), (13, 17), (17, 25), (15, 8), (22, 39), (12, 14), (25, 13), (35, 30), (35, 10), (1, 39), (20, 26), (19, 27), (23, 32), (21, 7), (13, 10), (25, 20), (9, 39), (0, 29), (15, 13), (22, 0), (29, 24), (41, 38), (7, 2), (12, 9), (2, 35), (22, 42), (4, 28), (11, 39), (17, 40), (7, 10), (40, 6), (24, 29), (33, 24), (3, 3), (38, 27), (5, 32), (36, 21), (40, 19), (11, 16), (17, 26), (30, 13), (16, 7), (14, 45), (27, 15), (14, 11), (20, 22), (10, 35), (13, 46), (16, 4), (28, 10), (32, 18), (9, 31), (26, 24), (15, 31), (2, 31), (0, 4), (1, 42), (20, 18), (14, 31), (31, 24), (22, 15), (1, 27), (28, 31), (5, 10), (1, 23), (15, 20), (29, 23), (5, 44), (10, 30), (6, 23), (35, 38), (22, 36), (34, 30), (28, 40), (32, 7), (19, 38), (15, 12), (9, 16), (31, 44), (2, 2), (24, 7), (12, 20), (29, 35), (14, 12), (16, 34), (9, 13), (37, 18), (37, 28), (26, 1), (19, 41), (36, 11), (28, 26), (7, 1), (26, 30), (35, 32), (32, 11), (10, 7), (29, 25), (13, 4), (6, 22), (29, 34), (20, 12), (32, 22), (18, 26), (24, 22), (24, 34), (13, 12), (10, 22), (24, 27), (8, 31), (34, 8), (19, 33), (2, 26), (27, 30), (19, 43), (5, 7), (13, 43), (28, 0), (10, 24), (28, 43), (41, 0), (3, 34), (11, 45), (38, 39), (4, 42), (32, 38), (15, 25), (14, 34), (31, 2), (34, 46), (27, 27), (1, 36), (33, 45), (8, 17), (4, 25), (29, 41), (33, 0), (27, 12), (30, 29), (7, 18), (12, 41), (18, 42), (5, 37), (13, 24), (5, 35), (16, 31), (41, 36), (29, 37), (18, 40), (30, 0), (29, 27), (18, 24), (32, 20), (24, 41), (17, 38), (4, 9), (40, 5), (38, 0), (4, 36), (18, 9), (41, 13), (15, 30), (2, 1), (28, 9), (11, 43), (13, 1), (39, 0), (21, 43), (30, 10), (39, 39), (20, 37), (6, 1), (15, 17), (22, 16), (10, 5), (38, 34), (1, 31), (33, 26), (30, 35), (4, 32), (11, 44), (31, 18), (34, 32), (12, 7), (30, 18), (34, 22), (13, 15), (12, 29), (39, 24), (21, 33), (3, 32), (3, 6), (31, 29), (40, 36), (29, 36), (8, 37), (35, 11), (39, 20), (18, 29), (39, 8), (30, 19), (9, 34), (18, 11), (22, 41), (27, 26), (27, 18), (14, 27), (34, 6), (19, 24), (37, 32), (24, 31), (27, 37), (34, 18), (5, 33), (11, 28), (37, 3), (28, 30), (15, 28), (20, 33), (6, 14), (13, 38), (18, 2), (35, 21), (26, 12), (10, 46), (29, 33), (33, 16), (5, 21), (4, 2), (16, 11), (4, 4), (3, 9), (3, 23), (12, 1), (10, 16), (19, 46), (26, 37), (22, 17), (7, 21), (16, 2), (27, 19), (26, 13), (1, 37), (41, 1), (15, 16), (13, 21), (2, 11), (16, 3), (22, 23), (34, 13), (30, 1), (36, 35), (41, 4), (25, 21), (40, 9), (34, 2), (25, 31), (32, 34), (24, 23), (5, 27), (31, 25), (21, 46), (15, 5), (3, 41), (26, 27), (32, 4), (16, 26), (15, 29), (34, 17), (41, 2), (14, 32), (40, 2), (15, 10), (40, 8), (10, 27), (33, 21), (18, 4), (2, 44), (10, 38), (7, 45), (21, 24), (25, 36), (38, 41), (39, 23), (20, 30), (20, 25), (26, 7), (19, 16), (9, 3), (5, 19), (34, 26), (2, 36), (3, 38), (32, 25), (14, 28), (12, 33), (15, 7), (25, 25), (35, 14), (34, 38), (41, 40), (37, 46), (7, 31), (22, 32), (40, 15), (19, 29), (34, 10), (27, 13), (27, 16), (5, 15), (37, 42), (25, 41), (29, 16), (28, 18), (6, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 29), (29, 12), (0, 8), (3, 1), (4, 16), (16, 3), (46, 18), (47, 12), (25, 2), (30, 43), (6, 19), (4, 40), (27, 37), (42, 39), (42, 40), (16, 25), (22, 19), (23, 38), (43, 4), (39, 0), (35, 48), (13, 8), (19, 5), (14, 18), (13, 9), (19, 30), (19, 7), (3, 45), (40, 11), (11, 10), (42, 47), (29, 16), (29, 3), (6, 36), (28, 36), (25, 31), (17, 38), (6, 6), (0, 12), (46, 14), (18, 45), (39, 43), (5, 3), (20, 37), (20, 17), (15, 17), (17, 46), (14, 1), (5, 9), (15, 5), (33, 24), (23, 11), (44, 43), (6, 44), (3, 22), (4, 13), (30, 3), (4, 30), (36, 31), (25, 15), (46, 12), (29, 5), (48, 7), (7, 47), (35, 21), (20, 38), (32, 19), (48, 14), (33, 11), (3, 36), (8, 30), (9, 23), (39, 36), (8, 45), (38, 28), (16, 11), (31, 13), (37, 41), (28, 31), (23, 24), (14, 25), (33, 13), (38, 42), (5, 33), (20, 19), (45, 43), (23, 27), (32, 45), (45, 34), (0, 15), (42, 25), (11, 43), (21, 18), (37, 42), (15, 23), (18, 32), (39, 25), (4, 22), (36, 29), (20, 9), (41, 42), (24, 43), (5, 1), (11, 41), (14, 36), (43, 6), (12, 27), (5, 42), (11, 17), (3, 30), (17, 31), (23, 17), (24, 2), (25, 9), (33, 18), (5, 26), (2, 20), (31, 27), (42, 24), (40, 37), (28, 39), (37, 5), (29, 37), (42, 32), (21, 6), (4, 31), (7, 7), (1, 11), (10, 11), (17, 0), (48, 12), (1, 1), (1, 44), (5, 11), (13, 0), (21, 29), (25, 32), (0, 13), (12, 15), (16, 9), (22, 6), (37, 6), (34, 26), (36, 47), (41, 23), (20, 3), (12, 18), (3, 15), (11, 20), (24, 3), (28, 11), (9, 7), (31, 22), (18, 33), (40, 0), (41, 13), (29, 21), (42, 7), (22, 18), (31, 28), (15, 37), (28, 15), (40, 9), (6, 30), (10, 25), (11, 30), (1, 48), (42, 1), (8, 34), (12, 30), (9, 15), (16, 30), (19, 23), (28, 33), (18, 12), (13, 31), (4, 7), (42, 8), (3, 48), (8, 5), (46, 23), (18, 31), (26, 43), (16, 19), (25, 28), (24, 32), (37, 24), (6, 24), (23, 26), (21, 38), (43, 15), (22, 4), (20, 34), (4, 48), (19, 14), (15, 35), (14, 34), (9, 18), (22, 21), (33, 40), (40, 6), (44, 30), (34, 38), (6, 45), (46, 2), (38, 23), (11, 6), (14, 31), (26, 17), (9, 37), (36, 12), (28, 35), (18, 47), (27, 15), (24, 46), (18, 40), (35, 28), (19, 17), (9, 22), (2, 21), (4, 5), (28, 30), (31, 36), (29, 38), (37, 13), (32, 21), (41, 17), (19, 19), (45, 41), (25, 23), (19, 2), (34, 48), (35, 29), (5, 23), (32, 43), (28, 10), (38, 24), (7, 33), (12, 40), (8, 25), (48, 29), (20, 40), (1, 10), (12, 23), (13, 48), (25, 36), (47, 31), (23, 39), (13, 13), (1, 26), (27, 0), (47, 45), (28, 6), (30, 1), (3, 29), (2, 43), (27, 14), (47, 47)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 21), (1, 14), (32, 41), (5, 16), (39, 0), (8, 39), (41, 24), (25, 38), (41, 36), (33, 9), (42, 5), (40, 32), (13, 32), (20, 24), (29, 11), (37, 37), (34, 33), (34, 40), (24, 19), (33, 6), (4, 17), (18, 37), (20, 42), (42, 22), (34, 13), (7, 35), (7, 41), (36, 30), (39, 43), (40, 24), (3, 26), (37, 4), (2, 16), (14, 30), (21, 32), (11, 6), (14, 16), (1, 25), (0, 42), (19, 31), (19, 7), (0, 2), (32, 14), (33, 22), (41, 25), (9, 20), (4, 28), (9, 1), (7, 11), (5, 33), (24, 34), (33, 41), (7, 43), (18, 15), (29, 17), (6, 7), (8, 4), (30, 25), (17, 27), (9, 3), (14, 8), (27, 27), (22, 5), (4, 18), (20, 25), (13, 30), (29, 22), (16, 40), (5, 15), (34, 7), (0, 38), (25, 31), (35, 17), (10, 43), (10, 28), (42, 33), (21, 8), (0, 18), (38, 1), (17, 6), (29, 34), (11, 5), (35, 41), (35, 0), (9, 31), (17, 16), (40, 20), (31, 28), (36, 12), (5, 5), (11, 12), (38, 7), (12, 29), (41, 37), (13, 40), (40, 27), (4, 35), (12, 4), (20, 37), (25, 29), (0, 4), (1, 28), (12, 2), (19, 8), (40, 6), (25, 12), (6, 14), (5, 6), (7, 28), (22, 33), (36, 35), (6, 43), (9, 10), (17, 29), (23, 3), (27, 6), (28, 32), (31, 15), (13, 16), (11, 38), (8, 26), (40, 21), (8, 28), (11, 17), (34, 9), (25, 25), (14, 20), (15, 41), (20, 29), (23, 26), (32, 17), (33, 25), (12, 3), (0, 29), (1, 12), (7, 19), (3, 42), (26, 4), (40, 16), (37, 8), (25, 10), (12, 20), (2, 30), (28, 12), (13, 0), (26, 26), (27, 42), (3, 3), (4, 42), (22, 38), (28, 34), (20, 27), (12, 16), (26, 43), (12, 8), (6, 38), (30, 20), (41, 13), (22, 18), (1, 31), (25, 24), (13, 6), (32, 23), (30, 6), (15, 31), (3, 37), (32, 13), (13, 19), (24, 27), (1, 11), (38, 27), (39, 13), (16, 6), (16, 18), (20, 40), (21, 12), (29, 41), (13, 4), (15, 15), (22, 19), (3, 29), (33, 18), (19, 33), (6, 32), (37, 9), (36, 25), (11, 25), (41, 42), (17, 32), (19, 21), (9, 4), (34, 11), (15, 42), (9, 34), (8, 31), (26, 39), (6, 28), (3, 30), (5, 27), (42, 3), (15, 36), (34, 19), (34, 17), (15, 22), (38, 33), (41, 5), (13, 34), (7, 17), (8, 42), (0, 40), (15, 11), (30, 1), (36, 26), (36, 37), (32, 38), (21, 34), (23, 43), (2, 22), (27, 34), (36, 14), (4, 4), (1, 6), (20, 5), (24, 12), (31, 22), (40, 34), (18, 18), (21, 30), (30, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 30), (18, 24), (17, 30), (15, 7), (28, 1), (2, 13), (14, 5), (31, 2), (18, 16), (33, 13), (27, 39), (28, 29), (16, 16), (25, 4), (14, 16), (20, 0), (24, 0), (8, 22), (32, 20), (40, 37), (34, 0), (20, 5), (19, 36), (35, 7), (7, 22), (8, 30), (30, 5), (39, 26), (32, 2), (2, 19), (7, 13), (1, 5), (1, 10), (18, 7), (42, 26), (37, 37), (7, 18), (13, 3), (27, 38), (24, 26), (38, 7), (10, 39), (35, 33), (28, 9), (28, 38), (1, 27), (8, 19), (2, 16), (16, 21), (21, 36), (17, 5), (33, 31), (17, 7), (37, 27), (43, 20), (31, 33), (38, 30), (13, 23), (42, 38), (10, 18), (16, 31), (32, 30), (1, 2), (18, 38), (40, 8), (14, 3), (21, 31), (37, 5), (7, 2), (39, 29), (14, 1), (32, 37), (30, 20), (7, 24), (34, 38), (38, 17), (21, 18), (5, 22), (40, 29), (9, 17), (35, 13), (29, 20), (4, 19), (37, 21), (32, 28), (32, 14), (31, 30), (25, 13), (25, 29), (26, 2), (14, 24), (36, 23), (13, 5), (14, 37), (3, 12), (12, 17), (3, 38), (0, 22), (16, 25), (39, 11), (26, 3), (1, 0), (33, 9), (40, 25), (23, 14), (15, 35), (0, 36), (37, 31), (13, 34), (16, 22), (1, 35), (41, 16), (43, 27), (26, 28), (40, 23), (19, 17), (36, 16), (24, 37), (40, 9), (5, 34), (22, 38), (12, 8), (23, 15), (35, 22), (35, 38), (9, 18), (2, 35), (35, 17), (19, 4), (43, 35), (34, 28), (23, 11), (26, 4), (0, 30), (0, 4), (30, 11), (33, 37), (26, 5), (23, 5), (23, 24), (17, 4), (27, 17), (35, 26), (22, 35), (14, 35), (41, 9), (31, 21), (38, 21), (32, 13), (30, 33), (19, 3), (16, 34), (9, 3), (12, 9), (13, 17), (27, 26), (12, 34), (41, 19), (43, 1), (31, 7), (20, 37), (39, 35), (32, 3), (10, 27), (14, 32), (6, 18), (41, 38), (32, 33), (6, 20), (35, 12), (39, 5), (39, 16), (13, 18), (42, 22), (27, 10), (18, 19), (7, 0), (27, 12), (6, 28), (28, 22), (33, 35), (22, 33), (28, 7), (28, 14), (16, 39), (24, 10), (14, 12), (26, 33), (2, 28), (6, 24), (24, 3), (9, 2), (41, 11), (20, 12), (6, 27), (26, 20), (5, 15), (21, 11), (17, 18), (21, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 37), (27, 8), (20, 5), (10, 34), (5, 32), (43, 40), (15, 38), (3, 17), (35, 39), (34, 40), (2, 9), (6, 17), (47, 20), (36, 25), (8, 18), (10, 20), (13, 7), (36, 20), (11, 33), (1, 4), (38, 13), (30, 31), (40, 12), (46, 26), (45, 27), (23, 19), (12, 2), (25, 28), (16, 30), (2, 8), (47, 6), (10, 16), (35, 12), (45, 0), (40, 17), (45, 28), (46, 20), (5, 38), (26, 7), (9, 38), (20, 39), (38, 23), (32, 41), (14, 0), (31, 11), (35, 10), (21, 29), (3, 11), (6, 2), (16, 19), (21, 16), (45, 39), (24, 6), (26, 31), (45, 26), (0, 35), (2, 33), (11, 40), (0, 21), (5, 1), (30, 7), (46, 31), (45, 5), (0, 22), (14, 29), (10, 30), (1, 21), (16, 35), (36, 23), (14, 32), (8, 9), (0, 6), (25, 20), (8, 22), (1, 5), (1, 40), (20, 35), (13, 9), (26, 22), (16, 31), (10, 13), (1, 9), (2, 17), (35, 2), (23, 32), (25, 26), (45, 16), (29, 29), (7, 18), (2, 3), (0, 26), (46, 17), (8, 36), (23, 4), (20, 25), (14, 13), (40, 3), (38, 32), (22, 10), (19, 32), (43, 15), (20, 10), (43, 35), (0, 20), (9, 17), (15, 15), (17, 6), (19, 10), (37, 40), (29, 34), (36, 6), (5, 9), (15, 37), (41, 39), (35, 8), (28, 5), (36, 28), (0, 38), (32, 12), (32, 29), (29, 3), (8, 33), (38, 27), (13, 32), (37, 28), (13, 22), (6, 31), (14, 17), (7, 16), (11, 20), (35, 23), (2, 23), (39, 1), (31, 24), (7, 32), (43, 33), (40, 40), (41, 19), (44, 10), (10, 33), (11, 0), (32, 22), (43, 22), (27, 14), (44, 22), (17, 2), (30, 23), (19, 33), (14, 31), (20, 20), (33, 11), (47, 32), (9, 41), (22, 38), (37, 12), (17, 17), (13, 29), (18, 38), (25, 34), (18, 29), (7, 34), (11, 32), (29, 14), (41, 3), (31, 3), (47, 1), (22, 29), (47, 19), (12, 41), (33, 36), (27, 10), (34, 28), (42, 19), (27, 23), (46, 29), (10, 32), (43, 10), (25, 16), (46, 16), (9, 22), (40, 34), (30, 37), (12, 36), (7, 7), (42, 35), (17, 13), (10, 37), (44, 20), (37, 35), (37, 37), (24, 10), (25, 36), (43, 16), (16, 11), (32, 33), (7, 8), (16, 33), (7, 41), (22, 37), (45, 36), (26, 14), (12, 18), (2, 31), (17, 36), (16, 14), (43, 1), (39, 28), (17, 11), (11, 38), (18, 26), (4, 12), (28, 18), (44, 31), (38, 6), (3, 34), (10, 26), (31, 39), (22, 39), (8, 6), (19, 2), (25, 2), (0, 9), (44, 33), (47, 34), (17, 27), (45, 40), (40, 2), (41, 29), (42, 4), (7, 6), (15, 31), (18, 3), (36, 1), (36, 4), (3, 25), (44, 19), (35, 5), (21, 11), (12, 13), (33, 33), (31, 9), (9, 26), (29, 31), (42, 16), (21, 22), (41, 28), (31, 12), (14, 1), (20, 31), (14, 8), (17, 5), (6, 9), (7, 2), (47, 38), (37, 18), (17, 30), (16, 24), (44, 17), (30, 22), (45, 14), (17, 32), (42, 36), (26, 6), (4, 0), (9, 21), (19, 20), (26, 16), (28, 29), (14, 15), (8, 19), (15, 39), (25, 12), (23, 25), (19, 1), (13, 3), (21, 36), (33, 31), (18, 37), (31, 1), (24, 14), (5, 10), (37, 17), (14, 14), (14, 6), (32, 37), (7, 0), (18, 28), (10, 39), (44, 25), (12, 15), (1, 31), (1, 24), (37, 26), (47, 31), (6, 1), (32, 30), (22, 8), (21, 3), (21, 33), (46, 1), (19, 5), (34, 33), (34, 34), (40, 4), (29, 26), (10, 29), (47, 29), (25, 22), (46, 6), (21, 41), (10, 7), (21, 26), (31, 30), (40, 38), (12, 25), (1, 26), (19, 37), (35, 17), (21, 32), (4, 20), (17, 4), (5, 12), (9, 2), (15, 25), (36, 31), (14, 36), (42, 11), (43, 24), (23, 29), (1, 36), (28, 2), (20, 13), (3, 19), (46, 40), (4, 39), (22, 21), (41, 31), (31, 5), (24, 17), (15, 22), (23, 40), (42, 25), (26, 32), (2, 34), (19, 18), (41, 41), (29, 9), (29, 37), (7, 25), (3, 10), (29, 4), (24, 28), (32, 10), (22, 11), (2, 37), (23, 17), (17, 37), (38, 26), (32, 26), (28, 32), (2, 14), (45, 23), (44, 41), (19, 27), (8, 16), (5, 39), (0, 12), (41, 38), (40, 20), (37, 10), (34, 22), (30, 25), (45, 38), (46, 25), (19, 15), (19, 22), (23, 27), (25, 27), (15, 5), (38, 28), (20, 6), (18, 0), (8, 10), (42, 24), (44, 18), (22, 30), (20, 19), (3, 27), (11, 16), (15, 32), (18, 30), (1, 0), (36, 37), (32, 31), (19, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 40x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 13), (24, 12), (18, 8), (2, 32), (4, 7), (17, 15), (20, 32), (4, 6), (35, 17), (16, 4), (19, 9), (12, 7), (4, 34), (11, 6), (28, 25), (31, 0), (32, 26), (9, 19), (4, 16), (13, 22), (19, 0), (22, 16), (9, 14), (22, 6), (38, 9), (23, 26), (31, 13), (15, 28), (0, 18), (11, 3), (20, 4), (30, 38), (20, 29), (27, 19), (13, 6), (37, 17), (0, 4), (19, 16), (35, 14), (15, 18), (4, 5), (22, 7), (0, 40), (7, 20), (14, 4), (2, 9), (17, 22), (22, 19), (7, 12), (26, 19), (27, 9), (1, 4), (31, 5), (6, 22), (19, 37), (39, 7), (24, 4), (6, 24), (30, 17), (6, 4), (16, 21), (34, 10), (2, 11), (1, 26), (20, 9), (0, 41), (0, 22), (25, 39), (10, 4), (22, 21), (31, 7), (30, 1), (21, 3), (27, 29), (3, 4), (32, 2), (24, 1), (12, 35), (32, 14), (10, 2), (22, 40), (4, 37), (25, 37), (29, 38), (4, 38), (7, 1), (34, 33), (27, 27), (1, 28), (8, 18), (16, 38), (33, 31), (0, 25), (3, 17), (29, 39), (29, 7), (34, 36), (34, 20), (11, 34), (27, 0), (31, 25), (34, 1), (3, 6), (34, 40), (34, 2), (35, 35), (14, 32), (0, 2), (28, 39), (3, 36), (17, 28), (13, 21), (20, 15), (5, 31), (32, 30), (6, 10), (2, 24), (38, 29), (12, 13), (27, 8), (10, 20), (0, 37), (8, 16), (20, 35), (7, 22), (6, 12), (6, 41), (9, 5), (31, 27), (16, 2), (6, 17), (35, 38), (34, 5), (26, 41), (36, 5), (11, 25), (15, 16), (20, 33), (11, 32), (35, 29), (36, 18), (6, 32), (28, 36), (32, 35), (34, 30), (14, 25), (15, 3), (7, 37), (15, 24), (14, 41), (15, 38), (16, 34), (11, 13), (11, 1), (28, 5), (18, 34), (16, 9), (19, 24), (33, 12), (19, 41), (33, 16), (31, 8), (21, 8), (33, 36), (1, 14), (29, 12), (21, 22), (12, 10), (20, 41), (15, 41), (14, 7), (6, 40), (14, 13), (31, 37), (12, 12), (33, 19), (1, 34), (28, 26), (21, 13), (26, 15), (36, 7), (23, 28), (17, 10), (8, 36), (9, 1), (19, 26), (29, 20), (26, 7), (10, 7), (0, 9), (37, 10), (33, 28), (31, 18), (32, 29), (27, 34), (33, 21), (26, 22), (17, 24), (7, 7), (3, 34), (18, 28), (29, 28), (37, 28), (28, 4), (17, 18), (13, 3), (26, 32), (7, 25), (8, 23), (3, 40), (3, 18), (16, 7), (28, 27), (27, 30), (13, 29), (37, 12), (21, 17), (26, 40), (19, 17), (14, 21), (24, 35), (11, 16), (10, 15), (24, 19), (25, 15), (0, 17), (21, 9), (21, 10), (33, 7), (16, 36), (0, 14), (33, 20), (5, 0), (27, 17), (32, 31), (18, 19), (25, 29), (10, 13), (27, 21), (23, 16), (33, 0), (15, 9), (0, 6), (5, 21), (5, 27), (30, 12), (26, 33), (1, 10), (18, 5), (15, 5), (36, 1), (25, 25), (29, 18), (8, 34), (23, 29), (32, 16), (39, 24), (28, 13), (14, 31), (36, 3), (33, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 40), (37, 5), (32, 33), (27, 1), (5, 11), (12, 7), (6, 10), (47, 32), (32, 23), (37, 33), (30, 36), (7, 23), (5, 14), (3, 31), (47, 36), (33, 29), (10, 38), (9, 23), (10, 17), (47, 30), (38, 27), (17, 1), (31, 13), (25, 27), (36, 3), (24, 2), (13, 21), (16, 1), (3, 5), (28, 36), (1, 37), (18, 26), (43, 20), (45, 41), (16, 34), (43, 3), (0, 5), (34, 36), (23, 33), (16, 19), (32, 17), (2, 9), (34, 12), (36, 6), (13, 12), (3, 2), (0, 32), (21, 25), (5, 31), (5, 22), (42, 5), (1, 4), (48, 31), (32, 7), (42, 39), (43, 37), (13, 35), (19, 2), (2, 18), (31, 26), (25, 0), (41, 10), (6, 0), (5, 13), (10, 3), (36, 7), (46, 28), (33, 31), (44, 34), (38, 4), (19, 0), (25, 20), (31, 30), (16, 18), (35, 0), (21, 8), (29, 25), (5, 28), (25, 24), (20, 37), (7, 41), (21, 13), (0, 28), (27, 41), (29, 2), (13, 11), (26, 13), (14, 10), (16, 8), (38, 12), (6, 2), (38, 15), (28, 19), (48, 34), (0, 15), (43, 21), (45, 8), (4, 12), (23, 35), (31, 4), (10, 24), (15, 3), (5, 0), (33, 12), (37, 40), (44, 13), (43, 11), (15, 21), (47, 34), (40, 0), (43, 6), (23, 9), (26, 38), (41, 15), (22, 5), (4, 2), (38, 23), (14, 11), (3, 0), (5, 3), (2, 21), (20, 21), (27, 29), (38, 13), (33, 20), (24, 24), (15, 1), (7, 12), (13, 0), (30, 34), (1, 35), (23, 29), (29, 18), (10, 16), (14, 9), (7, 15), (47, 28), (13, 16), (22, 30), (38, 39), (13, 30), (7, 8), (36, 5), (40, 23), (27, 25), (39, 28), (13, 19), (24, 12), (8, 10), (1, 16), (1, 36), (33, 7), (36, 10), (29, 14), (40, 36), (47, 26), (30, 8), (3, 15), (0, 33), (4, 18), (11, 14), (14, 12), (6, 21), (3, 23), (32, 15), (6, 32), (14, 21), (16, 21), (14, 41), (17, 41), (45, 31), (23, 11), (8, 36), (34, 11), (34, 14), (9, 9), (28, 23), (38, 6), (1, 15), (12, 26), (27, 40), (19, 30), (1, 11), (18, 4), (46, 25), (24, 3), (34, 15), (29, 40), (25, 30), (26, 3), (6, 11), (14, 7), (1, 21), (24, 15), (17, 12), (21, 6), (1, 2), (31, 15), (30, 40), (38, 28), (42, 21), (37, 28), (26, 18), (12, 5), (28, 35), (20, 13), (33, 8), (7, 16), (0, 12), (37, 2), (11, 18), (38, 11), (4, 1), (20, 5), (35, 35), (18, 5), (17, 20), (48, 37), (38, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 36), (31, 0), (48, 38), (11, 31), (9, 6), (13, 15), (38, 47), (41, 25), (40, 21), (36, 28), (9, 47), (38, 9), (23, 38), (47, 27), (26, 46), (45, 2), (46, 46), (1, 46), (19, 2), (43, 11), (30, 40), (4, 20), (4, 42), (37, 26), (10, 11), (37, 13), (0, 43), (8, 24), (2, 34), (28, 32), (33, 28), (21, 15), (8, 1), (39, 46), (33, 21), (28, 41), (26, 45), (6, 10), (10, 43), (44, 33), (45, 5), (39, 8), (0, 8), (7, 12), (13, 39), (31, 45), (12, 4), (23, 11), (15, 10), (19, 19), (38, 11), (0, 42), (18, 5), (28, 15), (36, 6), (6, 15), (48, 25), (23, 8), (25, 37), (26, 41), (31, 15), (31, 27), (10, 20), (11, 5), (26, 19), (28, 31), (1, 6), (16, 28), (34, 15), (33, 18), (13, 30), (6, 24), (37, 8), (45, 25), (28, 16), (17, 11), (17, 21), (30, 43), (10, 7), (0, 29), (19, 31), (39, 2), (39, 5), (34, 41), (22, 13), (37, 29), (16, 43), (24, 27), (24, 21), (7, 43), (3, 43), (36, 32), (31, 22), (13, 23), (45, 15), (29, 44), (8, 37), (41, 13), (3, 12), (30, 42), (23, 46), (44, 27), (9, 41), (23, 43), (28, 40), (3, 9), (36, 8), (28, 9), (40, 14), (41, 31), (41, 37), (23, 22), (0, 22), (36, 39), (44, 13), (43, 5), (23, 0), (32, 22), (14, 40), (47, 22), (22, 39), (31, 10), (32, 3), (39, 37), (38, 21), (40, 45), (37, 28), (18, 44), (37, 21), (24, 24), (0, 10), (7, 21), (18, 23), (2, 19), (30, 11), (46, 20), (32, 30), (3, 20), (26, 26), (34, 33), (38, 39), (34, 34), (45, 23), (33, 44), (34, 23), (21, 8), (3, 32), (1, 26), (17, 3), (35, 31), (47, 7), (22, 25), (47, 43), (34, 44), (36, 46), (18, 41), (19, 17), (45, 11), (23, 39), (28, 21), (43, 35), (9, 38), (12, 6), (11, 41), (4, 11), (13, 8), (21, 7), (12, 38), (36, 3), (8, 32), (33, 13), (10, 45), (22, 15), (21, 46), (2, 17), (42, 4), (18, 47), (19, 27), (35, 2), (24, 40), (16, 15), (43, 4), (18, 42), (34, 28), (5, 30), (9, 37), (38, 26), (34, 22), (33, 45), (23, 5), (23, 29), (25, 13), (7, 35), (15, 25), (4, 8), (38, 2), (10, 33), (26, 17), (11, 11), (9, 24), (20, 25), (39, 47), (5, 39), (9, 8), (47, 25), (11, 7), (10, 17), (3, 16), (43, 32), (22, 4), (23, 14), (13, 9), (22, 30), (4, 15), (8, 11), (37, 33), (8, 30), (1, 8), (21, 10), (37, 4), (40, 33), (21, 14), (26, 8), (18, 19), (21, 35), (16, 5), (10, 5), (22, 0), (31, 18), (28, 11), (22, 34), (28, 27), (1, 22), (13, 27), (28, 42), (26, 18), (16, 9), (8, 40), (13, 44), (31, 19), (9, 13), (0, 30), (1, 7), (16, 38), (32, 9), (43, 17), (7, 36), (12, 29), (7, 26), (43, 30), (15, 15), (43, 10), (27, 28), (43, 29), (34, 0), (35, 44), (46, 13), (40, 42), (12, 11), (42, 14), (10, 13), (42, 37), (18, 18), (41, 1), (4, 16), (20, 42), (7, 13), (26, 29), (36, 20), (33, 40), (44, 14), (12, 24), (45, 47), (7, 44), (44, 7), (12, 39), (23, 20), (8, 16), (30, 18), (40, 30), (5, 5), (27, 44), (37, 40), (24, 41), (0, 16), (41, 5), (15, 31), (19, 8), (7, 8), (9, 26), (41, 15), (42, 32), (9, 42), (29, 14), (15, 9), (14, 31), (28, 46), (46, 4), (3, 3), (8, 25), (31, 39), (5, 2), (37, 18), (9, 33), (8, 6), (1, 34), (45, 28), (40, 6), (15, 40), (4, 46), (13, 10), (38, 36), (28, 8), (10, 24), (10, 15), (18, 16), (10, 22), (32, 46)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 19), (0, 43), (6, 37), (12, 4), (3, 6), (33, 47), (2, 3), (41, 9), (4, 19), (44, 45), (32, 22), (2, 20), (1, 40), (30, 28), (33, 28), (36, 34), (16, 11), (12, 36), (29, 4), (18, 29), (19, 26), (1, 19), (23, 21), (36, 48), (44, 22), (17, 37), (1, 3), (7, 38), (17, 29), (5, 12), (14, 15), (31, 44), (9, 8), (10, 18), (27, 19), (23, 37), (20, 18), (39, 6), (45, 32), (21, 42), (2, 23), (45, 41), (24, 18), (1, 26), (42, 24), (10, 47), (23, 42), (36, 23), (33, 6), (21, 34), (21, 11), (23, 38), (18, 25), (43, 19), (18, 18), (6, 16), (36, 26), (30, 24), (41, 41), (1, 9), (43, 27), (42, 18), (25, 27), (16, 26), (19, 20), (44, 47), (35, 5), (9, 46), (10, 8), (29, 28), (18, 43), (3, 34), (28, 23), (25, 8), (21, 4), (34, 26), (10, 4), (0, 22), (0, 32), (3, 15), (15, 22), (0, 37), (19, 23), (12, 16), (40, 1), (39, 21), (21, 28), (20, 9), (0, 15), (23, 36), (1, 31), (28, 35), (15, 25), (19, 29), (32, 23), (1, 36), (13, 48), (43, 44), (8, 20), (26, 26), (31, 0), (15, 13), (23, 46), (38, 0), (12, 42), (20, 24), (24, 47), (33, 44), (16, 9), (37, 35), (26, 24), (34, 9), (30, 30), (18, 40), (22, 24), (3, 30), (22, 38), (1, 7), (9, 48), (43, 47), (34, 34), (21, 1), (2, 39), (9, 15), (34, 48), (19, 46), (28, 44), (11, 36), (14, 0), (12, 19), (7, 14), (31, 48), (16, 19), (18, 27), (29, 15), (22, 30), (42, 5), (12, 10), (27, 16), (41, 39), (35, 14), (32, 27), (29, 16), (23, 10), (18, 11), (26, 2), (5, 5), (34, 10), (8, 43), (15, 3), (30, 39), (4, 33), (16, 36), (14, 17), (7, 27), (42, 6), (37, 36), (41, 48), (27, 11), (29, 45), (41, 12), (15, 37), (41, 38), (12, 5), (37, 33), (0, 5), (7, 8), (18, 46), (4, 0), (32, 2), (13, 12), (30, 25), (38, 29), (44, 12), (27, 38), (12, 23), (30, 32), (6, 24), (31, 12), (22, 17), (30, 47), (28, 47), (1, 2), (39, 16), (37, 40), (12, 17), (2, 33), (20, 1), (22, 6), (29, 35), (21, 21), (35, 43), (4, 38), (26, 47), (33, 42), (30, 15), (16, 33), (22, 35), (41, 47), (23, 9), (5, 33), (35, 18), (34, 11), (13, 14), (5, 44), (27, 32), (25, 0), (13, 22), (1, 28), (27, 6), (4, 47), (5, 16), (36, 29), (12, 39), (12, 18), (21, 48), (17, 46), (38, 13), (27, 20), (40, 28), (37, 1), (45, 14), (31, 10), (29, 22), (22, 34), (40, 19), (40, 41), (0, 12), (19, 16), (31, 46), (43, 21), (25, 25), (39, 44), (38, 48), (45, 30), (27, 42), (8, 5), (39, 34), (5, 34), (14, 39), (21, 2), (27, 35), (5, 45), (17, 9), (17, 48), (33, 17), (10, 11), (44, 35), (15, 23), (35, 37), (41, 32), (6, 2), (24, 33), (36, 28), (41, 5), (21, 0), (12, 20), (5, 27), (35, 17), (29, 40), (5, 26), (31, 24), (24, 29), (7, 33), (38, 41), (13, 34), (41, 20), (26, 44), (19, 34), (23, 5), (14, 19), (45, 43), (45, 15), (8, 11), (15, 0), (43, 30), (14, 35), (45, 45), (24, 19), (17, 40), (21, 27), (31, 22), (14, 5), (18, 33), (30, 19), (23, 0), (38, 9), (0, 46), (1, 1), (31, 33), (4, 34), (16, 20), (31, 34), (24, 9), (23, 27), (0, 47), (29, 0), (44, 29), (16, 42), (37, 2), (18, 7), (40, 47), (4, 40), (14, 1), (3, 35), (10, 17), (4, 46), (39, 18), (16, 22), (3, 10), (13, 36), (17, 16), (16, 21), (25, 43), (15, 42), (11, 10), (10, 22), (6, 27), (15, 24), (29, 36), (3, 12), (26, 19), (42, 48), (13, 24), (40, 34), (16, 46), (36, 13), (13, 18), (0, 34), (21, 24), (26, 28), (45, 13), (9, 13), (1, 23), (36, 35), (8, 24), (22, 14), (35, 35), (25, 24), (11, 9), (7, 9), (29, 29), (4, 29), (40, 22), (42, 16), (3, 23), (32, 24), (7, 4), (0, 30), (13, 45), (17, 24), (36, 30), (25, 39), (40, 13), (24, 1), (7, 2), (17, 30), (15, 11), (13, 33), (25, 37), (15, 2), (6, 1), (6, 47), (3, 47), (38, 18), (0, 14), (1, 12), (20, 33), (21, 17), (29, 14), (14, 3), (2, 25), (10, 28), (2, 30), (12, 43), (41, 22), (28, 14), (32, 5), (20, 16), (36, 12), (22, 5), (31, 14), (40, 7), (20, 14), (17, 45), (37, 39), (14, 30), (20, 40), (35, 3), (38, 7), (36, 11), (28, 26), (24, 26), (17, 20), (41, 36), (42, 15), (20, 35), (14, 16), (21, 40), (42, 38), (44, 40), (24, 38), (41, 29), (4, 41), (17, 3), (33, 30), (11, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 29), (20, 15), (38, 14), (17, 6), (9, 27), (10, 35), (6, 0), (2, 31), (36, 10), (10, 1), (15, 13), (6, 40), (19, 16), (19, 2), (20, 19), (35, 40), (27, 15), (42, 6), (8, 36), (2, 5), (27, 37), (27, 13), (25, 2), (38, 40), (35, 16), (33, 39), (13, 5), (9, 31), (12, 7), (35, 24), (22, 6), (14, 21), (6, 30), (43, 24), (27, 4), (14, 3), (0, 5), (42, 25), (16, 4), (4, 6), (2, 11), (12, 26), (14, 25), (7, 30), (7, 27), (23, 31), (28, 29), (34, 40), (14, 16), (15, 8), (16, 34), (22, 38), (14, 38), (19, 38), (18, 19), (18, 18), (25, 12), (7, 37), (8, 40), (21, 39), (16, 14), (42, 19), (29, 2), (25, 22), (37, 8), (43, 20), (5, 17), (27, 6), (13, 32), (35, 26), (14, 33), (43, 30), (36, 36), (19, 0), (10, 29), (43, 34), (34, 19), (25, 16), (24, 7), (27, 40), (38, 36), (26, 7), (11, 4), (35, 35), (43, 1), (27, 16), (33, 2), (15, 16), (19, 35), (20, 18), (28, 10), (16, 17), (18, 31), (32, 15), (39, 35), (14, 0), (36, 0), (20, 21), (15, 12), (19, 14), (19, 7), (43, 6), (5, 21), (23, 20), (8, 29), (4, 0), (1, 10), (13, 15), (13, 40), (29, 26), (3, 28), (27, 20), (42, 24), (39, 7), (4, 18), (21, 17), (37, 1), (2, 22), (10, 34), (18, 9), (31, 31), (30, 0), (9, 4), (39, 14), (24, 39), (31, 6), (40, 39), (30, 2), (21, 22), (28, 18), (29, 30), (36, 29), (17, 23), (30, 32), (34, 39), (13, 20), (40, 11), (1, 22), (22, 33), (0, 30), (4, 15), (20, 4), (41, 24), (25, 31), (38, 32), (23, 38), (43, 35), (16, 15), (42, 40), (12, 19), (28, 20), (17, 4), (0, 20), (40, 29), (16, 30), (2, 21), (11, 7), (18, 25), (24, 12), (3, 25), (41, 5), (29, 36), (34, 3), (10, 30), (21, 25), (6, 1), (33, 4), (32, 3), (23, 2), (29, 9), (43, 0), (26, 32), (15, 17), (23, 35), (34, 0), (10, 38), (7, 8), (35, 33), (4, 22), (0, 14), (7, 36), (39, 9), (26, 5), (0, 10), (22, 1), (13, 28), (16, 6), (27, 30), (24, 1), (42, 37), (3, 19), (22, 4), (27, 34), (8, 33), (23, 11), (5, 20), (42, 16), (4, 16), (25, 11), (30, 13), (0, 9), (43, 25), (6, 5), (14, 32), (11, 14), (42, 28), (11, 39), (20, 32), (16, 9), (12, 32), (3, 7), (21, 32), (30, 16), (30, 23), (21, 23), (5, 32), (0, 11), (5, 38), (6, 17), (36, 6), (34, 16), (30, 29), (21, 7), (11, 0), (16, 8), (7, 12), (27, 38), (21, 15), (37, 26), (2, 9), (39, 40), (13, 29), (33, 21), (11, 30), (10, 0), (1, 15), (41, 10), (29, 37), (38, 1), (11, 40), (21, 36), (6, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 15), (25, 25), (4, 26), (0, 14), (23, 1), (29, 2), (6, 36), (19, 8), (10, 33), (19, 32), (23, 22), (3, 23), (4, 33), (6, 29), (24, 4), (11, 18), (27, 17), (0, 4), (27, 11), (33, 16), (3, 4), (2, 40), (37, 21), (13, 23), (15, 0), (42, 24), (44, 21), (26, 8), (39, 27), (25, 40), (40, 18), (15, 16), (46, 29), (11, 37), (22, 39), (33, 30), (24, 8), (33, 2), (10, 19), (23, 24), (27, 33), (11, 14), (31, 21), (8, 42), (15, 27), (25, 38), (42, 16), (1, 9), (18, 16), (7, 3), (44, 23), (39, 8), (2, 1), (8, 32), (36, 22), (19, 21), (8, 16), (32, 26), (1, 27), (32, 12), (13, 41), (32, 22), (25, 3), (17, 35), (40, 27), (13, 2), (33, 37), (23, 20), (2, 31), (24, 15), (13, 27), (2, 29), (13, 3), (31, 26), (26, 2), (43, 26), (31, 10), (40, 30), (41, 22), (39, 36), (22, 11), (1, 15), (44, 19), (35, 2), (22, 6), (21, 31), (35, 42), (45, 6), (8, 11), (46, 4), (37, 18), (21, 29), (1, 26), (39, 40), (36, 20), (13, 8), (36, 33), (35, 19), (28, 8), (28, 0), (0, 38), (40, 16), (29, 40), (23, 25), (11, 12), (43, 19), (8, 29), (22, 41), (39, 31), (34, 22), (24, 37), (14, 23), (32, 6), (38, 32), (5, 29), (13, 38), (29, 0), (11, 32), (45, 11), (46, 1), (6, 35), (41, 13), (28, 12), (46, 25), (26, 17), (11, 30), (40, 28), (42, 25), (6, 6), (40, 37), (21, 9), (28, 25), (31, 19), (28, 24), (19, 31), (17, 2), (29, 24), (29, 38), (18, 25), (16, 10), (29, 4), (37, 4), (31, 17), (21, 43), (8, 1), (7, 7), (28, 5), (18, 13), (1, 42), (15, 20), (40, 44), (0, 44), (36, 2), (0, 18), (8, 44), (25, 2), (3, 37), (8, 4), (31, 8), (31, 40), (46, 30), (7, 0), (44, 41), (4, 15), (27, 23), (23, 7), (16, 12), (38, 7), (10, 6), (40, 11), (28, 14), (42, 11), (8, 37), (8, 14), (32, 17), (28, 32), (12, 33), (10, 32), (42, 0), (26, 40), (38, 44), (45, 40), (34, 15), (6, 33), (9, 13), (36, 40), (42, 6), (39, 10), (7, 27), (33, 41), (43, 33), (5, 7), (15, 41), (19, 26), (15, 28), (22, 2), (26, 41), (26, 35), (21, 24), (11, 19), (34, 14), (26, 25), (35, 17), (28, 13), (10, 42), (22, 32), (26, 24), (11, 43), (19, 25), (6, 44), (8, 0), (28, 26), (24, 33), (8, 21), (36, 42), (9, 41), (21, 39), (39, 29), (13, 10), (45, 29), (13, 21), (45, 14), (32, 30), (44, 25), (1, 19), (40, 41), (43, 6), (9, 4), (5, 17), (27, 14), (37, 27), (25, 23), (31, 30), (15, 33), (18, 31), (35, 1), (44, 27), (14, 5), (44, 30), (4, 23), (9, 36), (28, 2), (39, 18), (29, 16), (26, 23), (23, 35), (27, 38), (4, 9), (13, 9), (42, 44), (25, 39), (38, 21), (9, 6), (24, 7), (18, 23), (1, 25), (37, 28), (19, 41), (31, 9), (2, 0), (41, 16), (4, 12), (11, 11), (16, 30), (44, 2), (21, 3), (14, 29), (26, 3), (39, 22), (5, 6), (41, 29), (46, 0), (18, 17), (19, 18), (21, 40), (4, 19), (2, 10), (38, 22), (41, 1), (34, 17), (7, 2), (13, 28), (25, 18), (17, 26), (15, 30), (40, 24), (37, 11), (30, 1), (27, 24), (21, 10), (35, 6), (25, 32), (45, 28), (26, 42), (40, 39), (19, 3), (46, 9), (34, 16), (18, 30), (43, 7), (15, 18), (6, 37), (19, 39), (12, 38), (5, 5), (12, 22), (9, 12), (11, 13), (44, 10), (5, 22), (28, 40), (32, 44), (10, 29), (42, 10), (41, 41), (2, 18), (45, 1), (45, 41), (37, 34), (25, 33), (33, 33), (1, 40), (44, 34), (7, 9), (12, 41), (37, 22), (10, 13), (38, 25), (38, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 39), (3, 31), (1, 11), (40, 29), (11, 40), (3, 19), (29, 20), (15, 2), (28, 30), (24, 3), (41, 15), (43, 21), (38, 30), (5, 38), (18, 10), (42, 6), (2, 5), (41, 21), (4, 36), (24, 40), (4, 18), (21, 6), (19, 3), (33, 2), (22, 35), (33, 8), (44, 37), (28, 15), (25, 37), (29, 19), (6, 9), (30, 36), (14, 6), (7, 15), (18, 17), (4, 28), (11, 21), (3, 36), (15, 3), (28, 7), (23, 26), (37, 2), (44, 31), (43, 20), (20, 6), (15, 26), (34, 28), (12, 27), (7, 33), (41, 11), (32, 25), (0, 18), (18, 29), (0, 22), (38, 7), (16, 13), (16, 5), (41, 2), (27, 35), (34, 16), (36, 2), (37, 22), (6, 33), (21, 15), (13, 39), (34, 30), (37, 26), (33, 34), (0, 29), (15, 4), (10, 22), (6, 4), (18, 36), (36, 20), (15, 0), (38, 5), (13, 29), (9, 11), (4, 30), (30, 28), (19, 40), (17, 10), (6, 15), (43, 26), (10, 1), (10, 12), (24, 33), (38, 22), (10, 18), (23, 40), (32, 5), (34, 2), (13, 15), (6, 1), (23, 3), (42, 38), (7, 7), (20, 40), (26, 29), (2, 11), (2, 2), (42, 1), (39, 39), (22, 11), (17, 38), (12, 29), (20, 12), (4, 34), (26, 20), (27, 20), (16, 40), (41, 35), (24, 39), (38, 28), (5, 20), (12, 18), (6, 30), (14, 39), (0, 38), (3, 10), (43, 36), (37, 19), (31, 5), (32, 30), (24, 14), (40, 6), (35, 40), (34, 35), (29, 23), (5, 4), (18, 26), (2, 18), (27, 16), (27, 32), (40, 30), (39, 14), (37, 31), (24, 38), (41, 14), (34, 0), (33, 4), (9, 21), (27, 11), (1, 35), (7, 37), (16, 25), (15, 21), (36, 34), (5, 5), (22, 19), (29, 21), (1, 18), (7, 31), (6, 19), (37, 27), (44, 18), (13, 30), (32, 26), (4, 1), (44, 26), (43, 4), (42, 32), (6, 40), (40, 28), (14, 36), (19, 10), (35, 24), (13, 38), (21, 14), (38, 11), (37, 18), (27, 24), (16, 24), (6, 2), (40, 5), (23, 38), (4, 26), (13, 12), (1, 16), (18, 7), (32, 7), (40, 8), (26, 30), (25, 20), (20, 16), (20, 22), (1, 10), (6, 29), (31, 36), (8, 32), (11, 0), (25, 36), (5, 40), (32, 23), (26, 10), (19, 31), (22, 28), (37, 36), (40, 2), (44, 17), (21, 30), (41, 36), (34, 5), (4, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 22), (0, 41), (18, 4), (44, 28), (42, 41), (15, 45), (43, 45), (41, 13), (40, 2), (10, 17), (35, 13), (4, 18), (42, 36), (31, 44), (18, 9), (44, 30), (7, 32), (0, 20), (14, 35), (27, 16), (28, 25), (1, 12), (16, 39), (21, 20), (12, 8), (0, 10), (2, 20), (38, 1), (40, 23), (24, 10), (26, 38), (23, 5), (31, 46), (25, 37), (20, 7), (39, 25), (37, 14), (26, 21), (42, 5), (37, 38), (10, 18), (27, 43), (30, 35), (13, 47), (24, 4), (40, 28), (4, 3), (36, 8), (13, 24), (39, 1), (21, 35), (40, 20), (11, 9), (22, 5), (25, 22), (21, 7), (16, 33), (22, 41), (30, 25), (39, 26), (31, 14), (22, 40), (1, 8), (24, 40), (18, 21), (36, 17), (26, 11), (33, 43), (0, 24), (5, 7), (35, 33), (17, 5), (37, 33), (23, 47), (36, 6), (5, 47), (20, 48), (36, 36), (1, 9), (27, 30), (24, 8), (17, 48), (7, 21), (28, 12), (4, 10), (42, 1), (8, 3), (39, 6), (37, 39), (42, 28), (45, 7), (12, 25), (6, 4), (32, 37), (22, 31), (14, 46), (42, 14), (19, 19), (34, 38), (18, 23), (29, 5), (28, 34), (0, 5), (29, 0), (13, 30), (44, 3), (22, 13), (42, 26), (2, 48), (38, 20), (16, 7), (24, 32), (45, 0), (34, 32), (39, 45), (7, 15), (35, 43), (33, 13), (21, 28), (20, 31), (14, 24), (24, 7), (11, 33), (33, 26), (11, 43), (43, 0), (23, 32), (28, 3), (21, 8), (10, 7), (5, 38), (41, 30), (29, 34), (22, 21), (19, 9), (34, 5), (12, 48), (36, 2), (33, 19), (32, 24), (28, 37), (33, 46), (21, 30), (32, 32), (35, 46), (13, 0), (16, 4), (45, 37), (5, 40), (2, 44), (3, 38), (8, 42), (28, 24), (11, 45), (24, 34), (1, 42), (38, 30), (43, 5), (6, 32), (38, 13), (33, 30), (13, 42), (6, 15), (10, 38), (30, 40), (12, 2), (1, 43), (18, 47), (31, 34), (38, 42), (45, 22), (4, 19), (31, 10), (30, 19), (4, 4), (18, 28), (8, 0), (9, 0), (19, 48), (1, 35), (18, 13), (30, 17), (5, 30), (10, 4), (11, 40), (17, 22), (34, 8), (22, 38), (38, 26), (36, 31), (25, 36), (7, 42), (13, 44), (43, 4), (7, 24), (24, 12), (4, 2), (42, 39), (35, 25), (32, 0), (7, 44), (34, 26), (23, 44), (44, 9), (22, 30), (2, 22), (9, 22), (27, 19), (37, 3), (10, 22), (27, 14), (2, 23), (44, 45), (16, 14), (38, 27), (31, 0), (34, 7), (17, 14), (7, 4), (42, 25), (10, 19), (39, 10), (38, 36), (21, 6), (15, 18), (31, 6), (12, 1), (41, 16), (15, 23), (2, 4), (26, 14), (4, 20), (4, 28), (39, 24), (35, 44), (18, 6), (3, 22), (37, 46), (26, 46), (22, 43), (34, 21), (23, 18), (2, 36), (9, 38), (14, 19), (18, 29), (2, 32), (45, 29), (26, 30), (13, 46), (0, 31), (45, 43), (4, 31), (25, 26), (25, 23), (32, 16), (41, 43), (24, 25), (41, 33), (8, 26), (19, 46), (5, 46), (2, 42), (14, 28), (38, 28), (3, 12), (32, 9), (36, 13), (0, 28), (12, 12), (7, 37), (0, 6), (7, 33), (24, 28), (19, 27), (33, 16), (36, 15), (12, 35), (2, 0), (32, 33), (23, 17), (20, 27), (39, 19), (2, 47), (22, 48), (45, 38), (39, 9), (18, 17), (7, 45), (6, 27), (0, 3), (3, 11), (32, 15), (35, 4), (6, 42), (20, 2), (9, 37), (39, 43), (25, 43), (38, 11), (37, 19), (19, 41), (15, 19), (34, 27), (24, 21), (2, 18), (12, 37), (22, 6), (6, 0), (15, 2), (32, 1), (23, 28), (29, 17), (3, 29), (43, 26), (42, 38), (20, 25), (32, 8), (30, 26), (45, 39), (25, 34), (4, 1), (5, 2), (33, 47), (10, 12), (7, 40), (17, 39), (19, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 40), (17, 13), (6, 0), (20, 31), (28, 36), (44, 1), (38, 26), (2, 5), (11, 36), (17, 12), (38, 29), (9, 10), (43, 18), (19, 25), (18, 16), (41, 37), (30, 29), (27, 0), (7, 16), (26, 11), (41, 31), (26, 17), (16, 5), (14, 1), (9, 15), (0, 32), (18, 8), (43, 29), (37, 23), (19, 20), (30, 1), (43, 32), (23, 19), (37, 32), (28, 40), (8, 19), (29, 19), (25, 23), (16, 11), (19, 11), (13, 33), (8, 4), (4, 39), (14, 8), (1, 11), (4, 1), (17, 32), (13, 14), (27, 15), (39, 25), (37, 37), (15, 20), (2, 35), (26, 9), (0, 38), (7, 24), (4, 8), (0, 21), (16, 22), (34, 28), (32, 19), (42, 15), (28, 17), (27, 6), (14, 37), (24, 38), (8, 0), (30, 6), (20, 14), (10, 17), (28, 29), (33, 1), (22, 32), (31, 9), (23, 30), (38, 25), (19, 38), (25, 27), (37, 3), (21, 22), (41, 30), (14, 18), (32, 31), (26, 30), (32, 4), (39, 5), (39, 37), (19, 14), (4, 27), (25, 8), (30, 4), (13, 31), (41, 11), (36, 36), (27, 35), (33, 29), (6, 36), (21, 36), (17, 18), (40, 3), (32, 3), (29, 3), (28, 1), (20, 4), (1, 15), (33, 37), (1, 22), (13, 34), (8, 23), (21, 26), (13, 28), (31, 29), (42, 6), (13, 36), (29, 23), (0, 35), (5, 25), (20, 9), (0, 29), (32, 13), (9, 19), (35, 38), (2, 9), (22, 34), (37, 22), (3, 30), (14, 40), (7, 14), (7, 25), (37, 5), (29, 1), (41, 10), (23, 23), (1, 9), (35, 31), (40, 20), (14, 0), (2, 23), (44, 12), (37, 31), (26, 18), (1, 4), (40, 37), (25, 4), (14, 28), (30, 39), (40, 2), (11, 0), (43, 38), (4, 36), (12, 34), (31, 36), (7, 21), (8, 12), (18, 5), (10, 26), (18, 14), (29, 16), (39, 40), (14, 9), (3, 9), (36, 20), (27, 24), (16, 27), (22, 16), (43, 4), (2, 11), (17, 30), (35, 15), (28, 27), (8, 29), (15, 23), (33, 7), (17, 37), (31, 8), (36, 30), (4, 32), (42, 31), (20, 16), (4, 31), (28, 23), (44, 19), (37, 17), (29, 30), (21, 32), (13, 38), (33, 9), (34, 38), (26, 23), (22, 35), (23, 26), (14, 39), (1, 25), (11, 39), (6, 1), (21, 10), (20, 11), (33, 16), (3, 18), (26, 4), (5, 2), (13, 0), (34, 24), (6, 12), (2, 21), (9, 2), (19, 10), (24, 20), (27, 1), (28, 38), (17, 29), (6, 37), (23, 5), (30, 40), (1, 14), (6, 20), (0, 40), (35, 32), (32, 14), (27, 16), (33, 31), (32, 18), (34, 32), (42, 17), (14, 10), (41, 3), (9, 34), (24, 17), (1, 1), (7, 40), (0, 11), (43, 25), (25, 36), (5, 34), (6, 11), (12, 5), (36, 38), (41, 34), (4, 4), (38, 7), (6, 15), (1, 35), (17, 40), (16, 23), (6, 34), (34, 8), (10, 40), (43, 22), (10, 19), (28, 16), (2, 36), (39, 32), (16, 13), (15, 16), (6, 28), (36, 16), (24, 14), (27, 33), (38, 12), (12, 18), (15, 38), (33, 6), (25, 22), (41, 32), (22, 20), (16, 16), (11, 19), (20, 0), (33, 34), (42, 27), (32, 37), (17, 22), (16, 19), (17, 9), (24, 12), (38, 8), (11, 25), (44, 20), (3, 13), (34, 39), (2, 30), (2, 38), (34, 36), (33, 36), (4, 22), (24, 9), (18, 23), (36, 13), (26, 33), (38, 15), (7, 18), (43, 3), (17, 17), (34, 31), (25, 30), (36, 39), (29, 13), (37, 29), (12, 13), (8, 11), (13, 23), (13, 22), (39, 31), (28, 26), (20, 27), (25, 1), (44, 7), (24, 8), (4, 18), (42, 10), (12, 12), (19, 37), (10, 30), (24, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 15), (18, 37), (26, 26), (5, 20), (42, 13), (42, 8), (3, 8), (19, 1), (14, 40), (14, 23), (24, 9), (44, 31), (28, 12), (18, 40), (38, 6), (21, 25), (22, 31), (45, 18), (24, 31), (27, 19), (20, 25), (31, 16), (43, 26), (21, 29), (21, 24), (11, 15), (17, 10), (10, 7), (37, 2), (42, 11), (8, 36), (30, 35), (41, 39), (2, 10), (3, 32), (37, 13), (6, 1), (15, 16), (2, 15), (45, 0), (4, 41), (3, 31), (2, 0), (28, 8), (18, 7), (26, 22), (46, 28), (35, 30), (29, 11), (33, 15), (2, 2), (2, 32), (24, 27), (14, 12), (9, 28), (35, 4), (5, 2), (26, 38), (11, 11), (16, 37), (27, 21), (3, 0), (41, 29), (44, 33), (44, 28), (20, 21), (5, 6), (39, 12), (3, 38), (10, 29), (45, 22), (31, 0), (2, 3), (4, 23), (0, 19), (25, 7), (36, 39), (19, 26), (43, 17), (9, 17), (29, 6), (14, 22), (7, 6), (21, 36), (28, 30), (1, 33), (40, 39), (27, 14), (6, 19), (30, 8), (16, 12), (3, 9), (44, 35), (9, 16), (13, 21), (33, 6), (30, 13), (30, 31), (8, 9), (5, 4), (13, 13), (44, 24), (8, 32), (40, 11), (19, 40), (10, 6), (39, 13), (0, 8), (29, 7), (44, 15), (19, 24), (2, 38), (15, 27), (14, 25), (16, 35), (43, 3), (11, 19), (9, 5), (28, 25), (25, 1), (3, 7), (20, 4), (39, 18), (0, 27), (32, 27), (37, 7), (13, 6), (38, 33), (37, 30), (6, 18), (29, 4), (14, 37), (2, 8), (27, 0), (26, 7), (19, 12), (2, 36), (33, 23), (16, 19), (28, 19), (30, 23), (7, 29), (20, 23), (12, 37), (6, 12), (24, 7), (29, 32), (31, 20), (38, 21), (40, 21), (42, 3), (33, 20), (12, 7), (40, 14), (45, 7), (17, 35), (21, 12), (7, 20), (21, 23), (28, 35), (9, 12), (44, 34), (38, 27), (32, 37), (32, 6), (23, 33), (41, 21), (2, 35), (26, 13), (17, 5), (36, 24), (7, 9), (30, 37), (12, 25), (22, 19), (7, 30), (15, 10), (24, 11), (9, 15), (37, 28), (43, 1), (20, 28), (20, 14), (35, 2), (14, 0), (10, 38), (9, 38), (4, 16), (8, 30), (43, 4), (19, 25), (24, 41), (28, 11), (25, 18), (14, 29), (7, 5), (19, 36), (31, 22), (8, 26), (4, 9), (16, 14), (8, 27), (14, 3), (39, 41), (32, 19), (32, 9), (37, 11), (13, 3), (10, 16), (24, 0), (8, 11), (12, 19), (7, 27), (4, 27), (21, 38), (22, 27), (11, 14), (23, 17), (46, 2), (36, 18), (24, 24), (14, 41), (27, 11), (31, 19), (19, 23), (33, 24), (42, 29), (32, 22), (13, 39), (26, 35), (28, 16), (34, 21), (45, 9), (21, 0), (45, 4), (19, 41), (2, 13), (41, 40), (1, 27), (33, 27), (8, 7), (23, 24), (1, 25), (39, 35), (25, 32), (22, 10), (40, 25), (46, 4), (15, 15), (31, 36), (18, 32), (31, 17), (33, 29), (15, 36), (1, 2), (46, 37), (22, 24), (20, 16), (29, 15), (12, 4), (45, 27), (38, 41), (46, 32), (19, 0), (14, 24), (23, 30), (20, 41), (2, 27), (24, 29), (32, 2), (28, 39), (23, 22), (27, 16), (22, 20), (1, 21), (22, 21), (23, 39), (0, 12), (44, 18), (13, 19), (5, 11), (25, 0), (2, 22), (13, 40), (15, 40), (11, 32), (15, 3), (16, 5), (43, 22), (17, 38), (4, 0), (24, 18), (19, 27), (18, 4), (29, 5), (42, 19), (13, 34), (34, 41), (6, 6), (39, 16), (24, 32), (42, 41), (31, 7), (20, 1), (7, 38), (19, 33), (46, 35), (23, 7), (30, 29), (38, 26), (35, 24), (41, 37), (2, 29), (46, 17), (12, 8), (37, 18), (21, 33), (39, 40), (0, 33), (13, 20), (10, 24), (35, 16), (2, 4), (15, 2), (27, 23), (19, 21), (25, 5), (44, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 24), (8, 45), (17, 13), (2, 35), (22, 0), (2, 45), (35, 28), (20, 1), (25, 1), (3, 9), (0, 27), (29, 40), (14, 39), (29, 7), (41, 27), (0, 20), (0, 30), (42, 40), (42, 13), (24, 44), (28, 32), (3, 12), (4, 15), (11, 8), (11, 25), (19, 33), (16, 21), (29, 19), (11, 36), (3, 4), (29, 13), (16, 6), (4, 42), (15, 36), (3, 10), (5, 20), (19, 31), (1, 27), (46, 30), (19, 36), (39, 10), (10, 2), (30, 21), (31, 45), (38, 10), (5, 25), (26, 22), (16, 38), (47, 24), (8, 1), (26, 8), (45, 35), (27, 7), (11, 45), (0, 45), (34, 29), (29, 8), (31, 5), (12, 29), (9, 17), (28, 19), (34, 8), (35, 20), (3, 7), (15, 10), (24, 28), (20, 18), (44, 25), (13, 7), (22, 37), (17, 41), (7, 1), (38, 20), (17, 40), (1, 37), (45, 45), (12, 14), (44, 43), (4, 40), (42, 1), (29, 22), (3, 0), (8, 21), (20, 28), (46, 8), (44, 37), (38, 5), (38, 7), (4, 38), (29, 29), (1, 13), (46, 16), (27, 23), (31, 8), (16, 15), (21, 16), (29, 35), (37, 6), (5, 2), (18, 29), (26, 14), (25, 8), (21, 8), (27, 32), (29, 43), (34, 22), (34, 10), (41, 44), (22, 14), (45, 15), (20, 25), (10, 6), (13, 14), (45, 10), (41, 0), (29, 3), (44, 29), (33, 34), (25, 20), (26, 32), (6, 20), (12, 35), (43, 9), (19, 21), (14, 36), (26, 7), (4, 6), (45, 41), (19, 44), (38, 1), (36, 4), (22, 31), (46, 9), (35, 44), (3, 8), (2, 12), (41, 3), (40, 34), (39, 19), (15, 9), (9, 23), (45, 39), (40, 10), (35, 0), (0, 40), (26, 10), (27, 10), (21, 20), (16, 20), (14, 3), (8, 29), (40, 27), (31, 10), (8, 23), (29, 41), (18, 8), (14, 9), (36, 32), (26, 1), (36, 28), (44, 34), (19, 25), (30, 9), (1, 25), (43, 0), (24, 21), (25, 43), (16, 32), (41, 16), (9, 24), (47, 12), (26, 30), (31, 9), (28, 30), (19, 20), (4, 37), (8, 28), (32, 12), (37, 1), (20, 8), (41, 24), (11, 43), (24, 22), (20, 6), (47, 26), (15, 20), (13, 9), (9, 39), (28, 3), (45, 25), (32, 33), (22, 5), (5, 11), (31, 43), (18, 9), (16, 41), (21, 13), (13, 44), (39, 0), (25, 15), (8, 17), (35, 13), (10, 26), (31, 44), (34, 40), (6, 9), (35, 24), (26, 19), (23, 40), (38, 40), (27, 0), (17, 19), (28, 23), (11, 35), (13, 1), (20, 37), (24, 23), (27, 15), (15, 16), (4, 22), (4, 26), (21, 4), (31, 3), (36, 35), (7, 22), (5, 19), (37, 13), (22, 26), (46, 32), (26, 13), (20, 27), (9, 34), (26, 12), (45, 17), (6, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 31), (44, 35), (14, 38), (15, 37), (2, 37), (25, 28), (15, 16), (26, 14), (6, 25), (15, 4), (17, 13), (30, 7), (16, 17), (28, 24), (6, 9), (42, 13), (18, 23), (3, 16), (0, 39), (17, 12), (17, 8), (35, 9), (41, 34), (1, 12), (9, 39), (38, 20), (33, 24), (23, 31), (41, 25), (29, 30), (20, 35), (29, 5), (17, 0), (40, 2), (40, 35), (28, 17), (9, 30), (16, 4), (14, 20), (18, 34), (0, 28), (13, 37), (26, 1), (34, 3), (46, 39), (5, 13), (30, 38), (8, 9), (19, 37), (16, 18), (43, 17), (22, 14), (1, 15), (36, 14), (45, 11), (8, 5), (0, 5), (39, 38), (38, 15), (18, 5), (2, 10), (5, 26), (1, 25), (31, 17), (38, 33), (25, 12), (25, 13), (41, 14), (34, 34), (7, 13), (45, 27), (23, 8), (28, 22), (23, 14), (21, 25), (11, 27), (23, 12), (5, 18), (16, 2), (12, 13), (30, 5), (15, 30), (24, 22), (13, 24), (3, 8), (30, 39), (34, 20), (24, 30), (29, 25), (43, 40), (17, 25), (28, 34), (4, 8), (37, 31), (46, 16), (37, 16), (11, 22), (4, 21), (37, 9), (46, 34), (2, 22), (30, 12), (31, 27), (37, 20), (30, 6), (15, 7), (22, 34), (21, 40), (10, 4), (41, 40), (29, 12), (37, 8), (24, 39), (31, 34), (31, 22), (18, 2), (5, 17), (18, 8), (12, 9), (24, 20), (9, 5), (38, 23), (25, 0), (39, 35), (39, 20), (29, 36), (14, 6), (19, 38), (27, 9), (4, 32), (43, 36), (22, 2), (12, 22), (43, 7), (46, 3), (23, 37), (12, 23), (8, 18), (39, 4), (36, 1), (34, 25), (4, 22), (7, 38), (18, 32), (45, 3), (41, 27), (39, 28), (9, 13), (23, 24), (34, 12), (18, 35), (24, 32), (24, 2), (16, 26), (11, 11), (15, 27), (32, 11), (14, 24), (39, 19), (33, 36), (13, 0), (19, 30), (2, 2), (40, 27), (42, 12), (16, 32), (18, 10), (25, 25), (16, 22), (32, 19), (43, 24), (32, 8), (19, 10), (2, 6), (44, 17), (36, 19), (2, 28), (9, 7), (4, 30), (42, 33), (37, 12), (14, 8), (11, 29), (16, 12), (40, 29), (8, 1), (6, 1), (38, 18), (20, 7), (35, 38), (44, 0), (10, 30), (20, 3), (13, 28), (19, 18), (16, 7), (43, 23), (26, 16), (5, 38), (10, 18), (2, 0), (45, 21), (33, 15), (38, 5), (42, 9), (11, 14), (22, 4), (23, 19), (28, 25), (41, 21), (4, 34), (17, 10), (25, 17), (34, 1), (39, 26), (24, 29), (22, 20), (2, 18), (21, 34), (16, 9), (30, 11), (39, 13), (15, 34), (4, 36), (26, 27), (9, 17), (21, 31), (30, 16), (3, 26), (34, 4), (21, 15), (40, 37), (2, 19), (25, 18), (42, 5), (37, 28), (11, 5), (1, 40), (16, 35), (32, 6), (43, 8), (33, 7), (44, 29), (35, 7), (3, 20), (43, 9), (24, 35), (42, 29), (2, 7), (28, 11), (25, 29), (29, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 40), (18, 12), (18, 33), (41, 8), (43, 29), (6, 1), (22, 32), (12, 26), (31, 3), (25, 41), (44, 5), (37, 1), (42, 38), (5, 16), (37, 43), (40, 0), (40, 32), (15, 25), (1, 18), (25, 0), (14, 20), (46, 39), (40, 11), (31, 42), (21, 4), (45, 20), (33, 39), (24, 0), (13, 13), (29, 2), (26, 28), (43, 17), (0, 16), (47, 2), (17, 22), (42, 39), (7, 35), (5, 33), (10, 0), (16, 20), (36, 39), (36, 38), (1, 36), (27, 32), (46, 3), (2, 9), (24, 34), (24, 25), (1, 16), (32, 32), (15, 35), (9, 20), (14, 26), (17, 4), (22, 5), (44, 33), (4, 25), (38, 22), (17, 31), (13, 24), (11, 7), (8, 7), (33, 15), (13, 36), (36, 7), (0, 14), (5, 26), (42, 42), (23, 29), (9, 21), (34, 41), (37, 30), (42, 22), (30, 3), (45, 14), (44, 31), (27, 16), (26, 40), (1, 33), (44, 40), (32, 25), (10, 38), (16, 8), (14, 22), (10, 32), (13, 16), (3, 37), (29, 26), (43, 27), (13, 28), (22, 31), (14, 24), (31, 15), (20, 5), (6, 17), (23, 32), (25, 6), (47, 10), (31, 30), (20, 42), (0, 12), (32, 20), (25, 21), (8, 19), (20, 32), (28, 15), (43, 1), (6, 19), (7, 8), (43, 20), (32, 29), (19, 34), (8, 24), (22, 22), (32, 24), (24, 8), (39, 2), (6, 14), (10, 23), (33, 1), (33, 17), (29, 4), (22, 6), (44, 16), (12, 19), (2, 23), (26, 31), (8, 3), (32, 1), (18, 11), (35, 2), (36, 28), (12, 1), (13, 12), (34, 34), (1, 39), (18, 22), (11, 2), (6, 26), (26, 7), (36, 42), (46, 27), (47, 29), (20, 41), (30, 13), (8, 6), (25, 2), (27, 43), (23, 6), (1, 4), (34, 13), (1, 25), (33, 23), (15, 24), (45, 22), (33, 20), (3, 16), (41, 0), (5, 11), (23, 19), (4, 24), (4, 4), (24, 1), (0, 1), (4, 16), (10, 5), (24, 14), (26, 27), (16, 41), (4, 11), (22, 19), (43, 30), (5, 38), (2, 7), (37, 41), (8, 43), (29, 12), (11, 17), (3, 20), (11, 21), (19, 26), (1, 7), (3, 13), (36, 9), (14, 30), (46, 4), (27, 40), (45, 30), (29, 8), (17, 3), (30, 14), (44, 37), (43, 36), (34, 38), (26, 4), (47, 5), (17, 1), (36, 21), (23, 4), (12, 14), (41, 27), (32, 21), (2, 40), (35, 30), (42, 30), (37, 18), (30, 16), (9, 11), (37, 21), (21, 41), (40, 36), (45, 31), (2, 18), (23, 31), (11, 28), (24, 18), (44, 18), (31, 29), (46, 26), (38, 13), (35, 40), (41, 7), (32, 4), (31, 8), (16, 32), (37, 40), (23, 38), (1, 1), (44, 23), (20, 19), (38, 43), (36, 27), (37, 31), (1, 9), (16, 27), (17, 16), (39, 0), (16, 39), (21, 29), (23, 0), (41, 10), (6, 10), (11, 33), (30, 11), (20, 37), (44, 26), (43, 37), (36, 13), (34, 12), (7, 37), (37, 35), (19, 32), (35, 23), (42, 7), (44, 4), (37, 36), (31, 34), (22, 38), (29, 40), (8, 20), (29, 3), (31, 7), (36, 3), (27, 30), (20, 0), (20, 12), (40, 35), (21, 40), (24, 30), (9, 13), (3, 10), (30, 19), (11, 13), (46, 21), (12, 37), (7, 10), (22, 28), (35, 7), (40, 1), (28, 31), (8, 31), (8, 37), (2, 27), (26, 19), (30, 31), (25, 43), (9, 31), (41, 4), (21, 1), (35, 11), (11, 32), (36, 29), (10, 33), (38, 39), (9, 19), (18, 1), (30, 38), (41, 22), (22, 23), (24, 42), (20, 14), (21, 7), (37, 11), (23, 40), (3, 0), (19, 2), (38, 26), (41, 15), (36, 18), (31, 27), (24, 23), (11, 25), (17, 11), (9, 6), (23, 2), (34, 24), (14, 31), (43, 9), (46, 0), (38, 24), (18, 26), (43, 24), (3, 26), (45, 26), (15, 34), (41, 17), (20, 17), (26, 23), (38, 23), (0, 5), (27, 6), (45, 38), (46, 37), (3, 41), (25, 28), (26, 13), (23, 30), (27, 9), (1, 35), (32, 7), (14, 17), (40, 17), (27, 18), (8, 9), (31, 35), (23, 5), (40, 13), (43, 15), (17, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 12), (12, 19), (16, 38), (26, 42), (41, 14), (28, 15), (40, 43), (26, 43), (5, 16), (4, 28), (12, 17), (9, 44), (13, 42), (21, 18), (22, 26), (37, 22), (31, 14), (3, 33), (14, 38), (29, 4), (33, 9), (3, 31), (40, 37), (34, 10), (18, 25), (15, 0), (5, 5), (14, 23), (6, 13), (0, 8), (18, 36), (20, 36), (22, 38), (1, 2), (19, 43), (4, 39), (6, 32), (4, 16), (8, 29), (39, 19), (4, 24), (9, 13), (33, 44), (19, 7), (40, 6), (36, 21), (38, 16), (24, 4), (29, 38), (25, 13), (31, 43), (9, 4), (41, 15), (37, 8), (27, 1), (25, 9), (21, 32), (5, 41), (6, 11), (39, 6), (5, 18), (20, 35), (40, 32), (36, 33), (21, 40), (34, 45), (27, 27), (10, 34), (16, 34), (34, 14), (13, 43), (23, 19), (7, 27), (10, 18), (30, 39), (38, 32), (32, 39), (12, 22), (16, 39), (10, 25), (5, 24), (38, 23), (35, 20), (31, 28), (3, 14), (39, 41), (3, 10), (23, 20), (26, 24), (37, 4), (16, 11), (40, 11), (40, 19), (10, 41), (21, 0), (32, 41), (41, 4), (4, 40), (9, 35), (28, 12), (10, 33), (37, 10), (17, 2), (14, 9), (34, 38), (21, 22), (34, 6), (27, 38), (11, 7), (25, 5), (30, 0), (9, 18), (15, 20), (8, 34), (21, 39), (24, 13), (15, 40), (25, 4), (31, 44), (27, 4), (28, 26), (35, 3), (13, 3), (36, 14), (21, 42), (11, 44), (2, 1), (28, 24), (32, 2), (7, 16), (27, 28), (7, 34), (9, 45), (15, 9), (14, 42), (10, 22), (3, 1), (23, 5), (17, 14), (37, 16), (6, 5), (11, 20), (3, 42), (32, 26), (6, 9), (24, 28), (8, 15), (3, 22), (25, 21), (9, 6), (30, 11), (11, 43), (34, 37), (33, 43), (24, 44), (6, 6), (10, 45), (23, 30), (10, 27), (35, 30), (26, 4), (19, 19), (9, 17), (5, 11), (2, 10), (18, 12), (35, 1), (40, 20), (34, 39), (36, 5), (18, 27), (15, 5), (17, 17), (22, 0), (0, 23), (12, 9), (16, 9), (39, 31), (17, 27), (33, 38), (26, 39), (38, 10), (30, 29), (22, 30), (5, 3), (8, 1), (16, 37), (36, 1), (9, 5), (0, 27), (22, 16), (8, 8), (26, 37), (40, 27), (5, 31), (41, 3), (31, 25), (32, 34), (23, 10), (6, 4), (7, 11), (28, 34), (36, 0), (27, 25), (41, 30), (3, 29), (34, 18), (3, 17), (13, 6), (23, 26), (12, 20), (1, 0), (23, 37), (18, 26), (17, 22), (32, 8), (6, 31), (3, 37), (28, 16), (2, 18), (28, 32), (11, 10), (40, 22), (11, 18), (34, 36), (19, 14), (37, 9), (34, 19), (22, 22), (31, 26), (4, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 2), (25, 35), (27, 8), (11, 40), (19, 28), (40, 35), (31, 20), (28, 9), (42, 22), (39, 15), (36, 16), (24, 17), (9, 18), (17, 37), (24, 32), (31, 14), (32, 6), (34, 34), (8, 30), (10, 34), (42, 28), (33, 27), (33, 40), (32, 31), (26, 23), (12, 37), (0, 8), (33, 31), (0, 20), (16, 27), (35, 38), (11, 30), (5, 4), (8, 21), (40, 20), (42, 6), (43, 35), (25, 18), (32, 32), (10, 0), (2, 39), (37, 42), (10, 14), (20, 12), (2, 21), (36, 32), (38, 19), (37, 39), (16, 11), (31, 18), (21, 9), (34, 42), (2, 19), (29, 20), (39, 24), (2, 4), (3, 12), (11, 11), (2, 43), (25, 37), (40, 4), (16, 39), (40, 42), (41, 17), (28, 29), (0, 32), (19, 31), (22, 33), (19, 30), (37, 37), (31, 29), (29, 16), (1, 5), (9, 31), (18, 41), (2, 14), (38, 6), (7, 11), (19, 38), (27, 6), (23, 34), (0, 29), (21, 36), (32, 39), (18, 1), (28, 18), (18, 10), (23, 19), (28, 13), (4, 31), (14, 9), (27, 28), (12, 33), (35, 13), (39, 12), (31, 12), (12, 10), (12, 26), (13, 18), (21, 0), (42, 35), (0, 24), (14, 20), (36, 33), (24, 16), (39, 43), (20, 25), (34, 7), (16, 40), (2, 36), (6, 23), (33, 24), (6, 41), (22, 7), (17, 33), (9, 24), (4, 35), (5, 19), (23, 2), (43, 26), (21, 4), (34, 27), (10, 35), (37, 31), (21, 43), (22, 22), (8, 32), (10, 31), (30, 19), (43, 22), (10, 8), (18, 26), (5, 6), (13, 8), (4, 25), (12, 22), (0, 31), (14, 26), (9, 38), (43, 12), (2, 5), (37, 40), (8, 42), (1, 37), (20, 27), (12, 31), (40, 6), (37, 1), (38, 13), (42, 29), (31, 10), (5, 7), (15, 30), (14, 11), (4, 5), (22, 13), (42, 1), (5, 26), (34, 1), (24, 24), (34, 25), (12, 38), (25, 9), (17, 29), (20, 16), (24, 3), (5, 8), (7, 16), (10, 39), (41, 20), (17, 17), (10, 21), (14, 3), (6, 3), (35, 29), (40, 5), (28, 39), (34, 26), (36, 41), (27, 30), (4, 3), (18, 38), (24, 39), (40, 32), (18, 28), (8, 34), (41, 42), (16, 7), (34, 3), (9, 26), (2, 35), (30, 30), (21, 21), (28, 32), (2, 2), (5, 23), (2, 37), (14, 42), (36, 8), (9, 2), (40, 14), (38, 1), (9, 13), (25, 41), (0, 6), (3, 20), (34, 0), (38, 26), (23, 7), (18, 9), (19, 22), (17, 26), (5, 9), (11, 8), (8, 24), (35, 2), (27, 29), (3, 29), (41, 27), (17, 1), (29, 26), (25, 16), (41, 29), (23, 38), (7, 34), (41, 14), (43, 10), (40, 1), (28, 10), (43, 32), (42, 43), (22, 11), (19, 29), (24, 31), (2, 32), (21, 16), (5, 38), (16, 42), (42, 21), (7, 38), (14, 41), (43, 5), (23, 40), (17, 24), (37, 2), (6, 35), (20, 26), (30, 4), (33, 21), (38, 35), (23, 20), (22, 31), (23, 5), (17, 39), (11, 38), (28, 37), (11, 22), (12, 27), (9, 23), (17, 5), (22, 34), (37, 14), (40, 22), (15, 28), (22, 8), (28, 14), (38, 29), (10, 19), (37, 23), (24, 8), (11, 9), (15, 20), (15, 11), (29, 24), (29, 30), (5, 42), (16, 0), (6, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 17), (17, 15), (45, 12), (29, 5), (5, 33), (6, 43), (31, 29), (36, 15), (39, 33), (11, 21), (41, 18), (38, 18), (9, 33), (38, 1), (3, 21), (42, 25), (13, 43), (37, 19), (40, 4), (13, 36), (46, 34), (43, 3), (46, 13), (4, 28), (5, 30), (14, 26), (42, 20), (12, 35), (46, 3), (10, 32), (8, 17), (3, 44), (37, 7), (24, 35), (39, 3), (38, 26), (45, 17), (27, 25), (38, 44), (32, 18), (33, 31), (32, 30), (9, 2), (18, 22), (2, 0), (4, 25), (0, 9), (35, 14), (34, 12), (37, 20), (41, 38), (45, 21), (23, 30), (39, 29), (35, 2), (36, 29), (0, 33), (1, 28), (41, 28), (22, 44), (5, 43), (42, 18), (39, 37), (4, 38), (8, 33), (38, 28), (0, 40), (28, 4), (29, 35), (27, 16), (2, 16), (36, 40), (43, 5), (3, 0), (11, 2), (16, 32), (30, 16), (7, 10), (30, 17), (25, 5), (42, 42), (7, 0), (47, 35), (23, 38), (28, 41), (5, 12), (3, 27), (4, 23), (12, 41), (15, 21), (36, 9), (9, 38), (31, 3), (38, 16), (47, 39), (27, 41), (20, 1), (15, 9), (11, 39), (30, 43), (30, 34), (8, 19), (16, 36), (12, 7), (31, 41), (41, 17), (14, 39), (14, 21), (23, 3), (14, 36), (27, 24), (26, 23), (2, 24), (27, 3), (37, 39), (1, 9), (37, 6), (12, 40), (35, 18), (44, 32), (35, 41), (20, 23), (16, 20), (22, 13), (10, 11), (3, 34), (3, 40), (1, 19), (6, 1), (7, 28), (42, 3), (17, 18), (17, 36), (45, 33), (9, 9), (26, 27), (10, 2), (17, 5), (41, 37), (43, 13), (0, 31), (2, 41), (0, 13), (14, 2), (18, 8), (34, 8), (21, 31), (7, 43), (32, 20), (30, 5), (12, 9), (37, 44), (35, 0), (23, 0), (9, 31), (45, 13), (28, 37), (30, 19), (22, 6), (25, 18), (32, 32), (10, 40), (11, 15), (19, 25), (21, 8), (0, 3), (44, 19), (2, 14), (13, 18), (31, 21), (34, 2), (38, 43), (2, 13), (38, 24), (21, 3), (28, 23), (31, 36), (16, 27), (31, 30), (25, 25), (12, 22), (36, 0), (41, 14), (29, 6), (26, 0), (19, 22), (14, 1), (36, 32), (37, 10), (18, 13), (42, 17), (22, 7), (36, 14), (39, 17), (16, 31), (38, 30), (41, 30), (0, 12), (21, 0), (24, 9), (31, 17), (43, 31), (4, 1), (46, 43), (23, 13), (9, 12), (39, 38), (8, 23), (20, 15), (7, 44), (38, 15), (22, 26), (18, 6), (34, 33), (4, 32), (11, 34), (2, 39), (2, 36), (13, 27), (17, 14), (3, 28), (22, 42), (36, 27), (39, 21), (26, 6), (17, 25), (16, 9), (33, 27), (23, 33), (22, 33), (43, 41), (0, 8), (23, 34), (13, 3), (15, 14), (4, 26), (47, 5), (4, 40), (42, 26), (27, 14), (23, 32), (35, 7), (38, 25), (1, 25), (20, 31), (29, 22), (43, 16), (7, 42), (0, 7), (36, 16), (36, 22), (38, 8), (6, 28), (10, 20), (28, 25), (6, 36), (40, 15), (14, 33), (15, 1), (33, 6), (43, 21), (21, 36), (27, 19), (0, 11), (29, 28), (40, 27), (33, 24), (17, 24), (28, 7), (4, 21), (6, 16), (5, 9), (29, 24), (42, 6), (29, 41), (42, 29), (14, 37), (22, 30), (33, 3), (8, 3), (47, 11), (19, 7), (8, 25), (35, 35), (26, 40), (9, 24), (33, 21), (43, 8), (31, 38), (12, 25), (33, 28), (10, 39), (33, 9), (35, 38), (9, 23), (20, 39), (37, 23), (11, 41), (21, 15), (25, 33), (8, 8), (31, 33), (14, 43), (23, 9), (17, 9), (34, 13), (0, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 10), (38, 1), (11, 13), (14, 35), (16, 15), (29, 17), (21, 21), (12, 6), (7, 28), (4, 23), (26, 36), (5, 32), (23, 29), (7, 14), (4, 24), (6, 17), (23, 18), (4, 3), (25, 39), (38, 42), (16, 3), (36, 11), (3, 9), (39, 12), (22, 6), (23, 15), (37, 30), (20, 31), (17, 26), (4, 39), (24, 34), (19, 12), (12, 4), (32, 0), (16, 37), (39, 10), (34, 22), (12, 34), (10, 27), (18, 40), (36, 22), (15, 9), (35, 26), (15, 20), (18, 14), (23, 8), (30, 37), (3, 7), (1, 28), (32, 6), (11, 0), (0, 29), (26, 41), (2, 21), (3, 37), (19, 41), (33, 36), (7, 20), (15, 31), (5, 9), (15, 11), (33, 30), (34, 33), (26, 40), (27, 9), (39, 31), (5, 23), (16, 10), (22, 0), (36, 7), (15, 12), (25, 33), (34, 13), (21, 32), (39, 36), (29, 39), (12, 28), (37, 5), (6, 30), (1, 1), (3, 36), (11, 9), (5, 28), (11, 6), (33, 3), (3, 11), (2, 31), (20, 35), (0, 41), (35, 5), (16, 12), (24, 31), (0, 37), (5, 20), (34, 24), (9, 32), (0, 13), (16, 26), (21, 20), (28, 20), (17, 39), (19, 16), (36, 32), (20, 23), (36, 3), (5, 19), (9, 35), (24, 17), (22, 1), (27, 22), (13, 17), (12, 3), (1, 14), (21, 16), (21, 2), (19, 39), (29, 38), (5, 10), (31, 23), (8, 19), (28, 14), (39, 24), (21, 15), (23, 7), (14, 42), (7, 23), (28, 12), (10, 24), (15, 37), (5, 3), (19, 32), (6, 19), (38, 29), (0, 39), (8, 27), (24, 5), (32, 35), (21, 36), (38, 27), (29, 20), (9, 29), (12, 43), (9, 28), (2, 4), (32, 1), (20, 43), (34, 42), (27, 33), (6, 6), (33, 4), (33, 12), (38, 28), (16, 1), (3, 43), (27, 14), (34, 18), (22, 27), (33, 27), (24, 36), (31, 37), (16, 41), (39, 6), (7, 7), (38, 14), (1, 7), (6, 24), (30, 2), (35, 28), (21, 0), (29, 11), (15, 29), (38, 40), (13, 39), (28, 36), (21, 9), (2, 2), (1, 25), (4, 17), (37, 35), (28, 13), (13, 34), (35, 10), (12, 5), (27, 20), (38, 32), (24, 30), (26, 4), (26, 24), (19, 2), (35, 7), (6, 12), (31, 28), (26, 18), (9, 18), (18, 34), (19, 1), (25, 14), (17, 3), (10, 12), (18, 1), (1, 11), (34, 10), (21, 25), (28, 28), (30, 11), (36, 26), (20, 42), (16, 5), (10, 29), (39, 25), (32, 9), (0, 17), (3, 15), (30, 30), (10, 23), (17, 19), (7, 37), (30, 18), (16, 33), (3, 40), (0, 32), (14, 0), (34, 41), (10, 11), (2, 43), (26, 2), (2, 3), (1, 0), (1, 38), (8, 20), (24, 33), (8, 5), (38, 16), (17, 29), (32, 16), (11, 4), (33, 10), (15, 39), (2, 25), (5, 13), (11, 30), (37, 15), (8, 43), (22, 34), (17, 35), (25, 12), (25, 29), (36, 37), (35, 11), (14, 31), (6, 20), (6, 31), (36, 0), (37, 11), (29, 24), (37, 24), (5, 1), (32, 21), (15, 4), (33, 8), (22, 28), (37, 9), (30, 26), (2, 7), (16, 18), (19, 28), (19, 29), (19, 27), (22, 4), (12, 24), (25, 19), (13, 20), (26, 21), (35, 12), (26, 0), (14, 11), (22, 16), (17, 37), (39, 2), (37, 8), (8, 28), (24, 14), (9, 0), (4, 13), (31, 3), (16, 14), (4, 26), (25, 4), (22, 10), (35, 0), (27, 42), (26, 15), (21, 17), (1, 22), (20, 22), (8, 17), (31, 7), (14, 28), (7, 6), (22, 13), (36, 25), (25, 41), (14, 17), (25, 2), (27, 31), (17, 6), (11, 12), (3, 33), (13, 42), (29, 23), (10, 2), (10, 33), (37, 20), (0, 34), (15, 26), (35, 41), (18, 35), (6, 29), (35, 21), (6, 26), (30, 21), (27, 1), (29, 6), (13, 8), (1, 9), (4, 35), (16, 29), (16, 21), (9, 41), (17, 22), (21, 7), (35, 34), (2, 6), (32, 18), (25, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 27), (3, 0), (33, 0), (28, 40), (33, 14), (1, 17), (9, 20), (26, 25), (37, 27), (46, 40), (5, 6), (35, 20), (8, 24), (14, 17), (12, 21), (7, 41), (11, 5), (14, 32), (27, 1), (5, 26), (38, 9), (0, 41), (38, 40), (42, 24), (24, 10), (37, 23), (27, 35), (18, 24), (45, 18), (27, 3), (1, 5), (39, 10), (11, 36), (28, 18), (13, 29), (7, 9), (45, 1), (35, 13), (43, 8), (16, 11), (38, 12), (16, 34), (27, 29), (33, 41), (38, 21), (46, 30), (11, 33), (41, 9), (14, 16), (22, 17), (0, 37), (22, 24), (27, 37), (39, 2), (21, 0), (19, 36), (42, 31), (24, 1), (7, 27), (42, 19), (16, 1), (23, 39), (25, 9), (33, 1), (5, 36), (30, 26), (44, 27), (26, 9), (1, 28), (21, 20), (11, 24), (21, 25), (2, 5), (19, 17), (46, 15), (26, 34), (20, 20), (12, 24), (2, 24), (18, 17), (4, 29), (20, 33), (40, 35), (42, 36), (45, 23), (47, 5), (43, 5), (18, 25), (12, 5), (2, 36), (39, 9), (43, 20), (25, 19), (19, 31), (3, 18), (6, 13), (27, 20), (45, 34), (35, 10), (39, 22), (9, 39), (40, 23), (44, 4), (44, 33), (2, 15), (9, 16), (33, 10), (5, 37), (39, 4), (24, 4), (17, 5), (0, 3), (10, 25), (4, 19), (16, 8), (15, 37), (1, 20), (43, 31), (45, 41), (15, 6), (26, 20), (22, 0), (31, 34), (41, 21), (20, 27), (45, 24), (11, 27), (28, 6), (41, 36), (4, 14), (31, 1), (22, 23), (27, 22), (5, 30), (27, 11), (29, 1), (44, 35), (45, 39), (14, 33), (5, 1), (1, 3), (6, 25), (1, 21), (36, 34), (11, 14), (43, 21), (30, 8), (39, 29), (37, 8), (28, 1), (25, 4), (46, 17), (2, 0), (37, 25), (9, 4), (18, 6), (23, 12), (46, 16), (7, 23), (47, 11), (27, 31), (22, 6), (16, 25), (18, 10), (29, 11), (16, 18), (35, 16), (22, 29), (27, 36), (3, 13), (32, 19), (47, 25), (1, 6), (25, 15), (47, 17), (26, 26), (29, 32), (36, 39), (35, 34), (25, 28), (3, 33), (16, 5), (30, 9), (33, 2), (5, 12), (12, 29), (33, 32), (20, 1), (10, 27), (41, 8), (18, 12), (29, 19), (20, 38), (33, 9), (34, 2), (25, 33), (2, 32), (40, 2), (21, 30), (31, 10), (37, 33), (28, 32), (45, 29), (34, 5), (30, 25), (32, 38), (36, 10), (17, 15), (2, 20), (44, 9), (46, 26), (26, 10), (14, 20), (23, 18), (12, 13), (46, 22), (14, 15), (22, 41), (21, 40), (25, 14), (0, 29), (44, 31), (15, 28), (47, 20), (36, 2), (6, 15), (26, 19), (15, 15), (8, 10), (9, 7), (2, 34), (38, 3), (1, 23), (0, 38), (10, 7), (30, 19), (12, 6), (44, 14), (35, 18), (1, 38), (29, 12), (26, 0), (44, 24), (33, 30), (1, 27), (6, 23), (6, 17), (28, 20), (12, 7), (21, 23), (32, 1), (16, 29), (37, 16), (5, 10), (41, 5), (5, 24), (39, 25), (0, 10), (5, 28), (17, 40), (4, 41), (13, 14), (43, 11), (7, 2), (37, 9), (35, 40), (37, 6), (31, 19), (8, 38), (32, 3), (19, 20), (40, 37), (23, 4), (24, 16), (12, 25), (19, 15), (7, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 36), (9, 44), (23, 3), (37, 25), (20, 19), (30, 14), (11, 19), (31, 18), (20, 22), (40, 32), (22, 29), (4, 12), (13, 25), (15, 14), (7, 21), (31, 41), (0, 31), (2, 36), (15, 36), (27, 22), (26, 9), (3, 7), (2, 26), (15, 20), (30, 37), (35, 24), (11, 7), (9, 43), (38, 24), (22, 17), (21, 20), (34, 1), (4, 44), (21, 4), (30, 36), (1, 5), (30, 34), (5, 22), (32, 23), (2, 39), (20, 27), (21, 24), (27, 44), (1, 4), (31, 8), (16, 45), (26, 10), (27, 3), (6, 38), (11, 22), (30, 40), (21, 1), (23, 46), (10, 11), (31, 1), (23, 6), (37, 5), (18, 43), (15, 46), (23, 45), (37, 31), (1, 18), (14, 0), (9, 13), (16, 33), (25, 10), (17, 11), (23, 32), (9, 25), (23, 25), (24, 40), (12, 0), (24, 35), (5, 30), (15, 1), (33, 17), (33, 12), (41, 27), (9, 35), (30, 13), (30, 7), (38, 19), (32, 31), (32, 12), (15, 18), (12, 32), (5, 37), (8, 14), (6, 13), (8, 5), (28, 19), (13, 15), (25, 4), (11, 6), (3, 2), (41, 8), (3, 30), (37, 17), (27, 23), (33, 35), (19, 39), (17, 42), (9, 34), (0, 3), (31, 21), (37, 24), (6, 7), (8, 28), (30, 1), (4, 5), (23, 40), (14, 29), (3, 15), (35, 4), (41, 32), (18, 3), (3, 26), (35, 38), (19, 11), (18, 12), (3, 32), (37, 13), (31, 30), (7, 0), (2, 8), (26, 21), (3, 42), (9, 20), (3, 6), (12, 25), (35, 34), (19, 31), (41, 42), (5, 21), (20, 5), (10, 0), (33, 13), (25, 27), (20, 45), (17, 35), (20, 23), (14, 19), (7, 32), (1, 13), (35, 22), (33, 24), (13, 10), (15, 7), (13, 0), (30, 31), (37, 12), (27, 6), (4, 20), (8, 23), (25, 42), (13, 3), (27, 1), (24, 37), (22, 4), (22, 27), (10, 35), (23, 22), (36, 19), (27, 15), (6, 12), (9, 28), (24, 8), (23, 11), (18, 37), (11, 18), (34, 3), (38, 17), (25, 46), (35, 36), (16, 36), (19, 23), (5, 28), (41, 15), (18, 10), (32, 10), (32, 3), (41, 29), (32, 5), (39, 13), (23, 13), (23, 27), (28, 2), (32, 34), (12, 27), (33, 33), (21, 39), (21, 9), (24, 43), (2, 20), (27, 30), (29, 38), (22, 43), (39, 19), (24, 10), (17, 24), (18, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 10), (42, 26), (15, 23), (5, 17), (35, 27), (42, 0), (30, 29), (10, 5), (26, 32), (41, 40), (35, 6), (28, 29), (41, 29), (3, 41), (14, 21), (7, 45), (35, 4), (21, 44), (29, 44), (41, 32), (9, 10), (35, 0), (43, 10), (28, 38), (0, 29), (32, 37), (20, 5), (12, 44), (8, 34), (16, 9), (4, 28), (33, 15), (23, 27), (22, 8), (31, 0), (10, 43), (37, 17), (45, 33), (47, 15), (29, 10), (38, 9), (17, 19), (6, 30), (19, 24), (36, 40), (11, 38), (26, 5), (18, 19), (10, 31), (26, 23), (24, 33), (27, 12), (5, 21), (10, 17), (34, 37), (10, 32), (27, 27), (20, 28), (10, 2), (35, 3), (18, 42), (44, 35), (33, 26), (0, 26), (1, 28), (11, 12), (33, 11), (40, 33), (10, 24), (5, 19), (6, 10), (23, 1), (16, 32), (8, 26), (43, 39), (1, 18), (14, 39), (10, 15), (16, 15), (47, 12), (6, 18), (21, 18), (34, 40), (25, 44), (35, 9), (3, 8), (30, 46), (13, 41), (26, 16), (40, 39), (46, 37), (24, 17), (14, 43), (29, 23), (40, 15), (38, 38), (36, 31), (46, 26), (31, 34), (33, 16), (3, 3), (9, 11), (3, 18), (0, 3), (45, 1), (4, 39), (8, 11), (43, 0), (40, 17), (34, 12), (40, 0), (42, 16), (4, 5), (10, 30), (22, 1), (28, 4), (32, 26), (13, 38), (3, 13), (36, 7), (4, 11), (28, 30), (16, 41), (24, 20), (3, 27), (32, 32), (40, 40), (0, 15), (7, 9), (17, 3), (47, 25), (30, 5), (16, 12), (27, 22), (35, 33), (4, 32), (12, 45), (36, 42), (22, 35), (8, 39), (29, 32), (13, 36), (3, 38), (35, 46), (4, 40), (6, 23), (11, 29), (46, 20), (31, 16), (44, 24), (16, 31), (5, 5), (12, 12), (31, 14), (11, 28), (40, 43), (9, 24), (23, 9), (4, 38), (31, 37), (20, 2), (28, 17), (12, 46), (15, 29), (22, 25), (22, 39), (13, 42), (37, 42), (2, 4), (11, 24), (18, 39), (31, 15), (20, 1), (24, 34), (20, 0), (45, 25), (35, 16), (30, 11), (28, 37), (30, 41), (3, 19), (23, 29), (25, 2), (36, 20), (40, 9), (2, 17), (6, 26), (0, 11), (11, 14), (22, 6), (12, 21), (28, 33), (9, 14), (6, 8), (19, 40), (37, 12), (19, 21), (14, 25), (1, 29), (11, 27), (6, 40), (6, 22), (28, 11), (8, 10), (5, 33), (26, 17), (8, 33), (38, 34), (9, 29), (35, 44), (41, 37), (7, 16), (40, 38), (42, 34), (9, 45), (34, 26), (21, 5), (26, 20), (34, 43), (25, 36), (18, 44), (42, 11), (17, 10), (42, 33), (40, 32), (11, 45), (26, 18), (17, 25), (6, 1), (1, 3), (42, 1), (44, 21), (36, 39), (19, 46), (14, 6), (1, 5), (29, 29), (18, 35), (21, 10), (47, 17), (42, 18), (38, 3), (22, 43), (12, 20), (27, 21), (5, 34), (19, 34), (22, 29), (5, 45), (17, 26), (32, 13), (27, 2), (4, 10), (16, 37), (0, 14), (5, 31), (12, 31), (47, 13), (5, 25), (2, 27), (14, 16), (27, 23), (44, 23), (20, 23), (47, 4), (41, 26), (42, 6), (10, 28), (13, 25), (25, 11), (20, 41), (9, 3), (33, 6), (6, 29), (0, 4), (23, 28), (21, 12), (11, 5), (5, 13), (27, 7), (6, 38), (19, 28), (18, 36), (11, 2), (22, 38), (24, 0), (47, 22), (43, 41), (45, 12), (41, 41), (23, 2), (20, 3), (36, 22), (22, 42), (21, 15), (40, 23), (15, 22), (24, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 17), (1, 27), (34, 12), (40, 30), (39, 22), (13, 45), (14, 13), (5, 36), (21, 5), (44, 28), (27, 1), (0, 44), (21, 36), (7, 10), (35, 3), (40, 36), (7, 29), (15, 20), (28, 33), (8, 39), (19, 17), (45, 6), (2, 20), (47, 29), (37, 8), (36, 6), (44, 3), (29, 1), (42, 36), (3, 16), (22, 32), (12, 1), (22, 3), (36, 24), (33, 16), (10, 45), (47, 26), (10, 37), (7, 18), (25, 16), (46, 14), (4, 39), (9, 43), (46, 31), (3, 12), (43, 40), (25, 41), (33, 39), (16, 27), (12, 24), (32, 9), (29, 11), (46, 2), (16, 33), (21, 13), (34, 43), (39, 12), (2, 36), (7, 35), (36, 33), (7, 3), (27, 16), (43, 8), (46, 34), (9, 26), (46, 39), (47, 3), (35, 45), (13, 38), (16, 44), (38, 0), (38, 16), (21, 37), (28, 42), (19, 30), (0, 20), (34, 33), (40, 19), (5, 19), (0, 23), (37, 20), (15, 3), (47, 12), (33, 23), (44, 2), (24, 26), (3, 29), (28, 31), (36, 28), (36, 36), (32, 26), (1, 11), (31, 7), (11, 39), (37, 2), (40, 34), (4, 43), (20, 7), (24, 35), (37, 34), (29, 4), (1, 17), (15, 38), (20, 35), (9, 0), (21, 18), (12, 45), (25, 20), (21, 29), (0, 40), (43, 16), (43, 3), (5, 24), (36, 21), (39, 29), (35, 29), (32, 37), (18, 23), (29, 25), (33, 15), (14, 34), (32, 12), (29, 29), (43, 4), (34, 16), (24, 28), (47, 24), (19, 16), (3, 7), (28, 1), (45, 1), (41, 6), (23, 25), (36, 8), (2, 19), (42, 32), (28, 27), (22, 26), (34, 32), (26, 37), (16, 41), (10, 12), (4, 14), (29, 18), (19, 14), (10, 39), (10, 35), (20, 3), (14, 7), (15, 13), (10, 14), (8, 30), (39, 6), (19, 23), (43, 28), (18, 0), (27, 4), (16, 26), (2, 44), (21, 45), (28, 11), (1, 43), (27, 24), (33, 26), (13, 22), (15, 37), (26, 17), (26, 45), (12, 16), (4, 1), (26, 43), (24, 21), (0, 39), (7, 27), (38, 5), (10, 19), (36, 4), (6, 17), (35, 44), (45, 23), (18, 36), (40, 42), (32, 30), (28, 9), (31, 10), (27, 14), (0, 11), (44, 40), (10, 42), (25, 7), (17, 11), (37, 27), (23, 34), (42, 11), (26, 1), (47, 16), (34, 6), (28, 18), (7, 45), (18, 24), (7, 8), (15, 32), (15, 4), (12, 29), (31, 27), (21, 20), (23, 39), (32, 8), (47, 22), (21, 17), (11, 10), (14, 20), (15, 22), (32, 42), (38, 14), (2, 32), (42, 20), (18, 25), (3, 38), (32, 5), (31, 6), (29, 43), (38, 17), (38, 32), (42, 10), (10, 34), (2, 11), (10, 18), (47, 39), (14, 28), (35, 41), (23, 4), (4, 29), (17, 22), (31, 23), (26, 3), (9, 20), (33, 36), (21, 4), (28, 7), (11, 43), (11, 44), (30, 14), (21, 2), (2, 29), (32, 36), (37, 18), (7, 30), (25, 19), (3, 36), (31, 33), (35, 20), (34, 18), (18, 9), (13, 25), (37, 22), (10, 5), (31, 32), (8, 12), (12, 34), (28, 15), (45, 20), (1, 39), (5, 43), (28, 30), (10, 25), (21, 22), (8, 13), (21, 19), (46, 10), (47, 1), (47, 33), (40, 43), (30, 28), (9, 34), (41, 0), (41, 22), (21, 32), (37, 26), (33, 45), (26, 24), (37, 23), (20, 40), (5, 26), (28, 5), (3, 6), (16, 10), (25, 6), (5, 45), (12, 4), (39, 37), (11, 13), (25, 27), (21, 31), (25, 1), (5, 35), (12, 15), (27, 35), (47, 8), (3, 41), (29, 3), (10, 43), (16, 9), (44, 14), (36, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 32), (17, 13), (19, 15), (30, 18), (3, 9), (28, 2), (5, 11), (18, 11), (1, 46), (38, 41), (34, 24), (38, 26), (22, 40), (9, 12), (15, 14), (29, 43), (34, 27), (3, 12), (18, 5), (32, 22), (20, 26), (0, 41), (31, 31), (32, 35), (11, 41), (14, 10), (8, 4), (8, 6), (7, 6), (7, 0), (5, 40), (39, 19), (2, 28), (12, 7), (12, 22), (6, 24), (9, 8), (36, 10), (23, 25), (32, 10), (36, 2), (33, 33), (8, 7), (39, 22), (28, 45), (10, 45), (22, 22), (23, 36), (5, 13), (4, 21), (6, 41), (37, 19), (9, 37), (17, 43), (9, 13), (29, 7), (2, 40), (31, 37), (20, 14), (0, 29), (10, 39), (5, 1), (3, 38), (15, 16), (21, 41), (9, 34), (7, 21), (11, 18), (22, 26), (40, 8), (32, 41), (16, 1), (9, 44), (25, 4), (12, 0), (38, 40), (30, 40), (33, 36), (17, 4), (25, 44), (21, 38), (35, 4), (8, 16), (36, 24), (13, 4), (39, 39), (13, 1), (25, 39), (18, 38), (34, 43), (36, 14), (19, 35), (10, 37), (0, 7), (2, 19), (30, 39), (34, 29), (31, 2), (40, 27), (9, 11), (13, 30), (2, 23), (6, 40), (32, 8), (40, 2), (39, 30), (20, 36), (21, 24), (20, 15), (22, 15), (23, 39), (24, 12), (7, 46), (39, 24), (5, 22), (40, 29), (8, 3), (35, 24), (12, 13), (8, 12), (21, 43), (39, 35), (1, 22), (15, 2), (1, 0), (11, 29), (7, 17), (2, 7), (4, 2), (38, 9), (17, 26), (0, 16), (0, 31), (30, 24), (13, 8), (40, 33), (3, 14), (9, 2), (13, 5), (28, 29), (8, 15), (33, 45), (0, 15), (25, 22), (6, 27), (1, 38), (4, 9), (34, 19), (40, 7), (27, 18), (29, 17), (18, 19), (38, 44), (0, 36), (29, 40), (9, 9), (2, 39), (39, 11), (37, 40), (10, 24), (8, 29), (8, 17), (13, 35), (14, 5), (7, 14), (15, 30), (36, 36), (14, 20), (31, 14), (39, 8), (7, 12), (15, 43), (7, 8), (21, 35), (38, 43), (23, 14), (10, 8), (18, 26), (8, 19), (2, 34), (16, 20), (27, 25), (10, 29), (10, 32), (13, 11), (9, 39), (0, 2), (12, 21), (17, 6), (12, 4), (31, 44), (27, 4), (3, 1), (21, 36), (12, 43), (17, 27), (11, 0), (27, 9), (31, 27), (16, 42), (3, 6), (16, 15), (35, 40), (17, 15), (29, 38), (27, 39), (19, 22), (29, 0), (37, 8), (10, 38), (28, 27), (39, 25), (16, 41), (37, 9), (30, 44), (32, 11), (37, 22), (16, 27), (19, 12), (9, 23), (7, 20), (34, 34), (22, 13), (6, 3), (20, 33), (38, 11), (14, 1), (0, 32), (36, 38), (11, 23), (38, 25), (14, 28), (0, 3), (39, 27), (37, 23), (31, 43), (21, 6), (16, 24), (9, 46), (11, 42), (7, 30), (3, 8), (1, 30), (24, 7), (1, 36), (12, 42), (24, 46), (11, 43), (1, 4), (1, 16), (36, 41), (29, 24), (0, 37), (38, 3), (27, 46), (33, 28), (12, 9), (31, 19), (2, 12), (34, 2), (7, 29), (9, 32), (6, 0), (32, 18), (23, 17), (35, 16), (18, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 39), (3, 13), (22, 13), (8, 33), (32, 31), (11, 3), (24, 43), (1, 42), (4, 6), (42, 0), (27, 31), (11, 15), (2, 10), (23, 31), (23, 36), (23, 44), (40, 21), (4, 8), (22, 25), (0, 17), (9, 42), (32, 32), (39, 44), (36, 16), (22, 30), (9, 19), (14, 23), (21, 28), (20, 11), (22, 19), (19, 44), (40, 26), (17, 44), (13, 33), (42, 10), (5, 24), (43, 39), (9, 20), (2, 28), (6, 10), (6, 5), (40, 27), (38, 21), (31, 14), (39, 7), (35, 3), (7, 29), (12, 41), (5, 22), (5, 29), (22, 37), (28, 32), (24, 5), (0, 6), (38, 8), (40, 17), (34, 12), (16, 36), (42, 37), (19, 27), (0, 18), (24, 21), (2, 35), (41, 42), (7, 14), (2, 13), (41, 21), (28, 2), (13, 22), (42, 9), (26, 24), (2, 25), (24, 41), (26, 43), (27, 15), (37, 41), (19, 26), (31, 5), (24, 42), (39, 4), (18, 4), (18, 5), (31, 30), (2, 15), (17, 39), (26, 44), (4, 38), (16, 24), (15, 14), (1, 3), (14, 17), (38, 18), (25, 32), (30, 16), (34, 24), (36, 40), (42, 1), (40, 1), (33, 41), (35, 1), (15, 33), (13, 27), (11, 11), (20, 21), (13, 3), (16, 14), (0, 44), (33, 2), (36, 13), (4, 45), (36, 9), (35, 44), (0, 16), (22, 15), (5, 3), (27, 38), (5, 26), (10, 37), (29, 11), (11, 32), (1, 21), (13, 34), (41, 9), (43, 37), (21, 0), (1, 38), (23, 27), (35, 2), (41, 20), (11, 21), (41, 35), (34, 41), (21, 32), (5, 14), (7, 39), (9, 39), (25, 11), (32, 2), (19, 30), (22, 44), (39, 15), (1, 30), (29, 45), (17, 30), (17, 21), (42, 45), (41, 33), (30, 35), (18, 28), (40, 44), (42, 16), (16, 28), (14, 11), (40, 16), (28, 13), (39, 38), (19, 36), (30, 15), (32, 16), (5, 32), (7, 3), (12, 26), (5, 21), (27, 34), (24, 17), (2, 20), (0, 9), (42, 40), (8, 10), (9, 28), (23, 43), (20, 30), (31, 45), (20, 36), (25, 29), (12, 32), (23, 4), (21, 1), (0, 26), (35, 45), (8, 38), (4, 26), (13, 40), (22, 14), (3, 6), (17, 20), (17, 36), (3, 10), (22, 33), (10, 4), (15, 40), (29, 43), (16, 39), (8, 25), (23, 39), (7, 23), (26, 0), (21, 9), (36, 39), (33, 30), (0, 22), (30, 10), (1, 10), (16, 9), (23, 16), (7, 6), (28, 16), (12, 44), (39, 11), (38, 34), (43, 36), (17, 25), (41, 26), (2, 43), (17, 19), (17, 14), (28, 7), (18, 17), (27, 39), (24, 28), (3, 41), (28, 4), (10, 8), (19, 16), (10, 45), (11, 20), (24, 40), (20, 31), (27, 25), (28, 41), (37, 26), (13, 0), (1, 12), (7, 7), (39, 36), (24, 36), (11, 17), (15, 0), (5, 45), (11, 22), (12, 17), (20, 5), (36, 42), (41, 45), (22, 5), (3, 20), (32, 33), (28, 39), (41, 2), (39, 29), (4, 21), (31, 1), (25, 26), (14, 18), (11, 13), (11, 24), (32, 11), (1, 36), (29, 41), (37, 36), (24, 22), (16, 35), (26, 1), (1, 19), (2, 12), (12, 40), (40, 30), (21, 17), (9, 8), (21, 18), (28, 26), (16, 32), (29, 3), (33, 32), (11, 4), (5, 42), (23, 29), (37, 17), (3, 33), (9, 23), (29, 28), (6, 21), (4, 24), (5, 33), (35, 13), (23, 18), (27, 37), (8, 7), (22, 7), (16, 5), (0, 33), (30, 38), (12, 25), (20, 20), (34, 16), (30, 27), (1, 26), (1, 14), (11, 30), (40, 0), (41, 43), (34, 42), (4, 31), (6, 13), (23, 35), (1, 27), (23, 7), (41, 12), (42, 42), (37, 13), (20, 34), (26, 36), (27, 41), (30, 45), (21, 26), (40, 23), (20, 24), (13, 10), (15, 31), (24, 13), (9, 10), (0, 27), (21, 27), (23, 8), (3, 28), (10, 29), (34, 30), (29, 29), (3, 42), (8, 31), (1, 31), (2, 17), (14, 43), (26, 6), (30, 8), (37, 10), (16, 20), (4, 42), (15, 29), (19, 29), (32, 42), (17, 3), (10, 41), (32, 28), (29, 25), (41, 28), (17, 31), (6, 14), (1, 23), (39, 40), (39, 9), (42, 5), (8, 21), (30, 1), (37, 15), (9, 2), (32, 7), (3, 39), (32, 19), (34, 13), (40, 32), (27, 0), (32, 37), (11, 28), (6, 19), (16, 41), (24, 8), (18, 31), (27, 45), (31, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 36), (23, 42), (0, 26), (18, 37), (27, 0), (33, 40), (14, 42), (25, 25), (8, 42), (25, 9), (20, 6), (13, 11), (14, 27), (19, 43), (30, 21), (10, 8), (33, 17), (10, 22), (34, 9), (39, 44), (8, 13), (7, 4), (28, 33), (30, 44), (5, 32), (2, 13), (4, 30), (15, 31), (1, 39), (37, 41), (22, 16), (10, 38), (2, 16), (19, 31), (28, 2), (5, 27), (3, 35), (0, 17), (35, 11), (18, 22), (29, 34), (10, 3), (5, 0), (14, 23), (21, 23), (27, 43), (26, 35), (31, 43), (6, 28), (3, 2), (14, 20), (32, 40), (30, 26), (36, 25), (21, 42), (33, 39), (1, 12), (5, 44), (14, 40), (4, 40), (1, 2), (33, 21), (0, 16), (26, 44), (14, 43), (17, 1), (35, 38), (9, 32), (16, 42), (6, 17), (20, 29), (24, 32), (38, 16), (5, 8), (3, 9), (31, 13), (24, 28), (23, 21), (37, 9), (0, 45), (38, 14), (21, 27), (13, 15), (27, 10), (0, 38), (39, 10), (7, 46), (27, 41), (34, 26), (32, 13), (34, 10), (10, 9), (25, 0), (28, 43), (4, 25), (23, 3), (31, 22), (8, 40), (5, 25), (38, 21), (4, 27), (32, 10), (36, 12), (10, 1), (14, 0), (10, 18), (36, 8), (2, 26), (7, 3), (36, 23), (17, 10), (2, 35), (11, 35), (18, 3), (16, 11), (18, 18), (21, 33), (34, 41), (20, 34), (2, 40), (3, 11), (19, 8), (25, 37), (12, 4), (30, 2), (25, 22), (16, 14), (36, 14), (23, 28), (28, 4), (18, 45), (29, 26), (22, 22), (1, 31), (25, 38), (0, 4), (7, 35), (35, 27), (39, 5), (26, 28), (17, 3), (14, 7), (30, 32), (15, 10), (0, 32), (29, 40), (7, 37), (23, 35), (15, 39), (16, 24), (1, 37), (36, 15), (0, 24), (1, 13), (33, 10), (2, 14), (12, 13), (31, 36), (12, 42), (34, 7), (37, 46), (9, 14), (3, 44), (15, 34), (21, 45), (37, 25), (16, 13), (24, 4), (17, 2), (21, 38), (22, 17), (33, 33), (13, 24), (4, 11), (4, 5), (6, 16), (33, 14), (32, 25), (3, 10), (33, 25), (1, 3), (23, 23), (18, 40), (36, 20), (16, 40), (32, 19), (18, 43), (1, 6), (24, 9), (15, 22), (15, 43), (1, 20), (25, 5), (39, 26), (23, 20), (38, 17), (8, 46), (17, 14), (17, 7), (14, 19), (39, 25), (2, 2), (12, 11), (18, 44), (7, 30), (21, 18), (19, 45), (31, 3), (34, 23), (1, 21), (35, 31), (8, 38), (20, 22), (2, 24), (13, 18), (27, 32), (25, 8), (17, 43), (22, 6), (29, 32), (33, 45), (34, 36), (27, 2), (16, 20), (38, 20), (26, 45), (37, 27), (0, 8), (18, 27), (4, 23), (4, 2), (34, 0), (20, 38), (27, 17), (26, 43), (27, 6), (9, 11), (9, 3), (27, 34), (35, 5), (3, 17), (38, 1), (19, 32), (24, 40), (31, 1), (28, 14), (17, 18), (14, 4), (27, 39), (9, 45), (28, 0), (9, 4), (16, 36), (22, 30), (3, 1), (13, 21), (10, 6), (39, 11), (3, 26), (18, 29), (24, 8), (37, 13), (19, 18), (2, 29), (21, 32), (15, 26), (16, 15), (12, 22), (8, 28), (38, 30), (12, 30), (16, 17), (34, 16), (21, 0), (18, 1), (24, 14), (38, 15), (38, 0), (34, 31), (39, 23), (6, 11), (4, 19), (37, 15), (9, 42), (17, 44), (5, 26), (5, 34), (25, 36), (6, 30), (21, 5), (39, 27), (24, 16), (13, 35), (36, 40), (6, 36), (17, 19), (3, 28), (5, 11), (24, 7), (21, 41), (2, 18), (4, 6), (10, 32), (28, 42), (21, 8), (14, 26), (5, 33), (2, 7), (37, 24), (36, 42), (31, 35), (3, 31), (7, 34), (26, 34), (37, 0), (29, 27), (0, 1), (3, 25), (28, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 21), (11, 19), (10, 21), (24, 5), (20, 21), (3, 13), (7, 10), (27, 32), (15, 32), (10, 16), (20, 25), (34, 43), (34, 31), (34, 17), (21, 34), (31, 4), (21, 40), (32, 31), (2, 12), (12, 36), (39, 26), (33, 32), (12, 43), (15, 40), (3, 3), (27, 13), (35, 17), (5, 13), (10, 43), (37, 19), (38, 38), (31, 14), (38, 8), (36, 37), (13, 22), (19, 2), (11, 7), (20, 35), (24, 39), (25, 24), (20, 8), (35, 5), (22, 13), (10, 15), (9, 43), (25, 18), (9, 10), (19, 22), (13, 32), (1, 34), (38, 5), (34, 20), (12, 4), (24, 25), (8, 39), (3, 37), (8, 37), (34, 15), (16, 6), (25, 14), (25, 29), (26, 13), (27, 14), (27, 3), (26, 21), (18, 11), (0, 33), (39, 27), (19, 13), (32, 17), (7, 43), (12, 18), (11, 23), (3, 38), (28, 4), (14, 33), (31, 44), (21, 17), (5, 11), (16, 14), (0, 31), (5, 28), (7, 3), (30, 28), (14, 36), (3, 6), (16, 17), (18, 8), (17, 8), (18, 26), (39, 39), (13, 16), (28, 14), (32, 40), (26, 44), (1, 24), (4, 3), (19, 39), (21, 35), (34, 34), (16, 26), (19, 25), (29, 31), (1, 12), (37, 15), (26, 3), (39, 24), (29, 44), (21, 43), (30, 40), (2, 19), (37, 29), (1, 14), (38, 12), (11, 2), (24, 30), (14, 24), (31, 15), (4, 6), (11, 6), (23, 35), (33, 28), (15, 11), (5, 8), (22, 30), (38, 27), (2, 40), (29, 0), (37, 31), (37, 7), (39, 17), (10, 3), (22, 41), (37, 32), (12, 12), (26, 19), (8, 22), (22, 10), (0, 2), (31, 13), (12, 14), (23, 40), (29, 27), (26, 5), (20, 12), (14, 16), (32, 24), (1, 22), (14, 19), (17, 33), (4, 20), (1, 26), (20, 13), (11, 15), (20, 2), (39, 32), (35, 38), (16, 37), (6, 32), (37, 1), (24, 2), (11, 34), (27, 17), (7, 36), (16, 8), (34, 33), (23, 41), (7, 34), (15, 33), (18, 24), (33, 19), (36, 43), (37, 36), (35, 15), (9, 4), (28, 26), (32, 33), (15, 19), (36, 21), (26, 23), (19, 17), (38, 0), (32, 25), (39, 7), (20, 34), (32, 2), (24, 17), (35, 25), (34, 23), (14, 32), (25, 40), (39, 12), (0, 42), (4, 34), (12, 31), (23, 38), (31, 24), (5, 32), (16, 22), (9, 28), (15, 9), (21, 5), (0, 44), (29, 9), (15, 16), (10, 29), (13, 0), (3, 28), (17, 43), (6, 0), (31, 7), (31, 30), (38, 23), (28, 27), (12, 13), (8, 9), (36, 24), (30, 8), (37, 22), (16, 40), (14, 40), (11, 30), (36, 8), (13, 1), (20, 24), (8, 20), (32, 8), (21, 26), (13, 19), (31, 43), (3, 19), (24, 41), (8, 40), (3, 10), (37, 37), (5, 17), (2, 5), (17, 22), (37, 44), (29, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (4, 14), (7, 33), (19, 34), (13, 26), (28, 2), (21, 29), (28, 23), (40, 17), (20, 23), (12, 12), (37, 12), (38, 16), (28, 30), (37, 14), (3, 8), (6, 5), (9, 23), (8, 27), (9, 38), (13, 6), (10, 16), (20, 37), (16, 36), (4, 6), (33, 29), (11, 22), (23, 10), (38, 17), (12, 32), (0, 8), (18, 19), (25, 15), (12, 25), (21, 40), (40, 37), (40, 22), (40, 28), (28, 24), (19, 11), (19, 16), (1, 8), (17, 14), (0, 11), (2, 1), (13, 2), (18, 24), (0, 16), (1, 12), (23, 15), (33, 20), (29, 12), (34, 7), (12, 37), (0, 26), (41, 2), (15, 32), (16, 34), (18, 21), (41, 37), (24, 17), (41, 27), (2, 15), (28, 19), (36, 11), (8, 30), (3, 5), (19, 4), (33, 14), (36, 6), (12, 29), (7, 32), (25, 30), (29, 11), (33, 28), (15, 22), (6, 2), (4, 27), (10, 1), (11, 31), (37, 27), (3, 13), (16, 8), (13, 36), (1, 25), (35, 20), (22, 34), (6, 25), (19, 37), (34, 9), (27, 2), (4, 31), (37, 11), (27, 24), (17, 18), (3, 10), (6, 27), (24, 26), (37, 28), (1, 18), (11, 35), (38, 30), (4, 17), (11, 23), (4, 26), (11, 18), (4, 7), (41, 18), (33, 21), (11, 14), (18, 23), (16, 2), (35, 40), (27, 18), (8, 4), (37, 4), (26, 30), (26, 33), (15, 28), (21, 18), (0, 38), (1, 3), (27, 6), (27, 34), (0, 34), (26, 11), (20, 38), (40, 7), (29, 24), (13, 1), (32, 21), (34, 36), (21, 2), (12, 3), (33, 11), (26, 4), (7, 27), (22, 31), (26, 8), (35, 31), (15, 37), (38, 7), (36, 24), (33, 38), (24, 38), (16, 7), (28, 5), (10, 24), (22, 1), (40, 19), (17, 23), (23, 13), (15, 12), (20, 6), (33, 17), (14, 27), (4, 18), (6, 3), (36, 9), (1, 14), (37, 33), (25, 37), (11, 30), (22, 25), (16, 4), (14, 37), (29, 0), (21, 27), (35, 2), (18, 5), (4, 23), (33, 2), (34, 13), (29, 17), (23, 0), (15, 35), (17, 7), (35, 11), (6, 40), (37, 23), (26, 26), (0, 19), (32, 15), (38, 8), (40, 31), (24, 16), (26, 9), (22, 12), (32, 3), (36, 1), (26, 3), (40, 1), (39, 34), (14, 24), (25, 34), (18, 29), (9, 19), (3, 7), (24, 2), (29, 18), (34, 28), (24, 23), (37, 37), (20, 27), (41, 5), (2, 34), (28, 26), (19, 0), (2, 7), (0, 30), (28, 35), (16, 15), (14, 40), (22, 22), (6, 21), (25, 25), (2, 6), (30, 11), (5, 8), (19, 1), (12, 6), (10, 33), (31, 17), (18, 17), (10, 14), (41, 10), (26, 40), (14, 29), (26, 12), (7, 24), (7, 40), (13, 18), (24, 3), (8, 38), (6, 15), (39, 22), (6, 36), (38, 11), (10, 20), (2, 35), (28, 6), (15, 29), (9, 30), (6, 16), (7, 10), (17, 37), (20, 10), (23, 32), (6, 4), (14, 28), (27, 37), (23, 38), (28, 4), (20, 11), (31, 33), (16, 16), (35, 1), (34, 29), (21, 23), (23, 30), (37, 24), (35, 5), (35, 35), (31, 19), (32, 38), (7, 3), (25, 26), (16, 40), (32, 5), (35, 4), (36, 33), (1, 21), (41, 6), (40, 36), (23, 33), (26, 25), (9, 37), (7, 16), (14, 20), (22, 2), (23, 28), (38, 18), (3, 27), (39, 25), (11, 1), (5, 0), (3, 28), (5, 21), (22, 11), (2, 2), (21, 5), (35, 7), (5, 23), (7, 11), (39, 8), (9, 28), (12, 40), (22, 39), (36, 14), (24, 36), (33, 34), (0, 40), (29, 13), (39, 12), (13, 10), (29, 27), (20, 16), (26, 5), (21, 20), (40, 10), (1, 38), (9, 11), (14, 17), (2, 10), (24, 33), (21, 22), (0, 33), (23, 14), (3, 25), (2, 20), (19, 30), (32, 4), (24, 15), (39, 2), (23, 35), (4, 37), (24, 24), (4, 8), (20, 21), (37, 32), (11, 8), (22, 5), (36, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 3), (20, 18), (0, 32), (35, 31), (14, 3), (11, 25), (45, 13), (12, 4), (17, 17), (13, 6), (12, 43), (43, 4), (10, 12), (27, 23), (13, 48), (8, 12), (37, 36), (33, 30), (16, 33), (32, 4), (29, 34), (39, 9), (12, 12), (24, 5), (44, 25), (44, 13), (35, 19), (43, 31), (4, 26), (22, 15), (14, 7), (13, 5), (6, 27), (25, 41), (47, 6), (41, 40), (42, 11), (31, 18), (45, 15), (3, 38), (34, 34), (46, 16), (23, 28), (26, 34), (30, 39), (45, 45), (27, 46), (45, 1), (24, 20), (6, 12), (37, 28), (19, 24), (24, 7), (20, 8), (36, 14), (33, 23), (32, 24), (45, 2), (21, 32), (31, 42), (33, 34), (8, 29), (21, 24), (33, 2), (18, 21), (40, 16), (5, 22), (9, 35), (9, 7), (11, 17), (39, 19), (44, 8), (30, 36), (19, 28), (11, 34), (4, 15), (0, 3), (47, 38), (32, 35), (4, 2), (39, 32), (7, 29), (9, 4), (29, 0), (42, 15), (2, 21), (45, 5), (31, 14), (22, 18), (12, 25), (3, 1), (19, 19), (44, 11), (25, 28), (38, 30), (28, 43), (44, 15), (11, 16), (39, 22), (42, 18), (44, 17), (42, 10), (32, 6), (20, 13), (19, 5), (39, 6), (15, 27), (13, 20), (7, 27), (41, 33), (31, 15), (23, 8), (18, 14), (3, 28), (39, 35), (7, 3), (40, 11), (33, 39), (41, 0), (12, 2), (38, 43), (2, 19), (40, 42), (32, 11), (29, 3), (3, 18), (4, 38), (3, 42), (39, 30), (32, 44), (10, 14), (23, 46), (39, 12), (16, 15), (0, 15), (27, 21), (34, 22), (26, 20), (13, 7), (3, 9), (19, 4), (32, 9), (8, 18), (43, 15), (5, 29), (9, 10), (22, 39), (36, 37), (10, 40), (16, 44), (21, 43), (41, 18), (30, 13), (1, 6), (32, 42), (28, 0), (42, 21), (37, 47), (31, 26), (0, 41), (31, 2), (3, 30), (35, 0), (11, 10), (6, 3), (10, 37), (9, 43), (47, 17), (23, 40), (43, 0), (4, 7), (36, 0), (24, 35), (13, 22), (5, 41), (4, 0), (26, 29), (36, 17), (26, 28), (6, 44), (27, 0), (40, 22), (43, 16), (31, 16), (32, 39), (10, 27), (22, 32), (43, 10), (42, 40), (13, 35), (6, 35), (44, 42), (41, 27), (0, 8), (8, 45), (23, 22), (18, 9), (16, 28), (46, 11), (23, 37), (12, 13), (40, 23), (6, 41), (35, 37), (22, 26), (47, 25), (17, 21), (35, 8), (12, 29), (26, 9), (44, 14), (3, 5), (7, 33), (32, 31), (29, 37), (38, 8), (22, 41), (4, 37), (25, 30), (14, 1), (12, 41), (29, 27), (45, 35), (43, 3), (25, 5), (32, 10), (28, 19), (13, 23), (5, 42), (8, 39), (2, 35), (15, 21), (10, 4), (13, 18), (16, 2), (47, 1), (9, 41), (37, 32), (29, 36), (4, 3), (47, 18), (33, 27), (40, 20), (47, 29), (7, 45), (31, 11), (19, 13), (20, 46), (9, 27), (9, 34), (10, 44), (32, 19), (3, 24), (39, 26), (14, 28), (2, 23), (42, 24), (10, 8), (23, 32), (40, 30), (6, 47), (44, 45), (4, 22), (15, 39), (41, 14), (43, 36), (8, 8), (38, 11), (1, 29), (5, 34), (21, 14), (29, 2), (31, 33), (17, 42), (40, 27), (18, 35), (5, 19), (20, 34), (24, 8), (37, 31), (10, 15), (38, 26), (21, 10), (44, 3), (39, 34), (35, 12), (32, 18), (20, 17), (41, 45), (17, 48), (45, 37), (32, 43), (36, 15), (37, 44), (33, 26), (20, 22), (41, 39), (24, 32), (17, 24), (3, 6), (43, 43), (17, 41), (43, 23), (0, 24), (22, 25), (40, 18), (10, 33), (42, 27), (14, 31), (24, 36), (18, 29), (46, 15), (14, 2), (13, 0), (42, 9), (41, 32), (47, 3), (39, 2), (16, 10), (47, 15), (22, 28), (9, 11), (42, 5), (17, 46), (12, 7), (34, 2), (13, 44), (33, 44), (36, 44), (30, 40), (4, 42), (34, 41), (1, 24), (20, 15), (35, 16), (26, 12), (18, 10), (6, 5), (34, 12), (0, 19), (47, 12), (11, 13), (41, 21), (9, 0), (0, 36), (21, 42), (24, 2), (22, 9), (36, 31), (38, 46), (29, 19), (1, 10), (22, 47), (18, 24), (35, 34), (23, 26), (21, 18), (14, 5), (46, 3), (13, 29), (16, 40), (27, 35), (37, 9), (8, 42), (1, 18), (34, 48), (23, 16), (1, 28), (36, 6), (29, 17), (4, 4), (19, 31), (38, 38), (38, 22), (27, 40), (41, 24), (41, 47), (30, 15), (27, 15), (30, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 36), (8, 25), (23, 42), (1, 36), (3, 30), (3, 9), (17, 18), (33, 42), (2, 20), (23, 38), (22, 0), (11, 9), (4, 28), (0, 22), (41, 46), (6, 43), (22, 42), (37, 8), (33, 12), (21, 2), (30, 29), (0, 9), (24, 41), (40, 37), (32, 3), (23, 9), (4, 26), (39, 0), (39, 41), (21, 5), (21, 29), (29, 30), (19, 31), (39, 46), (23, 24), (7, 15), (5, 47), (11, 31), (21, 1), (37, 15), (28, 11), (22, 19), (26, 44), (7, 35), (16, 42), (40, 41), (8, 34), (0, 4), (35, 43), (27, 22), (37, 1), (3, 5), (12, 6), (25, 29), (1, 1), (16, 20), (26, 29), (7, 31), (17, 28), (28, 25), (7, 30), (12, 14), (38, 30), (4, 42), (31, 46), (15, 9), (28, 10), (28, 19), (10, 23), (12, 25), (18, 38), (2, 46), (4, 5), (32, 2), (21, 13), (3, 16), (23, 45), (3, 8), (12, 9), (40, 31), (2, 27), (27, 12), (8, 22), (7, 32), (6, 17), (36, 47), (10, 7), (21, 38), (40, 29), (6, 37), (31, 21), (33, 19), (19, 28), (20, 40), (7, 2), (29, 40), (10, 31), (26, 14), (14, 44), (39, 11), (23, 15), (20, 31), (28, 22), (18, 39), (7, 37), (9, 5), (6, 35), (31, 45), (25, 37), (37, 32), (29, 36), (34, 19), (7, 40), (2, 13), (25, 3), (29, 8), (3, 44), (7, 14), (15, 36), (8, 7), (17, 24), (15, 46), (12, 10), (27, 46), (15, 24), (11, 42), (32, 11), (38, 1), (17, 25), (37, 25), (11, 47), (7, 16), (16, 22), (31, 19), (33, 27), (14, 35), (15, 26), (7, 0), (37, 33), (41, 12), (38, 11), (34, 35), (34, 37), (0, 32), (34, 12), (5, 7), (41, 18), (8, 43), (26, 47), (38, 40), (35, 12), (35, 11), (3, 41), (35, 47), (21, 45), (37, 13), (34, 14), (33, 7), (40, 35), (33, 28), (22, 8), (40, 10), (21, 40), (26, 4), (16, 15), (11, 12), (13, 46), (18, 32), (10, 43), (17, 2), (38, 21), (2, 23), (11, 28), (29, 1), (15, 2), (38, 15), (25, 41), (38, 47), (26, 6), (35, 35), (17, 43), (34, 21), (12, 30), (25, 9), (25, 38), (30, 7), (31, 0), (9, 29), (5, 34), (30, 10), (25, 40), (24, 24), (39, 15), (33, 24), (35, 10), (24, 21), (11, 36), (1, 31), (13, 16), (41, 38), (26, 24), (26, 23), (0, 7), (33, 44), (32, 9), (5, 2), (6, 45), (33, 11), (22, 9), (36, 37), (26, 19), (27, 11), (40, 4), (21, 16), (1, 19), (18, 42), (10, 1), (4, 37), (2, 19), (29, 22), (37, 9), (17, 35), (23, 20), (11, 0), (41, 32), (27, 1), (19, 42), (0, 8), (7, 18), (3, 3), (23, 25), (14, 37), (35, 30), (5, 17), (31, 43), (16, 30), (39, 32), (25, 22), (10, 0), (6, 21), (36, 28), (0, 36), (28, 20), (24, 9), (36, 7), (29, 25), (22, 40), (4, 6), (19, 11), (15, 28), (31, 35), (41, 17), (1, 15), (5, 37), (18, 43), (29, 7), (40, 23), (39, 33), (10, 3), (9, 11), (31, 29), (21, 10), (21, 7), (11, 30), (8, 17), (14, 32), (24, 39), (33, 45), (37, 20), (9, 31), (33, 10), (25, 4), (13, 6), (28, 24), (5, 39), (15, 17), (34, 38), (25, 21), (36, 26), (38, 2), (6, 12), (35, 6), (0, 33), (19, 21), (10, 26), (7, 46), (3, 4), (34, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 12), (11, 24), (18, 33), (19, 41), (22, 6), (34, 22), (1, 22), (17, 24), (3, 18), (21, 3), (23, 6), (39, 25), (35, 37), (10, 37), (16, 38), (7, 0), (39, 13), (33, 38), (1, 3), (4, 18), (2, 23), (8, 17), (29, 25), (25, 20), (20, 18), (21, 19), (27, 27), (8, 22), (28, 32), (4, 3), (10, 4), (5, 39), (32, 13), (34, 9), (34, 31), (32, 22), (38, 41), (23, 36), (28, 21), (25, 23), (16, 32), (27, 7), (24, 24), (35, 7), (17, 31), (2, 18), (12, 22), (1, 38), (24, 30), (15, 12), (16, 10), (4, 17), (28, 10), (31, 21), (3, 4), (1, 37), (6, 33), (32, 35), (10, 35), (13, 35), (7, 32), (34, 26), (16, 14), (16, 20), (19, 34), (35, 34), (37, 29), (31, 9), (25, 41), (15, 2), (12, 28), (2, 1), (37, 14), (3, 32), (6, 31), (25, 39), (4, 6), (8, 31), (21, 38), (35, 31), (31, 13), (20, 0), (27, 5), (16, 5), (28, 26), (34, 25), (29, 36), (3, 38), (39, 26), (2, 4), (24, 12), (24, 13), (8, 8), (16, 12), (21, 39), (36, 31), (16, 13), (6, 27), (3, 20), (26, 27), (32, 26), (18, 13), (39, 28), (25, 13), (37, 22), (31, 41), (1, 6), (33, 25), (5, 14), (7, 40), (11, 17), (20, 27), (7, 16), (23, 12), (38, 31), (31, 26), (15, 5), (28, 9), (4, 5), (12, 24), (39, 34), (7, 3), (37, 17), (27, 6), (33, 32), (27, 24), (6, 29), (25, 10), (4, 33), (34, 18), (5, 10), (27, 12), (11, 10), (9, 40), (39, 21), (9, 33), (30, 35), (16, 41), (18, 37), (22, 18), (7, 26), (19, 16), (24, 35), (0, 38), (39, 16), (10, 36), (35, 17), (14, 34), (0, 23), (29, 9), (8, 15), (37, 37), (33, 22), (23, 16), (11, 41), (14, 36), (3, 17), (33, 8), (15, 8), (7, 27), (11, 14), (38, 23), (6, 12), (15, 23), (8, 16), (4, 36), (17, 19), (24, 0), (5, 25), (17, 20), (25, 8), (17, 5), (33, 37), (4, 21), (38, 36), (0, 9), (2, 15), (1, 27), (19, 30), (0, 28), (5, 12), (35, 5), (2, 19), (21, 20), (28, 8), (17, 38), (1, 23), (11, 21), (11, 27), (23, 5), (15, 38), (19, 23), (31, 33), (9, 8), (21, 37), (1, 41), (36, 8), (18, 7), (10, 30), (11, 34), (36, 21), (27, 34), (26, 13), (12, 21), (11, 9), (39, 37), (30, 2), (20, 22), (32, 40), (18, 9), (4, 10), (35, 38), (33, 0), (2, 0), (28, 27), (4, 35), (20, 8), (29, 20), (9, 27), (23, 2), (11, 28), (13, 31), (28, 40), (10, 41), (26, 33), (17, 0), (7, 39), (28, 28), (17, 33), (27, 10), (3, 29), (23, 40), (8, 21), (30, 14), (21, 2), (12, 37), (38, 28), (21, 13), (37, 28), (14, 15), (33, 14), (21, 27), (11, 3), (39, 15), (15, 3), (7, 8), (16, 24), (15, 26), (3, 33), (13, 34), (24, 41), (34, 16), (33, 31), (17, 1), (10, 28), (25, 26), (2, 13), (9, 12), (29, 12), (1, 20), (8, 20), (30, 4), (23, 19), (8, 11), (0, 4), (16, 4), (20, 19), (15, 32), (35, 32), (19, 9), (22, 16), (19, 29), (23, 18), (5, 19), (31, 32), (23, 3), (4, 38), (30, 30), (29, 30), (24, 7), (1, 7), (8, 3), (10, 8), (27, 35), (39, 38), (21, 28), (6, 39), (32, 18), (31, 15), (14, 33), (3, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 26), (12, 42), (33, 41), (21, 0), (9, 31), (0, 8), (7, 19), (10, 1), (16, 36), (37, 6), (2, 38), (22, 2), (35, 20), (3, 12), (28, 26), (22, 43), (8, 40), (24, 13), (34, 4), (33, 0), (4, 32), (24, 12), (31, 28), (23, 29), (6, 9), (0, 18), (36, 8), (21, 44), (7, 14), (15, 2), (7, 39), (21, 9), (3, 8), (11, 43), (21, 5), (5, 32), (6, 3), (13, 16), (25, 17), (21, 19), (35, 28), (33, 43), (31, 10), (24, 29), (6, 29), (23, 40), (34, 19), (19, 6), (9, 29), (40, 31), (28, 34), (5, 13), (21, 20), (31, 21), (8, 20), (0, 25), (30, 15), (1, 15), (10, 26), (39, 18), (9, 28), (26, 44), (22, 29), (17, 11), (4, 4), (29, 34), (11, 5), (22, 14), (34, 17), (35, 29), (13, 25), (27, 13), (21, 1), (9, 11), (35, 4), (18, 30), (8, 0), (0, 16), (24, 26), (21, 26), (3, 35), (10, 32), (28, 10), (30, 41), (3, 21), (0, 42), (3, 22), (3, 10), (5, 3), (35, 19), (22, 16), (20, 4), (21, 27), (13, 22), (38, 27), (20, 5), (37, 35), (9, 34), (3, 33), (19, 27), (20, 44), (37, 12), (8, 41), (9, 33), (6, 18), (3, 42), (26, 2), (19, 42), (14, 27), (16, 3), (27, 38), (8, 2), (4, 3), (28, 31), (35, 21), (35, 41), (1, 33), (13, 26), (28, 25), (6, 25), (6, 5), (28, 15), (20, 13), (26, 14), (24, 30), (14, 13), (14, 31), (18, 40), (8, 43), (24, 42), (26, 38), (25, 25), (13, 4), (38, 17), (5, 7), (19, 23), (18, 34), (24, 34), (23, 26), (7, 22), (1, 3), (14, 16), (12, 41), (5, 19), (36, 14), (21, 17), (5, 34), (32, 41), (15, 43), (13, 13), (20, 7), (24, 43), (30, 26), (2, 23), (35, 27), (1, 9), (38, 32), (26, 32), (5, 12), (34, 10), (14, 33), (7, 28), (16, 23), (36, 23), (7, 16), (28, 28), (16, 43), (32, 20), (9, 16), (33, 29), (33, 13), (28, 42), (37, 33), (39, 44), (0, 3), (22, 38), (5, 35), (33, 4), (15, 27), (4, 33), (27, 17), (2, 34), (10, 44), (21, 31), (28, 35), (31, 2), (8, 36), (27, 44), (5, 28), (15, 1), (26, 0), (14, 40), (31, 42), (0, 4), (5, 41), (15, 19), (34, 11), (26, 37), (33, 7), (10, 25), (24, 33), (15, 44), (17, 27), (5, 1), (1, 0), (13, 23), (18, 10), (18, 23), (11, 9), (26, 17), (12, 14), (35, 0), (36, 26), (27, 1), (31, 43), (13, 41), (39, 11), (16, 25), (24, 37), (11, 6), (24, 39), (34, 29), (36, 31), (5, 11), (32, 5), (30, 34), (5, 5), (36, 34), (12, 19), (26, 31), (34, 3), (6, 42), (24, 25), (4, 14), (8, 12), (34, 30), (2, 20), (25, 15), (17, 24), (27, 25), (12, 15), (10, 33), (32, 36), (29, 16), (11, 12), (37, 26), (27, 36), (13, 2), (31, 29), (8, 30), (30, 16), (12, 44), (7, 20), (37, 17), (38, 20), (9, 35), (3, 39), (4, 30), (16, 8), (17, 44), (12, 2), (13, 34), (21, 43), (21, 13), (0, 36), (25, 26), (15, 29), (38, 29), (4, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 14), (16, 27), (17, 9), (43, 35), (18, 32), (11, 37), (36, 26), (3, 29), (39, 25), (35, 41), (0, 3), (14, 27), (39, 29), (16, 36), (2, 30), (5, 13), (26, 12), (32, 19), (24, 40), (38, 16), (8, 1), (13, 14), (13, 8), (11, 21), (25, 21), (2, 40), (15, 30), (12, 35), (24, 42), (36, 43), (37, 30), (9, 26), (31, 44), (14, 23), (38, 44), (24, 33), (43, 24), (16, 35), (22, 12), (17, 37), (22, 18), (15, 3), (40, 19), (44, 22), (9, 6), (32, 28), (24, 4), (1, 4), (26, 13), (21, 42), (30, 8), (33, 15), (14, 19), (44, 35), (37, 23), (31, 42), (40, 20), (4, 15), (8, 25), (24, 28), (21, 5), (30, 39), (22, 19), (26, 22), (1, 36), (41, 24), (9, 24), (15, 35), (15, 0), (40, 25), (31, 30), (15, 36), (19, 9), (30, 23), (32, 23), (5, 15), (3, 5), (34, 43), (6, 11), (32, 29), (33, 14), (7, 41), (35, 36), (2, 24), (27, 12), (32, 6), (30, 41), (4, 17), (11, 0), (1, 14), (35, 24), (6, 1), (18, 41), (39, 35), (38, 18), (28, 19), (23, 7), (7, 37), (42, 34), (2, 20), (0, 31), (33, 23), (39, 31), (2, 15), (29, 34), (11, 2), (15, 17), (29, 35), (7, 26), (21, 41), (12, 8), (0, 22), (24, 11), (31, 13), (26, 38), (18, 36), (13, 4), (42, 21), (10, 36), (22, 24), (16, 15), (18, 25), (42, 26), (40, 24), (28, 22), (13, 18), (25, 32), (9, 35), (2, 12), (29, 37), (1, 9), (20, 26), (29, 16), (15, 31), (40, 42), (10, 13), (0, 21), (43, 16), (37, 35), (6, 28), (23, 24), (4, 8), (44, 1), (39, 3), (10, 19), (3, 7), (41, 9), (31, 33), (3, 22), (39, 8), (36, 38), (41, 8), (1, 6), (2, 22), (2, 44), (5, 21), (36, 12), (25, 40), (32, 34), (30, 34), (20, 3), (25, 33), (4, 16), (19, 22), (3, 42), (4, 28), (34, 12), (28, 36), (12, 24), (3, 24), (22, 32), (14, 25), (20, 10), (14, 3), (26, 33), (36, 18), (16, 40), (12, 9), (40, 2), (7, 18), (35, 44), (13, 31), (44, 39), (5, 9), (14, 20), (28, 0), (14, 0), (7, 7), (41, 38), (13, 20), (42, 4), (1, 33), (42, 9), (3, 1), (4, 4), (28, 14), (36, 2), (14, 18), (8, 21), (1, 21), (2, 39), (26, 26), (14, 11), (20, 18), (21, 33), (41, 10), (18, 7), (2, 19), (38, 23), (12, 4), (7, 39), (10, 4), (24, 44), (40, 13), (8, 44), (8, 43), (43, 22), (29, 32), (41, 43), (40, 18), (36, 29), (40, 6), (6, 0), (8, 14), (39, 39), (17, 16), (21, 32), (11, 17), (33, 6), (11, 28), (19, 34), (24, 15), (31, 28), (34, 37), (23, 14), (17, 1), (21, 25), (11, 8), (18, 31), (22, 28), (30, 37), (26, 2), (20, 0), (10, 3), (7, 9), (38, 0), (28, 11), (25, 1), (27, 26), (44, 43), (43, 2), (3, 9), (6, 42), (0, 24), (35, 6), (12, 28), (15, 16), (22, 6), (28, 10), (30, 9), (3, 19), (15, 23), (22, 20), (15, 11), (23, 3), (3, 15), (9, 20), (0, 1), (30, 12), (34, 0), (41, 37), (21, 23), (13, 42), (41, 26), (37, 17), (42, 27), (35, 0), (36, 32), (27, 16), (12, 25), (2, 11), (23, 31), (43, 8), (11, 16), (17, 20), (34, 18), (43, 15), (24, 41), (37, 3), (37, 16), (23, 28), (7, 0), (37, 40), (26, 20), (27, 32), (8, 29), (44, 25), (5, 4), (7, 36), (26, 34), (7, 40), (40, 27), (29, 39), (26, 27), (31, 43), (42, 36), (0, 39), (38, 13), (43, 4), (22, 1), (8, 13), (35, 32), (19, 19), (44, 0), (9, 8), (17, 33), (3, 26), (25, 14), (34, 1), (20, 42), (25, 38), (37, 11), (23, 40), (42, 6), (10, 17), (27, 24), (26, 4), (38, 38), (30, 24), (30, 6), (30, 17), (18, 23), (35, 22), (15, 32), (22, 36), (0, 29), (23, 19), (9, 33), (12, 42), (41, 41), (19, 37), (36, 20), (14, 4), (5, 19), (19, 35), (10, 10), (14, 38), (43, 3), (14, 15), (40, 4), (29, 36), (1, 38), (25, 26), (12, 37), (1, 25), (31, 34), (18, 17), (17, 40), (36, 22), (21, 15), (17, 4), (39, 42), (23, 23), (4, 35), (26, 25), (2, 38), (38, 1), (18, 18), (32, 16), (19, 18), (23, 35), (18, 28), (24, 2), (15, 19), (6, 30), (26, 3), (14, 36), (30, 31), (5, 33), (32, 40), (26, 16), (34, 23), (15, 24), (8, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 49x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 36), (45, 38), (27, 7), (30, 37), (31, 20), (31, 0), (35, 21), (20, 18), (38, 22), (9, 29), (38, 14), (4, 15), (0, 14), (15, 35), (25, 17), (25, 3), (13, 35), (34, 19), (21, 5), (6, 39), (0, 23), (36, 33), (23, 8), (40, 5), (18, 11), (27, 21), (13, 34), (10, 27), (13, 9), (24, 3), (38, 9), (11, 18), (28, 34), (19, 13), (14, 27), (8, 3), (21, 36), (36, 2), (30, 9), (36, 35), (42, 11), (48, 4), (42, 20), (9, 21), (3, 34), (19, 5), (30, 19), (43, 6), (8, 22), (48, 30), (11, 37), (29, 14), (37, 2), (24, 38), (4, 25), (10, 23), (9, 23), (25, 20), (13, 29), (48, 10), (25, 18), (47, 23), (39, 32), (31, 5), (12, 11), (35, 0), (47, 16), (34, 31), (42, 3), (3, 29), (45, 31), (14, 23), (46, 25), (34, 39), (8, 10), (43, 15), (31, 17), (17, 18), (8, 19), (27, 0), (15, 13), (26, 26), (17, 30), (3, 21), (31, 24), (33, 0), (33, 36), (22, 17), (43, 36), (21, 23), (6, 20), (47, 19), (14, 19), (38, 2), (18, 24), (28, 30), (13, 25), (15, 8), (1, 13), (2, 27), (14, 37), (46, 31), (0, 36), (46, 34), (35, 8), (2, 33), (14, 36), (19, 4), (28, 26), (9, 35), (2, 29), (20, 4), (44, 8), (14, 35), (15, 21), (19, 1), (3, 13), (43, 22), (35, 3), (29, 11), (22, 28), (28, 20), (26, 18), (2, 11), (35, 9), (40, 27), (4, 24), (1, 0), (16, 35), (0, 31), (31, 35), (0, 4), (30, 34), (28, 6), (19, 31), (43, 9), (20, 31), (12, 15), (1, 11), (43, 12), (26, 36), (27, 24), (17, 7), (30, 18), (47, 7), (26, 22), (29, 24), (4, 33), (17, 15), (44, 15), (36, 25), (23, 0), (20, 15), (39, 7), (28, 33), (43, 27), (16, 34), (13, 12), (12, 5), (8, 21), (38, 7), (15, 23), (35, 4), (11, 30), (41, 4), (2, 19), (41, 32), (22, 29), (32, 16), (44, 12), (33, 38), (45, 19), (24, 10), (46, 19), (12, 38), (14, 25), (32, 2), (7, 11), (31, 21), (15, 38), (23, 10), (33, 17), (7, 1), (13, 23), (13, 32), (35, 16), (42, 4), (43, 10), (29, 38), (46, 5), (23, 22), (11, 29), (32, 28), (36, 24), (22, 3), (23, 20), (30, 11), (3, 31), (41, 30), (29, 26), (28, 36), (3, 27), (21, 31), (12, 13), (12, 7), (15, 32), (47, 33), (27, 2), (37, 32), (21, 20), (11, 13), (22, 16), (25, 24), (47, 6), (0, 19), (47, 9), (16, 28), (40, 8), (37, 11), (23, 34), (26, 38), (23, 29), (27, 34), (5, 7), (6, 5), (28, 13), (13, 20), (32, 6), (31, 37), (18, 15), (34, 18), (32, 0), (12, 1), (3, 4), (38, 21), (19, 22), (12, 24), (48, 19), (30, 15), (41, 1), (44, 4), (7, 8), (5, 14), (24, 7), (33, 34), (7, 21), (0, 18), (42, 14), (25, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 43), (10, 20), (27, 28), (11, 1), (40, 11), (9, 21), (41, 23), (1, 23), (24, 15), (13, 25), (29, 19), (2, 45), (7, 34), (15, 21), (23, 25), (25, 34), (8, 7), (39, 19), (14, 28), (38, 40), (25, 17), (21, 15), (11, 11), (38, 17), (9, 43), (34, 35), (13, 45), (20, 5), (41, 26), (23, 28), (26, 10), (7, 7), (0, 6), (19, 32), (40, 8), (7, 29), (41, 24), (20, 40), (18, 24), (39, 28), (15, 34), (24, 4), (34, 46), (19, 22), (37, 7), (29, 34), (6, 8), (42, 23), (13, 15), (22, 23), (44, 26), (21, 21), (41, 17), (42, 0), (27, 27), (17, 6), (38, 43), (11, 17), (44, 36), (12, 47), (30, 32), (20, 37), (40, 40), (25, 36), (43, 41), (10, 37), (18, 15), (23, 38), (12, 1), (34, 47), (7, 39), (15, 27), (42, 3), (26, 22), (6, 42), (37, 37), (30, 7), (20, 2), (6, 35), (30, 1), (42, 17), (28, 13), (29, 39), (18, 6), (28, 15), (38, 37), (34, 19), (1, 18), (34, 15), (16, 30), (17, 31), (37, 45), (5, 24), (16, 11), (8, 18), (18, 28), (19, 10), (6, 34), (15, 24), (11, 43), (14, 0), (26, 37), (22, 21), (14, 21), (43, 44), (11, 33), (2, 3), (26, 20), (27, 20), (18, 36), (27, 47), (4, 38), (22, 29), (34, 25), (8, 17), (26, 23), (24, 25), (6, 26), (35, 30), (30, 35), (42, 37), (41, 29), (37, 24), (29, 27), (19, 14), (32, 3), (29, 29), (23, 34), (31, 47), (18, 12), (31, 12), (12, 37), (2, 22), (25, 39), (39, 40), (29, 28), (43, 5), (32, 29), (17, 46), (5, 6), (16, 3), (17, 37), (12, 43), (19, 26), (33, 35), (11, 28), (22, 42), (15, 42), (41, 4), (19, 41), (27, 22), (29, 11), (26, 41), (22, 41), (26, 7), (22, 20), (12, 25), (1, 7), (40, 23), (34, 40), (21, 10), (10, 42), (29, 33), (30, 8), (25, 43), (1, 0), (33, 26), (4, 23), (21, 29), (8, 38), (38, 31), (3, 9), (38, 47), (39, 21), (7, 18), (2, 32), (22, 32), (26, 6), (32, 38), (0, 20), (30, 45), (24, 22), (22, 5), (42, 30), (35, 9), (14, 36), (33, 21), (11, 44), (44, 41), (29, 9), (1, 5), (12, 3), (38, 18), (5, 20), (10, 9), (30, 36), (12, 44), (4, 39), (7, 26), (8, 10), (43, 32), (36, 22), (40, 17), (41, 43), (15, 5), (7, 13), (20, 44), (0, 37), (4, 21), (41, 13), (15, 17), (28, 28), (37, 18), (12, 5), (25, 30), (42, 14), (38, 45), (39, 1), (36, 12), (13, 1), (15, 9), (16, 27), (7, 37), (0, 44), (16, 18), (5, 15), (5, 39), (25, 22), (5, 25), (15, 45), (17, 24), (20, 38), (23, 13), (32, 11), (2, 4), (38, 35), (19, 30), (31, 14), (10, 5), (44, 43), (42, 7), (11, 31), (40, 1), (31, 19), (28, 2), (26, 25), (23, 6), (27, 46), (3, 16), (43, 28), (9, 5), (29, 24), (32, 2), (43, 47), (24, 20), (2, 47), (44, 12), (6, 11), (18, 8), (19, 0), (3, 32), (38, 38), (18, 41), (17, 28), (16, 9), (34, 10), (12, 30), (15, 39), (23, 15), (41, 15), (35, 8), (42, 40), (11, 24), (8, 14), (17, 43), (31, 23), (13, 2), (34, 38), (43, 23), (20, 23), (2, 40), (5, 43), (30, 11), (15, 37), (42, 12), (25, 29), (36, 21), (22, 2), (18, 4), (18, 35), (34, 4), (40, 6), (26, 21), (21, 3), (8, 3), (39, 12), (32, 31), (1, 43), (31, 36), (29, 38), (43, 7), (39, 20), (3, 22), (4, 31), (26, 18), (34, 3), (20, 34), (24, 38), (6, 21), (23, 42), (6, 19), (18, 25), (14, 47), (28, 20), (25, 3), (35, 10), (7, 36), (13, 20), (31, 5), (37, 0), (16, 46), (41, 0), (24, 34), (16, 36), (30, 2), (4, 22), (32, 4), (5, 8), (16, 35), (21, 35), (42, 47), (0, 23), (38, 3), (37, 3), (34, 20), (20, 33), (5, 16), (16, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 36), (26, 24), (5, 5), (31, 12), (30, 19), (27, 17), (12, 13), (25, 4), (3, 4), (25, 18), (1, 4), (3, 41), (4, 21), (19, 21), (16, 23), (25, 21), (40, 14), (10, 4), (7, 3), (27, 32), (12, 6), (23, 29), (1, 35), (11, 29), (16, 20), (15, 39), (18, 21), (31, 27), (22, 37), (37, 41), (27, 29), (21, 17), (27, 8), (18, 32), (4, 32), (27, 39), (32, 19), (4, 39), (31, 29), (25, 12), (36, 15), (8, 38), (23, 40), (24, 36), (2, 4), (38, 1), (27, 7), (30, 0), (1, 15), (24, 13), (25, 26), (9, 0), (24, 21), (16, 32), (15, 24), (2, 13), (26, 35), (4, 16), (23, 20), (28, 21), (23, 12), (22, 36), (10, 13), (30, 31), (10, 8), (17, 26), (22, 38), (37, 31), (32, 23), (17, 36), (36, 10), (11, 33), (3, 28), (34, 25), (2, 18), (29, 16), (37, 10), (17, 8), (11, 16), (7, 15), (5, 37), (27, 4), (18, 4), (36, 18), (7, 16), (0, 28), (19, 18), (13, 25), (33, 10), (17, 31), (13, 6), (26, 9), (39, 21), (18, 2), (26, 7), (30, 16), (32, 20), (32, 34), (39, 25), (1, 2), (30, 13), (25, 19), (10, 17), (14, 18), (2, 33), (30, 5), (35, 4), (31, 33), (13, 9), (34, 0), (13, 41), (39, 16), (35, 21), (37, 18), (38, 22), (35, 9), (38, 7), (38, 12), (13, 31), (29, 1), (29, 28), (18, 30), (11, 27), (35, 19), (2, 39), (12, 21), (4, 26), (28, 8), (3, 12), (3, 32), (18, 40), (20, 36), (14, 38), (23, 18), (29, 15), (27, 6), (15, 14), (37, 8), (31, 2), (18, 34), (7, 12), (29, 24), (9, 15), (4, 1), (39, 4), (21, 4), (0, 17), (17, 7), (11, 14), (6, 31), (5, 16), (38, 19), (26, 34), (26, 32), (17, 16), (24, 4), (14, 11), (40, 34), (27, 34), (18, 28), (34, 10), (26, 4), (10, 37), (19, 38), (40, 7), (40, 16), (3, 18), (37, 12), (4, 28), (15, 37), (33, 32), (37, 2), (0, 23), (38, 30), (24, 17), (19, 13), (38, 35), (12, 30), (17, 13), (33, 17), (25, 24), (21, 28), (23, 24), (15, 35), (21, 0), (1, 27), (6, 6), (27, 33), (7, 2), (36, 27), (26, 16), (31, 31), (24, 30), (7, 34), (0, 6), (25, 15), (40, 10), (21, 30), (30, 32), (1, 5), (27, 31), (38, 17), (3, 21), (21, 37), (2, 2), (39, 26), (27, 25), (20, 2), (19, 12), (14, 0), (4, 9), (16, 29), (15, 26), (19, 4), (30, 2), (14, 4), (34, 8), (32, 32), (5, 0), (23, 21), (29, 35), (26, 31), (9, 40), (10, 2), (31, 0), (0, 35), (4, 19), (26, 15), (13, 24), (11, 39), (24, 33), (2, 31), (8, 21), (13, 14), (40, 1), (10, 24), (40, 36), (3, 16), (14, 22), (34, 26), (23, 14), (15, 38), (16, 27), (7, 28), (20, 22), (21, 29), (40, 19), (8, 28), (37, 22), (3, 25), (10, 39), (32, 8), (26, 29), (20, 8), (27, 22), (15, 12), (17, 17), (12, 33), (11, 8), (11, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 23), (9, 3), (35, 24), (4, 20), (35, 30), (14, 22), (17, 32), (4, 21), (38, 8), (16, 33), (22, 26), (6, 33), (40, 4), (1, 3), (13, 20), (34, 14), (38, 16), (22, 40), (41, 41), (18, 21), (22, 7), (7, 10), (40, 1), (7, 36), (22, 1), (27, 13), (24, 12), (11, 20), (11, 38), (15, 3), (33, 41), (28, 25), (12, 38), (36, 10), (39, 10), (30, 36), (24, 21), (23, 32), (34, 4), (9, 17), (30, 23), (39, 18), (11, 43), (33, 13), (17, 7), (4, 18), (14, 16), (30, 18), (19, 13), (0, 17), (3, 39), (12, 15), (10, 12), (1, 43), (41, 37), (26, 6), (16, 34), (26, 27), (11, 34), (40, 41), (36, 4), (13, 40), (14, 31), (19, 43), (20, 5), (36, 15), (24, 0), (38, 17), (1, 42), (24, 4), (20, 32), (38, 41), (40, 10), (20, 31), (18, 35), (30, 1), (24, 14), (6, 31), (39, 22), (16, 39), (4, 31), (3, 15), (31, 38), (18, 25), (3, 26), (36, 23), (38, 14), (36, 25), (37, 43), (4, 43), (15, 41), (9, 7), (17, 9), (41, 8), (10, 32), (6, 6), (0, 22), (15, 22), (38, 26), (20, 27), (20, 18), (32, 18), (8, 33), (37, 17), (35, 0), (17, 5), (32, 12), (25, 29), (21, 17), (12, 5), (4, 40), (33, 5), (33, 7), (19, 0), (21, 28), (7, 37), (16, 42), (17, 21), (26, 28), (13, 32), (23, 8), (15, 18), (27, 12), (39, 24), (19, 37), (10, 11), (9, 35), (4, 38), (19, 3), (5, 23), (0, 30), (32, 26), (30, 31), (33, 40), (23, 21), (19, 30), (18, 39), (20, 20), (30, 26), (22, 28), (19, 1), (40, 15), (31, 5), (20, 39), (29, 37), (33, 3), (23, 12), (12, 36), (18, 27), (22, 24), (12, 30), (7, 24), (31, 12), (12, 7), (2, 38), (36, 27), (4, 42), (21, 21), (9, 10), (3, 28), (6, 32), (5, 22), (25, 17), (7, 34), (14, 33), (35, 36), (22, 30), (12, 2), (24, 26), (12, 27), (21, 30), (12, 10), (25, 19), (24, 13), (16, 29), (31, 40), (4, 26), (25, 43), (28, 40), (41, 18), (33, 21), (8, 21), (30, 19), (2, 30), (19, 15), (33, 37), (4, 36), (14, 41), (27, 24), (8, 29), (11, 32), (21, 5), (19, 41), (29, 31), (4, 0), (39, 25), (0, 20), (12, 4), (15, 30), (19, 39), (32, 3), (9, 29), (14, 9), (19, 26), (29, 6), (0, 18), (25, 3), (8, 12), (19, 31), (3, 0), (23, 6), (16, 28), (13, 22), (15, 29), (41, 16), (16, 18), (37, 11), (4, 22), (3, 1), (20, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 38), (0, 26), (41, 13), (41, 10), (32, 31), (19, 2), (20, 29), (14, 30), (14, 2), (32, 29), (0, 27), (32, 2), (11, 32), (0, 31), (4, 16), (4, 2), (28, 1), (19, 12), (7, 30), (42, 2), (39, 39), (9, 8), (32, 24), (26, 10), (23, 29), (24, 37), (21, 16), (34, 22), (10, 31), (20, 12), (1, 39), (17, 18), (29, 1), (21, 37), (37, 14), (45, 28), (14, 13), (4, 12), (0, 19), (14, 35), (13, 34), (33, 4), (19, 31), (23, 31), (43, 11), (12, 4), (34, 24), (13, 0), (16, 9), (44, 35), (40, 0), (17, 26), (12, 28), (38, 16), (20, 3), (19, 1), (22, 13), (39, 17), (8, 25), (16, 8), (45, 0), (12, 15), (44, 19), (28, 32), (0, 13), (39, 27), (10, 34), (36, 1), (10, 12), (41, 39), (43, 26), (31, 36), (11, 28), (25, 23), (23, 21), (22, 37), (27, 9), (15, 2), (15, 23), (5, 35), (9, 6), (26, 19), (8, 36), (12, 2), (27, 14), (37, 0), (11, 4), (39, 6), (33, 38), (1, 31), (6, 23), (6, 34), (31, 6), (6, 14), (8, 6), (7, 2), (25, 33), (22, 18), (11, 33), (7, 5), (26, 5), (27, 31), (45, 38), (2, 13), (15, 37), (8, 11), (7, 21), (15, 5), (10, 20), (9, 27), (7, 34), (45, 21), (33, 27), (9, 30), (4, 14), (43, 7), (41, 9), (15, 30), (42, 11), (31, 27), (43, 28), (37, 26), (21, 0), (15, 28), (45, 27), (8, 32), (23, 17), (27, 16), (34, 28), (37, 40), (23, 9), (28, 26), (3, 21), (29, 14), (2, 20), (32, 30), (42, 34), (17, 39), (0, 32), (8, 38), (35, 24), (39, 14), (15, 6), (21, 26), (5, 9), (26, 20), (37, 9), (20, 26), (1, 35), (38, 25), (10, 27), (3, 2), (10, 6), (29, 19), (32, 15), (40, 38), (37, 29), (36, 3), (34, 4), (40, 18), (13, 22), (34, 23), (11, 0), (6, 8), (37, 32), (3, 23), (17, 28), (4, 31), (42, 37), (18, 24), (44, 6), (19, 22), (45, 20), (37, 20), (27, 1), (2, 21), (39, 29), (6, 25), (36, 37), (41, 34), (30, 3), (35, 33), (21, 21), (16, 25), (18, 2), (30, 1), (0, 40), (34, 32), (36, 21), (37, 34), (18, 26), (12, 5), (17, 21), (33, 15), (23, 34), (9, 18), (37, 17), (29, 3), (21, 19), (20, 32), (45, 26), (18, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 19), (25, 2), (10, 2), (35, 11), (1, 15), (45, 8), (29, 21), (32, 1), (16, 33), (18, 34), (46, 27), (23, 39), (32, 18), (28, 33), (36, 23), (12, 21), (33, 0), (4, 4), (48, 20), (22, 8), (42, 13), (44, 8), (45, 28), (41, 3), (15, 17), (47, 14), (42, 40), (29, 34), (38, 3), (13, 24), (39, 2), (9, 30), (28, 20), (5, 40), (19, 12), (13, 3), (39, 21), (21, 13), (27, 4), (14, 37), (10, 13), (13, 29), (14, 38), (8, 1), (14, 22), (48, 23), (29, 23), (43, 1), (40, 14), (7, 36), (28, 29), (9, 2), (25, 20), (3, 40), (44, 37), (41, 11), (31, 5), (16, 3), (2, 1), (40, 37), (34, 4), (1, 18), (2, 0), (38, 29), (14, 31), (29, 18), (47, 3), (30, 36), (5, 14), (20, 34), (35, 29), (11, 40), (45, 34), (46, 35), (46, 17), (2, 11), (43, 0), (37, 17), (16, 4), (7, 3), (11, 7), (20, 24), (38, 5), (46, 39), (31, 30), (40, 36), (45, 40), (48, 1), (4, 20), (31, 22), (24, 13), (21, 17), (20, 27), (10, 23), (4, 37), (14, 28), (39, 14), (7, 29), (30, 16), (31, 33), (21, 22), (14, 20), (16, 0), (36, 7), (42, 30), (24, 11), (8, 30), (17, 29), (38, 7), (21, 26), (38, 37), (15, 34), (3, 20), (4, 15), (47, 7), (44, 40), (43, 30), (4, 22), (21, 3), (39, 26), (6, 28), (6, 1), (0, 32), (34, 5), (13, 28), (22, 36), (4, 1), (4, 12), (7, 35), (27, 13), (5, 21), (9, 21), (14, 35), (45, 30), (12, 1), (41, 37), (20, 6), (11, 30), (30, 14), (7, 20), (16, 23), (6, 7), (15, 14), (22, 33), (48, 38), (48, 15), (28, 17), (6, 22), (24, 31), (29, 24), (48, 19), (37, 29), (32, 28), (9, 36), (32, 11), (30, 4), (16, 14), (38, 8), (12, 36), (44, 2), (42, 22), (25, 33), (39, 31), (13, 33), (29, 29), (0, 6), (22, 21), (9, 24), (7, 18), (9, 25), (43, 2), (19, 4), (17, 15), (47, 8), (15, 20), (25, 34), (23, 17), (37, 6), (20, 11), (34, 34), (4, 31), (16, 9), (47, 20), (48, 16), (27, 15), (27, 11), (28, 28), (40, 32), (26, 34), (23, 36), (37, 40), (7, 37), (7, 4), (3, 27), (46, 5), (11, 25), (17, 14), (37, 4), (45, 21), (4, 27), (6, 20), (12, 26), (38, 12), (20, 16), (34, 17), (24, 2), (37, 9), (21, 14), (10, 22), (36, 11), (43, 29), (8, 24), (47, 2), (36, 22), (16, 36), (17, 3), (11, 32), (39, 3), (40, 10), (39, 11), (9, 11), (35, 31), (16, 10), (37, 36), (43, 21), (0, 8), (5, 11), (17, 35), (34, 2), (37, 11), (34, 27), (19, 26), (25, 9), (12, 3), (22, 18), (5, 20), (45, 24), (24, 1), (38, 20), (46, 22), (27, 21), (5, 29), (14, 21), (23, 27), (39, 20), (0, 30), (7, 8), (18, 22), (20, 7), (29, 32), (39, 27), (21, 23), (25, 23), (32, 13), (14, 0), (46, 30), (22, 13), (0, 40), (35, 40), (26, 33), (4, 39), (46, 20), (7, 10), (36, 33), (8, 15), (41, 15), (6, 32), (6, 4), (10, 27), (8, 5), (28, 12), (34, 26), (6, 21), (40, 6), (10, 3), (12, 40), (46, 25), (48, 37), (16, 1), (29, 4), (28, 6), (42, 16), (29, 17), (20, 26), (33, 34), (15, 36), (42, 24), (19, 31), (24, 19), (15, 39), (19, 32), (1, 25), (23, 28), (10, 1), (0, 18), (10, 0), (45, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 19), (12, 25), (22, 21), (32, 9), (20, 7), (23, 22), (11, 37), (32, 13), (26, 9), (11, 8), (17, 31), (16, 15), (1, 37), (20, 34), (4, 0), (39, 8), (22, 5), (11, 11), (9, 5), (2, 41), (38, 1), (28, 25), (16, 32), (35, 24), (23, 32), (19, 35), (20, 40), (9, 14), (10, 32), (31, 23), (23, 31), (24, 19), (38, 5), (4, 29), (23, 24), (23, 17), (39, 12), (15, 0), (35, 25), (10, 10), (39, 40), (9, 25), (11, 9), (18, 24), (11, 15), (39, 6), (8, 38), (12, 31), (30, 27), (29, 29), (20, 39), (26, 13), (4, 34), (9, 10), (24, 0), (9, 30), (30, 31), (30, 10), (16, 36), (2, 19), (29, 40), (30, 24), (29, 21), (6, 5), (34, 35), (6, 10), (37, 13), (34, 31), (7, 9), (14, 9), (2, 0), (14, 12), (22, 14), (4, 14), (38, 21), (24, 32), (16, 1), (30, 4), (39, 18), (24, 16), (2, 30), (8, 10), (6, 15), (29, 11), (27, 31), (36, 4), (7, 24), (32, 30), (25, 32), (14, 32), (1, 11), (30, 30), (23, 8), (34, 30), (34, 32), (20, 37), (32, 18), (12, 36), (10, 23), (17, 21), (2, 22), (7, 30), (39, 39), (27, 36), (12, 29), (25, 23), (15, 27), (32, 7), (30, 40), (41, 8), (31, 40), (40, 41), (22, 11), (38, 8), (1, 31), (39, 10), (18, 1), (15, 29), (23, 2), (34, 25), (25, 27), (20, 6), (31, 30), (13, 35), (33, 13), (2, 11), (17, 30), (40, 11), (21, 16), (16, 6), (39, 0), (29, 26), (4, 40), (30, 9), (25, 33), (21, 0), (33, 11), (22, 7), (22, 17), (39, 32), (10, 26), (0, 26), (14, 37), (26, 0), (22, 9), (41, 18), (21, 39), (21, 19), (11, 33), (25, 34), (8, 40), (38, 16), (20, 15), (27, 41), (29, 24), (2, 13), (6, 39), (10, 33), (11, 4), (1, 1), (8, 22), (36, 16), (41, 10), (7, 13), (17, 15), (41, 19), (14, 7), (3, 10), (16, 28), (6, 32), (34, 33), (6, 0), (3, 18), (40, 20), (27, 34), (7, 29), (9, 6), (23, 16), (40, 35), (27, 23), (18, 40), (24, 5), (27, 10), (1, 2), (18, 30), (34, 27), (28, 9), (26, 32), (25, 39), (3, 9), (6, 23), (36, 40), (39, 34), (29, 1), (40, 28), (11, 34), (19, 30), (41, 20), (23, 10), (13, 17), (41, 2), (3, 4), (8, 33), (21, 15), (37, 34), (5, 32), (41, 14), (19, 37), (31, 25), (2, 12), (8, 20), (24, 36), (34, 42), (37, 32), (0, 42), (37, 23), (18, 27), (22, 16), (27, 5), (14, 5), (5, 33), (26, 34), (18, 31), (36, 33), (31, 29), (3, 42), (15, 22), (1, 34), (6, 16), (5, 8), (5, 29), (12, 3), (40, 17), (3, 38), (9, 27), (0, 29), (15, 15), (30, 16), (40, 6), (13, 39), (10, 29), (13, 0), (25, 28), (2, 29), (25, 24), (35, 22), (5, 36), (7, 32), (16, 16), (29, 41), (28, 22), (14, 38), (22, 4), (35, 40), (18, 29), (29, 33), (37, 14), (7, 31), (28, 7), (33, 21), (19, 24), (36, 27), (39, 1), (34, 11), (25, 37), (5, 24), (25, 2), (14, 36), (28, 29), (9, 3), (2, 20), (16, 35), (9, 13), (37, 11), (8, 16), (41, 23), (6, 33), (16, 19), (34, 9), (15, 26), (12, 17), (19, 18), (6, 42), (27, 30), (14, 6), (18, 23), (15, 41), (34, 8), (23, 39), (31, 14), (29, 14), (41, 0), (18, 21), (8, 36), (0, 36), (21, 23), (27, 37), (22, 33), (21, 22), (3, 16), (29, 30), (28, 38), (18, 26), (0, 24), (28, 24), (17, 36), (30, 14), (2, 35), (23, 20), (26, 11), (38, 11), (7, 19), (9, 20), (10, 37), (28, 0), (40, 42), (1, 19), (30, 19), (32, 34), (6, 4), (36, 6), (12, 7), (13, 21), (21, 2), (13, 12), (35, 42), (7, 2), (2, 7), (26, 16), (22, 35), (5, 35), (29, 18), (32, 21), (30, 21), (10, 36), (17, 17), (12, 20), (18, 32), (40, 13), (35, 18), (4, 9), (13, 37), (5, 21), (15, 38), (13, 7), (41, 21), (13, 40), (38, 27), (19, 33), (11, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 37), (23, 38), (10, 2), (22, 7), (2, 21), (5, 40), (32, 39), (29, 11), (31, 37), (17, 28), (33, 17), (5, 19), (11, 24), (29, 3), (33, 36), (37, 33), (41, 22), (19, 0), (0, 7), (2, 18), (20, 27), (1, 2), (29, 28), (40, 30), (30, 26), (40, 16), (12, 15), (30, 33), (18, 10), (9, 26), (37, 29), (9, 3), (8, 10), (32, 33), (5, 34), (32, 16), (0, 24), (38, 17), (41, 4), (37, 17), (14, 27), (23, 24), (5, 17), (23, 19), (12, 39), (30, 30), (16, 25), (24, 35), (38, 18), (15, 13), (24, 23), (11, 27), (3, 2), (14, 20), (34, 0), (41, 16), (29, 12), (30, 28), (36, 6), (15, 1), (21, 1), (10, 7), (5, 35), (27, 19), (14, 7), (34, 22), (28, 12), (24, 3), (22, 0), (40, 20), (38, 6), (0, 6), (23, 32), (41, 10), (38, 19), (10, 10), (23, 29), (1, 8), (34, 1), (8, 14), (33, 34), (9, 34), (16, 40), (13, 41), (40, 39), (26, 29), (1, 10), (17, 12), (39, 20), (39, 33), (18, 4), (30, 7), (28, 20), (7, 19), (9, 19), (9, 12), (15, 29), (18, 8), (21, 25), (36, 16), (29, 18), (0, 13), (41, 37), (8, 27), (40, 41), (12, 18), (29, 30), (0, 8), (17, 8), (29, 23), (37, 2), (41, 9), (6, 41), (18, 2), (4, 4), (8, 26), (14, 40), (17, 27), (24, 21), (7, 22), (37, 7), (20, 14), (36, 31), (28, 36), (21, 26), (12, 3), (12, 27), (38, 39), (4, 41), (39, 30), (26, 21), (41, 7), (37, 30), (38, 26), (39, 19), (0, 25), (39, 16), (15, 21), (1, 34), (32, 34), (36, 11), (18, 36), (28, 25), (22, 4), (12, 32), (6, 4), (11, 21), (8, 35), (5, 9), (15, 3), (29, 8), (29, 38), (14, 41), (38, 12), (6, 27), (11, 14), (37, 22), (5, 6), (35, 34), (4, 3), (39, 37), (9, 16), (2, 40), (20, 40), (26, 24), (37, 4), (24, 38), (7, 12), (20, 34), (2, 8), (30, 37), (32, 3), (29, 15), (17, 21), (16, 5), (34, 17), (7, 28), (31, 30), (38, 24), (19, 10), (0, 37), (31, 38), (2, 15), (27, 32), (32, 5), (39, 24), (39, 34), (39, 35), (23, 28), (21, 12), (19, 19), (30, 32), (2, 41), (40, 0), (34, 13), (32, 27), (15, 25), (39, 6), (17, 26), (31, 23), (30, 36), (1, 15), (7, 34), (11, 4), (35, 26), (10, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 3), (18, 18), (15, 24), (36, 24), (30, 13), (33, 21), (10, 2), (6, 33), (38, 12), (32, 10), (18, 29), (6, 35), (6, 47), (19, 5), (19, 40), (14, 17), (34, 6), (2, 12), (14, 0), (19, 36), (33, 31), (11, 5), (36, 30), (12, 11), (23, 23), (0, 42), (7, 44), (0, 1), (25, 37), (24, 1), (39, 35), (17, 0), (37, 36), (30, 30), (28, 8), (4, 30), (21, 31), (14, 8), (28, 45), (2, 13), (19, 26), (32, 38), (11, 28), (7, 18), (26, 46), (19, 28), (13, 38), (9, 25), (23, 8), (7, 37), (26, 23), (36, 29), (5, 42), (30, 9), (27, 0), (17, 41), (37, 2), (38, 32), (6, 34), (1, 24), (28, 19), (0, 39), (23, 37), (14, 27), (5, 7), (17, 17), (33, 18), (7, 40), (38, 47), (3, 12), (18, 17), (11, 13), (8, 1), (31, 41), (24, 42), (30, 17), (2, 18), (28, 17), (19, 25), (14, 3), (1, 22), (3, 41), (32, 2), (12, 26), (24, 10), (28, 6), (3, 36), (30, 27), (36, 10), (26, 1), (24, 15), (29, 41), (36, 28), (36, 45), (2, 27), (22, 4), (17, 47), (37, 16), (3, 47), (0, 24), (25, 10), (35, 0), (22, 22), (12, 46), (10, 36), (10, 21), (18, 44), (27, 36), (21, 9), (24, 16), (22, 8), (25, 14), (29, 19), (36, 47), (16, 21), (30, 42), (28, 34), (39, 43), (20, 46), (27, 19), (0, 33), (4, 26), (34, 5), (9, 7), (12, 16), (14, 39), (29, 21), (31, 7), (17, 42), (13, 45), (4, 18), (34, 38), (21, 39), (8, 41), (17, 31), (33, 20), (37, 28), (36, 32), (13, 44), (33, 15), (1, 10), (31, 24), (27, 9), (14, 5), (35, 30), (36, 38), (1, 23), (39, 44), (20, 26), (14, 36), (14, 34), (0, 30), (30, 24), (30, 21), (23, 40), (26, 15), (31, 27), (13, 3), (6, 3), (15, 41), (12, 19), (3, 46), (16, 36), (0, 27), (9, 20), (23, 31), (17, 1), (11, 47), (26, 22), (34, 27), (6, 32), (37, 19), (5, 36), (9, 41), (32, 14), (12, 41), (10, 12), (11, 3), (37, 34), (17, 43), (27, 46), (3, 7), (15, 32), (25, 17), (20, 35), (13, 10), (6, 38), (24, 46), (12, 23), (13, 6), (10, 38), (15, 8), (39, 12), (32, 47), (29, 4), (21, 27), (26, 36), (15, 39), (2, 5), (28, 31), (1, 1), (22, 27), (13, 28), (13, 23), (23, 6), (27, 34), (39, 45), (15, 25), (18, 12), (19, 30), (19, 0), (13, 25), (26, 0), (19, 46), (22, 0), (14, 14), (3, 19), (34, 25), (10, 5), (2, 44), (13, 17), (37, 6), (37, 41), (0, 4), (15, 10), (35, 22), (30, 25), (26, 3), (36, 16), (19, 38), (12, 4), (6, 19), (34, 2), (2, 35), (39, 20), (15, 20), (29, 23), (11, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 0), (32, 9), (7, 24), (33, 34), (16, 22), (15, 11), (11, 16), (30, 22), (22, 7), (33, 15), (21, 16), (21, 25), (24, 7), (3, 37), (13, 17), (23, 34), (38, 10), (33, 18), (9, 34), (40, 35), (25, 10), (18, 5), (31, 17), (6, 36), (5, 12), (19, 21), (8, 16), (28, 15), (27, 3), (24, 27), (3, 7), (23, 31), (1, 39), (35, 1), (20, 30), (10, 28), (35, 24), (9, 20), (1, 12), (15, 15), (22, 27), (39, 28), (1, 18), (16, 31), (8, 0), (19, 26), (6, 27), (3, 34), (0, 27), (23, 39), (5, 27), (5, 9), (32, 10), (0, 32), (21, 19), (10, 24), (32, 32), (19, 8), (31, 24), (36, 30), (12, 27), (33, 4), (2, 34), (0, 37), (25, 33), (19, 36), (14, 9), (0, 21), (26, 19), (29, 15), (9, 23), (12, 17), (26, 24), (8, 21), (22, 29), (29, 3), (20, 10), (30, 32), (28, 18), (18, 28), (34, 13), (13, 38), (6, 26), (13, 20), (29, 10), (22, 28), (26, 21), (18, 2), (30, 5), (18, 26), (26, 39), (6, 25), (14, 15), (30, 12), (7, 31), (18, 8), (21, 39), (17, 31), (24, 29), (5, 8), (25, 19), (16, 16), (18, 12), (31, 16), (33, 3), (8, 15), (32, 30), (21, 5), (17, 35), (29, 16), (3, 6), (31, 29), (17, 26), (37, 18), (23, 13), (39, 7), (1, 34), (33, 5), (36, 15), (5, 22), (20, 25), (8, 19), (19, 3), (4, 34), (5, 15), (12, 38), (38, 14), (10, 17), (3, 30), (37, 20), (23, 15), (8, 31), (29, 35), (31, 22), (23, 17), (28, 24), (38, 8), (10, 16), (37, 3), (36, 32), (8, 20), (26, 4), (24, 4), (35, 9), (30, 17), (30, 14), (14, 2), (7, 33), (16, 12), (39, 38), (5, 38), (10, 22), (18, 4), (19, 18), (2, 22), (19, 39), (25, 24), (16, 30), (6, 30), (19, 33), (14, 1), (40, 33), (28, 11), (12, 34), (23, 18), (13, 14), (14, 33), (5, 23), (24, 38), (4, 37), (23, 24), (0, 34), (16, 11), (29, 38), (5, 29), (11, 4), (14, 10), (34, 39), (17, 24), (5, 11), (27, 39), (30, 1), (22, 26), (28, 33), (32, 1), (4, 11), (23, 4), (25, 35), (14, 21), (15, 14), (7, 3), (29, 21), (25, 17), (28, 32), (29, 34), (29, 20), (14, 0), (40, 7), (29, 30), (8, 3), (32, 26), (27, 0), (24, 20), (24, 17), (29, 1), (15, 12), (10, 18), (35, 17), (33, 28), (9, 29), (24, 22), (7, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 20), (6, 29), (2, 8), (17, 22), (1, 22), (32, 46), (31, 23), (9, 4), (5, 29), (18, 11), (16, 27), (16, 41), (28, 33), (25, 46), (12, 22), (29, 2), (14, 19), (4, 2), (33, 42), (17, 23), (27, 3), (22, 26), (29, 5), (11, 1), (18, 18), (12, 2), (19, 40), (8, 42), (27, 30), (33, 4), (2, 30), (17, 38), (33, 23), (19, 37), (22, 15), (15, 38), (13, 41), (38, 37), (1, 38), (18, 47), (38, 25), (17, 28), (7, 36), (30, 27), (21, 34), (17, 30), (13, 44), (25, 47), (13, 39), (16, 26), (20, 44), (20, 22), (30, 9), (25, 44), (3, 4), (26, 38), (38, 11), (19, 36), (11, 48), (13, 0), (18, 9), (11, 26), (28, 18), (33, 27), (21, 30), (3, 27), (20, 7), (39, 41), (12, 32), (18, 24), (26, 0), (14, 14), (12, 41), (26, 1), (8, 30), (3, 20), (38, 19), (24, 15), (35, 43), (27, 1), (9, 1), (18, 44), (27, 44), (2, 47), (7, 23), (40, 27), (7, 19), (37, 11), (3, 6), (11, 43), (38, 9), (3, 0), (4, 22), (26, 22), (29, 32), (16, 33), (16, 37), (29, 45), (4, 26), (28, 7), (5, 36), (26, 39), (24, 13), (18, 21), (11, 2), (5, 14), (36, 40), (5, 3), (2, 22), (0, 17), (9, 48), (32, 31), (15, 47), (12, 24), (29, 40), (13, 19), (25, 10), (14, 40), (15, 15), (34, 28), (1, 0), (29, 6), (11, 4), (33, 28), (23, 38), (39, 18), (31, 20), (25, 11), (40, 9), (13, 1), (10, 39), (36, 12), (32, 41), (9, 44), (10, 43), (37, 43), (33, 48), (21, 45), (10, 1), (9, 31), (34, 36), (34, 19), (16, 15), (26, 17), (27, 0), (16, 44), (20, 47), (17, 31), (32, 23), (3, 7), (36, 42), (7, 22), (17, 12), (6, 14), (30, 38), (30, 43), (20, 43), (8, 32), (30, 31), (35, 47), (23, 21), (9, 40), (36, 14), (29, 27), (28, 20), (16, 1), (20, 37), (28, 5), (29, 3), (22, 34), (19, 4), (7, 33), (3, 5), (27, 31), (31, 32), (20, 23), (28, 30), (39, 45), (14, 15), (13, 22), (38, 10), (30, 19), (15, 13), (13, 21), (14, 43), (24, 24), (38, 24), (24, 18), (28, 39), (35, 44), (13, 42), (11, 33), (19, 25), (19, 16), (35, 40), (26, 44), (8, 4), (24, 4), (25, 37), (4, 23), (30, 4), (28, 31), (26, 48), (6, 18), (31, 14), (40, 40), (23, 37), (7, 41), (17, 33), (25, 20), (3, 17), (13, 46), (3, 25), (27, 40), (15, 7), (40, 29), (11, 23), (18, 20), (32, 47), (3, 45), (15, 30), (13, 36), (33, 46), (6, 7), (11, 42), (11, 47), (7, 1), (36, 46), (3, 13), (11, 0), (4, 18), (37, 22), (12, 44), (38, 3), (6, 5), (22, 27), (28, 9), (25, 1), (6, 0), (28, 15), (1, 24), (32, 22), (0, 6), (32, 12), (21, 7), (28, 1), (16, 23), (36, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 2), (41, 37), (26, 7), (18, 22), (22, 8), (8, 3), (38, 5), (7, 0), (28, 21), (18, 25), (1, 2), (22, 29), (2, 24), (8, 10), (26, 37), (17, 18), (27, 2), (24, 5), (11, 36), (33, 17), (34, 5), (34, 20), (15, 37), (34, 4), (25, 45), (3, 46), (10, 15), (37, 8), (15, 23), (15, 28), (37, 32), (14, 27), (39, 12), (39, 9), (21, 11), (42, 4), (42, 45), (22, 36), (40, 10), (11, 41), (14, 23), (20, 30), (17, 7), (28, 12), (37, 36), (20, 0), (35, 36), (22, 39), (34, 28), (24, 0), (2, 33), (20, 15), (30, 27), (16, 2), (8, 7), (30, 1), (42, 1), (30, 10), (41, 41), (6, 30), (24, 19), (19, 24), (5, 29), (34, 0), (21, 35), (21, 9), (41, 28), (39, 23), (26, 8), (35, 27), (25, 12), (26, 17), (36, 23), (36, 37), (35, 34), (40, 23), (16, 41), (41, 2), (29, 37), (34, 30), (26, 40), (35, 45), (38, 14), (37, 5), (9, 41), (2, 41), (37, 14), (24, 43), (3, 3), (20, 31), (26, 0), (20, 29), (19, 5), (33, 20), (29, 11), (32, 10), (12, 0), (9, 3), (39, 20), (18, 10), (15, 36), (31, 39), (21, 19), (31, 8), (32, 18), (21, 5), (8, 23), (31, 13), (32, 27), (25, 36), (26, 18), (20, 7), (20, 16), (8, 43), (25, 42), (10, 30), (34, 10), (32, 25), (9, 31), (39, 10), (35, 3), (38, 20), (38, 2), (38, 28), (32, 4), (7, 21), (28, 39), (25, 38), (36, 13), (35, 40), (22, 46), (9, 0), (8, 39), (15, 21), (40, 1), (31, 44), (13, 30), (38, 7), (1, 1), (35, 7), (31, 4), (38, 30), (34, 36), (34, 12), (21, 36), (10, 3), (5, 46), (6, 43), (3, 43), (42, 19), (4, 44), (3, 42), (21, 33), (14, 11), (7, 30), (23, 21), (22, 27), (26, 30), (9, 27), (0, 7), (6, 14), (15, 11), (21, 31), (22, 16), (5, 36), (24, 14), (20, 44), (3, 21), (29, 25), (28, 4), (38, 1), (38, 33), (15, 44), (10, 11), (26, 46), (6, 29), (7, 12), (28, 3), (40, 31), (25, 46), (41, 34), (36, 9), (14, 20), (14, 44), (34, 40), (28, 28), (24, 6), (2, 21), (27, 25), (22, 4), (0, 5), (21, 32), (23, 40), (20, 43), (33, 16), (25, 17), (30, 23), (18, 17), (24, 34), (19, 21), (5, 11), (29, 5), (39, 16), (39, 15), (33, 3), (38, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 15), (29, 3), (9, 14), (12, 40), (34, 33), (12, 11), (16, 35), (4, 0), (44, 12), (44, 23), (33, 33), (44, 21), (23, 37), (45, 31), (8, 21), (13, 10), (12, 10), (45, 15), (44, 37), (43, 36), (28, 7), (11, 9), (28, 9), (19, 15), (37, 12), (26, 11), (23, 28), (1, 17), (28, 5), (41, 18), (44, 5), (2, 40), (20, 2), (37, 15), (37, 38), (5, 38), (31, 5), (9, 35), (21, 23), (27, 14), (6, 26), (20, 27), (34, 22), (17, 29), (29, 32), (33, 13), (39, 20), (7, 36), (28, 8), (15, 11), (40, 8), (45, 18), (18, 27), (31, 4), (33, 27), (16, 28), (13, 24), (35, 36), (8, 18), (41, 20), (14, 7), (12, 28), (29, 30), (33, 7), (34, 11), (40, 35), (45, 8), (4, 16), (23, 9), (11, 19), (13, 33), (39, 3), (42, 22), (37, 20), (35, 25), (39, 11), (41, 35), (37, 17), (2, 19), (36, 20), (14, 9), (17, 39), (22, 9), (30, 37), (4, 9), (30, 3), (17, 26), (34, 35), (16, 2), (9, 22), (1, 33), (25, 8), (42, 4), (2, 20), (40, 29), (34, 20), (20, 11), (1, 10), (36, 12), (40, 15), (31, 23), (42, 28), (39, 23), (38, 36), (17, 40), (44, 3), (32, 13), (11, 36), (41, 23), (5, 4), (8, 0), (40, 2), (40, 1), (6, 1), (13, 31), (42, 23), (19, 4), (4, 10), (17, 14), (2, 22), (42, 20), (17, 4), (4, 28), (9, 13), (36, 11), (31, 8), (41, 15), (42, 30), (1, 27), (25, 5), (1, 8), (13, 29), (12, 35), (36, 6), (19, 21), (33, 39), (5, 32), (43, 14), (2, 16), (34, 12), (40, 26), (21, 32), (16, 4), (3, 10), (40, 5), (37, 13), (18, 38), (26, 7), (7, 16), (4, 32), (20, 26), (38, 40), (18, 1), (19, 38), (31, 2), (33, 31), (27, 16), (15, 12), (45, 16), (35, 12), (23, 0), (12, 16), (37, 11), (35, 3), (37, 22), (38, 15), (3, 1), (18, 18), (21, 0), (27, 25), (3, 37), (28, 17), (29, 10), (28, 15), (4, 29), (45, 6), (27, 28), (14, 27), (0, 29), (30, 10), (24, 4), (36, 30), (32, 29), (42, 35), (44, 30), (33, 28), (21, 38), (12, 12), (11, 1), (29, 16), (35, 40), (18, 36), (6, 13), (0, 40), (42, 9), (36, 3), (13, 16), (42, 26), (38, 22), (13, 28), (22, 17), (2, 24), (24, 27), (18, 13), (25, 16), (42, 12), (3, 39), (1, 29), (1, 15), (17, 37), (34, 2), (27, 3), (7, 0), (13, 30), (1, 7), (37, 39), (25, 4), (25, 7), (12, 26), (9, 3), (39, 34), (9, 24), (17, 9), (7, 1), (44, 22), (30, 12), (20, 38), (36, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 27), (28, 7), (4, 36), (47, 6), (3, 17), (2, 14), (17, 42), (11, 18), (25, 46), (43, 3), (21, 30), (29, 31), (14, 0), (13, 17), (35, 4), (32, 32), (41, 19), (2, 25), (26, 2), (11, 15), (22, 29), (1, 21), (19, 16), (19, 33), (29, 27), (28, 9), (3, 1), (28, 6), (46, 2), (1, 42), (36, 42), (13, 34), (25, 4), (15, 44), (26, 35), (29, 18), (33, 36), (17, 38), (37, 43), (2, 48), (36, 27), (34, 36), (25, 32), (31, 0), (19, 19), (12, 38), (2, 22), (41, 26), (42, 37), (41, 43), (39, 3), (9, 47), (1, 12), (28, 30), (14, 34), (16, 46), (45, 20), (33, 42), (35, 21), (6, 8), (32, 26), (27, 27), (43, 26), (38, 4), (9, 8), (25, 30), (23, 10), (26, 4), (32, 24), (37, 40), (21, 2), (25, 43), (17, 35), (6, 38), (42, 8), (3, 44), (40, 42), (31, 16), (4, 17), (29, 33), (13, 47), (9, 31), (23, 34), (18, 11), (11, 8), (13, 23), (31, 31), (10, 7), (46, 22), (5, 1), (35, 45), (14, 25), (4, 30), (21, 23), (36, 46), (10, 20), (13, 35), (41, 24), (41, 14), (24, 37), (2, 38), (44, 39), (41, 30), (42, 25), (37, 22), (22, 26), (11, 3), (27, 7), (47, 24), (44, 10), (38, 26), (26, 47), (0, 8), (17, 7), (12, 9), (25, 42), (15, 47), (35, 22), (41, 41), (37, 20), (11, 28), (25, 23), (37, 14), (5, 11), (22, 19), (12, 18), (8, 15), (8, 4), (14, 7), (46, 17), (34, 16), (14, 12), (23, 2), (0, 26), (28, 4), (47, 5), (32, 1), (14, 47), (15, 6), (15, 23), (21, 24), (2, 34), (19, 14), (47, 22), (13, 30), (41, 36), (46, 4), (5, 38), (15, 17), (46, 28), (47, 0), (26, 48), (5, 19), (8, 28), (30, 45), (20, 27), (35, 36), (3, 19), (35, 29), (16, 18), (7, 35), (4, 3), (46, 26), (23, 18), (13, 39), (43, 41), (29, 37), (4, 15), (43, 22), (27, 14), (35, 1), (35, 5), (46, 47), (11, 11), (39, 18), (4, 23), (22, 27), (42, 48), (12, 26), (2, 4), (47, 45), (43, 35), (43, 7), (23, 12), (17, 28), (44, 28), (45, 39), (38, 18), (2, 19), (36, 36), (34, 5), (3, 9), (25, 9), (40, 3), (13, 41), (25, 24), (7, 38), (42, 46), (22, 12), (32, 21), (5, 9), (31, 25), (1, 43), (8, 6), (31, 9), (45, 36), (4, 47), (31, 32), (19, 22), (34, 26), (12, 21), (43, 31), (30, 5), (45, 15), (13, 29), (10, 30), (26, 46), (24, 43), (41, 35), (28, 27), (7, 9), (22, 1), (0, 5), (11, 9), (36, 34), (46, 38), (9, 14), (34, 8), (43, 40), (9, 5), (35, 2), (4, 34), (26, 34), (5, 2), (32, 16), (9, 16), (26, 18), (3, 22), (15, 13), (35, 13), (43, 5), (24, 42), (25, 6), (1, 36), (14, 5), (45, 1), (19, 43), (21, 29), (39, 41), (13, 33), (22, 30), (8, 35), (43, 37), (40, 25), (16, 24), (11, 5), (27, 9), (28, 20), (43, 38), (36, 7), (46, 44), (24, 26), (20, 20), (18, 41), (38, 39), (1, 3), (37, 32), (14, 41), (34, 48), (30, 17), (4, 26), (16, 8), (22, 14), (47, 32), (40, 14), (28, 33), (46, 0), (12, 17), (17, 47), (31, 26), (2, 12), (34, 41), (29, 24), (8, 18), (16, 11), (39, 20), (40, 6), (41, 29), (29, 38), (20, 36), (31, 24), (8, 14), (12, 0), (32, 14), (17, 45), (33, 18), (42, 41), (44, 0), (27, 11), (24, 32), (34, 39), (25, 26), (22, 6), (14, 14), (41, 27), (18, 43), (2, 8), (26, 31), (21, 15), (28, 46), (18, 17), (11, 7), (26, 21), (4, 28), (32, 36), (11, 17), (20, 42), (3, 37), (3, 0), (30, 4), (20, 48), (42, 1), (34, 35), (2, 37), (40, 43), (22, 41), (16, 19), (25, 29), (35, 7), (17, 44), (21, 34), (6, 39), (35, 37), (20, 16), (3, 42), (25, 36), (43, 45), (44, 47), (19, 46), (10, 45), (32, 34), (9, 39), (12, 48), (20, 15), (23, 17), (30, 44), (0, 31), (12, 19), (3, 18), (23, 43), (29, 0), (47, 33), (21, 5), (27, 10), (33, 32), (23, 29), (27, 45), (6, 40), (8, 27), (27, 8), (44, 18), (12, 40), (39, 19), (21, 10), (23, 31), (41, 9), (23, 16), (14, 9), (13, 36), (34, 4), (43, 48), (29, 28), (6, 20), (30, 0), (39, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (47, 36), (36, 18), (25, 33), (24, 3), (16, 15), (45, 25), (3, 14), (45, 34), (20, 40), (24, 29), (28, 19), (6, 35), (41, 30), (0, 2), (41, 28), (47, 37), (38, 15), (21, 31), (13, 28), (3, 5), (12, 17), (4, 19), (38, 13), (21, 0), (12, 5), (39, 36), (18, 12), (22, 25), (5, 31), (11, 6), (33, 6), (27, 16), (42, 23), (29, 1), (38, 4), (46, 27), (5, 23), (28, 16), (19, 5), (16, 17), (31, 37), (4, 8), (1, 19), (33, 27), (44, 8), (33, 25), (34, 20), (8, 19), (39, 35), (41, 7), (20, 30), (34, 28), (30, 22), (44, 5), (30, 3), (5, 22), (48, 2), (47, 30), (7, 28), (12, 32), (15, 26), (43, 14), (44, 9), (45, 39), (10, 35), (13, 3), (28, 29), (21, 27), (16, 30), (14, 2), (15, 37), (47, 28), (43, 40), (45, 24), (18, 37), (15, 24), (26, 35), (26, 3), (28, 12), (19, 24), (0, 28), (42, 35), (15, 31), (24, 18), (39, 34), (30, 19), (35, 24), (26, 10), (15, 14), (12, 33), (22, 14), (42, 29), (42, 39), (3, 12), (23, 39), (33, 12), (9, 7), (34, 2), (19, 30), (25, 17), (2, 31), (33, 4), (48, 0), (20, 0), (1, 15), (40, 37), (37, 28), (25, 2), (41, 15), (28, 3), (25, 22), (5, 19), (13, 37), (13, 36), (18, 10), (25, 32), (40, 7), (26, 24), (29, 40), (42, 21), (3, 15), (15, 35), (46, 39), (22, 28), (11, 5), (27, 11), (47, 11), (36, 6), (12, 1), (1, 37), (35, 1), (2, 18), (5, 9), (34, 33), (0, 6), (27, 30), (37, 12), (18, 29), (15, 19), (39, 30), (1, 23), (42, 0), (6, 1), (0, 18), (7, 38), (37, 30), (13, 31), (18, 30), (14, 25), (44, 40), (9, 5), (47, 1), (35, 20), (6, 30), (47, 39), (27, 10), (37, 21), (10, 10), (44, 6), (45, 21), (13, 12), (10, 25), (30, 6), (34, 39), (46, 23), (17, 15), (9, 30), (0, 39), (46, 2), (21, 9), (40, 16), (11, 3), (24, 35), (44, 38), (19, 40), (38, 30), (32, 11), (8, 27), (33, 7), (46, 26), (6, 8), (13, 0), (1, 31), (43, 32), (45, 2), (14, 21), (38, 12), (16, 4), (8, 39), (42, 5), (25, 4), (4, 3), (5, 2), (27, 24), (22, 1), (19, 31), (39, 38), (19, 32), (37, 27), (0, 19), (31, 4), (14, 39), (19, 16), (46, 38), (22, 12), (34, 7), (16, 19), (15, 11), (9, 26), (11, 24), (18, 3), (16, 7), (12, 29), (5, 36), (5, 37), (40, 6), (47, 17), (31, 12), (44, 30), (22, 19), (45, 17), (30, 23), (9, 0), (8, 23), (16, 27), (3, 6), (26, 22), (40, 17), (12, 15), (1, 24), (6, 27), (47, 38), (17, 35), (25, 26), (33, 20), (31, 1), (23, 7), (31, 8), (29, 39), (27, 35), (0, 13), (43, 20), (25, 21), (12, 37), (4, 38), (2, 32), (18, 4), (47, 25), (24, 34), (46, 36), (24, 33), (23, 30), (40, 25), (14, 34), (27, 19), (29, 36), (37, 10), (29, 12), (2, 28), (21, 18), (46, 37), (2, 8), (48, 13), (41, 14), (10, 11), (18, 2), (41, 37), (8, 6), (6, 32), (13, 5), (10, 22), (41, 23), (44, 34), (36, 31), (23, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 42), (39, 25), (25, 38), (44, 22), (14, 42), (23, 27), (22, 45), (15, 20), (25, 15), (33, 24), (0, 41), (22, 1), (36, 46), (29, 28), (25, 40), (2, 4), (28, 13), (38, 6), (16, 27), (18, 39), (22, 31), (32, 19), (14, 21), (11, 46), (36, 32), (20, 32), (3, 45), (3, 5), (0, 6), (38, 31), (6, 41), (42, 15), (8, 42), (31, 25), (35, 5), (29, 12), (5, 47), (40, 40), (15, 39), (10, 9), (0, 15), (38, 40), (41, 1), (17, 11), (28, 21), (3, 16), (32, 13), (5, 26), (31, 33), (34, 17), (18, 46), (2, 26), (13, 24), (5, 10), (16, 36), (28, 12), (6, 1), (36, 43), (16, 29), (27, 33), (36, 28), (1, 47), (36, 19), (1, 2), (30, 5), (0, 23), (36, 36), (34, 26), (11, 19), (21, 18), (12, 6), (15, 27), (43, 13), (18, 37), (9, 17), (9, 35), (2, 41), (7, 5), (1, 26), (34, 32), (43, 19), (24, 1), (10, 32), (13, 0), (23, 18), (2, 42), (40, 45), (17, 40), (16, 9), (26, 5), (21, 31), (0, 24), (4, 10), (42, 20), (24, 8), (29, 14), (28, 5), (41, 4), (8, 46), (10, 24), (12, 30), (34, 3), (26, 26), (7, 19), (25, 18), (7, 45), (29, 10), (17, 34), (8, 38), (12, 38), (21, 16), (22, 44), (14, 40), (42, 27), (6, 20), (32, 33), (13, 12), (17, 16), (0, 13), (5, 45), (36, 5), (34, 7), (24, 27), (34, 25), (5, 0), (23, 29), (33, 9), (29, 47), (0, 31), (44, 33), (40, 10), (13, 29), (37, 42), (16, 35), (32, 0), (44, 40), (40, 9), (34, 35), (34, 37), (27, 6), (14, 11), (28, 26), (44, 9), (6, 38), (25, 42), (3, 22), (23, 8), (18, 7), (12, 7), (1, 11), (27, 23), (30, 25), (13, 38), (10, 6), (44, 29), (41, 30), (17, 15), (3, 46), (28, 28), (18, 8), (4, 12), (41, 11), (26, 15), (18, 29), (7, 21), (27, 43), (44, 13), (10, 35), (37, 15), (33, 47), (36, 9), (42, 19), (12, 26), (13, 25), (5, 35), (0, 1), (24, 39), (30, 11), (4, 39), (33, 19), (11, 23), (26, 41), (33, 11), (5, 39), (27, 32), (34, 24), (28, 11), (19, 39), (17, 4), (34, 22), (10, 14), (23, 16), (2, 45), (13, 31), (38, 34), (34, 31), (42, 16), (31, 13), (12, 8), (37, 29), (28, 32), (31, 28), (35, 14), (16, 14), (36, 25), (16, 41), (18, 30), (12, 3), (0, 4), (6, 18), (17, 9), (32, 38), (31, 14), (4, 20), (22, 26), (28, 45), (8, 4), (44, 12), (38, 8), (42, 47), (10, 44), (18, 12), (26, 39), (7, 18), (24, 3), (37, 46), (3, 4), (16, 16), (15, 25), (9, 30), (22, 39), (24, 33), (28, 24), (6, 26), (38, 43), (15, 23), (28, 17), (23, 46), (8, 34), (20, 34), (42, 35), (4, 26), (24, 40), (29, 21), (6, 35), (24, 17), (24, 7), (6, 7), (31, 2), (17, 14), (26, 24), (44, 36), (6, 8), (42, 22), (22, 3), (30, 35), (43, 32), (23, 32), (14, 13), (42, 14), (18, 1), (28, 41), (22, 11), (24, 25), (9, 18), (38, 19), (9, 42), (3, 33), (0, 46), (34, 6), (15, 22), (22, 36), (32, 2), (30, 26), (0, 14), (27, 40), (7, 22), (21, 28), (33, 2), (22, 21), (28, 39), (27, 25), (43, 29), (9, 25), (31, 39), (17, 33), (23, 34), (36, 7), (12, 34), (27, 14), (8, 27), (28, 3), (14, 34), (25, 33), (35, 28), (27, 3), (15, 33), (32, 25), (3, 8), (8, 7), (39, 33), (8, 24), (33, 30), (10, 39), (24, 18), (5, 2), (29, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 7), (27, 34), (24, 29), (30, 34), (34, 10), (29, 36), (40, 16), (7, 26), (35, 0), (3, 32), (36, 34), (29, 19), (16, 3), (38, 15), (39, 39), (35, 14), (9, 12), (27, 24), (5, 37), (22, 29), (22, 15), (38, 39), (13, 21), (31, 26), (32, 31), (25, 8), (24, 35), (4, 29), (35, 26), (18, 0), (40, 27), (39, 1), (36, 36), (37, 34), (13, 37), (17, 26), (36, 22), (26, 18), (9, 34), (15, 38), (7, 37), (31, 2), (6, 7), (31, 24), (38, 2), (4, 36), (23, 24), (3, 36), (37, 41), (33, 34), (31, 34), (2, 1), (21, 1), (28, 28), (15, 8), (35, 27), (0, 39), (38, 32), (18, 39), (23, 36), (34, 20), (2, 6), (31, 33), (35, 39), (6, 40), (21, 5), (25, 22), (20, 22), (17, 1), (17, 38), (1, 25), (4, 31), (31, 18), (21, 9), (32, 35), (16, 22), (9, 14), (39, 6), (31, 22), (11, 18), (36, 39), (3, 35), (16, 30), (4, 17), (11, 30), (27, 18), (5, 30), (36, 26), (36, 30), (0, 35), (5, 14), (32, 10), (19, 1), (31, 17), (17, 25), (26, 25), (6, 12), (16, 18), (14, 23), (36, 27), (39, 32), (27, 28), (32, 3), (36, 0), (18, 3), (34, 26), (14, 34), (9, 24), (20, 27), (39, 41), (33, 9), (8, 13), (1, 19), (1, 40), (10, 21), (16, 5), (38, 5), (38, 7), (1, 11), (25, 4), (5, 40), (18, 22), (3, 31), (23, 29), (40, 22), (38, 4), (8, 28), (26, 15), (18, 17), (20, 2), (3, 41), (17, 22), (22, 36), (26, 11), (40, 5), (20, 36), (27, 38), (29, 12), (14, 31), (22, 3), (17, 30), (39, 31), (27, 10), (6, 4), (30, 13), (15, 29), (14, 35), (4, 7), (36, 1), (36, 28), (1, 32), (17, 31), (8, 21), (30, 40), (32, 13), (8, 16), (22, 25), (33, 31), (35, 32), (29, 15), (9, 38), (0, 21), (8, 30), (33, 5), (9, 10), (20, 10), (37, 42), (26, 6), (5, 15), (7, 14), (40, 21), (10, 39), (1, 12), (36, 29), (22, 34), (10, 42), (14, 33), (6, 22), (4, 42), (31, 35), (30, 14), (5, 9), (19, 31), (32, 20), (14, 30), (22, 31), (32, 7), (34, 39), (35, 28), (5, 16), (27, 8), (27, 30), (14, 19), (11, 8), (37, 39), (3, 19), (5, 35), (26, 41), (0, 5), (33, 20), (5, 26), (19, 36), (5, 34), (2, 35), (24, 39), (7, 10), (6, 24), (15, 20), (14, 5), (22, 21), (15, 35), (12, 28), (38, 20), (16, 20), (6, 26), (3, 8), (19, 7), (20, 31), (17, 4), (18, 31), (24, 21), (28, 24), (2, 5), (5, 2), (18, 7), (7, 36), (19, 3), (23, 35), (19, 2), (17, 29), (20, 20), (25, 15), (16, 6), (17, 15), (16, 41), (27, 20), (3, 42), (29, 41), (27, 15), (2, 26), (8, 32), (7, 19), (28, 40), (22, 33), (35, 20), (24, 18), (9, 15), (12, 32), (33, 2), (24, 13), (33, 6), (37, 24), (9, 11), (23, 15), (9, 33), (5, 0), (3, 15), (7, 34), (31, 42), (4, 28), (19, 35), (6, 42), (18, 1), (8, 29), (34, 15), (0, 6), (33, 18), (20, 19), (11, 2), (10, 33), (2, 2), (28, 7), (12, 15), (27, 2), (12, 1), (26, 12), (2, 40), (37, 9), (5, 27), (7, 2), (33, 3), (17, 13), (30, 35), (36, 5), (24, 32), (13, 15), (36, 19), (21, 41), (39, 34), (31, 19), (26, 10), (38, 9), (3, 40), (9, 32), (26, 29), (30, 32), (26, 32), (19, 9), (26, 31), (23, 18), (6, 16), (20, 21), (11, 33), (36, 12), (19, 6), (23, 10), (7, 42), (2, 4), (19, 40), (7, 41), (3, 11), (11, 42), (10, 27), (31, 31), (22, 26), (39, 10), (30, 20), (30, 18), (24, 31), (10, 15), (14, 37), (22, 27), (39, 3), (38, 17), (6, 29), (29, 8), (35, 34), (14, 39), (36, 11), (23, 8), (8, 36), (19, 8), (33, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 44), (38, 21), (16, 16), (0, 41), (38, 14), (14, 34), (0, 10), (1, 20), (12, 14), (9, 43), (39, 21), (13, 41), (13, 43), (34, 43), (19, 2), (26, 7), (39, 5), (27, 20), (8, 44), (21, 12), (35, 37), (16, 39), (27, 15), (11, 17), (25, 30), (33, 5), (37, 20), (14, 42), (14, 26), (34, 26), (29, 32), (17, 2), (18, 42), (3, 43), (29, 9), (1, 0), (9, 39), (17, 44), (16, 43), (13, 8), (12, 44), (17, 42), (35, 28), (11, 10), (33, 2), (13, 10), (6, 19), (34, 0), (17, 7), (23, 2), (10, 27), (25, 12), (22, 36), (22, 24), (34, 31), (17, 40), (0, 31), (33, 24), (18, 9), (5, 30), (23, 37), (25, 14), (38, 10), (13, 14), (25, 40), (3, 1), (15, 43), (14, 0), (22, 12), (22, 39), (27, 0), (2, 37), (13, 35), (30, 9), (5, 36), (8, 0), (30, 31), (37, 35), (38, 22), (16, 23), (4, 9), (35, 33), (14, 8), (11, 12), (36, 30), (19, 40), (27, 34), (35, 39), (31, 28), (22, 18), (30, 19), (33, 6), (5, 29), (21, 21), (16, 34), (9, 20), (1, 11), (31, 5), (31, 19), (1, 5), (25, 39), (23, 31), (29, 6), (34, 24), (26, 2), (16, 12), (2, 41), (0, 26), (26, 33), (11, 29), (29, 12), (33, 29), (11, 36), (32, 29), (14, 17), (4, 23), (25, 27), (18, 15), (20, 34), (18, 31), (4, 39), (34, 3), (23, 3), (29, 28), (32, 25), (11, 7), (6, 16), (33, 9), (39, 0), (38, 42), (35, 30), (29, 40), (8, 24), (9, 22), (4, 1), (39, 23), (6, 38), (1, 23), (19, 14), (19, 10), (36, 36), (16, 42), (5, 27), (27, 30), (9, 2), (30, 34), (32, 41), (11, 32), (38, 7), (30, 10), (37, 31), (12, 16), (33, 37), (36, 15), (3, 13), (29, 37), (29, 5), (21, 5), (11, 41), (13, 18), (17, 39), (11, 30), (12, 20), (22, 7), (20, 43), (0, 44), (32, 19), (12, 28), (38, 35), (6, 9), (8, 41), (30, 33), (28, 39), (36, 28), (25, 16), (35, 1), (30, 29), (3, 2), (12, 4), (3, 28), (1, 17), (26, 4), (8, 4), (4, 11), (27, 29), (28, 41), (28, 3), (4, 16), (10, 17), (33, 14), (4, 43), (13, 2), (36, 44), (10, 36), (21, 10), (35, 27), (2, 40), (34, 18), (6, 25), (27, 12), (13, 40), (28, 7), (16, 0), (34, 2), (8, 35), (6, 0), (34, 10), (35, 7), (21, 33), (29, 23), (9, 38), (27, 32), (25, 44), (39, 8), (32, 40), (13, 6), (37, 39), (35, 20), (12, 5), (18, 29), (25, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 0), (4, 37), (22, 32), (31, 23), (25, 3), (4, 24), (6, 40), (25, 7), (3, 35), (20, 38), (36, 9), (22, 18), (18, 20), (22, 29), (39, 43), (13, 13), (35, 29), (2, 7), (3, 26), (18, 37), (37, 29), (3, 3), (34, 21), (15, 48), (19, 11), (9, 47), (19, 48), (20, 24), (1, 5), (26, 4), (46, 9), (17, 9), (39, 45), (35, 13), (34, 41), (30, 41), (27, 22), (32, 34), (27, 11), (34, 7), (32, 36), (34, 30), (26, 9), (11, 28), (12, 24), (40, 19), (1, 2), (40, 32), (10, 34), (43, 36), (6, 28), (36, 30), (5, 29), (3, 10), (35, 47), (33, 13), (13, 42), (36, 3), (38, 20), (17, 21), (37, 8), (23, 29), (42, 9), (43, 37), (26, 7), (25, 17), (41, 8), (28, 13), (0, 29), (32, 6), (10, 19), (1, 8), (38, 14), (4, 47), (6, 19), (33, 31), (7, 9), (26, 36), (44, 34), (17, 41), (10, 3), (14, 20), (4, 8), (30, 26), (0, 36), (1, 31), (9, 1), (40, 11), (5, 26), (6, 10), (16, 35), (33, 18), (20, 19), (9, 31), (13, 23), (46, 14), (8, 12), (18, 47), (4, 19), (7, 6), (12, 10), (22, 2), (30, 35), (46, 28), (20, 7), (27, 6), (9, 5), (17, 10), (35, 10), (12, 40), (36, 6), (36, 23), (36, 18), (14, 19), (9, 11), (15, 18), (2, 21), (33, 35), (46, 43), (5, 6), (17, 8), (19, 45), (18, 7), (13, 12), (36, 47), (46, 10), (35, 19), (36, 34), (0, 16), (19, 26), (16, 29), (21, 8), (16, 15), (16, 7), (3, 24), (25, 4), (46, 42), (23, 20), (6, 13), (30, 9), (9, 43), (35, 34), (9, 0), (26, 12), (13, 3), (1, 20), (24, 22), (18, 9), (29, 47), (33, 41), (42, 19), (19, 39), (37, 38), (31, 8), (44, 33), (42, 5), (8, 41), (4, 5), (12, 14), (22, 36), (39, 15), (9, 20), (1, 10), (46, 13), (44, 15), (7, 33), (19, 46), (42, 47), (39, 0), (27, 26), (31, 11), (24, 18), (12, 16), (42, 48), (36, 44), (12, 47), (21, 3), (31, 21), (45, 42), (14, 43), (25, 14), (43, 48), (12, 11), (7, 3), (33, 20), (39, 16), (38, 36), (31, 12), (8, 33), (36, 0), (45, 7), (4, 22), (27, 43), (35, 43), (7, 31), (35, 42), (7, 29), (19, 7), (22, 47), (18, 17), (5, 45), (14, 6), (36, 15), (18, 6), (4, 46), (41, 11), (31, 42), (39, 13), (3, 14), (46, 3), (19, 6), (5, 34), (21, 40), (30, 27), (16, 42), (4, 31), (31, 0), (44, 12), (7, 45), (25, 6), (28, 3), (24, 32), (9, 7), (26, 47), (33, 2), (34, 27), (23, 44), (20, 47), (18, 2), (16, 5), (4, 15), (13, 27), (9, 38), (28, 14), (45, 15), (15, 45), (1, 35), (2, 42), (16, 47), (6, 16), (0, 7), (11, 13), (18, 14), (9, 39), (25, 10), (17, 5), (13, 32), (6, 35), (36, 14), (29, 32), (19, 14), (5, 5), (11, 6), (34, 34), (44, 25), (45, 47), (3, 31), (4, 33), (28, 42), (3, 47), (0, 41), (2, 1), (16, 38), (35, 45), (9, 29), (29, 40), (11, 26), (11, 47), (5, 23), (30, 42), (33, 39), (26, 19), (2, 19), (22, 13), (3, 23), (2, 36), (39, 11), (12, 21), (13, 34), (43, 8), (21, 36), (31, 2), (22, 35), (29, 2), (12, 18), (17, 27), (27, 36), (36, 12), (22, 39), (33, 9), (21, 4), (46, 12), (14, 13), (4, 43), (8, 36), (7, 41), (44, 43), (19, 42), (23, 3), (2, 6), (23, 32), (18, 42), (20, 43), (19, 44), (46, 25), (20, 22), (26, 11), (23, 15), (0, 25), (39, 32), (20, 34), (16, 14), (18, 31), (22, 6), (14, 9), (13, 0), (16, 22), (23, 22), (32, 4), (17, 42), (18, 4), (45, 25), (45, 40), (26, 28), (16, 30), (16, 48), (1, 22), (3, 30), (46, 26), (25, 5), (34, 35), (35, 28), (7, 38), (44, 22), (5, 24), (38, 44), (28, 7), (10, 24), (6, 0), (1, 16), (42, 23), (19, 38), (42, 13), (8, 2), (20, 20), (6, 14), (11, 37), (0, 6), (17, 43), (22, 11), (8, 8), (5, 10), (32, 12), (31, 22), (44, 11), (15, 11), (38, 5), (33, 37), (21, 6), (36, 20), (11, 4), (4, 17), (23, 23), (12, 8), (35, 17), (40, 13), (16, 3), (43, 27), (34, 23), (24, 39), (6, 33), (19, 25), (33, 30), (23, 6), (32, 17), (17, 7), (11, 43), (2, 4), (27, 40), (10, 13), (16, 18), (20, 12), (33, 26), (45, 43), (25, 41), (15, 12), (9, 2), (28, 47), (2, 9), (38, 38), (41, 13), (12, 6), (32, 44), (24, 7), (8, 6), (13, 31), (46, 47), (21, 9), (27, 28), (11, 1), (21, 32), (20, 35), (2, 16), (41, 16), (38, 16), (44, 36), (20, 9), (10, 31), (18, 24), (43, 33), (35, 4), (26, 31), (2, 31), (1, 29), (31, 18), (24, 46), (10, 6), (27, 30), (43, 46), (3, 8), (16, 31), (22, 0), (39, 18), (38, 1), (36, 42), (46, 5), (0, 3), (19, 37), (34, 37), (7, 30), (40, 45), (10, 44), (24, 23), (30, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 14), (42, 28), (6, 2), (43, 1), (26, 24), (29, 40), (22, 3), (29, 21), (0, 31), (17, 31), (46, 22), (14, 23), (0, 36), (22, 23), (46, 10), (32, 40), (6, 36), (35, 43), (8, 15), (2, 28), (25, 21), (11, 32), (24, 45), (15, 17), (34, 27), (43, 21), (44, 17), (25, 25), (39, 36), (24, 48), (35, 5), (42, 38), (26, 28), (43, 24), (6, 35), (45, 21), (17, 0), (36, 27), (9, 1), (37, 16), (37, 27), (25, 24), (24, 13), (35, 9), (17, 10), (6, 22), (8, 44), (21, 48), (10, 0), (22, 43), (23, 23), (36, 36), (36, 2), (22, 1), (25, 22), (5, 24), (14, 7), (1, 29), (7, 48), (32, 15), (44, 34), (12, 43), (5, 41), (22, 11), (42, 29), (21, 43), (36, 43), (34, 6), (24, 30), (20, 29), (45, 27), (23, 34), (7, 33), (15, 34), (26, 48), (21, 35), (14, 41), (14, 8), (4, 29), (42, 17), (9, 6), (22, 38), (42, 39), (36, 25), (7, 10), (42, 11), (37, 9), (19, 33), (35, 42), (12, 25), (38, 7), (43, 15), (19, 36), (14, 10), (10, 9), (40, 36), (36, 1), (16, 38), (4, 16), (17, 27), (7, 39), (9, 41), (24, 8), (5, 11), (35, 24), (40, 16), (34, 26), (38, 27), (43, 14), (38, 39), (30, 9), (43, 12), (10, 45), (17, 8), (38, 19), (27, 31), (18, 20), (15, 16), (8, 7), (9, 21), (34, 37), (10, 39), (44, 30), (18, 1), (25, 48), (9, 32), (16, 16), (33, 47), (9, 45), (22, 14), (42, 14), (37, 1), (3, 47), (22, 29), (10, 33), (30, 45), (36, 17), (34, 44), (3, 12), (42, 27), (29, 45), (26, 44), (31, 40), (11, 7), (0, 44), (20, 5), (22, 37), (17, 21), (5, 43), (32, 22), (37, 40), (23, 6), (31, 26), (34, 22), (6, 11), (31, 46), (13, 29), (6, 48), (26, 41), (42, 35), (21, 16), (16, 4), (16, 44), (20, 8), (37, 45), (24, 39), (0, 1), (40, 27), (1, 9), (24, 34), (41, 21), (14, 14), (13, 34), (31, 6), (36, 31), (31, 19), (9, 22), (18, 26), (23, 0), (15, 0), (28, 34), (1, 21), (41, 0), (13, 14), (24, 46), (12, 31), (19, 11), (25, 0), (5, 47), (3, 15), (0, 47), (46, 19), (8, 40), (20, 11), (25, 40), (15, 41), (8, 11), (7, 26), (45, 28), (46, 2), (17, 12), (19, 27), (24, 2), (10, 23), (7, 4), (30, 31), (34, 10), (36, 14), (17, 30), (34, 13), (20, 47), (8, 41), (2, 24), (25, 28), (44, 33), (40, 25), (17, 9), (27, 28), (30, 21), (7, 6), (30, 3), (16, 11), (34, 43), (28, 19), (28, 42), (29, 41), (31, 25), (44, 21), (18, 12), (13, 22), (0, 30), (12, 9), (20, 37), (27, 1), (11, 23), (24, 29), (35, 7), (31, 10), (25, 23), (4, 37), (17, 23), (22, 36), (34, 42), (7, 32), (40, 15), (19, 40), (5, 5), (19, 31), (22, 25), (17, 39), (33, 4), (27, 24), (12, 35), (17, 25), (8, 45), (18, 45), (41, 9), (11, 46), (6, 14), (24, 40), (6, 10), (7, 42), (40, 47), (20, 16), (31, 9), (44, 10), (37, 35), (39, 0), (12, 18), (34, 15), (43, 32), (38, 31), (13, 44), (0, 34), (13, 23), (22, 6), (8, 26), (39, 1), (28, 48), (19, 25), (0, 9), (35, 26), (23, 12), (30, 47), (43, 11), (41, 7), (26, 18), (20, 13), (14, 9), (0, 16), (31, 22), (1, 47), (44, 32), (18, 25), (22, 9), (21, 6), (44, 18), (16, 35), (11, 40), (6, 39), (37, 11), (13, 10), (42, 15), (10, 10), (15, 30), (36, 16), (28, 5), (4, 45), (33, 40), (38, 0), (37, 30), (18, 36), (31, 44), (41, 30), (1, 24), (36, 26), (45, 44), (23, 36), (35, 18), (34, 1), (26, 9), (41, 1), (25, 45), (46, 31), (14, 25), (40, 44), (21, 29), (43, 25), (2, 30), (18, 41), (46, 35), (44, 12), (37, 12), (32, 39), (10, 1), (43, 16), (7, 11), (7, 47), (18, 17), (27, 43), (44, 4), (29, 31), (33, 33), (37, 13), (12, 38), (25, 16), (3, 23), (17, 28), (14, 37), (16, 29), (2, 8), (23, 13), (34, 0), (31, 34), (10, 32), (0, 7), (44, 42), (14, 30), (4, 31), (28, 20), (11, 21), (35, 37), (27, 41), (40, 19), (39, 16), (2, 45)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 36), (11, 44), (2, 24), (29, 39), (23, 40), (34, 17), (24, 44), (32, 37), (33, 39), (47, 46), (23, 21), (43, 0), (17, 36), (37, 38), (28, 35), (14, 24), (32, 45), (13, 4), (7, 17), (46, 7), (44, 40), (17, 37), (19, 26), (39, 42), (39, 20), (10, 47), (25, 1), (12, 32), (32, 26), (11, 3), (14, 12), (21, 13), (21, 12), (15, 29), (15, 22), (18, 47), (18, 43), (16, 42), (7, 10), (27, 2), (10, 19), (35, 35), (33, 46), (16, 37), (20, 11), (20, 3), (47, 21), (42, 39), (31, 13), (0, 8), (5, 10), (29, 43), (2, 8), (21, 14), (41, 35), (39, 31), (18, 24), (8, 17), (15, 47), (2, 38), (1, 40), (39, 47), (17, 48), (35, 20), (40, 1), (40, 9), (13, 13), (26, 1), (11, 45), (11, 42), (3, 3), (16, 35), (43, 25), (26, 39), (28, 42), (21, 22), (45, 16), (40, 19), (36, 27), (39, 26), (5, 35), (18, 12), (34, 24), (19, 5), (17, 29), (42, 29), (4, 2), (3, 5), (19, 38), (26, 26), (18, 32), (29, 44), (47, 12), (40, 0), (0, 9), (6, 16), (16, 24), (41, 31), (37, 21), (8, 21), (44, 24), (18, 23), (42, 34), (28, 13), (32, 19), (6, 2), (44, 34), (14, 10), (22, 9), (19, 21), (15, 11), (38, 25), (23, 20), (24, 18), (43, 1), (29, 31), (19, 30), (32, 21), (29, 17), (29, 25), (20, 31), (9, 5), (14, 35), (15, 20), (36, 36), (19, 32), (28, 30), (1, 8), (7, 7), (23, 45), (10, 36), (30, 23), (4, 28), (41, 39), (18, 16), (45, 22), (5, 1), (20, 41), (18, 28), (18, 41), (19, 9), (22, 39), (42, 41), (31, 12), (3, 1), (26, 20), (22, 28), (1, 36), (36, 32), (5, 8), (39, 44), (4, 47), (13, 32), (28, 48), (33, 36), (7, 5), (34, 10), (17, 22), (37, 11), (21, 25), (36, 41), (36, 34), (3, 0), (3, 26), (19, 35), (19, 40), (8, 22), (30, 6), (35, 11), (24, 23), (19, 33), (22, 36), (18, 39), (23, 27), (31, 5), (38, 3), (20, 8), (37, 4), (43, 43), (13, 25), (7, 40), (24, 28), (8, 15), (7, 37), (4, 31), (39, 22), (31, 46), (45, 40), (32, 28), (42, 12), (1, 29), (44, 18), (38, 14), (27, 0), (6, 5), (25, 39), (20, 37), (31, 37), (40, 30), (41, 0), (29, 33), (43, 30), (35, 17), (2, 28), (44, 5), (2, 9), (42, 48), (2, 16), (35, 34), (5, 24), (9, 2), (14, 23), (38, 40), (0, 16), (11, 20), (36, 43), (29, 0), (35, 4), (3, 4), (23, 33), (30, 47), (26, 3), (34, 9), (46, 29), (16, 11), (46, 43), (25, 19), (33, 9), (2, 22), (10, 38), (13, 34), (25, 17), (40, 8), (32, 8), (1, 28), (28, 24), (13, 11), (35, 26), (1, 27), (11, 16), (31, 29), (2, 13), (27, 47), (4, 19), (27, 37), (7, 16), (38, 13), (9, 15), (31, 24), (18, 17), (22, 26), (40, 24), (43, 23), (40, 31), (20, 33), (38, 30), (21, 47), (28, 6), (32, 3), (34, 13), (12, 9), (3, 48), (9, 33), (36, 28), (39, 40), (0, 23), (35, 21), (17, 3), (6, 0), (37, 23), (17, 19), (38, 0), (3, 46), (7, 42), (21, 24), (5, 14), (45, 24), (35, 38), (9, 38), (43, 35), (34, 5), (26, 19), (10, 17), (26, 13), (4, 18), (35, 6), (23, 29), (44, 11), (20, 36), (21, 5), (41, 18), (5, 18), (34, 21), (41, 22), (41, 48), (4, 10), (0, 43), (3, 11), (10, 33), (47, 34), (47, 30), (32, 2), (37, 25), (27, 21), (8, 8), (30, 39), (45, 6), (1, 33), (43, 31), (26, 32), (14, 36), (3, 32), (15, 33), (9, 12), (44, 33), (25, 35), (18, 31), (13, 31), (47, 29), (21, 28), (39, 38), (21, 20), (1, 12), (11, 21), (7, 9), (39, 30), (28, 9), (8, 42), (0, 15), (26, 4), (31, 42), (17, 27), (5, 19), (35, 47), (23, 1), (13, 39), (43, 6), (14, 0), (31, 30), (36, 12), (23, 18), (20, 17), (35, 46), (45, 48), (31, 4), (27, 46), (43, 24), (36, 26), (43, 4), (30, 13), (20, 28), (38, 24), (16, 3), (41, 43), (30, 21), (43, 46), (31, 0), (43, 8), (21, 19), (22, 45), (20, 39), (27, 18), (0, 34), (26, 30), (40, 15), (24, 35), (13, 6), (26, 8), (0, 47), (44, 47), (1, 45), (37, 7), (45, 7), (11, 35), (4, 3), (3, 20), (46, 45), (24, 15), (26, 34), (15, 36), (20, 29), (27, 31), (35, 22), (9, 11), (42, 36), (13, 38), (6, 39), (29, 9), (28, 34), (12, 28), (16, 0), (45, 2), (33, 38), (15, 0), (32, 29), (6, 25), (0, 13), (15, 23), (17, 23), (21, 42), (13, 41), (43, 13), (29, 21), (23, 10), (14, 22), (26, 43), (12, 21), (0, 41), (35, 8), (19, 3), (3, 38), (38, 39), (8, 38), (3, 18), (8, 0), (33, 27), (7, 2), (27, 30), (36, 45), (36, 4), (20, 24), (38, 2), (22, 21), (4, 36), (6, 17), (47, 28), (33, 28), (6, 48), (33, 11), (8, 16), (3, 36), (33, 5), (14, 14), (27, 48), (30, 11), (8, 1), (13, 45), (10, 7), (31, 7), (37, 5), (21, 17), (30, 48), (35, 42), (30, 2), (13, 19), (0, 44), (21, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 13), (30, 13), (10, 8), (38, 9), (46, 28), (9, 17), (13, 32), (41, 26), (10, 27), (7, 33), (43, 25), (47, 37), (41, 37), (46, 24), (25, 34), (19, 2), (1, 5), (6, 24), (35, 11), (29, 14), (30, 28), (9, 40), (36, 12), (42, 35), (12, 32), (32, 8), (25, 35), (46, 8), (38, 6), (28, 8), (14, 22), (25, 23), (37, 18), (0, 34), (45, 34), (41, 16), (15, 19), (7, 40), (14, 18), (5, 39), (20, 34), (17, 20), (19, 39), (39, 7), (16, 29), (38, 17), (37, 0), (7, 12), (40, 1), (16, 13), (25, 24), (26, 8), (14, 29), (46, 5), (44, 7), (14, 36), (30, 5), (7, 0), (6, 27), (34, 27), (13, 25), (38, 1), (36, 14), (15, 20), (34, 13), (39, 33), (45, 20), (4, 1), (15, 33), (4, 13), (28, 28), (0, 3), (0, 25), (6, 37), (0, 14), (37, 13), (29, 1), (36, 38), (15, 40), (40, 12), (7, 27), (48, 4), (9, 7), (22, 15), (34, 5), (13, 23), (15, 32), (31, 6), (17, 37), (44, 39), (4, 30), (45, 0), (45, 3), (22, 5), (45, 22), (45, 6), (43, 4), (29, 38), (48, 15), (26, 23), (45, 39), (14, 12), (2, 16), (43, 6), (2, 35), (4, 31), (10, 9), (42, 2), (19, 29), (38, 24), (15, 9), (13, 10), (8, 8), (12, 36), (12, 39), (9, 34), (18, 22), (27, 2), (25, 15), (2, 36), (28, 1), (17, 8), (23, 0), (33, 36), (27, 38), (21, 1), (18, 6), (45, 7), (20, 7), (6, 5), (36, 33), (7, 19), (28, 9), (13, 38), (0, 31), (4, 38), (30, 19), (16, 37), (22, 40), (13, 30), (33, 16), (22, 13), (30, 33), (37, 14), (32, 4), (13, 28), (8, 37), (4, 37), (34, 11), (25, 11), (8, 11), (39, 3), (14, 40), (13, 17), (16, 33), (42, 8), (39, 37), (41, 8), (34, 6), (36, 28), (31, 31), (28, 27), (39, 9), (27, 31), (36, 35), (26, 2), (39, 19), (26, 7), (12, 5), (34, 34), (6, 38), (18, 32), (40, 15), (19, 24), (38, 35), (16, 9), (38, 3), (43, 19), (38, 22), (22, 10), (45, 23), (30, 26), (31, 27), (13, 14), (36, 9), (11, 24), (29, 22), (29, 39), (22, 24), (1, 40), (15, 30), (5, 34), (18, 5), (4, 36), (17, 0), (43, 28), (8, 31), (43, 31), (7, 22), (31, 30), (13, 7), (33, 20), (9, 9), (40, 22), (6, 17), (23, 9), (3, 22), (6, 18), (11, 12), (7, 17), (26, 32), (13, 8), (13, 24), (37, 34), (14, 34), (12, 23), (33, 24), (4, 34), (0, 35), (39, 24), (38, 4), (27, 1), (13, 3), (46, 33), (32, 35), (4, 20), (23, 28), (43, 35), (33, 34), (19, 40), (37, 5), (20, 39), (18, 28), (4, 7), (37, 4), (34, 36), (42, 12), (28, 20), (25, 10), (48, 26), (33, 5), (36, 39), (42, 22), (41, 31), (45, 24), (25, 1), (26, 12), (42, 24), (36, 11), (26, 24), (20, 10), (24, 15), (3, 40), (5, 27), (18, 15), (27, 23), (8, 3), (1, 11), (12, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 9), (14, 22), (11, 8), (5, 43), (9, 28), (11, 13), (23, 15), (12, 36), (25, 3), (24, 24), (32, 37), (18, 19), (42, 12), (1, 3), (37, 36), (34, 20), (23, 38), (33, 19), (37, 17), (4, 24), (18, 7), (23, 18), (38, 7), (38, 30), (13, 22), (23, 27), (32, 2), (23, 23), (10, 47), (10, 29), (17, 35), (2, 12), (30, 45), (24, 9), (17, 13), (39, 0), (4, 41), (26, 11), (28, 35), (32, 13), (7, 25), (7, 1), (13, 48), (0, 1), (2, 47), (21, 25), (4, 12), (24, 23), (19, 45), (24, 5), (25, 27), (19, 14), (35, 17), (19, 34), (36, 26), (15, 28), (3, 15), (33, 43), (25, 4), (1, 5), (21, 26), (36, 3), (12, 5), (29, 13), (5, 23), (9, 39), (22, 2), (16, 23), (42, 9), (8, 45), (4, 35), (14, 11), (36, 24), (13, 20), (33, 0), (0, 2), (16, 48), (26, 32), (8, 6), (27, 28), (16, 42), (22, 6), (7, 38), (8, 25), (35, 5), (21, 31), (10, 37), (39, 45), (20, 26), (33, 40), (41, 38), (27, 32), (38, 32), (15, 25), (37, 0), (7, 45), (32, 4), (41, 41), (42, 31), (25, 36), (7, 29), (15, 0), (23, 4), (34, 44), (25, 8), (22, 20), (23, 37), (7, 26), (29, 14), (26, 45), (9, 40), (5, 20), (13, 12), (23, 36), (17, 33), (16, 3), (30, 9), (7, 41), (14, 17), (40, 34), (25, 5), (34, 24), (15, 15), (0, 18), (11, 12), (33, 41), (16, 24), (9, 16), (33, 2), (40, 39), (4, 40), (14, 47), (19, 16), (2, 41), (14, 39), (2, 17), (21, 0), (20, 13), (3, 11), (0, 43), (5, 5), (24, 35), (41, 20), (38, 20), (7, 42), (18, 17), (14, 33), (13, 37), (9, 12), (19, 13), (15, 27), (38, 34), (16, 43), (13, 35), (24, 22), (39, 41), (38, 31), (12, 25), (6, 10), (32, 35), (27, 48), (8, 40), (36, 39), (37, 10), (32, 10), (32, 8), (34, 47), (36, 42), (5, 30), (15, 14), (4, 33), (17, 37), (9, 41), (39, 43), (39, 15), (8, 44), (32, 16), (0, 29), (16, 44), (1, 34), (35, 43), (8, 42), (11, 10), (2, 1), (26, 14), (21, 1), (5, 12), (4, 2), (0, 37), (4, 43), (36, 44), (8, 14), (25, 30), (22, 36), (39, 48), (26, 10), (3, 23), (29, 32), (33, 23), (30, 2), (22, 9), (15, 9), (28, 19), (24, 30), (34, 41), (38, 47), (42, 39), (6, 17), (3, 40), (13, 13), (23, 0), (23, 45), (38, 19), (21, 46), (20, 41), (19, 3), (4, 0), (33, 47), (23, 46), (20, 0), (23, 13), (12, 11), (30, 37), (7, 23), (5, 3), (34, 18), (42, 25), (19, 10), (28, 14), (35, 30), (2, 14), (18, 6), (22, 45), (42, 43), (34, 26), (15, 24), (38, 24), (3, 47), (2, 16), (15, 7), (0, 8), (24, 6), (32, 30), (24, 38), (26, 38), (40, 8), (4, 20), (41, 7), (7, 35), (17, 23), (6, 45), (6, 0), (34, 42), (27, 7), (36, 46), (32, 41), (6, 36), (3, 44), (19, 28), (12, 48), (34, 37), (25, 39), (24, 3), (11, 2), (4, 28), (7, 15), (15, 46), (32, 38), (34, 40), (36, 34), (42, 26), (22, 25), (17, 3), (30, 12), (15, 34), (25, 41), (12, 42), (37, 3), (2, 42), (21, 3), (17, 30), (4, 44), (13, 0), (5, 45), (40, 48), (11, 22), (19, 18), (0, 9), (13, 42), (41, 5), (29, 26), (14, 9), (16, 41), (27, 4), (35, 46), (8, 24), (7, 18), (16, 45), (6, 7), (42, 46), (10, 38), (12, 12), (33, 8), (32, 23), (18, 27), (30, 11), (3, 45), (0, 44), (22, 27), (30, 26), (37, 24), (41, 1), (27, 17), (13, 4), (31, 14), (9, 27), (9, 11), (34, 31), (16, 18), (37, 2), (22, 33), (28, 2), (37, 26), (14, 18), (18, 21), (25, 16), (34, 34), (25, 26), (6, 29), (35, 11), (8, 4), (15, 42), (12, 35), (37, 39), (35, 38), (31, 19), (2, 3), (14, 6), (19, 32), (28, 33), (17, 43), (0, 7), (21, 40), (4, 15), (14, 21), (17, 22), (35, 8), (22, 17), (31, 15), (26, 46), (24, 34), (41, 10), (31, 21), (16, 0), (2, 37), (28, 3), (0, 20), (28, 45), (4, 29), (38, 48), (6, 38), (19, 8), (1, 29), (1, 13), (29, 2), (23, 26), (33, 30), (9, 17), (41, 17), (37, 45), (39, 30), (23, 29), (13, 30), (1, 17), (30, 32), (6, 14), (40, 27), (41, 28), (2, 34), (34, 32), (3, 35), (28, 12), (10, 10), (42, 20), (8, 7), (3, 10), (27, 31), (29, 3), (42, 8), (38, 27), (20, 16), (12, 44), (32, 43), (7, 19), (21, 17), (32, 7), (33, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 25), (8, 8), (28, 33), (37, 22), (23, 9), (43, 20), (18, 8), (30, 9), (13, 29), (22, 11), (1, 14), (25, 46), (23, 19), (43, 43), (11, 20), (15, 31), (18, 17), (2, 3), (8, 5), (20, 14), (13, 43), (41, 41), (6, 21), (4, 42), (19, 31), (43, 23), (32, 35), (9, 22), (19, 9), (16, 44), (27, 23), (20, 27), (3, 18), (9, 7), (18, 28), (16, 41), (2, 8), (31, 45), (5, 20), (41, 14), (34, 7), (28, 11), (15, 15), (41, 45), (36, 15), (3, 42), (29, 38), (26, 33), (26, 14), (4, 14), (36, 24), (8, 24), (19, 25), (26, 9), (28, 44), (11, 31), (13, 32), (11, 0), (20, 13), (9, 26), (1, 12), (9, 23), (23, 26), (41, 21), (42, 22), (23, 3), (26, 6), (36, 43), (13, 36), (29, 26), (28, 14), (32, 34), (32, 27), (24, 26), (18, 19), (43, 38), (23, 45), (16, 33), (26, 15), (8, 46), (8, 38), (2, 45), (16, 27), (20, 32), (28, 22), (8, 30), (9, 31), (20, 1), (10, 21), (4, 39), (10, 9), (25, 34), (21, 36), (31, 26), (10, 41), (37, 40), (4, 24), (12, 6), (10, 32), (4, 37), (20, 24), (8, 7), (23, 46), (35, 28), (31, 2), (20, 2), (37, 38), (38, 46), (2, 31), (10, 37), (12, 46), (4, 6), (36, 8), (38, 1), (10, 23), (42, 9), (18, 44), (3, 7), (29, 5), (12, 27), (0, 9), (0, 35), (39, 22), (38, 29), (13, 31), (36, 2), (33, 39), (2, 41), (10, 44), (2, 42), (37, 14), (33, 22), (16, 36), (22, 32), (1, 44), (42, 17), (3, 14), (43, 6), (30, 15), (5, 44), (18, 20), (22, 25), (43, 22), (9, 42), (3, 26), (41, 37), (17, 11), (20, 16), (12, 21), (24, 17), (5, 1), (13, 1), (3, 2), (10, 15), (14, 19), (0, 22), (3, 23), (9, 20), (10, 18), (34, 36), (7, 12), (0, 17), (15, 22), (43, 35), (0, 45), (42, 15), (35, 46), (43, 34), (24, 11), (26, 39), (34, 34), (42, 11), (23, 8), (29, 15), (38, 35), (26, 2), (34, 26), (31, 1), (21, 14), (38, 33), (40, 7), (5, 41), (1, 45), (0, 23), (6, 24), (11, 10), (20, 15), (13, 25), (23, 16), (24, 13), (28, 12), (43, 4), (29, 14), (2, 16), (19, 44), (40, 31), (30, 12), (42, 37), (18, 45), (33, 36), (24, 33), (2, 34), (39, 44), (14, 17), (18, 4), (4, 2), (33, 14), (38, 15), (18, 16), (26, 26), (24, 42), (5, 13), (30, 40), (35, 12), (37, 28), (4, 0), (42, 12), (41, 26), (6, 17), (28, 30), (41, 1), (0, 6), (0, 11), (25, 42), (7, 38), (33, 28), (17, 26), (26, 30), (0, 10), (34, 28), (23, 36), (17, 23), (22, 8), (34, 38), (26, 3), (15, 23), (23, 7), (19, 28), (38, 21), (26, 24), (38, 3), (7, 5), (19, 8), (23, 2), (22, 24), (29, 39), (43, 13), (42, 18), (15, 19), (8, 12), (33, 32), (11, 1), (17, 35), (16, 35), (39, 41), (39, 10), (6, 19), (6, 8), (20, 31), (14, 44), (13, 46), (33, 40), (42, 2), (22, 14), (20, 8), (7, 45), (8, 44), (22, 6), (42, 23), (18, 5), (9, 41), (34, 37), (11, 22), (38, 0), (24, 32), (24, 35), (39, 26), (21, 19), (7, 3), (21, 39), (18, 22), (32, 37), (36, 28), (22, 28), (19, 39), (30, 27), (21, 22), (43, 28), (23, 29), (7, 16), (8, 31), (13, 2), (29, 34), (4, 22), (42, 39), (1, 24), (42, 14), (22, 34), (31, 17), (39, 24), (14, 22), (41, 9), (12, 31), (38, 45), (28, 5), (34, 43), (29, 42), (3, 11), (14, 38), (21, 23), (13, 34), (17, 9), (35, 0), (26, 13), (15, 1), (13, 10), (4, 43), (3, 9), (6, 14), (22, 7), (0, 33), (43, 25), (30, 17), (5, 46), (18, 26), (21, 17), (3, 3), (17, 17), (9, 17), (9, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 23), (17, 16), (12, 28), (12, 40), (1, 38), (34, 36), (21, 13), (34, 10), (35, 40), (19, 45), (16, 27), (26, 18), (0, 7), (20, 27), (0, 29), (8, 12), (6, 29), (40, 35), (7, 44), (29, 42), (39, 47), (2, 21), (26, 22), (30, 28), (6, 6), (25, 25), (7, 40), (23, 36), (17, 38), (33, 20), (6, 5), (15, 37), (0, 8), (24, 33), (8, 42), (31, 36), (32, 41), (0, 1), (28, 41), (22, 0), (28, 20), (22, 36), (12, 7), (25, 32), (32, 33), (20, 18), (28, 35), (25, 36), (36, 46), (13, 5), (19, 25), (33, 10), (25, 45), (26, 45), (17, 35), (19, 42), (20, 16), (40, 11), (4, 15), (33, 21), (22, 42), (2, 1), (5, 10), (21, 14), (7, 38), (18, 4), (21, 15), (9, 17), (3, 37), (13, 27), (11, 0), (33, 18), (16, 28), (11, 19), (10, 38), (2, 22), (8, 34), (20, 32), (15, 18), (22, 30), (26, 27), (31, 7), (11, 37), (30, 35), (2, 43), (17, 4), (23, 15), (26, 9), (9, 12), (18, 41), (36, 17), (19, 39), (5, 14), (21, 10), (35, 15), (18, 10), (29, 29), (22, 17), (0, 42), (24, 47), (6, 11), (35, 29), (36, 20), (9, 31), (17, 11), (30, 3), (0, 9), (22, 6), (0, 26), (17, 34), (40, 27), (9, 13), (10, 35), (30, 7), (11, 30), (5, 41), (33, 46), (23, 12), (10, 15), (3, 40), (11, 39), (16, 26), (22, 18), (39, 26), (39, 30), (1, 21), (19, 46), (10, 17), (38, 42), (24, 9), (0, 28), (24, 25), (18, 45), (25, 7), (30, 10), (1, 35), (2, 27), (23, 45), (20, 3), (17, 43), (38, 11), (6, 1), (26, 36), (7, 16), (2, 5), (14, 36), (14, 5), (17, 27), (13, 18), (9, 22), (24, 38), (23, 6), (17, 45), (17, 12), (28, 22), (13, 24), (31, 14), (35, 32), (35, 17), (0, 38), (36, 34), (32, 10), (8, 1), (17, 7), (35, 12), (20, 41), (40, 20), (10, 40), (1, 30), (27, 7), (7, 8), (29, 9), (1, 15), (8, 43), (15, 46), (38, 37), (32, 36), (13, 31), (38, 47), (8, 40), (11, 13), (20, 11), (16, 11), (17, 26), (1, 6), (9, 40), (33, 30), (31, 39), (16, 37), (20, 44), (37, 30), (27, 13), (16, 36), (17, 15), (32, 47), (11, 4), (3, 14), (15, 17), (27, 41), (35, 42), (31, 42), (14, 0), (13, 17), (25, 19), (33, 28), (3, 31), (10, 27), (34, 8), (33, 44), (36, 45), (34, 33), (13, 45), (26, 1), (8, 2), (23, 0), (23, 14), (38, 16), (9, 35), (35, 46), (27, 11), (37, 23), (3, 47), (37, 8), (14, 42), (23, 35), (34, 16), (6, 30), (28, 40), (4, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 22), (25, 36), (10, 31), (9, 12), (8, 17), (27, 27), (14, 33), (18, 19), (12, 16), (24, 14), (20, 1), (26, 0), (0, 33), (25, 1), (33, 30), (13, 0), (18, 20), (1, 21), (14, 11), (23, 15), (23, 35), (11, 41), (20, 5), (29, 19), (24, 40), (6, 4), (12, 15), (21, 41), (3, 31), (30, 12), (39, 11), (28, 31), (28, 13), (7, 12), (36, 20), (11, 17), (13, 5), (25, 14), (32, 12), (35, 32), (14, 39), (24, 19), (34, 37), (1, 10), (20, 3), (35, 25), (27, 29), (32, 40), (25, 35), (5, 0), (4, 35), (2, 11), (35, 17), (15, 41), (12, 19), (34, 24), (26, 37), (24, 7), (25, 10), (31, 5), (29, 24), (13, 33), (3, 23), (13, 20), (40, 31), (11, 33), (25, 25), (39, 0), (10, 15), (16, 29), (18, 26), (22, 41), (3, 37), (36, 38), (9, 8), (38, 18), (34, 12), (10, 22), (33, 33), (33, 16), (11, 0), (21, 39), (33, 38), (18, 23), (37, 5), (8, 19), (9, 19), (24, 29), (31, 12), (0, 19), (8, 8), (37, 12), (5, 22), (26, 16), (7, 14), (15, 26), (0, 26), (18, 37), (41, 40), (30, 22), (35, 1), (22, 32), (17, 25), (28, 22), (41, 3), (10, 41), (10, 3), (39, 39), (12, 28), (19, 35), (7, 8), (25, 34), (41, 13), (21, 26), (35, 38), (17, 37), (24, 4), (1, 9), (40, 3), (2, 6), (29, 15), (11, 38), (18, 13), (18, 0), (25, 26), (19, 26), (35, 3), (10, 20), (11, 29), (7, 31), (15, 22), (17, 14), (18, 32), (20, 28), (14, 36), (40, 33), (23, 10), (31, 19), (14, 0), (36, 0), (15, 6), (22, 1), (15, 24), (13, 19), (11, 11), (8, 12), (34, 30), (31, 28), (3, 20), (21, 12), (7, 21), (4, 15), (3, 9), (17, 30), (23, 21), (35, 23), (11, 16), (36, 27), (9, 5), (35, 13), (6, 6), (13, 22), (0, 22), (21, 40), (24, 35), (4, 6), (9, 28), (29, 16), (38, 8), (3, 19), (3, 22), (6, 39), (38, 30), (22, 14), (10, 35), (27, 23), (34, 18), (38, 32), (18, 36), (30, 10), (0, 41), (9, 11), (16, 13), (22, 15), (20, 38), (41, 19), (18, 2), (39, 24), (37, 29), (36, 31), (0, 2), (7, 0), (9, 23), (23, 33), (22, 0), (39, 28), (1, 17), (7, 1), (28, 10), (4, 16), (0, 14), (28, 34), (7, 22), (5, 12), (31, 23), (13, 34), (8, 5), (17, 23), (18, 34), (21, 9), (18, 27), (0, 21), (12, 35), (27, 34), (15, 23), (23, 17), (9, 35), (23, 5), (21, 6), (30, 40), (40, 22), (15, 5), (26, 10), (24, 39), (9, 30), (23, 6), (28, 40), (8, 32), (39, 14), (12, 5), (24, 30), (3, 36), (32, 21), (11, 8), (32, 38), (22, 23), (13, 40), (2, 27), (11, 20), (37, 24), (2, 20), (15, 0), (23, 40), (3, 24), (16, 3), (19, 20), (26, 27), (27, 19), (15, 33), (0, 30), (25, 15), (11, 34), (37, 25), (33, 12), (14, 23), (1, 35), (40, 28), (40, 4), (3, 39), (32, 4), (12, 25), (28, 27), (30, 39), (32, 35), (7, 4), (7, 29), (16, 7), (3, 15), (27, 13), (19, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 44), (9, 30), (23, 42), (19, 23), (18, 20), (24, 13), (4, 17), (20, 40), (1, 21), (7, 18), (44, 13), (44, 31), (29, 28), (17, 19), (42, 2), (18, 15), (13, 9), (22, 24), (21, 5), (4, 26), (42, 3), (9, 24), (11, 19), (24, 20), (7, 35), (44, 7), (37, 44), (22, 6), (32, 0), (31, 38), (38, 30), (3, 41), (37, 10), (23, 44), (9, 0), (39, 34), (39, 44), (39, 36), (14, 11), (31, 9), (32, 38), (40, 1), (8, 3), (38, 20), (0, 8), (5, 24), (11, 21), (35, 10), (14, 34), (3, 13), (20, 32), (29, 10), (8, 22), (22, 3), (9, 29), (37, 40), (43, 14), (24, 1), (37, 25), (21, 2), (19, 6), (41, 22), (27, 25), (7, 19), (15, 6), (3, 18), (5, 21), (28, 30), (12, 14), (17, 44), (5, 28), (17, 21), (8, 4), (17, 34), (43, 25), (42, 33), (25, 36), (6, 21), (20, 31), (0, 26), (4, 31), (27, 23), (33, 40), (29, 34), (30, 11), (20, 7), (22, 23), (25, 35), (41, 27), (2, 36), (10, 1), (34, 38), (8, 2), (24, 17), (37, 17), (26, 32), (0, 33), (36, 29), (16, 22), (33, 4), (12, 7), (15, 0), (5, 31), (4, 40), (17, 2), (29, 16), (25, 31), (10, 29), (38, 37), (28, 27), (26, 43), (28, 20), (18, 1), (28, 42), (26, 9), (43, 3), (39, 43), (17, 4), (25, 23), (20, 24), (20, 5), (10, 33), (20, 11), (7, 32), (23, 24), (43, 19), (17, 25), (3, 10), (25, 24), (4, 38), (21, 21), (25, 0), (35, 3), (43, 35), (16, 23), (6, 27), (13, 41), (29, 27), (39, 0), (30, 38), (11, 13), (32, 2), (36, 12), (21, 25), (43, 2), (15, 1), (0, 29), (22, 22), (18, 3), (27, 10), (42, 14), (32, 42), (9, 18), (9, 2), (40, 28), (14, 13), (26, 40), (30, 30), (25, 5), (23, 17), (42, 25), (11, 3), (7, 30), (37, 18), (43, 11), (44, 17), (10, 43), (24, 30), (38, 13), (39, 26), (28, 36), (42, 37), (6, 28), (18, 39), (35, 29), (36, 11), (44, 37), (40, 41), (43, 26), (19, 38), (16, 36), (21, 38), (18, 8), (4, 22), (2, 43), (15, 29), (4, 43), (42, 40), (4, 24), (16, 11), (10, 2), (6, 11), (23, 32), (13, 34), (20, 9), (3, 34), (5, 36), (0, 2), (44, 11), (0, 14), (18, 11), (15, 32), (8, 41), (29, 21), (27, 32), (38, 43), (17, 30), (7, 27), (21, 15), (10, 21), (16, 15), (33, 25), (32, 44), (40, 24), (15, 31), (3, 20), (36, 43), (21, 35), (41, 43), (42, 21), (43, 27), (7, 14), (38, 28), (42, 11), (12, 16), (22, 43), (4, 36), (23, 31), (44, 6), (19, 24), (20, 41), (11, 25), (43, 31), (23, 20), (33, 34), (22, 40), (25, 26), (14, 42), (37, 32), (30, 6), (33, 35), (4, 23), (20, 0), (22, 31), (6, 43), (34, 33), (4, 44), (1, 36), (14, 24), (32, 34), (13, 42), (24, 40), (1, 2), (4, 5), (26, 12), (12, 8), (6, 36), (3, 19), (7, 12), (37, 15), (24, 0), (33, 44), (29, 41), (6, 19), (18, 25), (35, 42), (35, 17), (12, 34), (36, 42), (25, 14), (35, 37), (25, 13), (9, 27), (7, 13), (42, 32), (8, 5), (7, 24), (18, 12), (8, 0), (8, 43), (38, 17), (23, 2), (23, 11), (26, 27), (8, 25), (37, 23), (6, 9), (12, 1), (19, 5), (36, 41), (25, 39), (43, 44), (28, 35), (4, 27), (31, 35), (44, 30), (20, 42), (33, 20), (30, 26), (39, 29), (12, 26), (35, 0), (14, 19), (33, 16), (3, 27), (4, 10), (10, 19), (9, 6), (44, 0), (26, 6), (17, 37), (38, 39), (13, 21), (32, 7), (13, 14), (20, 18), (31, 27), (41, 23), (41, 26), (26, 42), (11, 20), (4, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 23), (35, 29), (14, 13), (8, 34), (6, 4), (11, 26), (39, 35), (26, 43), (2, 20), (19, 27), (6, 41), (1, 23), (1, 2), (31, 42), (3, 7), (25, 18), (1, 38), (30, 23), (18, 25), (10, 8), (9, 36), (40, 38), (31, 27), (22, 5), (31, 40), (23, 23), (20, 2), (10, 1), (8, 25), (29, 33), (9, 35), (8, 16), (27, 35), (3, 15), (34, 28), (27, 7), (0, 40), (18, 30), (10, 17), (24, 3), (5, 42), (26, 37), (22, 19), (31, 39), (35, 36), (11, 18), (31, 20), (36, 13), (29, 16), (18, 7), (29, 37), (5, 19), (0, 27), (0, 24), (10, 25), (29, 0), (20, 10), (18, 3), (16, 13), (9, 41), (16, 19), (20, 21), (17, 8), (6, 0), (19, 33), (16, 37), (5, 12), (18, 33), (29, 25), (6, 38), (28, 23), (25, 15), (11, 37), (7, 10), (39, 13), (39, 33), (39, 41), (24, 5), (15, 37), (32, 9), (15, 18), (12, 29), (26, 14), (13, 19), (0, 33), (7, 40), (14, 14), (0, 14), (32, 14), (12, 21), (9, 43), (8, 38), (23, 36), (38, 10), (15, 31), (8, 26), (18, 36), (2, 9), (7, 43), (29, 39), (20, 13), (3, 23), (14, 11), (1, 43), (30, 28), (24, 2), (19, 9), (29, 23), (1, 18), (18, 13), (22, 15), (17, 36), (9, 37), (3, 28), (14, 29), (17, 15), (30, 5), (2, 37), (8, 6), (15, 42), (40, 12), (5, 39), (11, 23), (24, 21), (22, 31), (12, 9), (34, 5), (11, 40), (25, 2), (37, 19), (17, 42), (14, 23), (6, 33), (4, 33), (39, 21), (11, 42), (21, 18), (35, 5), (4, 11), (17, 32), (18, 37), (30, 9), (34, 7), (38, 15), (40, 41), (23, 7), (27, 12), (25, 22), (10, 5), (37, 42), (38, 33), (31, 3), (35, 24), (13, 7), (10, 16), (33, 20), (40, 7), (1, 32), (22, 40), (11, 31), (27, 27), (27, 28), (12, 34), (24, 24), (37, 30), (0, 3), (36, 34), (31, 34), (17, 1), (31, 28), (30, 4), (15, 3), (18, 14), (30, 0), (35, 0), (24, 29), (4, 40), (1, 21), (13, 10), (34, 31), (9, 25), (14, 8), (28, 16), (23, 12), (35, 31), (39, 1), (8, 13), (25, 26), (6, 17), (7, 16), (3, 29), (39, 23), (34, 14), (28, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 5), (27, 29), (5, 33), (6, 30), (0, 35), (5, 3), (28, 22), (6, 5), (23, 36), (17, 30), (25, 9), (1, 11), (41, 21), (22, 34), (39, 24), (32, 7), (26, 28), (15, 7), (10, 29), (4, 0), (38, 2), (26, 38), (35, 4), (11, 9), (14, 33), (28, 34), (28, 11), (20, 33), (24, 30), (16, 5), (1, 14), (11, 35), (33, 19), (41, 13), (27, 22), (36, 14), (4, 2), (2, 11), (30, 26), (25, 16), (4, 20), (23, 25), (40, 7), (36, 0), (19, 24), (38, 6), (24, 7), (33, 0), (18, 2), (1, 10), (28, 4), (38, 17), (41, 9), (37, 10), (37, 26), (35, 39), (21, 8), (40, 3), (25, 24), (10, 13), (20, 24), (25, 6), (24, 2), (14, 12), (27, 2), (33, 40), (37, 33), (20, 8), (13, 35), (15, 11), (28, 8), (17, 37), (3, 14), (0, 11), (1, 31), (36, 2), (7, 6), (27, 26), (27, 17), (30, 6), (21, 5), (33, 22), (0, 3), (25, 23), (36, 30), (1, 2), (6, 20), (20, 15), (37, 22), (19, 3), (32, 35), (4, 1), (16, 23), (2, 29), (18, 8), (31, 30), (31, 4), (4, 8), (25, 3), (5, 26), (3, 35), (9, 40), (9, 6), (39, 27), (15, 10), (39, 23), (35, 22), (6, 22), (41, 35), (6, 32), (26, 21), (18, 18), (41, 28), (13, 0), (5, 21), (9, 21), (36, 21), (39, 22), (30, 38), (20, 30), (21, 15), (23, 37), (30, 25), (0, 19), (3, 38), (26, 6), (20, 13), (37, 28), (7, 1), (5, 34), (2, 40), (25, 26), (15, 33), (14, 11), (38, 37), (29, 27), (35, 13), (15, 35), (30, 14), (7, 35), (19, 34), (41, 37), (17, 17), (0, 30), (5, 40), (37, 19), (10, 30), (5, 8), (29, 6), (0, 13), (14, 3), (6, 33), (7, 17), (24, 11), (28, 10), (17, 29), (14, 0), (31, 25), (33, 26), (1, 39), (40, 27), (12, 2), (12, 31), (7, 28), (29, 22), (16, 22), (41, 10), (30, 37), (1, 4), (3, 0), (35, 28), (3, 6), (14, 39), (35, 10), (17, 38), (34, 12), (40, 1), (24, 12), (21, 31), (35, 14), (15, 36), (30, 12), (21, 33), (24, 25), (35, 31), (19, 22), (33, 28), (29, 17), (31, 39), (31, 17), (15, 14), (40, 6), (13, 25), (35, 2), (4, 16), (20, 20), (11, 13), (1, 7), (27, 34), (20, 22), (17, 25), (0, 6), (5, 28), (1, 20), (29, 3), (7, 16), (27, 31), (22, 25), (36, 19), (40, 16), (36, 12), (11, 25), (28, 16), (32, 28), (33, 39), (8, 7), (30, 1), (23, 22), (1, 0), (34, 4), (31, 11), (34, 34), (0, 15), (13, 8), (7, 32), (7, 24), (13, 26), (12, 16), (20, 16), (30, 15), (2, 12), (8, 25), (15, 28), (32, 27), (1, 9), (14, 35), (26, 16), (26, 34), (4, 14), (16, 8), (41, 3), (29, 16), (30, 32), (15, 13), (39, 10), (38, 29), (37, 36), (14, 10), (4, 13), (9, 35), (22, 26), (5, 29), (5, 1), (5, 17), (30, 8), (5, 35), (12, 36), (13, 15), (22, 21), (28, 21), (5, 14), (33, 12), (26, 23), (2, 36), (24, 39), (9, 22), (38, 7), (32, 33), (26, 2), (41, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 29), (5, 16), (2, 37), (3, 32), (23, 43), (40, 6), (26, 31), (23, 15), (35, 14), (16, 37), (38, 36), (39, 13), (10, 37), (17, 1), (1, 19), (10, 9), (34, 15), (35, 9), (21, 18), (10, 32), (1, 22), (30, 12), (2, 19), (36, 23), (39, 36), (17, 29), (3, 4), (12, 22), (9, 19), (7, 46), (39, 17), (5, 5), (23, 23), (33, 38), (26, 16), (22, 36), (22, 7), (7, 17), (12, 17), (34, 11), (39, 19), (31, 20), (39, 6), (27, 30), (0, 20), (28, 46), (1, 41), (17, 14), (4, 3), (12, 32), (36, 5), (6, 42), (15, 20), (34, 40), (35, 48), (23, 33), (18, 23), (39, 39), (2, 46), (4, 38), (36, 40), (29, 5), (19, 25), (9, 27), (15, 34), (13, 48), (4, 18), (21, 0), (17, 28), (14, 10), (16, 25), (11, 17), (2, 33), (19, 0), (41, 32), (9, 10), (31, 22), (36, 36), (19, 12), (16, 40), (32, 12), (23, 31), (27, 41), (38, 39), (7, 22), (35, 44), (20, 37), (9, 45), (26, 9), (12, 25), (20, 29), (34, 13), (39, 40), (0, 37), (36, 25), (25, 29), (37, 11), (38, 13), (6, 25), (13, 25), (28, 36), (13, 27), (21, 1), (23, 45), (4, 10), (37, 14), (38, 45), (24, 4), (13, 16), (33, 39), (28, 35), (22, 18), (15, 10), (17, 10), (1, 10), (14, 7), (15, 23), (0, 21), (31, 12), (21, 43), (24, 46), (15, 14), (6, 7), (10, 16), (3, 36), (8, 21), (18, 45), (10, 17), (7, 19), (38, 40), (33, 15), (6, 37), (7, 5), (23, 21), (7, 14), (40, 13), (39, 35), (25, 31), (33, 7), (19, 33), (41, 34), (22, 28), (27, 2), (2, 48), (35, 1), (15, 1), (14, 29), (25, 16), (32, 34), (22, 48), (4, 19), (18, 18), (15, 5), (8, 41), (21, 26), (1, 25), (21, 17), (10, 2), (41, 43), (38, 26), (36, 43), (29, 15), (37, 44), (32, 44), (30, 20), (41, 40), (14, 44), (20, 48), (6, 12), (18, 0), (33, 28), (38, 33), (22, 14), (2, 45), (19, 24), (5, 35), (5, 4), (13, 11), (3, 1), (21, 6), (36, 21), (34, 24), (20, 39), (21, 23), (24, 32), (7, 24), (14, 33), (1, 39), (1, 8), (18, 24), (2, 25), (28, 39), (32, 48), (15, 15), (19, 15), (1, 27), (2, 1), (7, 33), (8, 47), (30, 32), (10, 11), (19, 48), (12, 18), (38, 8), (5, 44), (13, 47), (20, 26), (40, 25), (21, 44), (26, 43), (26, 36), (14, 27), (19, 28), (26, 46), (33, 47), (34, 9), (36, 38), (10, 23), (34, 39), (22, 33), (26, 12), (4, 0), (23, 32), (34, 37), (4, 24), (37, 27), (7, 13), (24, 16), (2, 44), (32, 41), (23, 41), (17, 30), (41, 6), (27, 13), (39, 38), (24, 25), (37, 26), (12, 39), (10, 47), (12, 19), (20, 28), (0, 4), (20, 33), (8, 3), (20, 19), (19, 41), (16, 47), (18, 39), (27, 26), (32, 0), (23, 10), (18, 10), (35, 21), (41, 18), (19, 31), (7, 6), (8, 14), (29, 4), (14, 5), (14, 15), (30, 38), (29, 40), (2, 29), (14, 2), (30, 29), (27, 31), (19, 43), (13, 33), (39, 31), (21, 25), (11, 22), (25, 19), (20, 15), (0, 35), (18, 7), (38, 42), (24, 11), (35, 5), (17, 32), (22, 16), (10, 39), (3, 3), (31, 9), (23, 4), (38, 23), (6, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 1), (13, 25), (40, 34), (12, 13), (28, 28), (7, 23), (0, 20), (18, 40), (20, 33), (29, 34), (17, 13), (24, 16), (44, 21), (6, 22), (9, 36), (18, 27), (28, 21), (36, 40), (20, 13), (5, 29), (17, 6), (12, 10), (42, 20), (16, 18), (0, 34), (32, 10), (39, 30), (22, 13), (36, 9), (0, 38), (0, 4), (38, 37), (16, 16), (22, 10), (2, 29), (19, 13), (8, 32), (40, 10), (17, 12), (32, 20), (9, 30), (30, 7), (24, 39), (43, 36), (0, 11), (29, 29), (42, 28), (24, 19), (2, 5), (39, 36), (4, 25), (18, 24), (17, 8), (19, 21), (10, 20), (44, 17), (20, 19), (15, 1), (45, 28), (25, 20), (44, 37), (9, 33), (27, 0), (45, 39), (36, 35), (45, 13), (38, 36), (5, 16), (31, 4), (29, 13), (35, 23), (30, 13), (8, 7), (45, 21), (28, 31), (31, 12), (36, 10), (22, 18), (13, 7), (4, 21), (34, 19), (9, 39), (43, 9), (39, 32), (25, 39), (2, 10), (33, 20), (10, 6), (7, 25), (11, 4), (22, 27), (39, 35), (14, 14), (16, 28), (19, 20), (2, 22), (23, 33), (17, 14), (23, 38), (26, 29), (38, 23), (22, 3), (8, 23), (8, 10), (42, 6), (29, 39), (40, 13), (42, 21), (32, 24), (14, 25), (9, 8), (12, 18), (22, 30), (7, 22), (22, 5), (37, 11), (37, 1), (11, 23), (33, 6), (1, 22), (22, 17), (17, 39), (41, 1), (29, 5), (16, 32), (27, 11), (44, 0), (18, 37), (41, 20), (17, 23), (12, 20), (44, 27), (38, 17), (32, 32), (17, 33), (24, 21), (25, 35), (35, 39), (15, 31), (28, 36), (21, 40), (38, 9), (10, 3), (28, 15), (1, 11), (5, 19), (3, 35), (39, 28), (29, 18), (21, 34), (9, 12), (1, 14), (34, 13), (29, 25), (32, 33), (35, 22), (45, 36), (18, 8), (37, 21), (39, 11), (20, 2), (3, 36), (3, 28), (33, 15), (44, 22), (11, 32), (30, 23), (40, 30), (30, 4), (27, 28), (14, 38), (23, 1), (41, 35), (25, 13), (1, 16), (26, 20), (42, 34), (18, 1), (41, 12), (14, 4), (8, 25), (12, 33), (25, 6), (34, 10), (41, 39), (31, 10), (0, 36), (13, 24), (41, 18), (3, 37), (17, 11), (30, 17), (33, 0), (9, 11), (2, 13), (37, 39), (24, 12), (25, 18), (39, 26), (19, 12), (4, 39), (30, 38), (15, 13), (24, 34), (23, 25), (28, 18), (39, 23), (0, 28), (25, 21), (25, 7), (30, 26), (30, 21), (42, 36), (1, 6), (12, 31), (3, 39), (16, 30), (33, 25), (36, 2), (7, 34), (3, 24), (8, 3), (9, 1), (12, 24), (19, 25), (26, 17), (24, 9), (35, 14), (44, 16), (24, 4), (39, 37), (44, 5), (37, 22), (33, 26), (6, 31), (26, 6), (36, 20), (0, 17), (5, 20), (0, 18), (6, 32), (27, 4), (35, 25), (37, 3), (3, 30), (34, 8), (36, 0), (32, 1), (20, 27), (22, 33), (21, 37), (10, 26), (29, 1), (18, 13), (43, 1), (31, 36), (24, 31), (43, 16), (34, 39), (44, 30), (14, 10), (31, 7), (24, 2), (31, 34), (7, 2), (42, 30), (18, 4), (15, 25), (21, 5), (44, 25), (9, 35), (21, 22), (34, 6), (31, 9), (2, 15), (5, 26), (11, 35), (36, 21), (5, 0), (3, 33), (18, 25), (32, 29), (33, 40), (28, 2), (43, 40), (19, 1), (13, 9), (24, 27), (14, 27), (30, 25), (33, 39), (38, 21), (8, 8), (14, 5), (34, 37), (0, 3), (38, 1), (30, 6), (36, 32), (39, 34), (40, 0), (34, 31), (38, 35), (6, 28), (41, 22), (18, 18), (30, 8), (17, 37), (36, 30), (8, 28), (8, 17), (25, 34), (30, 32), (28, 17), (8, 11), (5, 28), (14, 0), (23, 31), (17, 27), (13, 40), (38, 7), (5, 39), (26, 21), (23, 8), (33, 28), (8, 40), (15, 16), (8, 18), (38, 40), (41, 24), (35, 3), (22, 0), (35, 6), (18, 33), (24, 15), (43, 29), (32, 38), (31, 11), (39, 39), (33, 3), (39, 15), (34, 27), (11, 15), (43, 38), (5, 35), (7, 8), (16, 12), (24, 35), (24, 18), (0, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 46), (37, 18), (12, 46), (19, 20), (33, 17), (13, 2), (23, 48), (3, 22), (10, 20), (33, 18), (45, 44), (6, 29), (30, 7), (37, 34), (38, 46), (8, 44), (7, 21), (40, 18), (1, 37), (29, 16), (40, 17), (2, 46), (35, 29), (34, 3), (32, 42), (5, 13), (25, 16), (45, 19), (37, 36), (45, 17), (12, 38), (29, 9), (15, 30), (13, 34), (37, 14), (4, 7), (19, 9), (38, 25), (42, 43), (31, 40), (12, 36), (48, 47), (7, 0), (44, 46), (23, 11), (31, 18), (46, 6), (21, 46), (13, 11), (36, 26), (8, 25), (3, 37), (23, 24), (31, 31), (1, 11), (40, 15), (20, 23), (14, 21), (42, 7), (7, 17), (33, 9), (14, 36), (37, 32), (13, 43), (10, 27), (25, 25), (20, 38), (27, 21), (19, 29), (44, 20), (35, 12), (26, 8), (30, 41), (36, 40), (20, 37), (16, 23), (16, 0), (36, 23), (27, 41), (32, 5), (44, 29), (32, 29), (41, 15), (14, 12), (22, 35), (36, 27), (6, 24), (42, 34), (10, 48), (15, 26), (16, 34), (42, 44), (28, 47), (15, 3), (6, 15), (17, 9), (39, 5), (38, 26), (9, 36), (3, 12), (17, 29), (24, 35), (0, 35), (26, 28), (16, 29), (38, 14), (38, 10), (28, 31), (17, 42), (39, 25), (41, 5), (45, 37), (37, 23), (38, 32), (48, 6), (16, 21), (18, 40), (11, 9), (23, 30), (23, 21), (14, 25), (20, 16), (26, 19), (39, 27), (12, 35), (43, 45), (16, 44), (10, 7), (42, 48), (0, 6), (31, 47), (27, 44), (5, 0), (31, 34), (23, 44), (37, 25), (26, 7), (44, 6), (43, 23), (23, 38), (3, 32), (44, 44), (46, 46), (43, 34), (37, 15), (15, 9), (12, 15), (6, 38), (44, 0), (39, 36), (37, 26), (48, 8), (3, 43), (15, 29), (5, 10), (8, 21), (6, 47), (6, 5), (1, 32), (23, 14), (2, 4), (32, 24), (21, 0), (3, 41), (9, 13), (41, 23), (46, 15), (39, 15), (47, 26), (17, 32), (23, 5), (39, 38), (42, 8), (34, 24), (19, 26), (7, 3), (34, 47), (28, 27), (22, 33), (15, 34), (9, 6), (42, 30), (19, 41), (0, 9), (19, 21), (36, 17), (40, 8), (45, 28), (3, 30), (16, 46), (24, 19), (10, 29), (31, 44), (45, 16), (24, 40), (27, 47), (27, 20), (36, 35), (9, 25), (43, 14), (1, 46), (46, 31), (40, 27), (24, 32), (2, 25), (28, 43), (29, 12), (1, 41), (23, 4), (48, 40), (37, 9), (15, 4), (34, 32), (11, 12), (30, 25), (1, 28), (11, 41), (0, 34), (9, 23), (32, 2), (44, 16), (31, 15), (14, 39), (39, 28), (26, 41), (46, 35), (26, 4), (14, 2), (31, 27), (6, 43), (46, 30), (19, 8), (31, 43), (46, 18), (21, 28), (40, 45), (13, 0), (45, 36), (6, 11), (22, 7), (14, 3), (7, 42), (5, 32), (6, 27), (11, 4), (24, 3), (18, 35), (13, 30), (26, 17), (33, 29), (7, 34), (27, 37), (11, 16), (47, 13), (40, 24), (44, 42), (9, 17), (5, 43), (39, 2), (14, 0), (37, 48), (29, 28), (8, 9), (24, 26), (17, 27), (5, 7), (31, 20), (16, 9), (5, 35), (41, 19), (44, 23), (32, 32), (22, 18), (34, 12), (30, 28), (6, 10), (45, 32), (37, 43), (39, 12), (23, 16), (11, 45), (16, 24), (39, 18), (8, 47), (2, 43), (32, 41), (35, 8), (14, 43), (37, 42), (33, 4), (20, 19), (17, 7), (37, 4), (45, 11), (3, 17), (4, 19), (3, 35), (7, 20), (18, 5), (15, 11), (31, 5), (42, 14), (8, 29), (18, 20), (39, 10), (9, 20), (16, 43), (10, 31), (38, 35), (10, 3), (30, 32), (26, 35), (35, 20), (35, 47), (33, 34), (47, 28), (33, 20), (12, 20), (8, 11), (11, 26), (26, 10), (40, 30), (27, 8), (19, 43), (8, 35), (39, 8), (7, 36), (4, 35), (11, 13), (35, 42), (45, 33), (46, 23), (17, 13), (33, 41), (41, 45), (13, 16), (10, 34), (30, 12), (13, 9), (48, 41), (27, 1), (7, 9), (31, 8), (45, 47), (5, 22), (22, 19), (6, 12), (8, 22), (5, 5), (33, 28), (32, 40), (17, 37), (30, 18), (36, 7), (48, 0), (2, 13), (38, 42), (35, 16), (1, 40), (21, 9), (15, 16), (7, 32), (46, 10), (32, 27), (47, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 44), (35, 10), (48, 17), (32, 27), (15, 19), (48, 20), (20, 10), (46, 2), (12, 20), (36, 6), (29, 23), (37, 22), (17, 15), (24, 38), (19, 11), (20, 18), (21, 25), (0, 35), (39, 7), (9, 31), (44, 29), (28, 27), (47, 18), (45, 3), (4, 34), (17, 31), (38, 4), (29, 27), (6, 9), (15, 38), (7, 10), (16, 38), (24, 14), (29, 26), (20, 43), (24, 34), (27, 8), (44, 22), (10, 5), (13, 20), (5, 38), (13, 25), (11, 42), (38, 43), (23, 16), (14, 40), (10, 17), (32, 13), (37, 43), (24, 35), (48, 16), (40, 41), (3, 43), (7, 17), (35, 22), (47, 5), (41, 8), (1, 14), (47, 21), (44, 32), (2, 5), (14, 20), (13, 8), (46, 17), (48, 11), (10, 16), (35, 12), (31, 31), (31, 24), (47, 8), (32, 32), (27, 11), (23, 42), (19, 25), (42, 38), (35, 36), (33, 41), (33, 3), (8, 7), (22, 0), (35, 28), (31, 29), (31, 3), (2, 7), (40, 19), (1, 28), (27, 44), (8, 24), (27, 40), (23, 11), (2, 11), (45, 23), (41, 29), (15, 17), (39, 4), (26, 12), (43, 24), (28, 36), (46, 0), (42, 6), (0, 32), (16, 30), (11, 25), (8, 40), (15, 6), (22, 10), (33, 39), (24, 3), (2, 41), (28, 22), (2, 4), (38, 32), (0, 22), (8, 0), (17, 14), (28, 5), (11, 29), (47, 13), (41, 33), (14, 1), (24, 29), (47, 7), (36, 33), (24, 10), (14, 5), (7, 1), (0, 11), (31, 35), (43, 12), (35, 5), (25, 19), (40, 23), (45, 44), (39, 28), (9, 40), (34, 5), (44, 38), (41, 38), (44, 6), (35, 14), (5, 27), (25, 20), (22, 39), (13, 5), (19, 12), (47, 22), (24, 30), (45, 22), (19, 15), (35, 44), (16, 5), (10, 10), (7, 31), (24, 36), (25, 42), (26, 8), (16, 7), (22, 34), (35, 24), (33, 19), (34, 21), (10, 15), (32, 18), (5, 25), (40, 29), (40, 39), (32, 33), (46, 10), (46, 42), (37, 26), (4, 14), (21, 41), (15, 9), (7, 38), (1, 15), (35, 42), (0, 24), (7, 7), (1, 43), (47, 31), (10, 3), (45, 19), (18, 4), (15, 14), (1, 37), (29, 25), (32, 9), (7, 41), (18, 24), (1, 40), (3, 29), (16, 22), (28, 17), (48, 34), (5, 6), (48, 5), (34, 25), (15, 27), (24, 33), (2, 9), (5, 33), (41, 42), (0, 21), (44, 7), (29, 6), (42, 44), (30, 11), (21, 14), (38, 14), (0, 9), (11, 6), (41, 10), (8, 15), (14, 39), (36, 10), (34, 38), (37, 27), (34, 30), (2, 42), (1, 42), (44, 23), (27, 34), (9, 4), (25, 35), (40, 18), (0, 42), (43, 11), (28, 31), (44, 10), (46, 4), (32, 41), (48, 18), (10, 32), (38, 19), (0, 18), (9, 28), (20, 39), (48, 2), (43, 18), (29, 18), (18, 25), (37, 30), (16, 42), (21, 29), (10, 28), (31, 18), (43, 10), (29, 5), (6, 43), (5, 8), (1, 41), (37, 18), (13, 31), (12, 19), (4, 21), (12, 41), (48, 24), (44, 43), (47, 34), (20, 25), (41, 4), (34, 8), (34, 31), (5, 3), (1, 19), (16, 40), (35, 8), (17, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 15), (38, 30), (29, 9), (35, 37), (42, 17), (6, 8), (39, 25), (5, 11), (4, 32), (4, 22), (26, 22), (39, 0), (32, 19), (42, 23), (4, 26), (32, 38), (24, 24), (31, 11), (18, 16), (31, 8), (31, 27), (29, 6), (19, 12), (38, 3), (9, 14), (21, 35), (41, 32), (8, 33), (29, 29), (32, 22), (35, 25), (37, 28), (7, 30), (14, 14), (5, 14), (8, 14), (14, 2), (36, 6), (3, 24), (9, 34), (33, 9), (34, 37), (25, 32), (9, 27), (32, 12), (39, 7), (12, 13), (17, 16), (21, 13), (35, 39), (9, 38), (15, 27), (15, 38), (8, 34), (9, 4), (23, 9), (17, 19), (20, 19), (26, 14), (22, 16), (10, 4), (27, 31), (19, 27), (3, 4), (7, 31), (25, 26), (19, 26), (11, 16), (22, 11), (0, 28), (20, 24), (28, 31), (9, 9), (5, 26), (37, 20), (6, 28), (7, 16), (16, 15), (28, 21), (13, 17), (9, 33), (39, 22), (31, 10), (1, 14), (36, 16), (14, 1), (20, 10), (26, 26), (12, 3), (0, 10), (41, 19), (28, 16), (19, 7), (28, 4), (20, 17), (35, 19), (21, 34), (30, 19), (26, 35), (29, 34), (26, 24), (0, 17), (0, 5), (39, 12), (2, 24), (10, 19), (20, 9), (2, 29), (14, 5), (27, 2), (1, 21), (30, 34), (38, 16), (8, 16), (23, 12), (34, 28), (9, 5), (33, 15), (10, 5), (15, 29), (14, 13), (1, 11), (22, 21), (29, 32), (1, 12), (17, 27), (12, 35), (36, 0), (35, 3), (22, 12), (20, 36), (5, 17), (19, 30), (13, 28), (11, 33), (6, 36), (15, 36), (30, 35), (22, 35), (11, 29), (12, 12), (6, 31), (34, 17), (24, 8), (29, 36), (6, 5), (29, 12), (26, 15), (35, 31), (21, 27), (38, 10), (26, 3), (16, 5), (13, 5), (9, 28), (26, 4), (31, 22), (16, 37), (16, 16), (4, 37), (36, 26), (18, 34), (36, 24), (36, 29), (39, 39), (12, 22), (33, 24), (37, 35), (0, 14), (9, 29), (23, 19), (16, 12), (25, 12), (28, 34), (15, 3), (42, 30), (2, 20), (31, 38), (11, 4), (35, 17), (37, 29), (20, 26), (40, 9), (1, 35), (24, 12), (16, 13), (33, 22), (29, 23), (4, 1), (14, 23), (22, 26), (21, 32), (42, 14), (34, 36), (26, 2), (27, 0), (2, 12), (14, 31), (19, 36), (0, 32), (19, 16), (36, 20), (12, 20), (15, 9), (5, 36), (20, 28), (42, 26), (17, 11), (38, 32), (2, 30), (0, 29), (33, 20), (41, 6), (33, 35), (34, 4), (17, 7), (7, 8), (21, 7), (0, 9), (24, 5), (7, 26), (32, 5), (18, 3), (4, 23), (15, 18), (16, 25), (17, 20), (24, 9), (37, 16), (12, 17), (17, 12), (27, 10), (14, 8), (42, 4), (9, 19), (31, 36), (13, 11), (11, 31), (23, 38), (15, 37), (27, 8), (5, 4), (22, 6), (11, 14), (24, 22), (26, 0), (29, 2), (11, 38), (41, 28), (18, 7), (21, 6), (29, 25), (12, 16), (14, 18), (36, 31), (9, 8), (26, 1), (9, 36), (6, 18), (10, 25), (28, 29), (36, 5), (27, 27), (13, 24), (9, 20), (7, 25), (13, 19), (8, 8), (4, 11), (32, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 26), (43, 1), (6, 35), (17, 40), (28, 22), (18, 8), (41, 39), (9, 42), (21, 34), (22, 30), (17, 45), (30, 4), (0, 44), (28, 8), (24, 31), (24, 4), (33, 10), (20, 32), (24, 13), (38, 20), (1, 19), (14, 33), (14, 18), (14, 1), (1, 13), (29, 25), (34, 4), (6, 7), (20, 36), (16, 8), (10, 18), (19, 20), (25, 28), (35, 22), (0, 23), (14, 31), (36, 17), (31, 26), (31, 30), (34, 21), (37, 26), (36, 36), (35, 0), (27, 21), (32, 45), (33, 36), (33, 43), (20, 30), (9, 20), (33, 30), (27, 37), (31, 32), (1, 36), (9, 24), (38, 28), (36, 46), (33, 6), (43, 8), (38, 10), (11, 30), (12, 27), (19, 39), (33, 34), (18, 27), (9, 40), (23, 6), (28, 30), (40, 45), (7, 12), (26, 44), (1, 4), (21, 43), (12, 32), (13, 22), (23, 21), (11, 42), (35, 30), (29, 4), (25, 14), (35, 5), (2, 45), (37, 20), (30, 14), (16, 26), (20, 10), (2, 26), (11, 20), (18, 23), (41, 28), (35, 13), (23, 34), (17, 46), (14, 35), (39, 15), (19, 17), (35, 39), (15, 34), (25, 4), (6, 45), (43, 16), (7, 4), (37, 17), (1, 3), (0, 40), (12, 14), (39, 2), (9, 30), (13, 0), (25, 5), (38, 37), (7, 3), (43, 13), (38, 31), (3, 41), (36, 22), (19, 34), (39, 42), (4, 32), (17, 24), (34, 7), (4, 33), (43, 0), (18, 19), (33, 33), (34, 17), (30, 9), (39, 46), (21, 19), (41, 26), (31, 15), (40, 41), (13, 16), (27, 27), (43, 40), (38, 4), (11, 10), (24, 20), (35, 18), (23, 26), (43, 42), (17, 39), (41, 30), (40, 20), (25, 29), (14, 27), (13, 44), (27, 42), (14, 19), (5, 8), (7, 35), (16, 6), (15, 17), (13, 27), (25, 2), (28, 24), (41, 6), (7, 45), (36, 23), (9, 45), (34, 12), (36, 42), (17, 31), (38, 21), (9, 19), (16, 7), (17, 11), (36, 26), (22, 32), (17, 5), (11, 22), (13, 36), (37, 28), (37, 9), (41, 1), (17, 21), (26, 1), (29, 31), (5, 45), (24, 9), (29, 33), (33, 38), (42, 34), (17, 14), (2, 34), (24, 12), (31, 1), (17, 8), (8, 21), (8, 40), (29, 12), (37, 12), (37, 37), (40, 17), (10, 7), (21, 3), (29, 35), (0, 32), (37, 34), (41, 3), (23, 13), (4, 11), (32, 6), (23, 23), (36, 39), (17, 12), (2, 20), (2, 43), (43, 33), (7, 9), (40, 32), (18, 2), (4, 45), (38, 2), (10, 27), (2, 10), (27, 10), (23, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 38), (26, 39), (38, 42), (38, 18), (19, 3), (14, 7), (8, 34), (43, 9), (20, 9), (13, 41), (24, 29), (46, 32), (29, 17), (45, 43), (22, 9), (28, 19), (5, 6), (18, 15), (6, 17), (24, 34), (32, 6), (39, 9), (5, 32), (31, 39), (10, 21), (32, 2), (42, 43), (17, 32), (22, 10), (20, 23), (45, 1), (24, 2), (11, 11), (30, 0), (31, 25), (43, 20), (12, 1), (9, 6), (29, 15), (10, 0), (19, 9), (45, 19), (0, 8), (3, 46), (25, 36), (38, 19), (11, 16), (23, 41), (37, 3), (19, 12), (20, 11), (1, 6), (4, 31), (13, 33), (24, 28), (31, 0), (26, 2), (6, 14), (42, 21), (36, 19), (2, 42), (4, 37), (14, 2), (8, 42), (2, 32), (16, 36), (6, 25), (29, 37), (5, 0), (28, 41), (1, 31), (9, 4), (10, 17), (46, 36), (18, 38), (9, 27), (26, 4), (26, 22), (10, 29), (11, 10), (16, 17), (22, 17), (16, 47), (45, 18), (6, 45), (12, 22), (30, 18), (38, 20), (14, 0), (2, 47), (2, 2), (9, 25), (30, 40), (23, 11), (23, 13), (34, 6), (4, 32), (15, 29), (26, 21), (8, 15), (22, 20), (42, 29), (15, 23), (19, 26), (41, 8), (9, 18), (40, 11), (39, 25), (23, 8), (20, 5), (42, 27), (6, 37), (35, 40), (26, 12), (35, 32), (40, 4), (32, 28), (27, 11), (17, 30), (41, 2), (17, 2), (17, 43), (22, 26), (40, 3), (5, 24), (3, 27), (20, 38), (9, 36), (31, 33), (12, 27), (0, 29), (19, 46), (37, 11), (16, 34), (3, 35), (34, 46), (41, 40), (30, 19), (42, 11), (27, 13), (42, 33), (14, 36), (34, 36), (30, 22), (11, 19), (44, 21), (42, 39), (12, 35), (24, 17), (12, 13), (43, 6), (10, 9), (16, 18), (11, 22), (4, 26), (0, 24), (41, 20), (21, 37), (31, 36), (15, 30), (8, 16), (33, 34), (0, 27), (23, 15), (7, 45), (34, 47), (24, 10), (17, 23), (18, 30), (38, 27), (17, 15), (2, 7), (43, 5), (29, 32), (22, 2), (42, 31), (8, 5), (30, 12), (18, 10), (20, 17), (7, 37), (7, 2), (21, 7), (15, 35), (18, 11), (32, 34), (23, 7), (0, 44), (38, 38), (13, 28), (46, 8), (36, 7), (19, 38), (22, 8), (21, 33), (6, 31), (14, 9), (45, 10), (34, 37), (35, 36), (27, 47), (37, 18), (18, 24), (20, 27), (8, 31), (44, 41), (33, 29), (32, 8), (42, 7), (16, 8), (0, 4), (39, 26), (8, 35), (12, 33), (8, 46), (7, 10), (14, 12), (11, 2), (37, 27), (8, 23), (18, 27), (11, 45), (29, 24), (6, 35), (46, 9), (16, 37), (12, 2), (44, 10), (12, 26), (14, 13), (39, 12), (46, 24), (29, 27), (8, 29), (19, 21), (42, 42), (13, 9), (19, 10), (14, 38), (22, 33), (38, 40), (27, 26), (16, 23), (9, 43), (1, 5), (41, 10), (20, 36), (23, 5), (13, 8), (3, 14), (15, 2), (39, 33), (14, 27), (7, 25), (10, 2), (0, 15), (1, 21), (8, 44), (4, 21), (15, 18), (26, 36), (24, 44), (18, 31), (1, 18), (31, 26), (43, 23), (22, 35), (1, 47), (14, 20), (12, 0), (37, 15), (25, 45), (25, 4), (17, 44), (11, 15), (33, 45), (7, 34), (33, 12), (30, 34), (35, 30), (46, 1), (35, 3), (28, 2), (2, 34), (13, 1), (18, 28), (41, 7), (38, 17), (14, 35), (11, 26), (14, 26), (3, 47), (17, 19), (7, 22), (33, 47), (32, 39), (7, 15), (40, 16), (3, 39), (16, 28), (12, 3), (46, 34), (16, 6), (38, 33), (18, 32), (43, 16), (1, 36), (7, 12), (45, 21), (34, 45), (45, 3), (7, 39), (14, 40), (2, 25), (45, 29), (5, 17), (17, 41), (10, 8), (25, 23), (10, 38), (0, 25), (0, 12), (33, 35), (1, 34), (42, 9), (36, 44), (36, 31), (7, 32), (35, 11), (40, 19), (19, 8), (32, 32), (38, 36), (26, 42), (42, 36), (14, 4), (25, 44), (43, 10), (8, 22), (40, 22), (39, 22), (21, 5), (32, 1), (39, 10), (33, 38), (19, 20), (4, 10), (22, 43), (24, 8), (0, 37), (10, 3), (1, 22), (46, 26), (40, 21), (15, 6), (34, 26), (10, 44), (24, 30), (19, 28), (3, 15), (13, 12), (40, 45), (0, 38), (7, 30), (38, 5), (46, 10), (37, 21), (44, 34), (25, 2), (15, 12), (34, 15), (44, 19), (26, 15), (33, 46), (44, 36), (20, 44), (26, 11), (38, 21), (20, 13), (33, 2), (37, 13), (36, 32), (30, 45), (40, 40), (37, 37), (9, 34), (29, 45), (40, 39), (20, 14), (28, 14), (8, 39), (15, 0), (31, 19), (0, 31), (2, 9), (27, 12), (9, 15), (23, 44), (25, 11), (8, 7), (36, 9), (6, 38), (46, 19), (35, 20), (13, 27), (7, 23), (34, 16), (38, 10), (42, 16), (39, 46), (34, 3), (14, 3), (1, 35), (30, 36), (1, 23), (19, 0), (24, 25), (33, 39), (43, 42), (2, 35), (37, 23), (14, 28), (12, 15), (0, 30), (5, 36), (42, 24), (1, 15), (35, 37), (1, 46), (10, 34), (6, 19), (26, 9), (36, 39), (22, 15), (34, 25), (22, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 11), (31, 12), (48, 22), (6, 8), (29, 30), (3, 27), (32, 38), (37, 42), (40, 42), (15, 24), (21, 26), (27, 8), (27, 29), (41, 1), (27, 24), (38, 3), (27, 41), (30, 27), (17, 7), (18, 2), (34, 1), (12, 3), (41, 0), (1, 41), (8, 31), (2, 12), (7, 7), (20, 10), (25, 2), (13, 37), (26, 10), (36, 27), (41, 24), (47, 8), (41, 40), (38, 34), (3, 37), (32, 7), (6, 1), (25, 34), (45, 2), (29, 9), (1, 15), (3, 24), (9, 16), (24, 9), (26, 23), (16, 8), (48, 32), (22, 8), (41, 23), (28, 34), (19, 28), (42, 37), (42, 15), (41, 18), (9, 39), (2, 19), (16, 31), (20, 41), (42, 25), (32, 5), (47, 9), (32, 35), (30, 25), (7, 34), (23, 40), (29, 23), (2, 40), (3, 19), (28, 40), (23, 42), (38, 31), (5, 32), (44, 8), (44, 6), (23, 30), (38, 10), (33, 42), (18, 34), (20, 24), (13, 4), (20, 40), (11, 32), (28, 13), (40, 36), (44, 13), (14, 27), (39, 29), (8, 11), (41, 14), (4, 18), (40, 12), (5, 25), (18, 37), (45, 11), (5, 13), (29, 0), (8, 34), (1, 5), (6, 22), (11, 17), (31, 33), (27, 1), (48, 2), (41, 37), (21, 36), (44, 37), (1, 18), (5, 11), (13, 24), (30, 17), (32, 20), (46, 1), (15, 37), (23, 10), (43, 10), (12, 12), (22, 2), (17, 0), (15, 28), (18, 22), (4, 26), (32, 4), (17, 20), (38, 12), (33, 35), (11, 15), (40, 10), (44, 33), (48, 30), (14, 33), (35, 3), (43, 2), (46, 20), (24, 26), (45, 6), (11, 37), (42, 34), (30, 20), (25, 32), (43, 41), (36, 4), (45, 39), (37, 17), (35, 14), (28, 28), (1, 30), (44, 18), (0, 11), (14, 17), (45, 4), (23, 2), (36, 28), (42, 40), (22, 34), (45, 26), (21, 5), (2, 9), (23, 0), (42, 4), (43, 15), (17, 32), (7, 26), (5, 6), (8, 7), (16, 0), (38, 13), (19, 33), (31, 1), (38, 25), (33, 36), (43, 28), (12, 1), (8, 10), (33, 17), (32, 17), (8, 30), (47, 13), (44, 28), (39, 42), (25, 17), (15, 42), (25, 24), (7, 25), (46, 32), (9, 9), (16, 6), (9, 6), (34, 24), (3, 42), (46, 36), (34, 31), (18, 18), (39, 11), (31, 0), (22, 13), (23, 5), (25, 5), (33, 14), (28, 6), (38, 27), (41, 11), (29, 37), (33, 7), (16, 39), (34, 12), (33, 18), (6, 24), (4, 19), (29, 3), (17, 10), (21, 32), (38, 36), (36, 7), (39, 28), (15, 36), (27, 7), (6, 19), (48, 21), (14, 28), (9, 28), (33, 23), (34, 19), (31, 39), (15, 13), (25, 21), (43, 4), (5, 36), (28, 15), (32, 24), (20, 30), (33, 1), (19, 5), (41, 7), (35, 31), (45, 1), (43, 0), (43, 27), (47, 33), (37, 5), (38, 15), (11, 35), (10, 0), (37, 41), (31, 27), (5, 1), (32, 34), (13, 18), (16, 38), (24, 37), (17, 28), (22, 36), (8, 14), (45, 16), (21, 31), (48, 13), (15, 16), (13, 10), (7, 38), (15, 14), (44, 40), (20, 17), (36, 29), (6, 34), (18, 14), (48, 25), (27, 13), (46, 18), (37, 23), (22, 19), (23, 28), (30, 42), (14, 8), (45, 41), (32, 21), (8, 23), (11, 23), (19, 24), (10, 19), (4, 32), (18, 32), (19, 4), (16, 5), (40, 32), (10, 6), (27, 42), (5, 31), (28, 25), (31, 13), (6, 35), (5, 21), (44, 25), (2, 37), (0, 8), (17, 2), (13, 31), (37, 13), (7, 32), (40, 28), (9, 13), (0, 13), (18, 28), (46, 14), (34, 16), (22, 24), (22, 31), (28, 37), (30, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (19, 31), (8, 28), (37, 4), (33, 7), (12, 30), (26, 22), (40, 11), (24, 44), (28, 1), (38, 39), (37, 26), (42, 23), (25, 27), (19, 39), (17, 7), (46, 1), (38, 1), (17, 2), (25, 28), (43, 3), (3, 5), (33, 1), (21, 3), (8, 10), (18, 6), (42, 18), (14, 45), (21, 28), (42, 41), (22, 27), (2, 6), (38, 44), (34, 44), (44, 31), (31, 18), (44, 30), (10, 8), (47, 15), (11, 40), (31, 28), (43, 15), (2, 15), (36, 5), (34, 43), (22, 40), (38, 35), (13, 28), (33, 36), (16, 27), (24, 21), (8, 8), (46, 19), (1, 38), (25, 36), (45, 11), (31, 21), (22, 36), (30, 43), (38, 32), (7, 45), (44, 18), (20, 22), (18, 20), (29, 15), (14, 10), (31, 17), (8, 21), (12, 26), (22, 33), (28, 14), (43, 30), (18, 5), (20, 44), (6, 41), (9, 29), (44, 38), (26, 31), (26, 29), (5, 5), (7, 22), (13, 42), (8, 17), (21, 29), (47, 18), (16, 5), (27, 40), (0, 39), (39, 2), (22, 11), (0, 22), (6, 19), (27, 41), (11, 15), (25, 40), (39, 25), (25, 39), (29, 17), (47, 23), (18, 2), (8, 15), (7, 31), (28, 10), (14, 34), (11, 34), (26, 6), (28, 9), (22, 43), (37, 22), (38, 27), (36, 10), (12, 27), (17, 1), (13, 34), (31, 24), (7, 0), (47, 44), (5, 13), (31, 31), (9, 13), (37, 30), (14, 2), (8, 20), (34, 11), (41, 11), (25, 1), (2, 35), (29, 2), (18, 19), (47, 21), (46, 5), (9, 11), (38, 42), (1, 43), (23, 31), (38, 10), (44, 8), (27, 10), (16, 43), (34, 32), (40, 3), (8, 26), (23, 34), (11, 42), (20, 27), (17, 30), (16, 4), (1, 17), (16, 33), (37, 9), (17, 34), (10, 14), (19, 32), (42, 19), (24, 31), (27, 39), (44, 22), (21, 13), (37, 0), (44, 26), (16, 42), (7, 13), (1, 1), (44, 3), (40, 0), (19, 13), (41, 42), (7, 35), (39, 42), (1, 11), (7, 19), (28, 20), (1, 7), (36, 29), (10, 44), (44, 34), (39, 33), (20, 14), (47, 37), (45, 15), (19, 33), (12, 10), (12, 35), (11, 24), (7, 5), (33, 32), (24, 43), (39, 3), (43, 23), (26, 1), (7, 26), (36, 45), (8, 30), (1, 31), (38, 31), (34, 39), (22, 15), (2, 39), (26, 5), (19, 22), (31, 10), (37, 24), (8, 0), (33, 8), (8, 31), (33, 40), (9, 34), (5, 26), (0, 38), (33, 29), (15, 39), (31, 30), (18, 40), (21, 10), (33, 9), (45, 40), (36, 11), (24, 42), (44, 1), (5, 35), (21, 32), (1, 18), (47, 0), (35, 32), (23, 35), (8, 36), (14, 20), (15, 45), (14, 36), (42, 26), (18, 17), (13, 6), (6, 5), (31, 9), (27, 34), (33, 2), (32, 37), (3, 1), (4, 28), (42, 28), (14, 19), (40, 34), (28, 22), (6, 13), (18, 30), (7, 15), (41, 4), (38, 4), (8, 22), (20, 34), (15, 8), (19, 38), (3, 38), (38, 43), (15, 36), (42, 16), (27, 5), (10, 34), (24, 32), (30, 24), (27, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 20), (40, 16), (2, 27), (6, 43), (9, 43), (37, 3), (41, 34), (31, 38), (15, 7), (3, 34), (13, 23), (23, 41), (3, 0), (7, 46), (29, 2), (39, 40), (41, 35), (39, 25), (12, 35), (37, 38), (31, 16), (41, 41), (24, 2), (16, 22), (14, 33), (36, 12), (10, 2), (20, 1), (29, 19), (4, 33), (34, 35), (33, 39), (2, 32), (25, 31), (38, 21), (37, 22), (11, 19), (33, 0), (33, 38), (4, 30), (2, 2), (10, 46), (11, 4), (27, 29), (20, 24), (13, 8), (22, 6), (15, 9), (21, 45), (2, 46), (21, 36), (41, 36), (18, 1), (9, 14), (39, 24), (6, 27), (0, 45), (29, 12), (19, 43), (33, 28), (29, 45), (34, 42), (21, 5), (14, 47), (25, 40), (19, 46), (13, 41), (30, 43), (21, 39), (1, 42), (28, 35), (13, 44), (16, 45), (33, 22), (17, 9), (26, 33), (35, 44), (34, 4), (6, 40), (15, 18), (27, 31), (32, 14), (37, 25), (5, 8), (30, 35), (38, 18), (32, 43), (3, 20), (37, 6), (8, 19), (41, 38), (10, 23), (35, 0), (39, 10), (4, 39), (34, 21), (24, 33), (31, 0), (30, 46), (31, 44), (25, 8), (12, 29), (4, 14), (2, 14), (25, 16), (33, 47), (26, 44), (1, 2), (34, 38), (28, 22), (25, 2), (18, 25), (39, 15), (13, 12), (36, 16), (3, 8), (27, 15), (13, 4), (15, 0), (19, 36), (5, 43), (35, 9), (29, 6), (5, 0), (41, 13), (39, 34), (12, 31), (17, 2), (40, 20), (20, 22), (27, 43), (23, 33), (5, 7), (16, 3), (9, 20), (31, 36), (13, 6), (1, 33), (14, 6), (19, 18), (11, 6), (31, 6), (1, 18), (41, 32), (27, 22), (17, 35), (0, 21), (10, 21), (10, 20), (5, 19), (19, 23), (17, 47), (32, 1), (40, 21), (8, 45), (39, 37), (9, 15), (39, 9), (29, 16), (11, 21), (29, 13), (36, 47), (19, 8), (8, 18), (21, 8), (19, 19), (2, 6), (17, 7), (24, 6), (17, 16), (39, 45), (38, 6), (14, 4), (15, 4), (25, 44), (4, 46), (22, 10), (19, 21), (40, 35), (35, 19), (10, 13), (5, 17), (35, 3), (37, 47), (30, 34), (18, 8), (37, 11), (36, 45), (7, 38), (25, 3), (32, 37), (39, 41), (23, 4), (5, 41), (41, 45), (26, 6), (31, 28), (30, 14), (35, 15), (38, 10), (27, 12), (0, 42), (35, 6), (35, 21), (1, 35), (24, 29), (33, 42), (22, 5), (31, 10), (36, 1), (34, 26), (14, 3), (35, 14), (23, 37), (39, 2), (37, 20), (1, 7), (16, 18), (15, 45), (33, 2), (35, 39), (24, 47), (22, 40), (9, 30), (16, 26), (10, 12), (30, 7), (33, 6), (25, 0), (38, 29), (5, 20), (17, 24), (19, 10), (20, 18), (17, 39), (24, 39), (32, 8), (24, 9), (6, 23), (0, 41), (1, 32), (27, 13), (40, 44), (33, 44), (18, 30), (35, 33), (26, 32), (17, 37), (37, 44), (9, 9), (39, 5), (1, 46), (31, 43), (15, 32), (6, 18), (3, 24), (32, 19), (13, 43), (1, 23), (21, 14), (20, 2), (31, 12), (32, 24), (14, 11), (18, 12), (3, 22), (26, 27), (10, 4), (28, 20), (1, 13), (15, 24), (20, 26), (31, 23), (23, 31), (15, 38), (9, 8), (6, 29), (31, 7), (2, 11), (37, 14), (15, 36), (20, 16), (0, 44), (16, 31), (21, 1), (39, 29), (36, 42), (37, 5), (33, 20), (33, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 41), (21, 22), (6, 2), (11, 11), (2, 4), (35, 38), (1, 25), (22, 12), (18, 16), (20, 43), (30, 45), (2, 38), (13, 7), (8, 43), (16, 22), (2, 37), (1, 45), (28, 40), (6, 14), (39, 34), (31, 36), (30, 21), (23, 34), (30, 34), (3, 16), (13, 1), (33, 33), (23, 11), (39, 30), (16, 24), (4, 44), (10, 42), (9, 29), (27, 42), (22, 3), (24, 16), (12, 33), (30, 5), (7, 0), (0, 25), (6, 30), (2, 42), (4, 4), (26, 21), (27, 17), (35, 27), (16, 32), (2, 5), (33, 2), (41, 26), (11, 2), (35, 28), (14, 45), (21, 30), (23, 0), (0, 3), (30, 10), (11, 17), (0, 5), (35, 15), (32, 39), (37, 3), (36, 13), (0, 20), (30, 23), (36, 20), (35, 31), (4, 1), (37, 26), (25, 22), (32, 13), (12, 19), (28, 1), (17, 40), (38, 5), (29, 3), (27, 13), (19, 0), (15, 26), (19, 21), (0, 37), (32, 44), (14, 2), (16, 4), (30, 0), (41, 34), (6, 22), (33, 4), (41, 5), (7, 32), (24, 38), (1, 29), (38, 19), (14, 26), (3, 25), (10, 24), (36, 4), (21, 1), (37, 7), (17, 10), (31, 17), (0, 19), (5, 14), (34, 24), (12, 11), (23, 19), (22, 10), (32, 3), (31, 13), (33, 12), (5, 2), (1, 33), (12, 15), (2, 29), (16, 5), (31, 27), (8, 9), (30, 19), (33, 25), (6, 31), (27, 22), (25, 39), (16, 16), (15, 24), (8, 44), (37, 38), (1, 18), (8, 3), (32, 31), (30, 9), (4, 24), (4, 8), (39, 16), (11, 42), (32, 1), (15, 4), (7, 30), (36, 34), (9, 33), (15, 15), (17, 39), (15, 34), (25, 43), (31, 2), (17, 34), (40, 34), (18, 3), (38, 38), (8, 13), (11, 10), (24, 7), (19, 39), (29, 27), (5, 23), (32, 41), (13, 34), (16, 34), (14, 19), (10, 5), (26, 18), (36, 28), (10, 7), (0, 26), (13, 33), (1, 43), (37, 37), (36, 22), (5, 38), (8, 15), (20, 38), (3, 19), (24, 3), (38, 21), (10, 19), (2, 40), (32, 4), (23, 28), (37, 34), (14, 44), (6, 15), (34, 11), (38, 6), (15, 11), (4, 26), (21, 41), (0, 27), (4, 12), (1, 31), (8, 23), (31, 34), (36, 26), (23, 35), (38, 28), (37, 0), (9, 44), (21, 29), (20, 4), (16, 38), (15, 43), (24, 45), (29, 6), (38, 10), (0, 24), (10, 28), (31, 45), (36, 30), (36, 21), (31, 25), (9, 31), (22, 34), (19, 29), (23, 13), (29, 22), (40, 44), (2, 9), (24, 8), (15, 37), (10, 12), (39, 25), (22, 8), (23, 40), (18, 24), (11, 1), (30, 6), (18, 28), (26, 26), (38, 39), (0, 38), (17, 14), (31, 42), (10, 4), (34, 13), (10, 21), (37, 15), (11, 18), (5, 37), (11, 5), (15, 21), (29, 39), (40, 29), (28, 10), (20, 16), (41, 33), (37, 18), (6, 17), (21, 45), (33, 44), (24, 14), (4, 10), (8, 7), (18, 23), (21, 39), (41, 13), (31, 35), (21, 17), (22, 36), (14, 29), (17, 16), (32, 30), (37, 28), (32, 29), (11, 21), (12, 5), (22, 15), (22, 7), (21, 15), (7, 10), (31, 3), (34, 39), (13, 26), (39, 3), (19, 2), (32, 15), (21, 14), (20, 27), (5, 32), (13, 42), (19, 38), (23, 2), (16, 18), (23, 3), (28, 30), (33, 31), (1, 42), (7, 2), (26, 14), (18, 35), (3, 30), (10, 41), (13, 36), (33, 19), (25, 37), (19, 12), (34, 31), (25, 42), (28, 42), (11, 40), (6, 23), (29, 16), (1, 1), (19, 7), (29, 31), (25, 6), (12, 12), (24, 10), (28, 28), (12, 14), (41, 2), (39, 12), (2, 36), (16, 28), (31, 40), (22, 1), (33, 3), (2, 26), (15, 29), (14, 16), (33, 28), (8, 29), (10, 35), (5, 40), (7, 12), (3, 33), (25, 11), (4, 38), (3, 7), (10, 44), (21, 23), (36, 16), (7, 44), (30, 22), (27, 20), (11, 24), (17, 19), (0, 36), (18, 12), (0, 40), (33, 26), (18, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (48, 0), (19, 46), (14, 14), (25, 24), (10, 5), (15, 40), (33, 24), (11, 16), (4, 23), (35, 13), (46, 26), (26, 45), (35, 21), (47, 18), (38, 37), (38, 46), (32, 26), (18, 11), (47, 24), (47, 43), (1, 33), (47, 40), (4, 43), (36, 2), (22, 37), (25, 11), (30, 18), (14, 15), (16, 30), (40, 5), (15, 18), (5, 12), (42, 47), (5, 6), (47, 42), (26, 7), (37, 1), (0, 34), (0, 11), (14, 8), (24, 26), (3, 14), (6, 12), (31, 40), (41, 5), (13, 1), (8, 17), (27, 2), (37, 4), (36, 25), (18, 16), (19, 41), (38, 31), (5, 32), (33, 1), (7, 34), (18, 8), (13, 13), (30, 27), (7, 27), (12, 28), (8, 4), (36, 5), (21, 13), (29, 16), (16, 20), (18, 28), (26, 5), (43, 37), (21, 15), (42, 0), (25, 42), (25, 27), (26, 12), (12, 24), (43, 16), (48, 43), (27, 20), (44, 20), (17, 40), (46, 33), (17, 29), (43, 1), (7, 17), (2, 21), (34, 21), (16, 44), (20, 32), (42, 9), (27, 25), (11, 31), (26, 8), (12, 31), (22, 30), (45, 43), (12, 38), (13, 9), (17, 1), (35, 43), (38, 1), (21, 10), (41, 36), (23, 38), (2, 18), (33, 22), (6, 7), (11, 10), (4, 5), (1, 40), (3, 4), (27, 16), (45, 21), (30, 8), (43, 44), (4, 4), (9, 15), (1, 38), (23, 14), (22, 19), (35, 22), (43, 42), (45, 32), (19, 27), (2, 14), (30, 16), (25, 34), (37, 46), (21, 24), (13, 10), (4, 3), (41, 19), (32, 7), (35, 25), (43, 8), (15, 47), (34, 19), (3, 46), (15, 9), (8, 21), (24, 1), (7, 5), (21, 35), (2, 47), (11, 35), (45, 47), (15, 16), (29, 5), (17, 21), (35, 6), (41, 12), (33, 23), (11, 5), (38, 28), (4, 36), (40, 25), (33, 12), (13, 35), (35, 1), (47, 39), (22, 5), (42, 40), (23, 43), (13, 45), (2, 29), (27, 11), (5, 36), (28, 37), (44, 46), (37, 32), (38, 36), (7, 30), (2, 1), (44, 7), (13, 40), (5, 22), (2, 43), (31, 22), (4, 13), (46, 11), (17, 14), (42, 26), (29, 37), (4, 27), (46, 41), (17, 2), (33, 33), (19, 24), (33, 34), (37, 19), (18, 24), (14, 28), (7, 32), (39, 1), (36, 16), (23, 3), (40, 35), (40, 1), (0, 13), (35, 38), (43, 45), (20, 7), (46, 46), (21, 37), (40, 3), (15, 33), (32, 17), (23, 27), (22, 45), (35, 45), (7, 18), (37, 29), (48, 27), (38, 14), (24, 29), (20, 39), (32, 30), (21, 0), (36, 22), (23, 6), (12, 2), (3, 32), (10, 27), (13, 4), (34, 3), (27, 45), (31, 9), (11, 6), (19, 36), (36, 26), (19, 30), (40, 19), (33, 13), (1, 18), (4, 18), (20, 37), (22, 15), (48, 36), (23, 29), (16, 8), (5, 43), (34, 45), (1, 16), (15, 17), (14, 47), (20, 12), (7, 37), (16, 15), (40, 32), (0, 15), (13, 15), (23, 9), (8, 35), (2, 7), (25, 19), (35, 16), (28, 25), (46, 28), (6, 26), (33, 42), (42, 43), (10, 43), (17, 32), (34, 13), (36, 47), (0, 32), (38, 5), (32, 3), (32, 21), (13, 43), (18, 40), (25, 16), (22, 47), (39, 15), (2, 40), (48, 12), (14, 2), (40, 42), (7, 29), (34, 44), (31, 20), (1, 15), (32, 1), (18, 18), (10, 18), (38, 11), (13, 17), (37, 43), (30, 45), (28, 26), (42, 24), (8, 45), (27, 15), (6, 30), (2, 27), (26, 22), (12, 9), (17, 12), (48, 14), (26, 14), (14, 39), (3, 16), (10, 35), (28, 24), (25, 15), (3, 34), (38, 26), (14, 11), (45, 14), (44, 22), (13, 32), (3, 11), (18, 42), (47, 34), (17, 41), (47, 37), (32, 37), (19, 14), (47, 12), (10, 9), (44, 26), (9, 12), (33, 21), (23, 42), (9, 43), (15, 26), (17, 31), (41, 13), (26, 31), (43, 7), (3, 17), (13, 47), (41, 0), (17, 17), (28, 11), (23, 44), (33, 2), (48, 22), (31, 1), (36, 17), (19, 22), (8, 18), (42, 21), (31, 36), (47, 27), (47, 21), (43, 0), (17, 20), (13, 20), (37, 36), (24, 21), (44, 5), (3, 28), (4, 22), (48, 20), (3, 2), (31, 44), (34, 20), (35, 19), (27, 39), (33, 16), (3, 43), (27, 43), (20, 33), (8, 38), (7, 36), (22, 40), (11, 26), (35, 47), (46, 29), (25, 8), (20, 17), (1, 27), (47, 47), (4, 26), (47, 45), (7, 4), (42, 11), (2, 19), (24, 0), (13, 21), (30, 42), (23, 20), (0, 43), (31, 3), (10, 20), (47, 20), (21, 20), (29, 21), (36, 39), (3, 3), (12, 13), (39, 19), (5, 7), (46, 19), (26, 10), (8, 26), (26, 28), (29, 36), (23, 28), (21, 5), (28, 44), (45, 19), (19, 44), (14, 6), (0, 10), (41, 18), (30, 12), (15, 45), (45, 18), (26, 42), (24, 15), (14, 32), (29, 25), (1, 47), (38, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 32), (39, 26), (36, 15), (13, 7), (11, 19), (11, 30), (9, 29), (24, 35), (38, 32), (25, 36), (22, 4), (34, 6), (6, 27), (36, 4), (15, 39), (33, 3), (37, 38), (31, 28), (25, 4), (32, 33), (33, 9), (37, 8), (0, 30), (22, 31), (1, 9), (39, 21), (36, 32), (10, 26), (5, 35), (17, 22), (27, 21), (3, 4), (2, 38), (23, 16), (20, 10), (30, 34), (19, 14), (1, 13), (27, 30), (38, 13), (2, 32), (13, 2), (16, 25), (33, 16), (29, 12), (15, 0), (28, 0), (1, 33), (22, 14), (20, 7), (9, 32), (27, 3), (20, 36), (17, 36), (20, 15), (26, 8), (0, 19), (23, 21), (2, 10), (29, 25), (11, 37), (16, 5), (36, 2), (14, 7), (24, 29), (17, 13), (29, 26), (37, 26), (31, 19), (3, 25), (14, 24), (20, 8), (7, 9), (0, 28), (26, 33), (1, 8), (36, 9), (34, 25), (33, 24), (1, 11), (25, 31), (29, 24), (11, 0), (16, 10), (25, 40), (31, 39), (5, 31), (9, 9), (23, 38), (19, 2), (0, 1), (20, 35), (13, 25), (5, 15), (21, 29), (15, 33), (22, 37), (9, 22), (12, 39), (19, 1), (8, 26), (24, 25), (26, 28), (0, 14), (38, 0), (31, 20), (22, 9), (3, 7), (37, 9), (9, 17), (39, 18), (37, 23), (30, 39), (22, 8), (10, 17), (1, 14), (33, 10), (36, 36), (13, 33), (16, 4), (32, 21), (4, 11), (8, 35), (39, 12), (21, 5), (32, 24), (17, 31), (35, 27), (12, 13), (35, 13), (26, 17), (9, 26), (3, 27), (29, 33), (11, 5), (4, 27), (28, 9), (9, 15), (27, 29), (12, 23), (31, 22), (5, 32), (12, 4), (7, 36), (4, 26), (9, 35), (14, 29), (9, 24), (14, 28), (29, 14), (8, 20), (3, 26), (8, 6), (31, 4), (14, 16), (11, 4), (28, 15), (26, 37), (15, 18), (18, 3), (16, 34), (10, 23), (16, 39), (3, 8), (22, 2), (16, 8), (7, 25), (32, 13), (24, 6), (24, 10), (32, 1), (11, 6), (28, 5), (1, 10), (34, 14), (26, 13), (6, 11), (16, 24), (22, 40), (15, 2), (16, 23), (14, 1), (28, 31), (37, 35), (20, 14), (20, 38), (3, 16), (7, 15), (0, 36), (1, 20), (24, 5), (11, 36), (25, 30), (15, 3), (11, 3), (15, 38), (33, 18), (25, 13), (35, 11), (11, 9), (30, 32), (36, 38), (35, 36), (23, 29), (9, 0), (34, 2), (2, 6), (8, 11), (2, 2), (12, 28), (16, 31), (31, 29), (25, 23), (18, 10), (14, 36), (18, 30), (25, 32), (4, 38), (24, 34), (3, 3), (16, 7), (14, 34), (22, 28), (17, 35), (16, 17), (4, 18), (5, 24), (19, 37), (20, 34), (8, 14), (10, 11), (22, 27), (10, 2), (0, 9), (0, 5), (32, 32), (19, 22), (3, 29), (21, 38), (5, 5), (9, 12), (19, 4), (12, 37), (32, 16), (19, 29), (21, 24), (9, 21), (4, 25), (3, 33), (24, 39), (24, 14), (15, 13), (13, 9), (8, 24), (26, 6), (0, 32), (1, 21), (18, 35), (29, 21), (4, 28), (39, 0), (24, 23), (24, 9), (5, 7), (23, 26), (36, 40), (36, 39), (30, 30), (26, 32), (36, 21), (11, 31), (11, 24), (12, 35), (25, 20), (9, 5), (13, 20), (13, 1), (24, 8), (25, 28), (34, 38), (26, 27), (6, 32), (5, 37), (37, 1), (6, 6), (19, 6), (21, 7), (36, 29), (32, 12), (37, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 40x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 3), (35, 7), (34, 8), (3, 21), (19, 7), (32, 0), (18, 12), (27, 25), (34, 9), (21, 8), (26, 28), (23, 22), (33, 26), (17, 30), (38, 31), (28, 22), (22, 34), (13, 16), (1, 22), (31, 21), (21, 25), (20, 32), (14, 21), (35, 18), (34, 11), (22, 15), (6, 38), (17, 17), (13, 18), (1, 25), (12, 3), (10, 33), (19, 37), (15, 19), (15, 14), (22, 27), (13, 24), (20, 8), (7, 12), (15, 39), (27, 12), (22, 30), (15, 0), (10, 37), (9, 11), (0, 24), (39, 10), (19, 21), (35, 12), (34, 36), (8, 8), (35, 15), (2, 11), (7, 5), (11, 25), (13, 11), (32, 25), (12, 11), (12, 15), (0, 6), (1, 8), (35, 3), (4, 39), (27, 11), (16, 25), (1, 4), (1, 23), (6, 6), (11, 9), (33, 16), (16, 13), (38, 40), (37, 39), (31, 20), (23, 29), (20, 23), (17, 35), (7, 7), (16, 36), (13, 41), (31, 1), (2, 29), (34, 23), (3, 4), (36, 4), (34, 10), (8, 24), (35, 24), (32, 32), (22, 41), (4, 15), (39, 2), (4, 10), (24, 31), (21, 0), (1, 20), (39, 39), (17, 29), (35, 34), (10, 19), (37, 40), (6, 13), (5, 5), (27, 9), (6, 19), (32, 40), (21, 40), (24, 15), (13, 20), (0, 19), (10, 38), (17, 28), (20, 22), (7, 37), (20, 28), (1, 27), (27, 8), (28, 3), (22, 5), (3, 14), (10, 30), (25, 35), (29, 4), (19, 9), (33, 39), (15, 16), (21, 12), (27, 23), (10, 29), (36, 28), (13, 2), (19, 16), (7, 19), (11, 35), (33, 1), (15, 17), (25, 22), (25, 14), (10, 35), (34, 1), (9, 20), (18, 25), (30, 9), (7, 11), (8, 39), (6, 34), (20, 4), (24, 23), (25, 23), (18, 0), (11, 3), (21, 22), (8, 33), (18, 32), (28, 0), (34, 32), (22, 7), (7, 9), (30, 30), (39, 27), (21, 17), (28, 39), (11, 13), (8, 20), (37, 30), (25, 28), (32, 28), (37, 9), (28, 26), (33, 10), (11, 26), (27, 21), (26, 16), (36, 39), (19, 24), (9, 5), (37, 24), (9, 39), (14, 32), (22, 13), (29, 5), (39, 7), (38, 36), (16, 15), (17, 26), (25, 1), (24, 14), (7, 18), (37, 3), (34, 29), (14, 38), (36, 12), (0, 13), (11, 37), (13, 26), (28, 23), (12, 33), (4, 22), (23, 0), (5, 27), (17, 33), (6, 21), (5, 12), (35, 35), (28, 9), (25, 18), (23, 23), (31, 3), (2, 5), (13, 39), (27, 5), (12, 2), (30, 32), (39, 36), (29, 16), (3, 7), (36, 33), (24, 21), (1, 10), (23, 31), (7, 28), (31, 5), (35, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 0), (32, 26), (30, 31), (6, 29), (22, 17), (3, 20), (41, 23), (35, 0), (7, 27), (23, 22), (25, 18), (18, 17), (17, 32), (22, 35), (9, 16), (15, 15), (14, 6), (14, 3), (19, 26), (11, 4), (8, 6), (19, 20), (39, 30), (3, 12), (38, 30), (9, 6), (35, 28), (37, 26), (13, 9), (41, 30), (15, 29), (22, 31), (31, 6), (24, 21), (46, 2), (37, 24), (32, 32), (21, 19), (9, 0), (2, 1), (8, 7), (29, 16), (31, 16), (19, 38), (16, 1), (8, 1), (39, 24), (13, 17), (40, 36), (45, 16), (28, 8), (23, 25), (20, 32), (1, 11), (32, 38), (44, 35), (5, 1), (30, 23), (31, 36), (41, 15), (18, 7), (31, 12), (26, 0), (37, 9), (23, 6), (1, 7), (32, 39), (45, 30), (7, 9), (19, 18), (36, 34), (27, 7), (42, 4), (15, 25), (42, 9), (11, 32), (21, 37), (23, 10), (41, 7), (28, 36), (32, 9), (12, 22), (17, 1), (10, 34), (45, 3), (15, 1), (33, 7), (24, 35), (46, 1), (30, 28), (39, 5), (23, 39), (9, 20), (44, 9), (20, 39), (1, 9), (29, 39), (35, 12), (7, 26), (31, 27), (39, 33), (0, 26), (42, 37), (2, 6), (16, 12), (46, 31), (20, 11), (19, 25), (1, 25), (25, 11), (44, 7), (38, 19), (42, 12), (44, 13), (21, 34), (4, 33), (3, 7), (43, 0), (3, 21), (31, 39), (34, 23), (36, 26), (0, 35), (1, 38), (29, 4), (35, 10), (32, 28), (4, 27), (26, 5), (0, 33), (28, 11), (20, 28), (1, 2), (19, 13), (4, 23), (16, 21), (18, 21), (29, 34), (11, 30), (0, 38), (23, 26), (0, 7), (2, 30), (29, 38), (14, 22), (12, 19), (18, 24), (42, 32), (28, 21), (5, 18), (44, 27), (42, 33), (20, 4), (43, 21), (5, 28), (40, 1), (10, 32), (23, 23), (18, 23), (5, 36), (9, 17), (41, 28), (31, 8), (26, 12), (17, 28), (20, 6), (25, 21), (19, 2), (12, 36), (2, 3), (21, 13), (27, 37), (33, 35), (33, 10), (11, 7), (40, 31), (37, 8), (0, 3), (43, 16), (2, 23), (23, 12), (45, 0), (0, 24), (4, 10), (13, 27), (35, 1), (43, 18), (32, 31), (0, 28), (9, 24), (20, 24), (23, 3), (23, 13), (40, 14), (43, 3), (7, 32), (13, 24), (3, 17), (39, 36), (5, 14), (2, 13), (25, 32), (9, 28), (45, 7), (16, 32), (20, 12), (22, 0), (41, 6), (30, 20), (13, 13), (38, 8), (18, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 44), (34, 34), (21, 20), (6, 40), (0, 2), (5, 43), (21, 14), (36, 20), (14, 3), (31, 44), (18, 0), (11, 26), (33, 38), (19, 11), (39, 19), (40, 16), (28, 5), (45, 7), (19, 23), (22, 10), (17, 33), (30, 36), (21, 23), (29, 44), (27, 25), (15, 16), (46, 22), (8, 22), (26, 2), (20, 17), (33, 19), (13, 25), (46, 0), (23, 6), (9, 37), (22, 30), (18, 22), (30, 0), (7, 19), (44, 0), (9, 36), (29, 32), (28, 36), (3, 7), (46, 14), (34, 17), (2, 26), (21, 3), (9, 47), (38, 0), (5, 41), (26, 18), (44, 13), (16, 34), (8, 1), (15, 36), (41, 4), (43, 40), (17, 39), (46, 26), (41, 7), (1, 12), (28, 47), (8, 23), (3, 42), (20, 36), (33, 22), (3, 5), (40, 44), (25, 31), (38, 22), (32, 39), (31, 35), (25, 25), (9, 15), (26, 34), (27, 16), (28, 38), (35, 14), (14, 8), (27, 29), (26, 21), (15, 46), (18, 40), (41, 3), (18, 1), (43, 5), (13, 37), (24, 1), (7, 12), (39, 30), (45, 27), (2, 28), (2, 45), (22, 13), (38, 19), (15, 31), (37, 25), (19, 45), (38, 13), (39, 1), (27, 23), (10, 44), (7, 27), (37, 11), (8, 12), (33, 15), (2, 14), (26, 25), (41, 47), (1, 40), (35, 6), (37, 29), (13, 17), (14, 9), (9, 27), (39, 13), (28, 28), (37, 0), (21, 33), (17, 38), (9, 3), (15, 6), (40, 31), (27, 41), (1, 39), (40, 10), (31, 39), (3, 4), (23, 10), (38, 27), (31, 9), (26, 12), (21, 28), (37, 24), (2, 41), (8, 45), (39, 2), (9, 29), (30, 16), (30, 30), (32, 3), (25, 22), (33, 21), (17, 37), (16, 14), (44, 22), (34, 12), (21, 13), (23, 9), (26, 39), (30, 4), (47, 44), (25, 11), (10, 15), (7, 9), (31, 8), (19, 5), (30, 5), (19, 28), (1, 8), (35, 30), (7, 18), (7, 47), (5, 20), (23, 28), (23, 43), (13, 3), (38, 47), (32, 4), (8, 16), (46, 23), (2, 16), (10, 17), (14, 18), (10, 36), (1, 32), (46, 11), (17, 16), (16, 35), (42, 41), (37, 46), (41, 42), (34, 29), (26, 19), (26, 8), (31, 13), (11, 40), (47, 46), (42, 25), (47, 19), (22, 4), (30, 22), (47, 38), (23, 26), (16, 39), (32, 36), (15, 5), (7, 4), (3, 26), (21, 8), (47, 41), (3, 32), (14, 19), (28, 43), (25, 10), (4, 31), (46, 21), (44, 44), (30, 9), (47, 39), (13, 5), (11, 5), (28, 25), (0, 17), (26, 16), (16, 38), (16, 45), (39, 43), (43, 2), (23, 47), (10, 35), (43, 38), (34, 6), (3, 8), (1, 25), (14, 30), (35, 34), (40, 13), (27, 28), (31, 3), (40, 28), (19, 13), (28, 44), (31, 5), (46, 15), (18, 15), (19, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 44), (13, 27), (30, 10), (15, 37), (27, 39), (14, 0), (22, 24), (25, 36), (32, 16), (27, 6), (35, 36), (39, 9), (0, 42), (35, 12), (19, 36), (43, 19), (44, 9), (5, 22), (2, 31), (41, 4), (42, 25), (3, 42), (46, 27), (15, 36), (25, 17), (5, 2), (23, 43), (43, 1), (43, 36), (5, 8), (28, 25), (9, 31), (18, 33), (1, 0), (0, 22), (18, 36), (6, 9), (27, 13), (6, 6), (10, 41), (17, 23), (29, 9), (30, 31), (25, 27), (22, 13), (15, 22), (32, 32), (14, 16), (3, 2), (20, 17), (37, 30), (27, 15), (22, 17), (33, 36), (32, 29), (19, 12), (6, 38), (11, 43), (3, 12), (9, 34), (42, 19), (16, 38), (11, 26), (40, 39), (5, 28), (4, 7), (31, 25), (16, 6), (33, 16), (1, 17), (36, 42), (15, 11), (2, 16), (39, 32), (17, 31), (5, 18), (20, 28), (20, 11), (37, 22), (38, 1), (44, 1), (26, 21), (28, 19), (19, 31), (7, 42), (15, 40), (37, 35), (33, 2), (45, 44), (38, 4), (23, 33), (38, 22), (42, 17), (40, 34), (13, 45), (39, 33), (46, 11), (10, 32), (23, 1), (18, 20), (20, 16), (45, 36), (16, 28), (33, 37), (15, 38), (12, 11), (26, 41), (23, 4), (13, 29), (22, 28), (46, 25), (32, 19), (24, 25), (11, 16), (8, 35), (18, 3), (29, 5), (30, 6), (34, 23), (22, 4), (45, 10), (39, 7), (39, 43), (43, 4), (8, 25), (6, 28), (6, 1), (13, 35), (19, 33), (10, 17), (19, 1), (0, 8), (34, 6), (2, 15), (38, 39), (21, 44), (42, 34), (46, 4), (40, 1), (11, 37), (13, 11), (44, 44), (38, 35), (7, 5), (25, 6), (43, 30), (0, 18), (1, 35), (23, 40), (36, 21), (28, 37), (15, 16), (1, 27), (35, 6), (8, 13), (27, 35), (43, 35), (27, 24), (17, 5), (20, 32), (34, 12), (39, 18), (33, 34), (40, 14), (2, 10), (44, 22), (3, 13), (29, 44), (15, 27), (5, 36), (2, 34), (28, 7), (42, 22), (40, 23), (22, 39), (12, 2), (26, 33), (25, 42), (28, 28), (15, 0), (28, 12), (44, 28), (24, 27), (12, 26), (28, 24), (23, 16), (0, 25), (0, 43), (6, 14), (35, 18), (28, 3), (45, 21), (34, 3), (31, 2), (41, 13), (25, 2), (15, 23), (4, 32), (27, 25), (17, 28), (16, 44), (46, 16), (27, 32), (5, 37), (46, 12), (3, 8), (41, 26), (6, 25), (11, 34), (44, 24), (15, 31), (45, 15), (31, 24), (38, 40), (8, 37), (1, 7), (38, 21), (0, 3), (36, 25), (24, 8), (19, 34), (20, 13), (41, 34), (0, 40), (24, 3), (13, 23), (17, 25), (42, 8), (40, 10), (42, 20), (26, 1), (16, 26), (42, 37), (4, 18), (43, 2), (20, 18), (12, 19), (22, 19), (44, 3), (37, 43), (16, 22), (37, 12), (8, 33), (11, 7), (17, 24), (9, 1), (37, 20), (34, 29), (38, 20), (4, 6), (35, 19), (37, 40), (25, 22), (44, 41), (15, 32), (4, 5), (14, 27), (14, 4), (35, 13), (3, 36), (30, 0), (41, 35), (39, 25), (30, 14), (10, 13), (33, 31), (7, 21), (34, 38), (17, 37), (35, 30), (30, 16), (38, 45), (1, 12), (5, 9), (1, 2), (39, 39), (22, 41), (29, 12), (14, 5), (39, 8), (24, 7), (4, 27), (0, 4), (8, 10), (13, 3), (28, 8), (36, 32), (14, 6), (33, 10), (39, 19), (13, 17), (36, 38), (32, 7), (32, 44), (17, 33), (30, 36), (14, 28), (21, 45), (17, 8), (24, 0), (10, 11), (35, 26), (34, 30), (29, 36), (30, 7), (4, 30), (17, 15), (16, 24), (0, 24), (41, 14), (1, 39), (12, 41), (26, 43), (45, 1), (39, 42), (14, 26), (28, 38), (16, 34), (11, 31), (10, 26), (16, 25), (43, 9), (9, 22), (20, 40), (26, 23), (45, 18), (20, 15), (37, 28), (11, 8), (38, 32), (13, 10), (19, 21), (6, 31), (4, 22), (5, 40), (17, 38), (23, 10), (20, 12), (21, 29), (12, 43), (15, 33), (37, 19), (12, 23), (39, 5), (30, 11), (32, 45), (3, 45), (12, 28), (13, 24), (23, 0), (13, 32), (10, 0), (30, 45), (6, 24), (5, 5), (11, 23), (19, 30), (32, 43), (30, 15), (11, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 11), (28, 12), (19, 38), (30, 8), (14, 44), (2, 18), (21, 7), (18, 11), (33, 2), (32, 43), (9, 39), (25, 8), (7, 13), (20, 10), (24, 4), (5, 31), (29, 6), (12, 31), (13, 11), (1, 26), (10, 21), (23, 38), (38, 31), (42, 42), (20, 46), (7, 6), (6, 4), (39, 1), (27, 39), (0, 17), (4, 16), (0, 16), (37, 32), (29, 7), (33, 45), (39, 17), (13, 40), (42, 17), (44, 27), (7, 32), (14, 8), (28, 4), (35, 27), (4, 18), (30, 34), (9, 11), (6, 40), (13, 21), (27, 22), (45, 17), (0, 37), (15, 29), (28, 11), (44, 37), (15, 32), (36, 33), (32, 5), (31, 12), (6, 39), (19, 11), (37, 45), (40, 5), (20, 13), (7, 47), (5, 15), (25, 18), (35, 19), (3, 46), (40, 3), (26, 0), (34, 4), (13, 19), (41, 19), (38, 27), (43, 9), (1, 37), (18, 24), (13, 6), (31, 3), (19, 35), (24, 6), (18, 43), (32, 6), (9, 36), (20, 36), (38, 35), (21, 15), (20, 32), (7, 9), (4, 4), (39, 42), (4, 6), (18, 30), (21, 2), (27, 19), (29, 35), (24, 40), (40, 1), (35, 15), (35, 12), (38, 13), (15, 33), (24, 24), (5, 12), (13, 0), (28, 15), (5, 19), (4, 38), (27, 8), (13, 20), (11, 31), (42, 41), (26, 46), (25, 5), (25, 7), (38, 16), (14, 31), (9, 13), (9, 33), (11, 32), (38, 3), (28, 26), (36, 44), (8, 27), (12, 43), (14, 23), (18, 16), (3, 27), (0, 35), (27, 32), (42, 25), (12, 42), (28, 45), (31, 36), (5, 40), (2, 30), (31, 23), (24, 19), (13, 17), (3, 44), (32, 4), (31, 1), (34, 42), (8, 1), (2, 39), (17, 31), (38, 23), (1, 36), (14, 25), (30, 28), (44, 32), (4, 33), (44, 2), (14, 32), (32, 13), (15, 22), (4, 35), (9, 3), (19, 15), (10, 1), (37, 35), (8, 17), (41, 38), (30, 10), (42, 39), (11, 4), (31, 28), (34, 10), (9, 42), (15, 2), (3, 38), (15, 34), (11, 28), (11, 21), (20, 3), (21, 1), (20, 28), (32, 35), (45, 28), (13, 22), (39, 27), (33, 36), (29, 12), (28, 7), (8, 9), (34, 33), (0, 22), (16, 27), (7, 39), (17, 43), (2, 17), (29, 37), (19, 44), (18, 18), (11, 36), (17, 17), (23, 21), (5, 47), (22, 44), (33, 35), (16, 26), (3, 7), (37, 27), (45, 2), (10, 27), (0, 44), (9, 38), (24, 21), (36, 38), (37, 34), (29, 32), (8, 24), (33, 42), (28, 37), (10, 23), (32, 10), (1, 42), (42, 33), (35, 31), (34, 1), (35, 22), (28, 20), (44, 5), (10, 42), (35, 42), (7, 25), (33, 25), (17, 33), (36, 25), (43, 16), (7, 41), (20, 5), (4, 8), (38, 15), (33, 41), (11, 15), (19, 32), (44, 21), (36, 27), (39, 14), (5, 2), (39, 32), (5, 43), (27, 34), (30, 5), (38, 9), (15, 28), (25, 10), (24, 26), (41, 17), (7, 45), (5, 5), (16, 8), (27, 15), (35, 17), (9, 31), (41, 25), (19, 5), (8, 46), (19, 22), (37, 13), (37, 12), (26, 18), (41, 21), (21, 36), (34, 11), (32, 17), (34, 28), (36, 36), (30, 30), (35, 6), (34, 36), (15, 27), (3, 19), (45, 38), (33, 21), (32, 30), (7, 33), (16, 36), (11, 19), (2, 11), (21, 11), (44, 16), (9, 15), (8, 45), (40, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 0), (33, 12), (37, 29), (7, 40), (11, 5), (37, 1), (10, 29), (8, 2), (41, 32), (36, 22), (37, 7), (13, 22), (17, 12), (39, 10), (38, 8), (13, 34), (2, 31), (2, 40), (8, 12), (23, 41), (2, 7), (38, 19), (40, 25), (13, 19), (12, 6), (43, 34), (35, 3), (16, 24), (6, 5), (28, 27), (14, 0), (3, 8), (41, 19), (41, 41), (2, 17), (11, 33), (7, 37), (4, 11), (39, 28), (21, 9), (11, 40), (16, 13), (3, 30), (22, 1), (31, 34), (2, 32), (7, 1), (1, 39), (27, 1), (24, 39), (0, 9), (16, 23), (18, 37), (7, 24), (6, 25), (36, 39), (1, 35), (17, 8), (3, 22), (8, 3), (3, 41), (7, 3), (31, 8), (38, 29), (41, 24), (21, 30), (5, 7), (43, 24), (12, 9), (38, 9), (23, 19), (26, 22), (40, 40), (19, 12), (34, 32), (22, 5), (3, 29), (21, 29), (29, 6), (31, 12), (40, 3), (19, 25), (42, 5), (43, 30), (5, 42), (1, 38), (18, 9), (40, 6), (21, 13), (39, 13), (39, 35), (37, 18), (0, 11), (5, 12), (32, 31), (33, 36), (5, 3), (1, 25), (29, 8), (1, 20), (41, 20), (2, 20), (25, 27), (18, 30), (43, 26), (1, 7), (12, 37), (22, 8), (6, 33), (2, 26), (35, 17), (2, 2), (26, 35), (26, 34), (22, 26), (13, 37), (21, 34), (22, 13), (12, 39), (31, 17), (14, 13), (28, 28), (32, 1), (34, 17), (37, 23), (33, 41), (2, 3), (42, 42), (37, 36), (6, 2), (5, 36), (0, 22), (40, 23), (35, 30), (42, 18), (31, 42), (2, 8), (30, 28), (23, 13), (27, 22), (16, 39), (27, 8), (26, 31), (18, 26), (8, 11), (34, 5), (32, 16), (2, 5), (35, 4), (35, 26), (28, 15), (8, 38), (4, 24), (43, 8), (19, 29), (13, 1), (16, 42), (12, 25), (32, 3), (17, 40), (35, 19), (21, 6), (14, 34), (14, 6), (12, 8), (25, 24), (28, 38), (29, 20), (16, 28), (6, 15), (15, 35), (41, 29), (15, 7), (30, 17), (14, 28), (22, 14), (39, 24), (36, 17), (11, 22), (0, 31), (34, 3), (29, 16), (29, 3), (20, 26), (38, 40), (13, 26), (15, 33), (9, 40), (9, 1), (28, 36), (26, 27), (5, 40), (37, 21), (40, 22), (0, 28), (16, 26), (4, 27), (38, 11), (37, 24), (5, 41), (19, 21), (20, 2), (39, 21), (5, 32), (16, 4), (2, 34), (3, 19), (23, 20), (12, 5), (33, 31), (10, 27), (5, 39), (27, 17), (39, 1), (27, 16), (39, 22), (1, 24), (23, 39), (24, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (46, 17), (37, 29), (24, 32), (40, 33), (45, 17), (39, 18), (0, 12), (46, 14), (9, 41), (11, 43), (35, 44), (42, 19), (31, 8), (9, 16), (16, 28), (16, 13), (13, 29), (6, 24), (28, 8), (41, 5), (27, 18), (40, 28), (15, 2), (45, 34), (36, 2), (18, 42), (31, 3), (26, 44), (12, 21), (39, 10), (42, 26), (4, 32), (23, 15), (42, 33), (4, 15), (12, 7), (17, 41), (20, 1), (35, 22), (34, 23), (44, 30), (43, 14), (1, 23), (27, 25), (31, 5), (35, 41), (27, 44), (10, 20), (36, 26), (13, 24), (38, 24), (1, 44), (18, 18), (43, 0), (28, 23), (36, 8), (30, 0), (3, 11), (31, 44), (34, 45), (30, 18), (34, 41), (30, 19), (12, 38), (1, 21), (6, 17), (47, 6), (22, 24), (3, 40), (19, 23), (24, 18), (44, 21), (7, 30), (1, 2), (0, 8), (25, 11), (1, 39), (17, 26), (42, 7), (10, 8), (35, 35), (11, 34), (11, 12), (8, 10), (13, 42), (20, 0), (7, 11), (29, 27), (17, 4), (9, 9), (46, 38), (16, 0), (10, 30), (14, 6), (38, 32), (34, 3), (26, 32), (38, 12), (8, 0), (32, 20), (33, 31), (7, 37), (22, 34), (44, 27), (15, 45), (13, 7), (43, 23), (45, 36), (42, 45), (27, 23), (18, 27), (45, 27), (16, 24), (44, 28), (1, 7), (5, 39), (11, 41), (44, 26), (19, 9), (46, 4), (26, 41), (20, 7), (39, 34), (44, 34), (10, 38), (30, 36), (10, 34), (39, 7), (26, 8), (9, 29), (37, 36), (13, 44), (38, 4), (14, 22), (15, 10), (13, 14), (1, 37), (5, 19), (45, 18), (29, 21), (29, 2), (31, 22), (24, 35), (11, 0), (24, 3), (33, 37), (27, 32), (41, 20), (3, 27), (42, 41), (16, 35), (8, 13), (13, 36), (28, 43), (45, 13), (0, 40), (1, 27), (41, 14), (3, 41), (10, 32), (5, 4), (5, 42), (23, 12), (4, 43), (34, 25), (38, 30), (35, 1), (10, 13), (29, 15), (33, 22), (38, 1), (43, 22), (46, 11), (6, 7), (29, 24), (14, 14), (42, 3), (21, 12), (21, 18), (8, 38), (16, 39), (36, 32), (30, 17), (2, 2), (10, 10), (33, 45), (34, 30), (18, 5), (40, 27), (6, 34), (9, 0), (40, 9), (34, 9), (5, 24), (38, 36), (21, 0), (7, 42), (21, 3), (10, 5), (42, 22), (33, 6), (15, 9), (30, 15), (32, 0), (40, 15), (26, 26), (27, 12), (31, 21), (18, 45), (3, 10), (37, 43), (31, 23), (12, 35), (42, 34), (13, 28), (38, 39), (24, 16), (33, 43), (2, 12), (32, 26), (15, 0), (32, 12), (25, 4), (19, 21), (27, 16), (30, 25), (20, 35), (0, 33), (7, 14), (27, 34), (18, 36), (9, 4), (11, 14), (21, 43), (43, 26), (28, 29), (23, 35), (9, 30), (14, 9), (31, 19), (46, 36), (45, 44), (39, 1), (15, 35), (7, 5), (17, 36), (21, 38), (38, 3), (14, 40), (40, 3), (47, 41), (11, 13), (17, 3), (25, 31), (21, 26), (2, 34), (47, 12), (46, 15), (19, 7), (40, 23), (37, 22), (32, 7), (40, 6), (6, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 8), (6, 5), (38, 41), (12, 1), (38, 39), (11, 15), (14, 16), (3, 42), (6, 7), (38, 0), (15, 37), (5, 3), (35, 12), (7, 44), (32, 23), (23, 20), (25, 37), (22, 16), (39, 9), (10, 9), (34, 15), (0, 18), (19, 23), (3, 7), (27, 0), (41, 26), (41, 24), (9, 24), (27, 29), (0, 14), (31, 14), (7, 12), (33, 37), (26, 34), (19, 28), (24, 36), (37, 6), (39, 43), (42, 14), (26, 15), (36, 29), (42, 19), (36, 25), (27, 20), (2, 4), (1, 9), (22, 14), (31, 17), (16, 41), (37, 13), (19, 5), (11, 42), (12, 41), (6, 4), (12, 21), (33, 3), (23, 34), (38, 5), (9, 14), (10, 31), (30, 41), (32, 40), (20, 3), (25, 4), (2, 16), (17, 29), (29, 20), (31, 31), (7, 29), (8, 20), (9, 8), (21, 34), (18, 18), (5, 1), (40, 4), (25, 28), (19, 32), (17, 30), (15, 6), (9, 44), (36, 39), (20, 21), (18, 25), (28, 8), (38, 6), (10, 10), (37, 37), (17, 9), (8, 26), (3, 1), (1, 1), (33, 10), (15, 18), (38, 8), (32, 20), (22, 21), (12, 33), (22, 39), (24, 24), (5, 7), (5, 43), (16, 42), (41, 9), (13, 26), (34, 30), (8, 28), (37, 34), (15, 4), (22, 40), (11, 27), (29, 19), (42, 32), (38, 25), (6, 10), (2, 26), (35, 31), (35, 30), (32, 39), (27, 11), (29, 27), (23, 14), (21, 7), (7, 1), (17, 31), (18, 33), (14, 22), (35, 44), (1, 44), (7, 20), (35, 23), (28, 6), (14, 13), (35, 39), (30, 8), (10, 35), (26, 25), (26, 27), (2, 19), (11, 19), (29, 10), (4, 44), (28, 36), (34, 12), (23, 29), (11, 33), (15, 20), (2, 2), (42, 17), (35, 41), (18, 31), (35, 15), (25, 26), (7, 43), (10, 43), (21, 6), (33, 41), (1, 10), (3, 17), (23, 17), (2, 20), (37, 29), (1, 17), (13, 19), (25, 15), (13, 1), (15, 42), (14, 4), (26, 0), (19, 21), (30, 25), (33, 7), (23, 1), (10, 3), (28, 38), (35, 24), (13, 4), (4, 30), (4, 36), (16, 4), (24, 12), (40, 20), (10, 39), (40, 37), (39, 27), (4, 10), (12, 22), (0, 7), (18, 14), (24, 7), (34, 38), (29, 23), (21, 32), (40, 39), (16, 29), (38, 12), (5, 40), (26, 2), (39, 42), (37, 16), (30, 16), (40, 28), (30, 18), (9, 39), (11, 23), (19, 4), (23, 7), (14, 15), (24, 25), (13, 6), (19, 14), (14, 28), (27, 39), (4, 39), (10, 17), (23, 21), (8, 38), (17, 39), (36, 17), (34, 3), (35, 40), (26, 32), (34, 2), (39, 13), (12, 12), (6, 21), (8, 32), (3, 6), (37, 23), (41, 10), (7, 42), (41, 25), (28, 13), (42, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (16, 18), (34, 7), (6, 43), (46, 30), (5, 18), (40, 5), (23, 26), (5, 20), (10, 32), (33, 36), (18, 32), (37, 33), (36, 26), (26, 0), (21, 4), (9, 27), (7, 34), (46, 7), (18, 7), (3, 13), (13, 3), (35, 16), (19, 14), (45, 43), (12, 9), (11, 5), (44, 19), (13, 38), (45, 12), (30, 4), (40, 11), (32, 0), (16, 26), (4, 18), (18, 0), (17, 4), (26, 19), (32, 23), (33, 34), (26, 20), (27, 25), (24, 10), (40, 10), (38, 17), (31, 26), (25, 40), (29, 42), (19, 40), (27, 18), (42, 27), (3, 16), (20, 27), (3, 18), (2, 35), (26, 36), (1, 31), (14, 3), (42, 14), (29, 5), (39, 14), (23, 18), (36, 18), (30, 6), (45, 33), (26, 33), (13, 36), (3, 40), (2, 26), (18, 16), (28, 14), (41, 29), (15, 30), (22, 9), (2, 44), (29, 28), (12, 1), (12, 23), (47, 22), (0, 2), (1, 22), (17, 1), (31, 36), (34, 28), (28, 13), (7, 43), (24, 40), (43, 39), (29, 24), (3, 7), (32, 20), (14, 2), (42, 26), (16, 20), (12, 7), (5, 12), (33, 19), (11, 8), (16, 2), (4, 26), (18, 10), (18, 4), (36, 9), (11, 20), (21, 1), (1, 0), (39, 1), (39, 4), (47, 20), (4, 8), (3, 19), (18, 29), (42, 28), (32, 41), (5, 28), (28, 4), (28, 41), (7, 3), (9, 11), (20, 7), (2, 2), (10, 7), (33, 44), (29, 31), (26, 6), (33, 6), (34, 17), (22, 19), (19, 3), (23, 21), (32, 6), (38, 16), (19, 21), (22, 7), (2, 30), (15, 13), (36, 25), (17, 8), (31, 29), (47, 4), (44, 5), (41, 18), (42, 38), (15, 26), (37, 13), (20, 0), (37, 43), (35, 5), (16, 0), (27, 26), (43, 21), (3, 17), (27, 19), (28, 30), (36, 44), (8, 8), (21, 0), (47, 36), (6, 1), (23, 28), (36, 24), (23, 16), (26, 29), (28, 18), (3, 43), (7, 7), (47, 17), (9, 44), (42, 41), (2, 39), (33, 43), (8, 3), (1, 43), (32, 12), (17, 44), (2, 25), (26, 38), (19, 0), (25, 3), (46, 33), (20, 1), (18, 24), (26, 10), (20, 2), (7, 41), (32, 1), (25, 30), (42, 22), (24, 42), (11, 10), (44, 34), (38, 13), (20, 16), (13, 4), (5, 8), (6, 30), (16, 25), (33, 4), (12, 16), (42, 7), (40, 1), (37, 16), (4, 33), (46, 17), (9, 32), (38, 39), (47, 33), (41, 40), (22, 10), (37, 19), (36, 42), (20, 4), (29, 8), (27, 39), (24, 24), (14, 29), (42, 43), (39, 2), (40, 24), (21, 31), (39, 3), (19, 44), (16, 41), (14, 44), (13, 27), (31, 23), (17, 28), (14, 14), (43, 38), (7, 29), (41, 3), (4, 43), (35, 20), (6, 41), (46, 8), (25, 23), (40, 9), (24, 2), (35, 31), (37, 44), (21, 35), (7, 27), (26, 13), (9, 33), (25, 5), (28, 36), (13, 44), (46, 9), (31, 6), (34, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 14), (21, 2), (38, 26), (23, 18), (26, 29), (20, 8), (19, 2), (14, 39), (5, 16), (15, 25), (5, 8), (33, 22), (21, 37), (5, 27), (14, 1), (37, 1), (26, 26), (17, 8), (25, 24), (5, 36), (40, 37), (36, 7), (22, 38), (38, 30), (5, 6), (21, 1), (16, 28), (26, 1), (13, 2), (14, 8), (15, 27), (40, 7), (18, 0), (29, 23), (38, 19), (16, 38), (4, 4), (39, 23), (14, 0), (8, 17), (34, 30), (17, 30), (10, 37), (19, 26), (12, 39), (6, 4), (29, 14), (5, 28), (12, 19), (26, 7), (18, 2), (40, 31), (31, 14), (14, 2), (2, 32), (27, 19), (21, 31), (36, 39), (28, 23), (7, 5), (33, 13), (30, 32), (5, 29), (8, 37), (14, 35), (9, 38), (4, 38), (33, 14), (4, 39), (41, 36), (2, 37), (30, 18), (26, 34), (16, 36), (33, 5), (21, 34), (19, 37), (34, 26), (36, 16), (27, 33), (7, 24), (23, 9), (10, 23), (38, 7), (2, 4), (32, 36), (8, 35), (5, 7), (16, 17), (0, 39), (28, 31), (25, 39), (13, 29), (31, 1), (21, 35), (18, 23), (3, 3), (19, 7), (31, 11), (17, 12), (19, 0), (13, 18), (40, 18), (15, 14), (27, 30), (26, 19), (0, 4), (16, 25), (16, 19), (34, 20), (41, 5), (1, 16), (18, 10), (6, 27), (40, 1), (35, 31), (1, 20), (31, 29), (40, 22), (21, 17), (28, 24), (9, 8), (2, 14), (20, 10), (7, 8), (12, 3), (30, 37), (36, 20), (12, 12), (6, 25), (13, 12), (23, 20), (6, 29), (7, 9), (15, 33), (11, 12), (25, 14), (15, 10), (27, 2), (41, 30), (16, 8), (35, 13), (37, 29), (13, 38), (30, 9), (27, 14), (20, 14), (11, 15), (22, 19), (11, 19), (8, 4), (19, 23), (35, 2), (12, 36), (18, 33), (29, 30), (37, 28), (24, 20), (37, 7), (11, 14), (10, 36), (5, 13), (9, 16), (2, 12), (19, 35), (6, 1), (8, 32), (1, 7), (15, 26), (7, 29), (19, 14), (18, 16), (20, 7), (41, 32), (4, 1), (23, 35), (30, 0), (13, 37), (27, 3), (39, 19), (15, 17), (27, 31), (1, 5), (19, 17), (30, 1), (13, 17), (24, 17), (24, 36), (29, 28), (12, 22), (10, 16), (22, 26), (37, 30), (12, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (20, 12), (20, 32), (5, 29), (34, 29), (31, 22), (22, 7), (28, 41), (46, 38), (6, 6), (15, 42), (16, 28), (18, 14), (12, 34), (13, 7), (39, 30), (14, 7), (37, 22), (8, 24), (31, 41), (17, 27), (19, 20), (29, 38), (17, 11), (13, 38), (14, 6), (35, 17), (33, 26), (21, 14), (47, 24), (29, 36), (6, 26), (21, 5), (9, 11), (21, 39), (39, 10), (47, 41), (12, 11), (27, 24), (33, 8), (2, 16), (4, 27), (6, 41), (0, 3), (10, 16), (35, 35), (46, 36), (27, 21), (20, 26), (10, 9), (23, 33), (25, 32), (10, 7), (36, 7), (0, 9), (33, 15), (29, 25), (7, 5), (1, 28), (29, 22), (47, 33), (21, 3), (21, 24), (33, 17), (24, 23), (1, 23), (25, 20), (9, 32), (21, 23), (39, 14), (17, 25), (35, 0), (7, 17), (36, 36), (33, 20), (39, 6), (6, 9), (10, 32), (18, 20), (33, 23), (2, 29), (2, 38), (0, 5), (47, 22), (2, 7), (20, 28), (28, 17), (38, 3), (35, 15), (33, 6), (2, 40), (19, 28), (27, 31), (24, 12), (23, 39), (25, 26), (29, 2), (11, 10), (46, 28), (37, 11), (47, 38), (16, 33), (20, 38), (25, 1), (27, 34), (12, 23), (32, 33), (28, 1), (37, 21), (12, 42), (47, 21), (4, 29), (27, 37), (25, 11), (30, 38), (26, 36), (18, 9), (21, 12), (39, 27), (34, 41), (5, 23), (4, 12), (16, 40), (9, 21), (42, 38), (7, 8), (0, 26), (30, 33), (4, 7), (43, 8), (3, 2), (0, 10), (37, 28), (39, 17), (26, 31), (35, 39), (4, 14), (27, 0), (18, 40), (29, 29), (43, 32), (31, 5), (16, 41), (33, 2), (7, 12), (10, 23), (18, 19), (5, 34), (31, 23), (27, 17), (37, 30), (15, 6), (44, 33), (29, 39), (10, 20), (38, 13), (9, 3), (33, 38), (38, 36), (42, 21), (12, 40), (4, 13), (23, 21), (6, 27), (16, 8), (34, 15), (16, 4), (12, 35), (46, 14), (28, 34), (21, 19), (19, 42), (23, 29), (5, 10), (19, 33), (43, 27), (39, 0), (22, 26), (34, 39), (21, 4), (10, 11), (30, 32), (17, 24), (34, 30), (6, 14), (28, 7), (44, 12), (28, 25), (3, 13), (35, 22), (41, 31), (4, 30), (19, 18), (30, 40), (31, 7), (22, 36), (17, 32), (8, 10), (14, 9), (41, 26), (37, 18), (0, 13), (9, 10), (3, 18), (39, 39), (40, 15), (6, 29), (37, 9), (5, 27), (27, 6), (22, 2), (24, 40), (24, 22), (13, 12), (17, 37), (44, 39), (39, 19), (24, 38), (8, 42), (0, 23), (27, 33), (34, 5), (39, 26), (16, 34), (17, 41), (9, 9), (14, 34), (6, 42), (46, 2), (1, 26), (4, 6), (28, 12), (46, 1), (36, 37), (14, 15), (31, 20), (11, 17), (36, 0), (8, 2), (8, 36), (2, 18), (43, 3), (14, 5), (2, 1), (5, 32), (16, 30), (46, 31), (9, 38), (35, 41), (19, 35), (31, 29), (32, 42), (15, 33), (10, 3), (5, 1), (14, 13), (35, 30), (25, 21), (25, 22), (24, 17), (43, 12), (8, 27), (4, 36), (41, 4), (38, 29), (39, 12), (29, 9), (7, 11), (4, 31), (40, 42), (20, 23), (13, 41), (47, 1), (15, 7), (20, 25), (19, 38), (30, 4), (19, 11), (0, 8), (24, 1), (13, 29), (26, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 48x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 34), (28, 38), (26, 0), (35, 17), (2, 30), (9, 10), (31, 10), (23, 8), (16, 2), (32, 37), (15, 27), (17, 1), (0, 7), (32, 8), (42, 40), (3, 37), (28, 26), (20, 0), (22, 22), (3, 12), (34, 11), (26, 34), (34, 2), (27, 5), (16, 10), (47, 24), (2, 17), (30, 3), (37, 11), (47, 5), (37, 17), (20, 29), (8, 9), (7, 10), (11, 15), (33, 26), (12, 31), (33, 0), (13, 6), (31, 38), (3, 6), (17, 26), (11, 20), (18, 38), (44, 9), (14, 38), (24, 23), (27, 37), (20, 4), (46, 8), (19, 22), (14, 0), (8, 15), (5, 12), (2, 23), (39, 38), (37, 4), (34, 3), (9, 21), (40, 33), (36, 35), (23, 5), (6, 39), (1, 13), (7, 6), (10, 15), (35, 8), (22, 1), (27, 9), (41, 30), (24, 39), (31, 26), (4, 5), (46, 4), (14, 2), (41, 24), (42, 32), (16, 18), (20, 25), (19, 33), (12, 16), (6, 15), (29, 25), (14, 12), (8, 8), (20, 41), (2, 40), (24, 38), (39, 23), (40, 17), (27, 22), (9, 19), (2, 12), (41, 34), (46, 14), (26, 10), (37, 30), (12, 22), (32, 24), (25, 22), (7, 13), (26, 29), (28, 10), (8, 41), (1, 22), (10, 7), (30, 24), (7, 4), (5, 19), (41, 19), (6, 41), (6, 14), (2, 39), (40, 0), (32, 40), (22, 2), (13, 18), (26, 41), (10, 28), (15, 34), (34, 35), (36, 34), (27, 25), (6, 30), (17, 25), (28, 15), (10, 18), (23, 36), (45, 34), (26, 26), (36, 7), (47, 26), (34, 34), (0, 5), (43, 23), (35, 33), (5, 41), (35, 18), (4, 10), (34, 14), (29, 42), (30, 30), (34, 36), (21, 25), (24, 4), (2, 29), (11, 3), (35, 25), (36, 41), (18, 29), (41, 9), (34, 8), (27, 27), (3, 38), (5, 20), (40, 41), (1, 35), (42, 16), (38, 22), (42, 14), (0, 1), (0, 22), (11, 23), (28, 16), (44, 25), (43, 28), (19, 14), (5, 39), (6, 18), (16, 16), (3, 3), (6, 29), (41, 11), (15, 2), (47, 18), (13, 1), (9, 27), (4, 28), (21, 10), (44, 14), (9, 7), (39, 3), (19, 39), (14, 31), (11, 0), (4, 42), (9, 16), (32, 23), (1, 41), (26, 37), (46, 0), (29, 40), (31, 34), (0, 27), (9, 41), (1, 38), (39, 41), (19, 29), (5, 42), (17, 34), (43, 14), (2, 24), (46, 10), (14, 37), (25, 36), (43, 41), (13, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 6), (2, 22), (15, 8), (18, 36), (25, 44), (24, 28), (30, 3), (10, 13), (13, 14), (42, 29), (26, 40), (11, 17), (42, 10), (42, 34), (6, 2), (34, 6), (16, 4), (24, 41), (5, 13), (14, 39), (44, 2), (18, 22), (17, 30), (4, 9), (24, 26), (2, 40), (27, 13), (30, 40), (9, 12), (2, 26), (6, 42), (38, 43), (28, 43), (36, 20), (36, 9), (14, 36), (44, 4), (39, 40), (44, 9), (44, 40), (38, 2), (23, 17), (15, 10), (43, 27), (17, 3), (35, 44), (20, 30), (23, 1), (7, 13), (10, 21), (23, 29), (3, 38), (30, 37), (25, 3), (19, 0), (37, 31), (27, 42), (7, 11), (41, 13), (29, 35), (36, 23), (6, 0), (32, 36), (24, 12), (3, 17), (29, 32), (41, 35), (6, 35), (4, 30), (6, 14), (37, 4), (32, 12), (12, 1), (3, 34), (29, 20), (24, 23), (9, 43), (20, 23), (22, 19), (27, 29), (7, 45), (7, 40), (7, 21), (11, 5), (30, 25), (34, 43), (15, 34), (12, 16), (30, 18), (21, 39), (40, 6), (39, 4), (26, 34), (29, 33), (31, 18), (21, 19), (18, 44), (7, 25), (28, 0), (11, 42), (8, 21), (9, 27), (12, 29), (1, 39), (40, 34), (12, 6), (20, 19), (16, 26), (33, 17), (0, 37), (18, 18), (20, 45), (42, 45), (7, 24), (12, 26), (8, 3), (43, 24), (36, 4), (27, 20), (16, 15), (6, 40), (34, 20), (42, 30), (34, 31), (23, 22), (5, 3), (23, 33), (32, 37), (34, 16), (30, 31), (6, 23), (26, 33), (17, 40), (22, 32), (20, 3), (24, 5), (11, 36), (13, 15), (21, 35), (35, 25), (43, 7), (27, 1), (14, 45), (16, 32), (1, 22), (10, 30), (19, 4), (8, 0), (36, 0), (43, 38), (1, 42), (13, 40), (1, 35), (1, 8), (13, 9), (41, 5), (19, 5), (38, 27), (35, 12), (15, 4), (3, 45), (6, 31), (19, 10), (34, 42), (11, 2), (35, 4), (44, 37), (39, 3), (20, 4), (8, 13), (24, 24), (40, 9), (35, 19), (44, 10), (29, 11), (32, 33), (23, 14), (9, 21), (41, 32), (40, 3), (39, 14), (29, 12), (5, 4), (0, 3), (39, 30), (15, 41), (10, 33), (10, 45), (42, 3), (8, 37), (0, 19), (32, 11), (18, 30), (26, 13), (20, 5), (32, 32), (20, 1), (4, 3), (36, 33), (36, 17), (21, 0), (23, 35), (14, 31), (19, 40), (35, 23), (9, 18), (36, 30), (17, 33), (22, 1), (26, 35), (18, 15), (39, 24), (32, 21), (20, 10), (41, 39), (18, 25), (6, 10), (1, 13), (7, 26), (33, 8), (7, 4), (0, 20), (12, 22), (34, 28), (23, 18), (14, 7), (0, 25), (13, 34), (28, 36), (28, 7), (1, 37), (18, 12), (12, 20), (1, 12), (1, 11), (34, 2), (34, 0), (26, 39), (2, 13), (20, 17), (33, 16), (6, 36), (28, 15), (2, 4), (2, 15), (42, 42), (27, 16), (34, 19), (38, 10), (0, 24), (5, 10), (38, 28), (35, 14), (20, 44), (34, 37), (32, 2), (22, 30), (3, 35), (40, 11), (37, 14), (18, 23), (32, 30), (31, 38), (8, 7), (25, 42), (14, 15), (19, 37), (7, 10), (13, 45), (25, 4), (4, 44), (41, 12), (18, 10), (8, 32), (2, 19), (28, 32), (27, 24), (13, 10), (15, 44), (28, 2), (30, 5), (2, 3), (34, 3), (4, 2), (17, 14), (29, 3), (26, 41), (27, 19), (22, 6), (35, 45), (38, 36), (30, 27), (2, 18), (40, 28), (21, 10), (5, 16), (5, 24), (35, 3), (21, 1), (14, 35), (7, 2), (33, 40), (34, 24), (6, 34), (31, 21), (13, 5), (24, 0), (28, 41), (25, 43), (2, 16), (3, 36), (19, 20), (11, 23), (20, 2), (8, 31), (31, 29), (40, 24), (33, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 20), (17, 26), (27, 34), (18, 24), (21, 7), (10, 40), (38, 7), (41, 8), (3, 22), (41, 9), (28, 8), (36, 45), (22, 36), (12, 13), (6, 40), (39, 8), (30, 47), (41, 38), (38, 1), (28, 44), (39, 32), (27, 11), (3, 47), (14, 29), (17, 0), (6, 5), (15, 2), (32, 21), (20, 29), (39, 0), (39, 15), (37, 41), (22, 6), (7, 20), (14, 23), (31, 13), (20, 17), (34, 41), (40, 38), (2, 47), (3, 38), (15, 39), (27, 16), (22, 43), (38, 2), (1, 7), (11, 5), (0, 35), (35, 44), (12, 7), (9, 29), (43, 39), (25, 29), (20, 14), (17, 39), (4, 39), (14, 18), (20, 5), (22, 28), (15, 46), (35, 13), (16, 26), (16, 43), (28, 28), (18, 46), (27, 29), (7, 16), (29, 20), (2, 30), (15, 12), (12, 12), (35, 0), (32, 44), (0, 28), (2, 34), (27, 17), (7, 12), (18, 34), (40, 46), (4, 16), (18, 22), (16, 1), (25, 41), (35, 30), (6, 3), (30, 5), (38, 29), (0, 19), (11, 29), (30, 37), (34, 28), (12, 44), (9, 19), (18, 0), (22, 26), (30, 41), (36, 5), (30, 38), (5, 47), (20, 47), (37, 46), (13, 13), (9, 2), (26, 33), (7, 0), (41, 10), (34, 44), (17, 10), (22, 42), (9, 8), (24, 36), (23, 9), (40, 4), (33, 37), (11, 8), (21, 38), (21, 13), (37, 44), (32, 12), (4, 46), (21, 20), (21, 17), (12, 32), (25, 7), (33, 22), (3, 0), (16, 20), (12, 42), (20, 3), (41, 12), (31, 30), (0, 38), (33, 46), (39, 37), (18, 21), (7, 31), (17, 45), (7, 4), (29, 40), (39, 45), (13, 45), (15, 3), (0, 42), (19, 12), (34, 6), (15, 35), (17, 43), (40, 19), (21, 10), (27, 45), (31, 31), (5, 21), (13, 24), (36, 6), (28, 17), (14, 3), (14, 4), (2, 21), (0, 6), (27, 2), (11, 6), (32, 45), (20, 31), (35, 9), (10, 11), (4, 33), (1, 14), (6, 8), (5, 0), (25, 37), (38, 10), (31, 6), (42, 20), (31, 3), (32, 36), (10, 4), (11, 24), (11, 45), (8, 31), (25, 35), (19, 32), (8, 9), (37, 16), (18, 30), (41, 11), (22, 31), (24, 23), (40, 43), (12, 47), (0, 40), (14, 7), (18, 44), (2, 38), (27, 23), (21, 23), (22, 40), (9, 10), (4, 43), (23, 41), (42, 5), (2, 3), (42, 10), (43, 28), (40, 5), (40, 13), (35, 15), (1, 1), (36, 33), (26, 42), (41, 19), (21, 36), (15, 47), (12, 21), (27, 41), (6, 26), (42, 16), (4, 2), (1, 15), (25, 46), (43, 26), (2, 4), (3, 16), (5, 33), (21, 22), (20, 22), (15, 14), (33, 45), (26, 10), (22, 46), (26, 28), (16, 12), (16, 15), (20, 23), (29, 28), (32, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 22), (18, 11), (14, 22), (16, 34), (11, 3), (15, 14), (31, 14), (29, 35), (36, 0), (4, 30), (11, 1), (37, 38), (31, 35), (41, 30), (3, 38), (23, 12), (31, 1), (33, 26), (39, 30), (9, 23), (33, 14), (21, 6), (8, 31), (31, 19), (9, 0), (41, 9), (11, 25), (25, 12), (3, 6), (21, 17), (7, 38), (32, 31), (17, 29), (41, 14), (27, 22), (4, 3), (4, 25), (7, 6), (30, 15), (11, 14), (28, 10), (39, 3), (28, 33), (34, 12), (21, 9), (0, 7), (15, 36), (38, 17), (5, 32), (34, 30), (21, 32), (17, 30), (27, 16), (13, 0), (9, 20), (21, 3), (37, 3), (0, 20), (35, 15), (20, 17), (20, 8), (14, 1), (24, 2), (41, 24), (39, 12), (23, 27), (28, 9), (0, 13), (3, 14), (1, 33), (31, 7), (3, 29), (39, 10), (17, 10), (35, 34), (4, 13), (32, 39), (36, 27), (2, 8), (3, 15), (34, 10), (5, 9), (30, 5), (8, 28), (26, 34), (5, 4), (15, 7), (30, 38), (5, 0), (27, 37), (32, 10), (38, 26), (6, 30), (25, 2), (28, 31), (10, 22), (3, 13), (3, 11), (2, 32), (18, 16), (37, 36), (12, 6), (32, 22), (25, 29), (39, 31), (38, 0), (41, 33), (4, 20), (12, 5), (7, 25), (1, 18), (35, 3), (22, 19), (18, 15), (0, 25), (15, 37), (5, 5), (24, 9), (10, 1), (38, 8), (33, 37), (8, 19), (10, 13), (13, 30), (40, 39), (29, 39), (19, 16), (10, 15), (26, 28), (12, 8), (11, 37), (27, 19), (28, 11), (12, 20), (0, 3), (28, 32), (37, 17), (37, 16), (0, 2), (39, 33), (16, 13), (9, 9), (11, 33), (28, 38), (7, 39), (33, 8), (13, 33), (18, 19), (23, 20), (13, 35), (41, 1), (29, 29), (17, 8), (0, 10), (1, 36), (10, 32), (33, 15), (20, 10), (41, 17), (6, 35), (6, 9), (4, 29), (39, 9), (26, 29), (34, 3), (30, 39), (39, 29), (20, 13), (23, 4), (30, 10), (6, 8), (5, 3), (3, 39), (8, 10), (41, 15), (39, 11), (31, 10), (31, 23), (33, 34), (0, 6), (40, 28), (14, 16), (26, 23), (3, 0), (2, 23), (20, 7), (15, 8), (30, 11), (26, 4), (15, 11), (11, 34), (9, 13), (37, 29), (18, 35), (33, 19), (4, 37), (5, 22), (4, 23), (27, 38), (27, 18), (10, 0), (39, 38), (38, 10), (34, 19), (6, 34), (5, 39), (21, 19), (9, 18), (3, 37), (16, 1), (17, 35), (12, 25), (26, 6), (3, 9), (23, 30), (6, 5), (12, 37), (16, 4), (23, 34), (23, 25), (11, 20), (21, 24), (29, 31), (17, 28), (38, 23), (33, 38), (40, 4), (13, 9), (14, 3), (7, 19), (21, 27), (37, 30), (33, 25), (14, 0), (3, 33), (28, 34), (10, 21), (13, 21), (13, 20), (34, 25), (2, 10), (8, 24), (16, 38), (37, 24), (31, 37), (16, 22), (20, 31), (25, 11), (0, 4), (35, 11), (13, 26), (33, 7), (29, 10), (19, 20), (14, 6), (14, 38), (9, 26), (23, 11), (30, 30), (25, 9), (30, 21), (41, 12), (19, 18), (31, 36), (28, 5), (2, 3), (27, 2), (0, 1), (23, 17), (24, 0), (1, 10), (5, 8), (22, 24), (19, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 21), (26, 31), (33, 36), (17, 24), (27, 40), (32, 17), (5, 26), (41, 38), (42, 6), (5, 3), (0, 8), (14, 1), (15, 42), (17, 10), (28, 18), (13, 6), (24, 11), (31, 15), (20, 12), (12, 1), (1, 30), (25, 33), (33, 5), (15, 39), (24, 3), (44, 43), (28, 45), (38, 1), (43, 46), (3, 25), (0, 26), (12, 11), (11, 20), (13, 5), (26, 47), (17, 26), (20, 40), (25, 13), (20, 14), (45, 35), (13, 40), (43, 5), (8, 11), (40, 36), (41, 2), (6, 16), (21, 35), (2, 37), (45, 7), (18, 4), (25, 28), (37, 39), (7, 13), (11, 22), (18, 43), (8, 1), (21, 41), (25, 37), (36, 17), (4, 38), (23, 16), (37, 10), (5, 39), (43, 0), (29, 15), (24, 13), (9, 25), (2, 1), (45, 9), (20, 26), (27, 17), (18, 34), (5, 40), (4, 28), (0, 27), (17, 17), (16, 42), (44, 3), (30, 46), (36, 24), (39, 31), (23, 44), (37, 45), (4, 36), (27, 38), (36, 46), (4, 12), (11, 37), (26, 0), (42, 22), (45, 34), (31, 13), (37, 42), (34, 42), (11, 11), (43, 35), (39, 39), (30, 44), (40, 10), (36, 18), (5, 29), (5, 2), (12, 32), (19, 34), (33, 33), (10, 33), (16, 3), (20, 32), (18, 23), (31, 24), (41, 18), (36, 39), (18, 10), (42, 34), (26, 16), (44, 0), (18, 36), (20, 9), (5, 47), (0, 4), (21, 39), (1, 32), (39, 40), (26, 8), (2, 26), (9, 28), (21, 26), (33, 46), (43, 32), (28, 4), (38, 13), (41, 34), (1, 43), (12, 31), (38, 40), (30, 15), (39, 5), (32, 28), (44, 17), (6, 22), (35, 37), (4, 15), (21, 30), (12, 22), (32, 12), (44, 14), (19, 15), (21, 10), (28, 3), (14, 6), (40, 45), (9, 8), (9, 4), (12, 0), (34, 11), (20, 10), (34, 17), (44, 21), (25, 16), (19, 14), (11, 18), (7, 21), (10, 20), (41, 17), (36, 1), (40, 23), (10, 40), (42, 3), (26, 43), (5, 4), (41, 10), (20, 22), (36, 23), (40, 34), (34, 29), (8, 8), (40, 28), (31, 23), (37, 4), (10, 12), (37, 0), (6, 4), (45, 30), (30, 45), (17, 34), (39, 41), (8, 9), (26, 23), (26, 1), (7, 39), (4, 8), (6, 23), (17, 11), (21, 16), (31, 26), (14, 15), (5, 16), (0, 9), (5, 17), (22, 1), (29, 38), (10, 4), (24, 31), (38, 19), (33, 37), (35, 35), (3, 2), (15, 19), (0, 28), (45, 28), (11, 43), (13, 25), (17, 30), (44, 25), (6, 26), (33, 30), (15, 9), (4, 6), (21, 20), (33, 15), (37, 20), (38, 17), (36, 2), (25, 22), (13, 2), (29, 45), (1, 0), (40, 8), (38, 14), (35, 46), (43, 17), (23, 45), (7, 14), (25, 31), (14, 31), (8, 18), (42, 5), (34, 27), (5, 6), (26, 15), (42, 27), (10, 9), (26, 21), (37, 40), (28, 10), (32, 2), (39, 6), (41, 16), (38, 8), (26, 34), (31, 17), (31, 37), (27, 36), (37, 1), (16, 0), (44, 40), (1, 21), (10, 21), (39, 32), (40, 31), (35, 4), (10, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 18), (6, 32), (47, 31), (24, 38), (5, 40), (43, 5), (35, 32), (45, 7), (30, 24), (36, 5), (36, 0), (30, 6), (21, 29), (9, 16), (47, 5), (12, 37), (29, 37), (25, 36), (32, 33), (37, 12), (41, 31), (11, 27), (9, 3), (3, 4), (10, 30), (28, 6), (11, 10), (14, 20), (10, 9), (12, 20), (22, 22), (24, 3), (9, 35), (18, 23), (3, 29), (23, 40), (4, 1), (30, 18), (37, 24), (24, 32), (25, 19), (41, 15), (35, 14), (0, 18), (15, 24), (25, 34), (26, 25), (14, 40), (6, 3), (40, 22), (39, 38), (20, 19), (22, 13), (29, 0), (18, 17), (41, 23), (23, 1), (32, 16), (39, 25), (12, 5), (7, 30), (2, 7), (4, 9), (42, 0), (17, 6), (26, 16), (3, 9), (21, 35), (8, 11), (22, 5), (33, 7), (9, 32), (29, 26), (19, 18), (32, 34), (40, 18), (39, 23), (11, 30), (9, 7), (0, 6), (0, 30), (31, 38), (25, 23), (24, 17), (37, 31), (0, 12), (26, 29), (44, 13), (17, 10), (21, 23), (46, 38), (13, 37), (1, 24), (22, 39), (45, 16), (44, 31), (7, 20), (36, 40), (7, 23), (29, 8), (25, 4), (28, 38), (20, 40), (0, 27), (1, 36), (20, 36), (22, 6), (3, 19), (34, 26), (16, 39), (15, 15), (27, 31), (37, 22), (16, 0), (2, 1), (35, 38), (8, 26), (31, 11), (19, 26), (23, 6), (34, 0), (22, 38), (45, 22), (1, 26), (10, 1), (16, 23), (32, 1), (35, 33), (2, 28), (36, 27), (4, 11), (29, 1), (45, 6), (27, 30), (40, 2), (16, 21), (41, 12), (28, 16), (42, 9), (20, 39), (20, 34), (36, 38), (12, 32), (17, 29), (44, 16), (8, 28), (46, 22), (18, 25), (32, 12), (23, 34), (7, 6), (34, 24), (11, 15), (0, 34), (8, 4), (33, 12), (23, 29), (43, 9), (1, 6), (13, 40), (41, 35), (28, 2), (33, 30), (32, 29), (19, 11), (47, 10), (34, 21), (40, 26), (39, 17), (15, 3), (39, 33), (40, 8), (0, 31), (33, 24), (10, 39), (39, 5), (35, 20), (23, 37), (34, 2), (0, 25), (33, 22), (46, 21), (4, 27), (3, 2), (30, 35), (33, 32), (37, 28), (2, 19), (15, 2), (25, 31), (17, 2), (2, 3), (43, 19), (22, 25), (41, 16), (4, 18), (28, 17), (5, 6), (8, 24), (25, 24), (8, 16), (32, 26), (11, 29), (40, 11), (35, 25), (30, 38), (39, 28), (26, 12), (21, 27), (38, 0), (36, 2), (17, 5), (4, 6), (0, 32), (0, 37), (32, 2), (23, 14), (37, 14), (43, 4), (38, 20), (11, 8), (47, 35), (23, 2), (46, 18), (1, 13), (8, 22), (37, 21), (0, 26), (27, 14), (37, 33), (5, 11), (34, 23), (19, 39), (24, 36), (30, 5), (21, 33), (34, 33), (43, 31), (14, 5), (23, 17), (28, 35), (47, 25), (6, 37), (41, 1), (14, 31), (12, 22), (18, 38), (43, 12), (31, 16), (35, 10), (7, 28), (31, 9), (28, 20), (30, 12), (19, 8), (30, 0), (29, 38), (32, 37), (0, 21), (16, 27), (45, 25), (43, 32), (32, 17), (44, 30), (41, 17), (34, 30), (9, 40), (21, 15), (14, 25), (27, 32), (2, 23), (11, 35), (19, 29), (37, 15), (45, 30), (42, 38), (17, 33), (27, 28), (26, 6), (8, 18), (30, 16), (38, 8), (28, 30), (42, 8), (18, 29), (38, 7), (9, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 2), (13, 32), (42, 2), (24, 5), (4, 4), (38, 31), (40, 9), (10, 12), (5, 1), (16, 17), (1, 26), (33, 4), (5, 30), (15, 23), (27, 2), (32, 35), (18, 33), (28, 7), (25, 36), (40, 13), (16, 8), (31, 15), (22, 18), (28, 29), (2, 6), (28, 11), (28, 26), (0, 7), (1, 10), (29, 11), (10, 39), (9, 31), (31, 8), (36, 27), (9, 41), (27, 40), (23, 9), (12, 42), (19, 14), (25, 23), (38, 14), (8, 25), (15, 15), (13, 16), (13, 4), (39, 12), (35, 26), (32, 9), (39, 0), (41, 11), (31, 17), (30, 21), (3, 28), (4, 37), (0, 30), (26, 6), (18, 34), (14, 30), (37, 38), (6, 5), (25, 39), (11, 14), (5, 25), (10, 30), (17, 33), (37, 12), (6, 34), (19, 35), (28, 22), (27, 32), (34, 36), (28, 2), (7, 14), (33, 13), (6, 19), (5, 39), (17, 42), (16, 2), (4, 14), (19, 39), (33, 20), (39, 37), (34, 19), (18, 10), (41, 27), (37, 34), (5, 5), (22, 6), (16, 39), (0, 33), (2, 37), (39, 2), (40, 21), (6, 30), (36, 22), (23, 5), (6, 20), (28, 42), (36, 39), (4, 36), (9, 42), (2, 34), (17, 22), (1, 25), (17, 15), (14, 17), (17, 3), (23, 14), (10, 42), (18, 23), (14, 7), (8, 16), (34, 12), (27, 3), (13, 20), (0, 8), (2, 24), (38, 38), (33, 6), (37, 5), (37, 7), (38, 2), (42, 13), (10, 32), (36, 34), (26, 8), (5, 7), (17, 34), (24, 40), (19, 21), (23, 38), (4, 1), (20, 5), (32, 3), (27, 24), (13, 42), (15, 6), (15, 40), (19, 10), (33, 32), (26, 33), (1, 20), (3, 14), (6, 24), (22, 22), (36, 33), (11, 33), (17, 24), (23, 23), (15, 32), (21, 24), (2, 18), (36, 17), (8, 34), (11, 26), (16, 16), (2, 10), (39, 10), (26, 32), (34, 41), (19, 3), (41, 0), (17, 31), (28, 17), (15, 20), (34, 21), (33, 29), (3, 33), (35, 33), (7, 28), (31, 7), (40, 14), (25, 24), (35, 40), (37, 17), (4, 9), (23, 1), (1, 3), (2, 43), (10, 43), (19, 38), (32, 11), (9, 29), (19, 15), (15, 11), (33, 34), (33, 18), (2, 14), (26, 7), (26, 41), (38, 15), (19, 18), (29, 5), (21, 28), (33, 43), (26, 42), (12, 39), (12, 2), (36, 2), (27, 8), (40, 17), (26, 36), (4, 40), (30, 27), (38, 4), (13, 21), (31, 6), (40, 19), (32, 24), (23, 15), (14, 34), (16, 14), (15, 36), (40, 31), (17, 7), (1, 29), (43, 19), (21, 2), (12, 24), (11, 23), (15, 42), (34, 13), (11, 6), (19, 26), (32, 32), (42, 35), (25, 12), (29, 36), (37, 43), (23, 26), (11, 7), (7, 5), (27, 25), (0, 36), (11, 18), (41, 38), (34, 1), (40, 25), (5, 34), (3, 20), (27, 15), (40, 24), (15, 31), (35, 11), (11, 0), (32, 40), (27, 7), (0, 29), (9, 35), (34, 31), (29, 3), (4, 5), (37, 8), (18, 7), (13, 37), (30, 17), (39, 13), (27, 16), (16, 40), (9, 33), (24, 20), (25, 2), (32, 33), (28, 28), (3, 9), (17, 28), (6, 4), (42, 0), (15, 4), (37, 14), (36, 36), (10, 15), (43, 8), (9, 18), (40, 28), (32, 16), (2, 5), (4, 3), (4, 22), (34, 33), (33, 15), (14, 10), (13, 43), (19, 27), (24, 9), (26, 11), (39, 25), (9, 25), (18, 12), (20, 28), (24, 10), (10, 18), (2, 9), (2, 32), (12, 21), (41, 21), (39, 35), (8, 39), (20, 40), (6, 29), (16, 5), (38, 35), (9, 9), (16, 6), (41, 24), (2, 17), (23, 2), (41, 35), (37, 31), (37, 15), (4, 27), (34, 28), (11, 31), (40, 12), (18, 31), (27, 11), (39, 41), (37, 2), (35, 6), (39, 20), (26, 4), (39, 24), (18, 35), (37, 21), (28, 32), (42, 34), (42, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 46), (30, 42), (27, 13), (16, 26), (12, 34), (5, 5), (10, 42), (20, 32), (38, 4), (10, 25), (16, 42), (40, 2), (1, 6), (45, 5), (40, 38), (16, 12), (19, 6), (7, 20), (42, 41), (8, 28), (17, 12), (2, 20), (44, 17), (42, 7), (40, 14), (9, 9), (39, 0), (41, 47), (29, 25), (7, 4), (36, 23), (19, 18), (0, 14), (33, 46), (33, 31), (39, 27), (25, 12), (26, 12), (26, 42), (3, 45), (17, 21), (42, 45), (12, 13), (1, 19), (36, 25), (22, 3), (30, 47), (23, 24), (20, 45), (0, 46), (24, 18), (43, 18), (38, 25), (46, 35), (33, 34), (47, 4), (46, 3), (5, 14), (44, 45), (7, 15), (15, 2), (31, 7), (20, 39), (29, 37), (7, 43), (32, 24), (47, 11), (13, 7), (46, 31), (18, 5), (5, 34), (14, 37), (45, 10), (21, 46), (21, 37), (47, 45), (13, 5), (14, 31), (39, 8), (33, 3), (2, 27), (25, 13), (0, 3), (38, 2), (31, 37), (15, 28), (14, 12), (42, 5), (11, 3), (33, 14), (14, 20), (37, 0), (35, 11), (34, 17), (18, 6), (22, 29), (25, 10), (34, 2), (47, 41), (35, 44), (23, 25), (20, 1), (22, 21), (15, 4), (9, 34), (21, 18), (13, 26), (13, 10), (29, 36), (12, 15), (17, 17), (36, 37), (18, 28), (42, 33), (37, 36), (23, 34), (25, 40), (23, 28), (43, 20), (12, 16), (3, 19), (46, 0), (34, 20), (25, 37), (3, 17), (47, 18), (38, 7), (30, 10), (13, 30), (32, 3), (11, 38), (33, 35), (19, 46), (33, 21), (41, 9), (24, 32), (1, 40), (25, 33), (24, 47), (6, 34), (4, 40), (27, 11), (17, 23), (0, 23), (19, 22), (36, 33), (26, 45), (25, 30), (24, 16), (5, 23), (28, 5), (34, 23), (4, 20), (37, 2), (22, 41), (39, 28), (45, 22), (28, 34), (14, 8), (19, 15), (28, 22), (13, 42), (11, 0), (23, 23), (1, 30), (11, 2), (41, 41), (21, 23), (39, 21), (10, 0), (7, 39), (33, 15), (13, 46), (5, 7), (34, 24), (24, 23), (24, 30), (12, 43), (40, 39), (34, 22), (10, 23), (34, 27), (8, 27), (25, 19), (37, 16), (17, 6), (9, 21), (4, 5), (21, 5), (45, 29), (16, 30), (33, 29), (38, 32), (32, 40), (36, 32), (16, 32), (31, 18), (26, 39), (15, 21), (11, 44), (42, 16), (47, 0), (31, 30), (1, 12), (21, 43), (45, 42), (46, 17), (40, 46), (20, 31), (1, 22), (28, 46), (34, 31), (30, 37), (37, 37), (9, 46), (8, 21), (42, 11), (9, 15), (25, 26), (8, 47), (27, 45), (17, 28), (36, 9), (34, 26), (35, 35), (4, 3), (17, 38), (6, 42), (39, 35), (20, 34), (27, 7), (8, 38), (6, 19), (16, 6), (33, 4), (32, 20), (10, 40), (21, 14), (29, 47), (20, 5), (1, 24), (0, 5), (6, 9), (20, 3), (46, 28), (15, 13), (28, 21), (23, 38), (1, 46), (18, 32), (46, 44), (42, 2), (16, 33), (46, 33), (12, 47), (17, 3), (4, 45), (0, 30), (39, 32), (12, 29), (6, 40), (32, 23), (41, 42), (10, 16), (9, 1), (27, 39), (40, 27), (42, 36), (22, 30), (4, 18), (29, 6), (0, 16), (1, 26), (3, 30), (8, 13), (16, 43), (6, 44), (30, 40), (6, 23), (37, 7), (34, 5), (2, 15), (29, 42), (13, 37), (44, 46), (26, 37), (26, 31), (19, 27), (16, 44), (44, 6), (23, 5), (17, 24), (44, 1), (13, 4), (32, 37), (22, 42), (44, 23), (10, 35), (33, 1), (30, 8), (29, 24), (2, 46), (20, 22), (44, 28), (28, 47), (15, 37), (2, 11), (4, 19), (5, 39), (21, 1), (25, 39), (18, 0), (8, 11), (29, 43), (40, 40), (9, 19), (40, 42), (9, 30), (40, 6), (1, 41), (39, 4), (41, 26), (30, 16), (21, 36), (9, 39), (15, 16), (41, 22), (40, 9), (14, 15), (2, 39), (31, 9), (28, 35), (19, 25), (0, 33), (36, 44), (6, 2), (29, 8), (41, 18), (22, 15), (13, 8), (47, 1), (41, 11), (4, 25), (29, 3), (5, 12), (38, 27), (21, 47), (35, 7), (6, 18), (22, 7), (17, 8), (10, 27), (39, 2), (45, 1), (1, 33), (47, 25), (29, 38), (46, 22), (23, 6), (14, 5), (3, 23), (38, 15), (43, 16), (43, 47), (6, 3), (8, 1), (3, 43), (16, 9), (30, 25), (13, 11), (3, 1), (11, 11), (29, 30), (28, 25), (38, 28), (24, 45), (36, 3), (2, 38), (30, 44), (6, 45), (22, 28), (13, 6), (31, 16), (9, 2), (20, 30), (28, 17), (37, 35), (5, 44), (15, 35), (30, 11), (13, 17), (46, 1), (2, 14), (27, 44), (13, 25), (2, 34), (3, 5), (31, 13), (1, 27), (4, 33), (22, 22), (20, 6), (34, 19), (12, 4), (41, 20), (7, 12), (3, 42), (21, 31), (35, 21), (15, 18), (28, 44), (21, 6), (0, 15), (15, 6), (38, 19), (22, 8), (40, 4), (24, 7), (41, 34), (40, 32), (10, 21), (19, 38), (6, 37), (20, 27), (34, 3), (20, 29), (32, 43), (23, 40), (15, 45), (36, 45), (14, 32), (16, 15), (39, 37), (45, 2), (2, 45), (32, 34), (11, 15), (6, 39), (12, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 13), (27, 39), (12, 24), (43, 21), (25, 12), (24, 0), (43, 17), (33, 32), (44, 24), (13, 22), (10, 3), (17, 22), (37, 32), (21, 10), (35, 38), (28, 39), (27, 28), (42, 0), (5, 24), (15, 21), (2, 16), (11, 22), (25, 24), (19, 12), (25, 33), (40, 20), (32, 25), (2, 21), (3, 0), (16, 15), (10, 37), (41, 21), (31, 16), (28, 11), (8, 36), (39, 1), (42, 4), (22, 32), (10, 28), (17, 34), (42, 24), (11, 12), (35, 33), (27, 19), (3, 26), (16, 27), (1, 7), (10, 15), (42, 17), (35, 8), (9, 39), (14, 18), (36, 5), (21, 21), (37, 15), (8, 28), (15, 14), (6, 28), (32, 18), (10, 21), (39, 29), (19, 11), (35, 16), (37, 38), (27, 25), (6, 7), (23, 10), (30, 18), (39, 24), (39, 23), (12, 30), (9, 28), (32, 8), (39, 9), (44, 0), (11, 29), (44, 19), (29, 32), (29, 10), (39, 16), (13, 8), (14, 4), (7, 24), (36, 8), (39, 26), (12, 29), (31, 32), (0, 16), (21, 20), (6, 14), (18, 1), (13, 16), (10, 35), (44, 15), (30, 3), (5, 31), (20, 20), (38, 24), (25, 26), (15, 38), (6, 6), (13, 26), (21, 31), (27, 17), (25, 31), (21, 6), (18, 29), (17, 2), (30, 26), (20, 21), (17, 7), (39, 11), (13, 18), (31, 15), (16, 24), (40, 2), (5, 32), (8, 30), (7, 37), (13, 10), (36, 12), (2, 2), (30, 2), (12, 34), (26, 8), (18, 23), (14, 15), (21, 30), (5, 0), (16, 26), (32, 31), (14, 25), (44, 4), (26, 31), (39, 19), (5, 19), (7, 26), (26, 16), (35, 11), (42, 22), (16, 39), (11, 2), (22, 20), (34, 1), (27, 36), (22, 3), (21, 37), (41, 28), (7, 30), (40, 11), (29, 21), (41, 1), (21, 14), (14, 2), (1, 17), (14, 10), (31, 6), (20, 32), (4, 37), (6, 10), (19, 13), (23, 20), (38, 22), (28, 2), (14, 9), (40, 8), (15, 12), (18, 34), (9, 33), (11, 26), (16, 1), (16, 10), (27, 3), (36, 38), (19, 26), (31, 10), (12, 6), (39, 15), (17, 15), (41, 3), (32, 33), (20, 8), (26, 9), (33, 35), (1, 26), (8, 33), (0, 8), (5, 27), (4, 28), (38, 15), (33, 7), (35, 6), (27, 2), (24, 31), (42, 37), (39, 2), (37, 24), (7, 14), (24, 3), (36, 21), (38, 8), (12, 37), (42, 27), (25, 38), (17, 1), (14, 23), (7, 38), (13, 11), (14, 0), (3, 2), (34, 3), (24, 20), (19, 28), (23, 22), (36, 27), (1, 27), (20, 6), (43, 32), (26, 11), (10, 36), (6, 1), (44, 6), (25, 19), (24, 10), (26, 25), (38, 2), (41, 13), (23, 4), (10, 22), (25, 21), (17, 24), (16, 0), (2, 5), (19, 36), (3, 24), (13, 5), (16, 8), (42, 5), (41, 14), (10, 0), (43, 11), (17, 18), (42, 31), (5, 5), (1, 15), (6, 39), (24, 23), (13, 7), (43, 23), (40, 7), (2, 29), (35, 13), (33, 12), (28, 34), (15, 18), (12, 23), (4, 2), (10, 1), (24, 11), (21, 23), (13, 1), (13, 30), (38, 9), (43, 33), (4, 9), (43, 39), (37, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 37), (30, 20), (3, 7), (4, 7), (10, 16), (32, 23), (14, 0), (35, 41), (21, 28), (25, 35), (27, 28), (27, 29), (25, 37), (38, 29), (36, 41), (10, 37), (38, 20), (0, 34), (33, 5), (10, 6), (29, 0), (28, 28), (30, 36), (19, 39), (5, 13), (28, 20), (31, 2), (17, 24), (40, 19), (10, 22), (6, 37), (36, 29), (15, 32), (27, 0), (15, 30), (21, 27), (22, 27), (2, 38), (37, 33), (12, 17), (13, 15), (18, 11), (11, 37), (25, 39), (29, 17), (29, 10), (11, 25), (19, 12), (4, 30), (16, 23), (21, 14), (37, 28), (38, 5), (7, 7), (18, 7), (11, 21), (34, 36), (32, 22), (40, 40), (32, 21), (5, 22), (24, 4), (2, 33), (30, 41), (27, 40), (21, 4), (23, 3), (23, 16), (0, 3), (39, 29), (2, 21), (19, 4), (7, 12), (25, 25), (38, 1), (33, 38), (17, 4), (11, 33), (0, 40), (20, 39), (5, 8), (32, 1), (37, 10), (23, 29), (25, 11), (4, 33), (37, 24), (7, 20), (29, 40), (24, 12), (28, 18), (0, 29), (9, 23), (22, 13), (21, 3), (1, 26), (10, 13), (32, 32), (5, 38), (8, 1), (5, 18), (27, 16), (30, 14), (28, 26), (37, 29), (24, 9), (40, 42), (32, 41), (36, 12), (19, 27), (36, 9), (39, 7), (31, 35), (40, 14), (14, 37), (25, 14), (8, 9), (1, 39), (13, 33), (10, 34), (1, 18), (16, 1), (4, 37), (21, 31), (39, 1), (33, 7), (17, 14), (40, 36), (12, 35), (19, 8), (26, 30), (8, 22), (12, 18), (7, 16), (21, 42), (1, 19), (25, 24), (17, 33), (35, 23), (23, 19), (24, 3), (27, 9), (13, 0), (4, 28), (10, 41), (17, 18), (30, 7), (30, 19), (3, 33), (28, 38), (8, 2), (20, 37), (3, 15), (20, 10), (16, 35), (29, 27), (6, 3), (6, 22), (17, 25), (35, 24), (19, 30), (18, 13), (37, 19), (11, 17), (36, 11), (28, 37), (14, 38), (18, 32), (15, 23), (6, 40), (18, 6), (40, 41), (33, 29), (39, 30), (17, 19), (2, 12), (13, 28), (1, 2), (26, 43), (21, 30), (29, 32), (14, 43), (35, 37), (16, 28), (22, 41), (1, 17), (5, 30), (0, 35), (14, 6), (24, 5), (4, 20), (34, 2), (21, 6), (1, 8), (30, 3), (2, 42), (18, 31), (37, 38), (25, 27), (21, 11), (23, 24), (4, 27), (18, 22), (22, 34), (31, 4), (8, 33), (14, 19), (7, 43), (19, 35), (30, 29), (4, 42), (26, 19), (31, 30), (22, 8), (26, 41), (28, 31), (12, 24), (28, 16), (36, 5), (26, 33), (23, 37), (0, 14), (16, 25), (13, 26), (40, 35), (16, 22), (17, 6), (14, 23), (34, 43), (17, 32), (23, 21), (19, 25), (21, 9), (15, 17), (31, 42), (26, 18), (20, 32), (0, 22), (25, 13), (33, 34), (38, 40), (23, 34), (11, 5), (6, 17), (30, 5), (27, 8), (39, 32), (35, 4), (27, 32), (16, 2), (1, 28), (14, 12), (14, 13), (0, 42), (0, 39), (8, 26), (5, 29), (12, 36), (26, 39), (13, 2), (2, 9), (18, 26), (1, 22), (17, 35), (2, 3), (25, 2), (14, 36), (9, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 11), (29, 1), (9, 24), (11, 38), (41, 14), (36, 9), (17, 33), (15, 8), (33, 37), (28, 26), (22, 42), (42, 27), (20, 38), (19, 2), (4, 27), (0, 45), (26, 3), (22, 44), (35, 4), (26, 43), (9, 1), (11, 42), (40, 36), (21, 13), (20, 5), (25, 4), (27, 24), (13, 25), (16, 6), (17, 3), (7, 0), (14, 21), (3, 46), (18, 9), (11, 5), (21, 16), (4, 24), (36, 1), (1, 6), (10, 1), (3, 27), (25, 18), (14, 28), (6, 8), (29, 12), (32, 27), (4, 43), (26, 18), (1, 9), (17, 28), (8, 42), (37, 43), (33, 22), (19, 23), (11, 16), (31, 42), (6, 11), (23, 46), (16, 3), (9, 31), (27, 5), (5, 37), (5, 16), (24, 6), (3, 38), (16, 8), (12, 2), (22, 5), (12, 15), (19, 42), (22, 33), (19, 28), (39, 12), (17, 31), (20, 13), (31, 25), (38, 1), (20, 4), (28, 14), (10, 32), (3, 40), (17, 46), (26, 45), (29, 28), (29, 15), (37, 12), (30, 27), (32, 13), (9, 46), (25, 42), (31, 40), (20, 35), (34, 14), (37, 18), (31, 31), (3, 14), (18, 35), (33, 0), (28, 24), (27, 25), (7, 13), (37, 33), (31, 0), (8, 29), (1, 41), (35, 37), (9, 42), (6, 34), (1, 29), (29, 27), (38, 37), (35, 23), (41, 33), (25, 20), (14, 1), (20, 22), (17, 42), (28, 21), (7, 46), (14, 25), (40, 3), (12, 12), (12, 29), (39, 13), (8, 36), (40, 30), (18, 41), (17, 7), (6, 10), (13, 31), (35, 14), (20, 20), (13, 41), (17, 4), (15, 12), (16, 27), (9, 41), (21, 42), (39, 30), (7, 14), (0, 28), (27, 42), (34, 12), (33, 21), (36, 33), (7, 40), (24, 37), (22, 11), (17, 29), (27, 17), (42, 41), (3, 30), (29, 2), (14, 42), (39, 41), (40, 23), (22, 40), (42, 29), (12, 39), (19, 37), (41, 6), (36, 42), (7, 25), (30, 32), (21, 6), (17, 1), (41, 31), (8, 39), (34, 13), (11, 0), (29, 45), (26, 0), (37, 27), (31, 24), (7, 31), (29, 36), (10, 36), (10, 39), (29, 10), (14, 7), (18, 43), (18, 27), (14, 8), (11, 19), (40, 1), (5, 28), (30, 5), (30, 31), (31, 2), (10, 44), (5, 19), (15, 10), (27, 11), (29, 21), (4, 10), (9, 13), (29, 4), (6, 37), (21, 41), (12, 9), (24, 35), (22, 17), (10, 40), (10, 24), (5, 46), (23, 28), (42, 3), (33, 2), (24, 15), (9, 36), (18, 15), (9, 26), (26, 28), (16, 23), (29, 17), (3, 39), (4, 4), (30, 2), (32, 24), (18, 2), (11, 17), (11, 33), (2, 42), (30, 22), (19, 27), (14, 31), (2, 15), (39, 39), (7, 42), (8, 5), (35, 6), (20, 17), (34, 46), (26, 9), (21, 37), (3, 20), (9, 20), (12, 16), (13, 7), (8, 13), (13, 39), (23, 15), (38, 8), (14, 45), (18, 12), (25, 5), (9, 2), (10, 7), (38, 17), (3, 25), (38, 11), (42, 42), (34, 35), (23, 4), (25, 3), (35, 12), (0, 38), (36, 12), (2, 26), (9, 37), (24, 5), (27, 28), (7, 18), (35, 13), (26, 7), (10, 27), (40, 6), (39, 42), (7, 34), (5, 42), (37, 9), (40, 27), (21, 44), (33, 33), (3, 4), (17, 27), (4, 25), (37, 22), (12, 26), (22, 21), (35, 15), (33, 9), (19, 41), (29, 30), (22, 34), (7, 5), (30, 9), (2, 7), (15, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 45), (22, 37), (33, 23), (5, 33), (33, 3), (35, 37), (24, 19), (19, 14), (31, 31), (19, 43), (21, 41), (20, 17), (16, 5), (43, 11), (1, 16), (2, 6), (8, 43), (35, 26), (15, 2), (30, 46), (42, 27), (1, 42), (42, 12), (31, 36), (20, 11), (17, 47), (30, 21), (23, 0), (24, 6), (11, 19), (5, 17), (38, 28), (36, 42), (40, 39), (31, 2), (23, 7), (27, 44), (37, 19), (26, 37), (6, 7), (5, 35), (43, 18), (3, 13), (1, 31), (19, 26), (5, 31), (24, 25), (32, 41), (38, 25), (8, 34), (37, 46), (6, 16), (42, 29), (22, 21), (35, 4), (14, 23), (20, 9), (40, 16), (7, 46), (23, 42), (39, 3), (34, 25), (24, 36), (2, 32), (37, 1), (5, 25), (2, 43), (40, 8), (26, 36), (16, 22), (2, 15), (33, 22), (7, 38), (15, 11), (37, 41), (31, 20), (3, 24), (38, 13), (29, 24), (31, 8), (1, 13), (30, 8), (7, 5), (34, 38), (11, 40), (8, 0), (4, 36), (7, 7), (9, 11), (16, 29), (18, 35), (15, 26), (11, 11), (20, 15), (24, 8), (30, 33), (7, 33), (31, 21), (13, 20), (33, 26), (1, 19), (17, 36), (41, 23), (31, 28), (11, 7), (37, 23), (29, 21), (21, 36), (43, 23), (5, 36), (33, 13), (35, 39), (24, 24), (28, 1), (18, 10), (27, 29), (20, 2), (34, 4), (25, 19), (26, 12), (32, 34), (24, 35), (32, 22), (30, 32), (24, 27), (39, 5), (32, 7), (4, 22), (0, 30), (21, 22), (22, 28), (3, 47), (23, 30), (43, 38), (36, 20), (21, 38), (16, 42), (33, 46), (35, 2), (28, 3), (20, 42), (18, 22), (33, 44), (18, 39), (41, 5), (9, 39), (34, 40), (8, 35), (23, 46), (42, 13), (43, 33), (22, 29), (25, 6), (25, 11), (3, 27), (39, 45), (12, 16), (16, 24), (23, 23), (9, 8), (40, 37), (24, 39), (14, 5), (8, 27), (21, 9), (26, 2), (38, 35), (39, 26), (23, 3), (16, 21), (14, 36), (0, 34), (33, 28), (35, 42), (25, 1), (11, 0), (25, 24), (31, 34), (7, 42), (4, 27), (27, 24), (2, 20), (41, 1), (42, 14), (24, 3), (31, 23), (42, 9), (7, 9), (30, 2), (36, 3), (29, 42), (32, 9), (31, 39), (28, 33), (4, 2), (15, 32), (19, 15), (11, 47), (29, 40), (7, 39), (35, 31), (29, 37), (0, 41), (14, 1), (12, 39), (4, 42), (26, 8), (20, 39), (42, 45), (3, 40), (13, 33), (21, 10), (0, 17), (41, 21), (11, 15), (39, 39), (6, 17), (1, 20), (23, 22), (4, 25), (12, 6), (22, 40), (42, 46), (21, 35), (34, 13), (5, 28), (9, 24), (12, 12), (35, 16), (26, 33), (7, 3), (20, 47), (31, 19), (40, 6), (28, 26), (15, 6), (33, 30), (22, 31), (31, 5), (32, 26), (28, 24), (28, 38), (20, 33), (39, 28), (4, 30), (22, 30), (39, 9), (30, 42), (29, 45), (21, 43), (39, 0), (29, 34), (13, 11), (36, 37), (2, 37), (10, 30), (21, 27), (4, 7), (30, 18), (26, 20), (15, 25), (21, 23), (10, 12), (5, 38), (19, 0), (8, 16), (4, 19), (37, 29), (11, 42), (18, 29), (25, 27), (10, 17), (5, 11), (29, 0), (43, 2), (32, 43), (35, 35), (27, 35), (34, 32), (20, 19), (12, 19), (30, 26), (27, 18), (25, 44), (8, 4), (37, 6), (33, 5), (36, 21), (24, 1), (29, 36), (11, 37), (18, 45), (38, 20), (6, 6), (39, 24), (22, 19), (32, 40), (6, 43), (32, 1), (40, 46), (29, 17), (17, 4), (38, 43), (14, 19), (17, 18), (26, 26), (43, 21), (19, 44), (33, 42), (35, 33), (39, 30), (0, 47), (26, 38), (25, 23), (38, 11), (17, 17), (15, 13), (29, 43), (8, 2), (11, 16), (7, 1), (0, 5), (21, 17), (35, 36), (23, 21), (30, 36), (11, 25), (14, 40), (16, 26), (42, 26), (25, 32), (41, 6), (39, 33), (38, 9), (26, 0), (19, 16), (31, 4), (22, 4), (30, 25), (18, 1), (19, 28), (26, 16), (38, 17), (26, 32), (35, 25), (38, 22), (23, 24), (12, 10), (34, 29), (39, 47), (5, 3), (30, 43), (43, 8), (34, 12), (28, 37), (43, 37), (37, 8), (23, 15), (35, 13), (16, 47), (35, 18), (29, 15), (18, 9), (34, 19), (25, 22), (43, 26), (17, 10), (22, 16), (29, 47), (10, 2), (2, 4), (15, 0), (6, 4), (35, 40), (38, 26), (5, 26), (6, 39), (9, 26), (40, 11), (26, 45), (40, 43), (6, 10), (3, 16), (33, 45), (25, 46), (36, 23), (34, 37), (5, 24), (8, 25), (32, 47), (12, 45), (43, 30), (24, 18), (15, 30), (20, 44), (37, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 0), (19, 43), (12, 3), (33, 17), (35, 28), (17, 12), (25, 27), (6, 22), (27, 40), (24, 0), (14, 19), (14, 25), (11, 3), (24, 13), (22, 11), (40, 31), (33, 2), (0, 30), (10, 19), (6, 1), (6, 35), (29, 9), (30, 1), (26, 23), (41, 26), (12, 18), (36, 41), (17, 2), (32, 5), (45, 4), (7, 10), (41, 37), (44, 22), (18, 9), (14, 10), (19, 29), (13, 20), (35, 5), (27, 22), (23, 1), (5, 35), (46, 30), (5, 29), (40, 22), (20, 13), (5, 33), (9, 4), (7, 30), (44, 20), (15, 25), (39, 11), (44, 0), (38, 13), (44, 32), (11, 26), (18, 33), (22, 43), (0, 15), (44, 41), (39, 26), (38, 24), (36, 3), (31, 10), (38, 39), (23, 30), (43, 42), (11, 37), (12, 29), (0, 18), (24, 12), (23, 38), (1, 14), (3, 4), (12, 14), (39, 31), (0, 23), (42, 3), (1, 0), (10, 33), (9, 22), (12, 38), (27, 30), (39, 21), (21, 7), (7, 36), (44, 1), (16, 33), (44, 8), (13, 43), (13, 30), (11, 12), (7, 34), (47, 12), (46, 16), (26, 25), (35, 8), (5, 20), (37, 29), (42, 37), (46, 15), (40, 23), (47, 5), (8, 13), (47, 24), (19, 24), (37, 38), (35, 10), (22, 28), (6, 7), (7, 28), (45, 28), (10, 4), (35, 7), (2, 17), (12, 11), (5, 39), (11, 15), (35, 6), (3, 6), (38, 40), (23, 15), (17, 27), (24, 10), (18, 5), (35, 25), (45, 38), (40, 8), (3, 12), (42, 11), (34, 37), (21, 25), (41, 2), (7, 21), (12, 7), (46, 43), (35, 40), (9, 3), (16, 0), (29, 8), (31, 2), (47, 31), (28, 41), (13, 9), (25, 0), (6, 25), (37, 16), (46, 41), (15, 29), (7, 29), (41, 7), (35, 13), (9, 30), (15, 14), (27, 20), (10, 28), (32, 36), (18, 20), (34, 31), (44, 12), (42, 31), (30, 18), (28, 27), (28, 8), (35, 11), (32, 9), (29, 10), (9, 18), (47, 32), (6, 6), (20, 3), (46, 20), (30, 19), (16, 43), (17, 31), (40, 42), (47, 25), (0, 19), (35, 21), (19, 22), (11, 10), (43, 41), (42, 24), (32, 12), (16, 9), (43, 20), (35, 26), (21, 8), (16, 16), (28, 1), (17, 9), (20, 10), (10, 16), (6, 2), (39, 40), (23, 27), (42, 36), (43, 34), (33, 27), (38, 2), (6, 3), (6, 31), (11, 11), (3, 24), (2, 8), (46, 4), (40, 34), (9, 27), (10, 40), (5, 17), (5, 42), (46, 22), (46, 13), (20, 22), (17, 18), (27, 12), (13, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 27), (11, 32), (1, 37), (27, 16), (15, 45), (31, 1), (20, 41), (17, 9), (5, 15), (33, 43), (31, 31), (38, 3), (43, 21), (37, 25), (40, 37), (9, 7), (16, 6), (36, 13), (9, 15), (44, 12), (11, 14), (12, 31), (12, 28), (46, 42), (23, 30), (0, 22), (15, 22), (25, 22), (23, 25), (9, 44), (38, 18), (27, 22), (32, 16), (45, 29), (4, 36), (5, 12), (15, 27), (21, 39), (10, 35), (30, 7), (10, 45), (35, 46), (9, 41), (26, 24), (4, 37), (27, 15), (20, 36), (3, 23), (41, 30), (38, 41), (46, 8), (46, 46), (0, 1), (41, 23), (37, 44), (17, 19), (23, 28), (34, 35), (45, 22), (4, 38), (28, 34), (46, 35), (3, 33), (18, 28), (19, 6), (3, 16), (46, 1), (14, 13), (18, 17), (29, 11), (10, 37), (35, 4), (0, 9), (12, 21), (22, 44), (43, 45), (44, 31), (20, 33), (23, 36), (8, 7), (38, 8), (4, 2), (1, 17), (30, 32), (36, 11), (40, 20), (8, 15), (26, 22), (15, 4), (6, 26), (17, 10), (8, 39), (16, 38), (42, 15), (17, 18), (7, 0), (34, 39), (38, 31), (0, 20), (20, 46), (7, 23), (35, 18), (25, 10), (34, 24), (11, 34), (10, 11), (21, 44), (6, 14), (28, 28), (18, 20), (28, 15), (28, 32), (19, 23), (42, 0), (35, 22), (8, 23), (19, 42), (22, 7), (7, 36), (4, 35), (21, 19), (1, 40), (45, 21), (3, 2), (46, 37), (0, 46), (2, 15), (21, 30), (25, 44), (29, 3), (42, 3), (35, 3), (43, 23), (42, 14), (28, 33), (18, 19), (4, 31), (10, 7), (19, 12), (33, 23), (21, 29), (40, 1), (5, 5), (8, 22), (8, 45), (24, 8), (26, 34), (7, 40), (39, 43), (16, 40), (27, 21), (47, 33), (11, 30), (44, 32), (26, 12), (7, 13), (21, 46), (7, 37), (34, 26), (2, 8), (10, 33), (45, 31), (22, 26), (18, 21), (9, 36), (41, 25), (46, 33), (23, 34), (36, 15), (31, 5), (47, 19), (47, 29), (6, 46), (31, 37), (40, 24), (6, 44), (1, 31), (26, 16), (3, 39), (2, 37), (5, 33), (12, 22), (31, 0), (26, 32), (14, 27), (8, 21), (12, 42), (17, 46), (24, 12), (44, 5), (21, 11), (34, 11), (30, 10), (26, 23), (2, 32), (30, 19), (29, 8), (38, 32), (12, 9), (37, 8), (39, 7), (4, 40), (32, 15), (3, 40), (1, 39), (12, 0), (36, 1), (3, 31), (34, 23), (9, 18), (31, 41), (0, 12), (14, 45), (37, 10), (20, 43), (2, 35), (34, 25), (34, 38), (43, 41), (30, 3), (15, 16), (24, 20), (12, 44), (6, 33), (36, 40), (47, 41), (34, 34), (43, 16), (5, 20), (14, 46), (0, 14), (45, 40), (9, 2), (33, 12), (38, 42), (45, 26), (41, 33), (18, 13), (26, 39), (36, 19), (41, 8), (39, 21), (3, 30), (47, 21), (14, 34), (19, 35), (44, 19), (0, 38), (35, 9), (43, 46), (11, 6), (13, 24), (42, 25), (2, 29), (6, 6), (23, 35), (15, 15), (1, 1), (22, 4), (15, 28), (45, 7), (38, 37), (21, 15), (13, 0), (34, 13), (47, 26), (37, 46), (39, 6), (39, 3), (30, 43), (14, 10), (21, 3), (6, 22), (38, 6), (18, 46), (46, 23), (37, 24), (5, 17), (13, 44), (15, 35), (27, 6), (33, 29), (44, 38), (14, 32), (38, 27), (26, 31), (6, 35), (4, 18), (14, 14), (18, 0), (37, 15), (20, 23), (21, 13), (21, 23), (36, 35), (7, 33), (4, 12), (28, 35), (29, 22), (12, 29), (45, 42), (47, 1), (16, 2), (26, 21), (1, 13), (4, 34), (24, 4), (4, 1), (7, 38), (30, 44), (21, 6), (16, 46), (32, 45), (25, 15), (16, 34), (41, 0), (26, 33), (25, 20), (23, 13), (24, 10), (9, 21), (39, 28), (27, 2), (29, 34), (7, 7), (4, 15), (26, 7), (26, 38), (29, 45), (24, 31), (37, 6), (43, 26), (6, 45), (45, 27), (18, 27), (39, 45), (23, 17), (47, 30), (45, 17), (35, 29), (43, 37), (17, 37), (25, 18), (39, 12), (29, 27), (13, 29), (45, 44), (29, 23), (20, 37), (33, 10), (41, 14), (6, 34), (10, 9), (47, 42), (19, 34), (25, 35), (16, 13), (15, 26), (14, 4), (35, 27), (37, 1), (8, 28), (17, 16), (42, 38), (45, 20), (12, 17), (42, 46), (27, 1), (16, 29), (34, 29), (40, 44), (21, 2), (31, 22), (37, 12), (29, 24), (5, 42), (33, 3), (44, 0), (30, 13), (38, 1), (37, 23), (15, 18), (9, 26), (27, 3), (21, 20), (28, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 36), (20, 9), (24, 8), (23, 23), (16, 38), (17, 35), (7, 23), (21, 17), (6, 20), (39, 16), (17, 6), (39, 14), (37, 30), (5, 29), (35, 13), (10, 15), (30, 8), (33, 24), (2, 3), (4, 11), (33, 22), (24, 22), (1, 36), (36, 40), (13, 3), (15, 34), (5, 5), (15, 11), (37, 22), (40, 4), (32, 11), (2, 12), (22, 9), (10, 5), (13, 1), (33, 37), (11, 25), (14, 25), (10, 4), (35, 1), (33, 38), (8, 5), (5, 36), (32, 3), (6, 38), (13, 22), (23, 22), (23, 29), (20, 28), (0, 23), (27, 1), (11, 14), (36, 41), (2, 37), (24, 1), (23, 35), (16, 14), (27, 21), (16, 36), (26, 15), (19, 29), (4, 22), (35, 37), (8, 28), (33, 5), (2, 11), (20, 3), (25, 1), (3, 34), (30, 5), (31, 39), (25, 27), (5, 24), (33, 11), (12, 25), (35, 5), (28, 12), (31, 38), (2, 17), (18, 37), (17, 27), (35, 10), (17, 39), (11, 23), (28, 0), (1, 35), (1, 16), (3, 17), (18, 34), (20, 6), (15, 9), (38, 29), (17, 42), (30, 41), (13, 29), (8, 31), (4, 35), (32, 40), (30, 10), (2, 20), (18, 0), (37, 9), (13, 25), (30, 19), (40, 19), (34, 37), (15, 40), (28, 30), (26, 35), (26, 32), (25, 13), (13, 15), (37, 17), (22, 38), (0, 20), (6, 8), (40, 13), (11, 36), (18, 23), (6, 26), (39, 32), (3, 13), (17, 33), (13, 33), (26, 3), (28, 6), (16, 7), (14, 8), (40, 7), (7, 10), (21, 10), (36, 2), (9, 20), (33, 17), (3, 16), (6, 9), (12, 3), (23, 18), (18, 41), (33, 35), (12, 36), (40, 2), (20, 40), (36, 15), (35, 11), (17, 38), (11, 20), (24, 37), (0, 4), (18, 12), (26, 26), (14, 16), (21, 7), (37, 3), (29, 40), (31, 24), (6, 28), (24, 15), (7, 32), (19, 34), (27, 18), (0, 37), (8, 25), (40, 22), (16, 19), (34, 39), (1, 23), (4, 40), (31, 3), (18, 11), (20, 42), (5, 6), (20, 4), (30, 20), (0, 12), (9, 22), (36, 19), (20, 10), (15, 23), (7, 1), (23, 28), (0, 9), (16, 32), (14, 34), (15, 4), (33, 26), (12, 22), (38, 42), (40, 20), (31, 15), (21, 16), (16, 17), (11, 37), (23, 5), (38, 27), (37, 7), (4, 32), (9, 1), (0, 2), (34, 36), (28, 3), (14, 19), (7, 2), (6, 29), (6, 4), (1, 8), (34, 12), (10, 7), (38, 9), (33, 28), (31, 18), (4, 18), (15, 27), (37, 31), (0, 3), (3, 41), (23, 8), (7, 4), (15, 5), (13, 8), (38, 28), (5, 1), (40, 3), (21, 13), (28, 13), (5, 8), (29, 30), (25, 32), (15, 8), (6, 33), (35, 12), (27, 39), (4, 41), (37, 1), (34, 24), (6, 14), (0, 17), (8, 20), (12, 42), (34, 6), (34, 13), (28, 25), (25, 28), (3, 0), (14, 11), (12, 39), (21, 3), (27, 33), (38, 21), (34, 35), (15, 36), (12, 19), (29, 0), (6, 19), (21, 4), (16, 41), (26, 7), (7, 30), (21, 6), (13, 11), (37, 32), (35, 29), (29, 41), (37, 23), (40, 21), (38, 23), (38, 13), (15, 17), (1, 24), (29, 7), (9, 36), (39, 29), (12, 37), (7, 41), (30, 23), (36, 9), (8, 2), (39, 30), (10, 37), (20, 1), (11, 40), (16, 0), (1, 26), (24, 38), (11, 26), (13, 9), (10, 38), (20, 5), (27, 8), (9, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 39), (36, 32), (29, 40), (2, 44), (28, 23), (36, 38), (42, 7), (2, 15), (41, 18), (14, 0), (20, 9), (20, 14), (17, 31), (45, 45), (46, 28), (8, 25), (32, 44), (26, 23), (7, 14), (47, 1), (34, 1), (7, 10), (8, 0), (46, 32), (16, 31), (12, 24), (41, 28), (9, 43), (10, 4), (13, 27), (42, 4), (17, 23), (0, 1), (13, 19), (21, 8), (42, 1), (28, 6), (16, 45), (15, 21), (34, 28), (14, 31), (14, 20), (46, 6), (43, 42), (26, 34), (34, 25), (30, 10), (44, 37), (42, 15), (38, 25), (6, 20), (30, 14), (41, 10), (32, 19), (19, 37), (33, 16), (41, 37), (1, 41), (11, 5), (27, 24), (31, 31), (4, 10), (14, 12), (43, 23), (21, 4), (36, 0), (31, 37), (22, 45), (21, 3), (30, 40), (38, 6), (10, 30), (24, 9), (20, 37), (13, 32), (39, 20), (10, 43), (2, 32), (0, 19), (9, 45), (9, 39), (4, 2), (48, 42), (15, 26), (29, 37), (38, 45), (43, 8), (33, 39), (22, 23), (16, 24), (5, 16), (12, 32), (12, 20), (40, 44), (18, 45), (0, 35), (9, 15), (18, 7), (38, 39), (28, 12), (40, 3), (46, 20), (18, 20), (28, 3), (9, 7), (35, 4), (30, 24), (43, 44), (25, 14), (16, 7), (22, 7), (3, 11), (13, 3), (48, 44), (7, 18), (17, 25), (42, 3), (42, 38), (32, 1), (19, 35), (21, 29), (46, 2), (8, 21), (0, 37), (37, 22), (27, 9), (17, 15), (33, 4), (35, 8), (16, 10), (2, 25), (18, 29), (44, 22), (36, 1), (23, 10), (45, 14), (14, 36), (3, 41), (45, 41), (6, 42), (44, 19), (33, 25), (45, 44), (28, 8), (19, 6), (19, 42), (3, 20), (7, 21), (5, 41), (22, 12), (34, 29), (0, 40), (36, 14), (19, 41), (9, 19), (38, 22), (9, 2), (14, 11), (21, 24), (33, 30), (46, 1), (24, 31), (12, 0), (5, 11), (28, 28), (37, 39), (9, 42), (34, 39), (44, 24), (30, 35), (25, 34), (36, 20), (16, 11), (24, 39), (22, 10), (28, 43), (29, 21), (28, 10), (5, 7), (22, 24), (3, 1), (47, 14), (19, 39), (1, 17), (35, 1), (4, 29), (1, 13), (41, 31), (1, 6), (19, 2), (10, 3), (31, 34), (1, 32), (39, 38), (45, 11), (27, 39), (0, 17), (18, 2), (27, 30), (17, 17), (48, 13), (4, 35), (1, 4), (47, 10), (48, 23), (14, 25), (3, 44), (40, 19), (20, 18), (44, 0), (40, 31), (21, 13), (37, 38), (27, 15), (31, 22), (45, 36), (28, 42), (26, 45), (46, 34), (46, 9), (19, 16), (27, 21), (28, 26), (18, 16), (33, 3), (41, 3), (16, 17), (28, 21), (34, 22), (27, 42), (18, 39), (6, 9), (40, 25), (4, 18), (5, 27), (20, 28), (45, 22), (19, 31), (2, 8), (42, 25), (31, 6), (15, 5), (23, 4), (19, 45), (17, 9), (7, 22), (27, 23), (10, 1), (14, 34), (4, 45), (43, 5), (42, 29), (42, 26), (28, 37), (46, 38), (15, 27), (33, 14), (28, 33), (42, 41), (6, 11), (3, 25), (46, 0), (5, 18), (30, 18), (17, 35), (18, 23), (41, 6), (31, 38), (47, 39), (37, 11), (32, 41), (17, 13), (30, 8), (35, 35), (46, 7), (39, 27), (8, 22), (44, 33), (1, 9), (28, 14), (39, 26), (41, 42), (24, 16), (45, 28), (23, 21), (23, 16), (48, 18), (9, 8), (39, 3), (18, 19), (18, 10), (21, 18), (38, 20), (36, 12), (5, 28), (3, 34), (0, 9), (31, 15), (12, 36), (35, 28), (18, 9), (2, 3), (8, 45), (8, 2), (13, 45), (36, 4), (21, 5), (48, 30), (30, 42), (29, 15), (10, 11), (29, 22), (22, 5), (20, 23), (2, 6), (30, 2), (45, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 36), (42, 22), (17, 12), (25, 26), (32, 27), (43, 28), (12, 23), (32, 36), (31, 2), (20, 5), (21, 8), (43, 29), (13, 30), (26, 14), (10, 5), (24, 20), (1, 40), (42, 11), (2, 39), (12, 25), (39, 9), (33, 17), (14, 3), (11, 18), (1, 7), (20, 38), (10, 4), (21, 41), (31, 13), (20, 31), (2, 29), (18, 17), (27, 3), (11, 12), (3, 6), (1, 36), (38, 10), (5, 41), (19, 38), (12, 26), (31, 31), (26, 37), (6, 34), (16, 13), (16, 7), (39, 34), (36, 24), (21, 39), (33, 5), (18, 5), (22, 24), (11, 15), (11, 23), (34, 27), (35, 36), (27, 27), (31, 6), (19, 39), (18, 13), (25, 23), (32, 31), (24, 32), (20, 27), (9, 30), (13, 19), (1, 30), (22, 30), (26, 1), (34, 9), (18, 32), (15, 5), (9, 35), (13, 24), (28, 33), (42, 19), (26, 12), (42, 28), (19, 31), (18, 28), (27, 17), (37, 13), (0, 9), (32, 29), (22, 27), (37, 37), (9, 25), (42, 15), (42, 38), (19, 7), (7, 24), (39, 11), (26, 2), (35, 37), (25, 2), (42, 37), (19, 20), (32, 20), (45, 26), (4, 24), (27, 34), (25, 17), (33, 28), (31, 9), (10, 18), (36, 31), (34, 3), (0, 22), (22, 31), (44, 9), (42, 31), (31, 22), (32, 8), (2, 8), (25, 35), (12, 35), (11, 0), (8, 30), (44, 20), (7, 8), (33, 13), (22, 8), (39, 10), (27, 0), (17, 40), (40, 4), (29, 17), (0, 14), (44, 24), (39, 15), (5, 35), (13, 33), (25, 24), (41, 29), (38, 31), (31, 12), (9, 28), (21, 5), (39, 38), (5, 5), (43, 36), (18, 40), (23, 8), (37, 4), (2, 23), (23, 32), (2, 16), (45, 25), (36, 9), (23, 6), (42, 27), (41, 32), (22, 39), (35, 21), (1, 41), (33, 22), (30, 20), (13, 21), (5, 37), (12, 37), (31, 0), (43, 37), (17, 5), (22, 17), (2, 12), (28, 5), (22, 22), (19, 32), (32, 33), (37, 30), (31, 33), (14, 6), (36, 33), (16, 27), (30, 25), (18, 8), (30, 36), (5, 9), (37, 25), (14, 16), (16, 11), (45, 32), (34, 22), (37, 34), (16, 6), (4, 6), (12, 36), (20, 2), (33, 19), (22, 32), (34, 13), (25, 3), (8, 19), (40, 18), (15, 25), (37, 22), (22, 9), (13, 38), (30, 39), (3, 31), (22, 29), (10, 34), (37, 24), (45, 7), (4, 21), (2, 36), (43, 0), (31, 10), (34, 40), (31, 3), (18, 18), (41, 24), (33, 26), (8, 29), (30, 9), (33, 29), (24, 31), (8, 11), (23, 15), (18, 33), (20, 37), (28, 40), (19, 34), (25, 9), (13, 23), (12, 40), (11, 10), (22, 41), (20, 28), (17, 31), (9, 26), (9, 1), (35, 32), (28, 8), (31, 18), (37, 6), (7, 10), (38, 8), (20, 10), (42, 13), (4, 10), (17, 25), (24, 1), (12, 9), (14, 0), (24, 13), (26, 32), (38, 36), (1, 31), (3, 40), (28, 17), (22, 19), (38, 6), (13, 5), (2, 30), (11, 16), (24, 4), (29, 15), (15, 15), (13, 3), (29, 18), (24, 0), (12, 24), (35, 25), (5, 23), (12, 31), (3, 8), (9, 10), (28, 28), (43, 6), (0, 40), (30, 38), (24, 37), (30, 22), (3, 25), (8, 22), (2, 10), (37, 2), (22, 20), (12, 13), (44, 8), (40, 38), (32, 16), (2, 14), (33, 38), (31, 32), (12, 11), (40, 21), (6, 5), (20, 14), (6, 22), (18, 27), (6, 40), (33, 21), (7, 18), (5, 26), (33, 8), (20, 1), (24, 6), (0, 27), (7, 5), (19, 40), (32, 13), (7, 4), (8, 27), (41, 13), (5, 24), (31, 39), (0, 5), (40, 37), (45, 33), (39, 41), (17, 22), (2, 26), (41, 30), (32, 3), (45, 18), (23, 9), (20, 19), (33, 9), (18, 39), (36, 37), (20, 40), (42, 20), (7, 3), (22, 15), (45, 15), (18, 10), (42, 4), (3, 22), (6, 33), (36, 2), (4, 33), (34, 18), (34, 36), (21, 28), (30, 10), (13, 25), (45, 1), (22, 7), (1, 3), (16, 5), (13, 15), (8, 1), (1, 35), (39, 20), (19, 5), (19, 30), (23, 26), (5, 25), (19, 17), (12, 16), (12, 34), (42, 17), (5, 1), (14, 11), (31, 16), (39, 7), (8, 20), (4, 41), (41, 3), (0, 37), (9, 11), (24, 8), (14, 14), (1, 22), (23, 30), (36, 17), (15, 10), (34, 37), (38, 32), (44, 38), (12, 1), (23, 36), (32, 12), (24, 7), (41, 16), (14, 22), (0, 13), (17, 26), (41, 9), (33, 20), (43, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 20), (3, 35), (14, 8), (17, 18), (32, 11), (4, 9), (22, 34), (38, 31), (10, 31), (8, 16), (11, 36), (21, 12), (9, 36), (2, 39), (36, 36), (36, 1), (1, 35), (35, 19), (16, 39), (1, 5), (3, 2), (35, 29), (30, 20), (3, 30), (33, 9), (20, 22), (38, 0), (35, 34), (40, 23), (8, 19), (33, 25), (10, 15), (7, 38), (23, 21), (15, 29), (18, 39), (0, 24), (33, 17), (29, 17), (33, 23), (27, 20), (3, 9), (34, 25), (1, 29), (38, 15), (16, 16), (19, 37), (28, 25), (26, 6), (7, 28), (26, 26), (27, 16), (38, 21), (40, 27), (11, 30), (17, 15), (27, 10), (32, 2), (8, 28), (35, 38), (38, 4), (26, 7), (27, 14), (19, 0), (40, 17), (23, 14), (18, 4), (22, 23), (39, 35), (8, 29), (36, 9), (39, 17), (5, 20), (21, 7), (39, 11), (5, 11), (29, 13), (12, 2), (12, 13), (9, 12), (4, 21), (29, 14), (12, 22), (7, 20), (35, 36), (29, 31), (16, 25), (38, 29), (26, 16), (34, 16), (25, 34), (27, 24), (6, 5), (23, 4), (12, 11), (31, 38), (12, 17), (22, 8), (30, 13), (40, 18), (20, 0), (37, 31), (36, 23), (37, 11), (14, 33), (40, 28), (30, 8), (11, 31), (34, 1), (9, 11), (32, 26), (19, 10), (15, 11), (28, 21), (24, 17), (12, 4), (15, 30), (23, 34), (40, 9), (20, 37), (3, 10), (0, 36), (18, 9), (10, 7), (38, 34), (9, 34), (8, 25), (31, 21), (40, 16), (17, 11), (36, 39), (18, 36), (33, 19), (29, 33), (25, 10), (25, 17), (15, 13), (14, 26), (1, 34), (12, 0), (24, 12), (37, 13), (30, 19), (18, 23), (40, 35), (5, 4), (30, 32), (22, 6), (19, 7), (4, 22), (33, 37), (6, 33), (20, 4), (11, 4), (35, 20), (38, 24), (22, 14), (37, 6), (25, 20), (31, 16), (19, 13), (17, 9), (25, 18), (21, 17), (31, 28), (6, 17), (28, 39), (6, 35), (37, 10), (40, 12), (35, 1), (29, 36), (21, 35), (11, 21), (40, 38), (4, 31), (24, 5), (4, 13), (29, 35), (15, 27), (5, 22), (30, 7), (40, 15), (2, 9), (39, 5), (21, 1), (6, 8), (24, 1), (39, 15), (32, 39), (17, 12), (5, 5), (21, 21), (30, 30), (6, 38), (7, 13), (10, 26), (6, 27), (6, 3), (20, 38), (13, 33), (14, 25), (22, 18), (2, 20), (4, 20), (23, 29), (11, 27), (6, 10), (32, 36), (2, 36), (24, 14), (2, 24), (39, 38), (2, 21), (7, 7), (30, 29), (40, 2), (37, 39), (3, 15), (22, 17), (33, 14), (28, 20), (15, 6), (25, 19), (3, 13), (32, 27), (31, 18), (16, 33), (33, 12), (40, 34), (0, 6), (38, 16), (2, 28), (26, 5), (1, 3), (22, 11), (6, 26), (14, 35), (0, 16), (21, 27), (28, 34), (26, 0), (33, 20), (24, 39), (5, 1), (39, 20), (34, 11), (37, 38), (37, 18), (39, 1), (23, 36), (32, 16), (11, 19), (17, 21), (25, 35), (31, 37), (18, 28), (36, 17), (24, 37), (11, 12), (12, 7), (7, 2), (4, 2), (31, 24), (37, 0), (28, 14), (8, 0), (1, 37), (2, 26), (10, 6), (10, 27), (35, 33), (20, 13), (2, 32), (3, 17), (21, 0), (10, 8), (6, 39), (39, 13), (37, 16), (3, 7), (5, 18), (8, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 32), (7, 21), (33, 8), (8, 17), (13, 31), (13, 46), (36, 46), (33, 23), (34, 21), (16, 19), (27, 19), (42, 24), (16, 37), (15, 39), (33, 34), (30, 36), (12, 44), (36, 11), (23, 28), (3, 7), (3, 26), (18, 16), (6, 37), (15, 16), (34, 3), (21, 29), (33, 15), (28, 12), (17, 17), (34, 27), (13, 45), (6, 36), (1, 39), (19, 21), (3, 2), (20, 46), (29, 45), (15, 31), (2, 5), (40, 41), (44, 19), (37, 27), (31, 42), (28, 22), (28, 37), (1, 12), (43, 47), (12, 32), (3, 38), (3, 42), (11, 33), (32, 32), (21, 32), (44, 12), (36, 43), (39, 9), (46, 15), (9, 44), (18, 4), (36, 7), (14, 43), (43, 20), (30, 14), (37, 12), (38, 40), (9, 19), (39, 32), (20, 14), (5, 1), (28, 36), (34, 29), (11, 35), (5, 4), (2, 19), (47, 46), (43, 27), (11, 31), (9, 2), (39, 0), (0, 29), (9, 11), (34, 18), (47, 43), (32, 35), (30, 47), (21, 35), (0, 44), (27, 16), (28, 45), (42, 11), (27, 45), (15, 2), (22, 5), (21, 39), (36, 32), (6, 19), (40, 39), (40, 29), (45, 43), (21, 15), (7, 29), (30, 3), (44, 4), (11, 30), (7, 19), (15, 21), (24, 11), (16, 25), (0, 39), (3, 12), (44, 7), (41, 41), (33, 28), (25, 21), (47, 44), (14, 35), (26, 37), (14, 34), (22, 43), (37, 2), (35, 19), (23, 9), (45, 2), (12, 9), (36, 2), (27, 47), (19, 42), (4, 31), (35, 30), (5, 25), (9, 46), (20, 2), (11, 22), (28, 18), (43, 3), (27, 2), (20, 0), (16, 38), (3, 17), (17, 6), (18, 8), (47, 21), (11, 32), (9, 16), (19, 1), (10, 46), (46, 2), (25, 37), (40, 17), (43, 9), (22, 26), (11, 10), (38, 37), (2, 24), (19, 14), (3, 1), (2, 21), (10, 6), (30, 34), (13, 35), (32, 15), (1, 6), (3, 34), (3, 16), (11, 8), (41, 25), (23, 47), (36, 29), (1, 7), (36, 3), (35, 22), (42, 32), (2, 2), (24, 28), (28, 10), (5, 18), (5, 27), (12, 7), (1, 36), (40, 26), (35, 5), (25, 5), (37, 22), (11, 41), (36, 45), (13, 41), (46, 27), (4, 25), (0, 7), (3, 19), (9, 26), (40, 2), (17, 11), (8, 2), (32, 47), (36, 6), (16, 42), (17, 30), (6, 38), (37, 35), (27, 3), (27, 10), (47, 28), (45, 34), (41, 6), (13, 30), (8, 7), (25, 25), (22, 38), (42, 37), (46, 18), (18, 47), (30, 33), (3, 10), (30, 28), (30, 24), (10, 42), (18, 2), (34, 31), (0, 12), (40, 18), (22, 30), (41, 5), (37, 45), (38, 3), (25, 13), (0, 22), (23, 40), (35, 24), (32, 26), (20, 24), (18, 3), (7, 35), (10, 34), (21, 24), (37, 16), (18, 22), (25, 2), (41, 18), (3, 44), (23, 17), (26, 9), (23, 22), (17, 22), (13, 34), (36, 4), (42, 40), (29, 8), (43, 39), (23, 20), (14, 13), (9, 5), (38, 0), (42, 33), (46, 26), (18, 17), (9, 42), (15, 27), (27, 37), (14, 15), (28, 38), (40, 12), (6, 27), (43, 14), (11, 5), (35, 15), (47, 35), (19, 8), (35, 17), (24, 9), (15, 18), (0, 46), (22, 4), (10, 3), (43, 36), (34, 26), (39, 16), (13, 39), (22, 13), (26, 47), (20, 12), (42, 31), (23, 12), (5, 20), (22, 24), (42, 19), (0, 15), (5, 16), (40, 11), (36, 15), (17, 7), (41, 38), (28, 0), (13, 18), (4, 0), (36, 9), (45, 39), (28, 32), (14, 29), (34, 10), (24, 30), (43, 44), (25, 46), (17, 47), (28, 11), (17, 46), (16, 31), (44, 3), (25, 14), (15, 14), (24, 15), (47, 0), (33, 29), (34, 42), (23, 18), (12, 5), (6, 46), (1, 11), (15, 12), (40, 6), (45, 3), (41, 29), (8, 25), (24, 36), (13, 11), (43, 16), (12, 43), (28, 33), (7, 16), (38, 47), (15, 1), (46, 1), (3, 24), (4, 26), (38, 43), (32, 38), (28, 26), (20, 47), (13, 20), (25, 15), (39, 46), (39, 31), (9, 30), (19, 32), (31, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 21), (42, 39), (41, 15), (31, 28), (19, 10), (27, 16), (38, 33), (9, 21), (15, 27), (27, 32), (22, 33), (32, 6), (9, 7), (10, 30), (4, 20), (42, 25), (10, 34), (12, 35), (23, 40), (43, 32), (6, 5), (30, 37), (3, 8), (22, 13), (7, 26), (14, 6), (23, 0), (41, 31), (12, 3), (33, 12), (5, 2), (8, 17), (28, 20), (19, 27), (6, 9), (5, 18), (42, 20), (23, 27), (32, 32), (34, 35), (41, 20), (22, 30), (31, 5), (10, 29), (22, 42), (1, 34), (33, 18), (17, 19), (25, 5), (30, 21), (33, 4), (37, 44), (29, 14), (35, 5), (43, 25), (5, 37), (22, 8), (12, 33), (0, 18), (2, 35), (33, 31), (23, 3), (29, 11), (41, 3), (13, 24), (36, 11), (0, 39), (21, 22), (37, 34), (15, 17), (38, 15), (20, 11), (24, 24), (8, 33), (2, 31), (1, 44), (25, 11), (5, 4), (26, 40), (15, 22), (22, 0), (37, 38), (21, 34), (33, 20), (15, 32), (12, 42), (6, 16), (1, 40), (21, 30), (4, 32), (17, 26), (23, 15), (39, 23), (10, 15), (35, 20), (6, 23), (40, 29), (33, 42), (11, 24), (30, 19), (23, 39), (0, 10), (38, 34), (15, 21), (40, 4), (37, 25), (21, 41), (23, 32), (21, 24), (9, 11), (14, 38), (36, 12), (43, 16), (14, 23), (4, 3), (11, 25), (4, 35), (10, 0), (33, 37), (35, 10), (19, 3), (5, 6), (24, 22), (37, 17), (7, 20), (23, 16), (38, 9), (28, 19), (1, 41), (3, 44), (38, 0), (39, 9), (21, 44), (31, 38), (41, 11), (40, 35), (27, 2), (16, 31), (41, 24), (33, 7), (18, 27), (1, 1), (11, 36), (37, 23), (30, 26), (5, 33), (15, 40), (34, 2), (13, 11), (22, 5), (34, 39), (12, 25), (15, 36), (37, 14), (38, 39), (14, 28), (13, 43), (15, 33), (1, 20), (5, 40), (34, 38), (40, 12), (12, 43), (37, 30), (37, 21), (29, 2), (27, 19), (15, 11), (10, 17), (1, 16), (9, 29), (13, 22), (24, 40), (30, 8), (16, 23), (42, 13), (16, 13), (0, 13), (26, 13), (40, 44), (10, 2), (38, 42), (43, 11), (16, 6), (22, 12), (35, 11), (33, 27), (5, 12), (7, 12), (27, 13), (6, 30), (20, 42), (24, 4), (18, 4), (2, 2), (22, 31), (36, 22), (32, 10), (8, 32), (33, 35), (29, 42), (29, 34), (6, 27), (25, 10), (40, 43), (10, 24), (36, 39), (7, 34), (39, 35), (23, 17), (12, 41), (23, 33), (35, 19), (34, 36), (8, 41), (27, 35), (5, 43), (25, 30), (32, 15), (8, 3), (24, 2), (34, 3), (36, 18), (1, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 38), (23, 32), (15, 39), (9, 9), (16, 8), (4, 13), (31, 14), (10, 12), (12, 13), (1, 0), (40, 9), (7, 7), (0, 36), (20, 16), (35, 22), (26, 16), (30, 18), (37, 12), (3, 9), (4, 36), (4, 20), (10, 8), (32, 21), (19, 5), (17, 31), (3, 15), (27, 23), (13, 23), (29, 21), (17, 17), (35, 21), (3, 26), (25, 16), (30, 31), (26, 31), (19, 30), (0, 29), (14, 31), (13, 15), (30, 37), (21, 15), (32, 29), (18, 15), (15, 5), (35, 25), (15, 14), (32, 33), (23, 18), (4, 12), (1, 2), (18, 5), (31, 22), (1, 4), (17, 32), (26, 14), (8, 13), (7, 16), (25, 19), (15, 17), (3, 27), (15, 0), (16, 14), (39, 22), (39, 33), (12, 14), (9, 25), (33, 10), (1, 16), (14, 0), (8, 15), (1, 32), (8, 33), (14, 25), (13, 36), (7, 24), (1, 12), (3, 1), (17, 6), (9, 6), (38, 3), (21, 22), (28, 7), (30, 38), (22, 13), (14, 28), (14, 37), (12, 0), (13, 31), (4, 10), (26, 29), (13, 32), (25, 7), (3, 38), (33, 29), (37, 20), (20, 19), (30, 26), (3, 33), (18, 37), (34, 37), (38, 23), (25, 29), (37, 14), (2, 39), (23, 38), (5, 13), (15, 25), (6, 36), (28, 29), (35, 11), (13, 19), (36, 29), (34, 21), (15, 19), (11, 38), (2, 5), (10, 1), (20, 8), (38, 36), (19, 27), (28, 2), (1, 28), (23, 14), (11, 1), (36, 13), (17, 33), (24, 37), (32, 16), (23, 10), (15, 13), (8, 27), (40, 7), (35, 7), (40, 11), (36, 23), (24, 30), (12, 19), (37, 35), (31, 0), (0, 9), (13, 10), (15, 23), (32, 25), (38, 35), (32, 31), (28, 22), (34, 14), (38, 0), (25, 12), (10, 32), (20, 22), (40, 4), (4, 7), (20, 17), (2, 15), (2, 11), (34, 25), (6, 9), (1, 6), (8, 23), (4, 4), (3, 22), (27, 12), (31, 36), (7, 1), (13, 18), (38, 29), (21, 2), (11, 4), (30, 28), (13, 28), (16, 37), (18, 19), (22, 33), (3, 5), (23, 3), (34, 13), (35, 36), (34, 7), (0, 33), (11, 16), (26, 25), (15, 9), (29, 22), (1, 18), (0, 28), (8, 8), (11, 7), (39, 32), (6, 0), (4, 15), (25, 24), (35, 38), (23, 16), (2, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 16), (13, 10), (40, 20), (45, 1), (33, 2), (38, 23), (2, 5), (34, 33), (3, 36), (39, 19), (0, 41), (7, 3), (20, 15), (26, 14), (31, 24), (42, 24), (44, 23), (40, 16), (13, 20), (34, 4), (41, 41), (45, 10), (31, 12), (15, 19), (14, 5), (32, 18), (13, 9), (45, 29), (1, 22), (15, 16), (3, 28), (46, 3), (29, 38), (9, 18), (35, 36), (46, 33), (43, 15), (12, 24), (40, 1), (9, 1), (15, 11), (17, 14), (18, 37), (25, 15), (35, 6), (32, 0), (34, 32), (34, 15), (30, 19), (11, 24), (5, 11), (0, 23), (1, 0), (16, 12), (40, 30), (29, 37), (11, 15), (38, 26), (27, 26), (26, 38), (24, 29), (4, 35), (21, 30), (4, 22), (15, 14), (43, 10), (16, 14), (30, 18), (31, 19), (26, 1), (14, 13), (19, 34), (45, 41), (1, 39), (45, 32), (44, 42), (40, 21), (37, 39), (13, 8), (11, 12), (10, 33), (27, 7), (35, 34), (2, 33), (38, 35), (15, 41), (1, 16), (36, 19), (44, 37), (24, 40), (42, 41), (24, 18), (40, 2), (0, 7), (45, 14), (18, 21), (9, 33), (46, 15), (29, 13), (35, 27), (29, 36), (39, 37), (24, 23), (43, 25), (4, 9), (44, 32), (3, 29), (21, 2), (30, 3), (28, 6), (31, 18), (14, 9), (4, 13), (29, 30), (31, 39), (27, 12), (9, 42), (7, 7), (31, 20), (36, 2), (26, 2), (10, 13), (43, 3), (37, 15), (34, 18), (9, 16), (15, 6), (5, 24), (36, 33), (29, 1), (22, 25), (2, 29), (44, 36), (17, 16), (38, 11), (29, 41), (18, 5), (6, 26), (30, 16), (46, 38), (28, 8), (37, 32), (9, 28), (5, 6), (6, 22), (1, 35), (11, 41), (24, 4), (30, 10), (31, 7), (27, 41), (27, 29), (9, 8), (46, 18), (7, 17), (15, 40), (4, 39), (2, 1), (33, 42), (26, 15), (11, 21), (27, 11), (41, 2), (5, 36), (12, 25), (41, 30), (13, 29), (0, 31), (23, 8), (13, 2), (23, 31), (30, 24), (13, 17), (35, 40), (36, 0), (27, 8), (29, 25), (26, 43), (38, 42), (42, 21), (9, 32), (9, 10), (26, 12), (31, 41), (11, 3), (45, 15), (46, 29), (38, 43), (3, 15), (21, 32), (3, 38), (26, 42), (0, 34), (33, 23), (14, 19), (45, 12), (45, 27), (42, 0), (15, 17), (37, 14), (13, 34), (3, 17), (34, 22), (20, 30), (41, 6), (41, 20), (6, 0), (7, 39), (26, 35), (1, 38), (32, 16), (41, 32), (11, 31), (13, 39), (25, 41), (22, 35), (40, 3), (13, 16), (5, 3), (19, 42), (43, 24), (11, 6), (41, 17), (22, 24), (40, 33), (29, 32), (26, 10), (3, 43), (17, 17), (13, 15), (12, 8), (30, 32), (38, 19), (34, 1), (33, 22), (13, 18), (29, 28), (30, 28), (44, 9), (30, 23), (28, 28), (0, 27), (40, 19), (28, 12), (46, 5), (45, 40), (6, 27), (27, 31), (30, 11), (4, 20), (32, 4), (25, 4), (11, 0), (1, 14), (2, 38), (31, 34), (5, 33), (18, 36), (23, 29), (17, 20), (38, 8), (1, 34), (32, 37), (44, 8), (3, 35), (19, 6), (41, 4), (19, 1), (7, 24), (4, 26), (27, 20), (46, 0), (43, 28), (45, 21), (13, 4), (42, 36), (34, 43), (15, 25), (2, 34), (16, 29), (5, 0), (39, 41), (15, 9), (38, 2), (7, 2), (44, 2), (29, 39), (5, 21), (8, 13), (2, 35), (2, 40), (26, 8), (43, 37), (30, 29), (2, 15), (43, 19), (19, 2), (1, 25), (13, 6), (42, 17), (3, 27), (19, 13), (12, 23), (20, 28), (20, 37), (15, 2), (42, 42), (37, 25), (24, 2), (19, 28), (37, 31), (21, 11), (12, 30), (4, 29), (41, 43), (8, 7), (3, 40), (8, 33), (6, 34), (21, 15), (5, 7), (28, 18), (10, 41), (21, 31), (33, 30), (37, 21), (23, 38), (9, 41), (28, 5), (32, 41), (10, 6), (0, 6), (25, 25), (11, 9), (3, 26), (20, 26), (46, 28), (1, 15), (42, 34), (39, 36), (45, 39), (14, 1), (23, 22), (32, 39), (46, 42), (41, 9), (23, 12), (12, 20), (13, 28), (9, 4), (41, 23), (2, 19), (24, 20), (13, 41), (21, 29), (25, 27), (11, 43), (45, 3), (1, 23), (9, 39), (1, 42), (8, 32), (39, 8), (39, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 3), (8, 31), (13, 11), (11, 37), (15, 32), (27, 12), (8, 34), (16, 36), (23, 5), (9, 9), (30, 23), (30, 36), (18, 10), (24, 2), (36, 35), (17, 4), (19, 28), (36, 27), (25, 16), (25, 1), (27, 16), (3, 7), (16, 37), (2, 8), (34, 29), (9, 2), (1, 30), (8, 27), (32, 4), (39, 33), (24, 9), (21, 7), (11, 35), (39, 29), (22, 33), (37, 29), (9, 1), (4, 17), (22, 0), (22, 26), (2, 11), (22, 9), (32, 1), (5, 34), (14, 4), (25, 29), (30, 5), (30, 38), (32, 31), (38, 37), (1, 26), (27, 29), (18, 25), (9, 15), (35, 22), (13, 9), (35, 20), (19, 17), (28, 18), (39, 31), (28, 20), (36, 21), (7, 10), (5, 13), (27, 0), (3, 9), (1, 33), (36, 11), (37, 14), (14, 14), (10, 8), (6, 18), (21, 33), (6, 28), (22, 7), (13, 18), (33, 18), (0, 8), (22, 13), (36, 14), (36, 16), (32, 26), (2, 27), (8, 7), (24, 31), (4, 25), (20, 13), (38, 22), (25, 39), (31, 32), (3, 6), (36, 25), (18, 39), (12, 21), (27, 14), (31, 27), (36, 15), (11, 32), (22, 22), (37, 17), (34, 21), (7, 31), (8, 11), (2, 20), (20, 7), (30, 4), (12, 4), (19, 20), (24, 39), (34, 0), (10, 17), (9, 14), (10, 35), (39, 21), (6, 14), (8, 1), (23, 8), (6, 12), (6, 39), (2, 12), (5, 33), (4, 32), (28, 32), (37, 35), (19, 38), (24, 27), (3, 13), (13, 21), (30, 24), (21, 10), (2, 16), (10, 32), (36, 6), (22, 32), (13, 35), (10, 27), (38, 2), (5, 16), (29, 25), (30, 10), (23, 4), (25, 20), (35, 11), (25, 5), (12, 34), (22, 12), (3, 23), (31, 16), (33, 7), (10, 16), (6, 11), (7, 30), (15, 30), (10, 30), (21, 18), (11, 34), (31, 23), (14, 16), (26, 11), (36, 2), (21, 3), (33, 2), (32, 21), (35, 31), (32, 7), (18, 4), (27, 34), (29, 0), (34, 36), (25, 4), (12, 13), (23, 12), (28, 26), (21, 11), (1, 19), (17, 33), (17, 5), (20, 0), (16, 11), (19, 30), (5, 8), (34, 10), (18, 0), (36, 30), (33, 23), (4, 7), (36, 33), (25, 6), (27, 2), (4, 12), (32, 16), (17, 2), (30, 15), (36, 1), (29, 24), (26, 7), (8, 21), (32, 33), (21, 12), (7, 18), (19, 22), (27, 38), (32, 34), (33, 0), (35, 9), (19, 6), (14, 2), (9, 18), (34, 14), (37, 0), (4, 13), (7, 8), (13, 13), (5, 12), (10, 14), (16, 38), (12, 14), (30, 26), (34, 32), (6, 3), (34, 3), (9, 0), (3, 34), (4, 28), (38, 33), (34, 28), (6, 9), (15, 28), (30, 21), (39, 12), (13, 30), (22, 20), (37, 12), (13, 26), (23, 17), (0, 34), (0, 26), (4, 16), (35, 33), (35, 35), (37, 19), (13, 10), (35, 21), (25, 36), (14, 9), (33, 35), (37, 39), (16, 0), (35, 10), (8, 38), (31, 33), (0, 31), (10, 36), (38, 4), (30, 8), (22, 15), (32, 35), (9, 5), (30, 3), (8, 24), (16, 34), (6, 26), (39, 15), (12, 30), (30, 1), (28, 30), (25, 26), (23, 9), (36, 18), (35, 8), (37, 15), (13, 24), (10, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 34), (31, 29), (40, 5), (40, 35), (24, 3), (17, 8), (21, 3), (24, 45), (13, 26), (12, 38), (26, 41), (21, 38), (3, 39), (24, 35), (10, 8), (18, 45), (20, 29), (14, 29), (27, 20), (35, 9), (23, 5), (5, 0), (23, 10), (39, 0), (40, 43), (10, 38), (15, 23), (24, 25), (39, 31), (35, 33), (31, 36), (6, 31), (0, 15), (33, 40), (19, 31), (8, 32), (3, 44), (2, 19), (36, 25), (6, 2), (4, 10), (1, 39), (34, 2), (21, 0), (23, 28), (36, 17), (14, 24), (16, 35), (15, 5), (22, 36), (37, 0), (14, 5), (23, 27), (17, 5), (33, 7), (4, 5), (13, 40), (39, 42), (1, 43), (17, 41), (15, 10), (31, 15), (38, 19), (4, 37), (19, 1), (32, 2), (21, 44), (2, 28), (27, 14), (22, 20), (41, 24), (39, 16), (3, 46), (2, 39), (3, 45), (26, 8), (1, 20), (37, 11), (36, 19), (27, 33), (2, 27), (36, 24), (7, 12), (0, 31), (1, 27), (30, 0), (20, 10), (25, 10), (12, 3), (4, 42), (1, 7), (11, 4), (10, 3), (32, 7), (8, 22), (22, 46), (21, 10), (26, 31), (0, 11), (36, 37), (32, 32), (4, 7), (38, 35), (19, 23), (27, 6), (18, 2), (39, 8), (11, 11), (13, 2), (27, 16), (16, 16), (24, 33), (33, 5), (30, 18), (5, 37), (38, 11), (12, 18), (16, 7), (40, 29), (3, 33), (10, 43), (35, 34), (28, 40), (32, 38), (32, 29), (23, 6), (17, 32), (14, 39), (17, 16), (33, 44), (32, 36), (2, 13), (40, 3), (3, 30), (25, 5), (21, 13), (37, 1), (40, 4), (36, 20), (31, 1), (20, 17), (22, 34), (1, 9), (28, 38), (23, 34), (12, 43), (10, 36), (27, 29), (6, 20), (5, 12), (1, 37), (17, 17), (0, 18), (25, 23), (28, 16), (11, 7), (29, 3), (34, 29), (35, 38), (31, 14), (13, 4), (37, 23), (25, 30), (17, 22), (18, 23), (38, 4), (12, 30), (40, 28), (0, 27), (15, 17), (0, 26), (12, 24), (7, 44), (21, 12), (22, 30), (5, 26), (36, 38), (41, 18), (9, 34), (7, 36), (12, 10), (26, 46), (30, 38), (11, 13), (11, 5), (40, 12), (0, 6), (23, 11), (10, 31), (41, 1), (2, 11), (40, 39), (32, 21), (39, 20), (19, 28), (9, 9), (14, 1), (9, 11), (4, 31), (33, 20), (27, 8), (17, 13), (37, 38), (22, 3), (36, 46), (38, 36), (25, 45), (34, 15), (24, 16), (25, 2), (18, 22), (6, 45), (19, 3), (37, 15), (35, 23), (5, 1), (22, 10), (8, 10), (24, 31), (39, 40), (39, 33), (2, 22), (4, 4), (8, 23), (37, 24), (2, 45), (33, 4), (20, 19), (38, 32), (34, 30), (25, 0), (30, 9), (10, 19), (25, 9), (11, 22), (27, 38), (37, 20), (9, 7), (6, 11), (17, 2), (14, 15), (23, 14), (8, 11), (32, 14), (6, 13), (26, 27), (40, 22), (35, 4), (8, 7), (11, 36), (5, 9), (1, 23), (38, 39), (37, 2), (8, 37), (30, 36), (24, 18), (19, 19), (29, 14), (26, 34), (17, 36), (10, 29), (16, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 10), (41, 15), (8, 2), (5, 32), (42, 45), (7, 14), (21, 26), (7, 42), (41, 10), (41, 44), (44, 13), (15, 40), (44, 6), (23, 25), (8, 14), (28, 5), (23, 47), (16, 26), (41, 27), (26, 45), (22, 31), (30, 16), (17, 37), (2, 37), (37, 38), (14, 25), (14, 39), (28, 28), (6, 42), (16, 46), (9, 39), (35, 20), (27, 24), (35, 44), (6, 32), (32, 33), (9, 35), (36, 20), (31, 23), (43, 42), (25, 24), (26, 33), (23, 38), (42, 28), (1, 38), (15, 1), (7, 15), (41, 43), (41, 41), (21, 22), (35, 17), (17, 11), (31, 21), (15, 3), (36, 39), (28, 43), (42, 38), (25, 0), (19, 26), (44, 15), (43, 45), (8, 40), (27, 16), (15, 39), (44, 34), (3, 26), (27, 39), (10, 39), (14, 15), (15, 13), (42, 30), (7, 25), (44, 19), (3, 10), (14, 18), (33, 9), (2, 24), (12, 23), (42, 41), (22, 32), (18, 18), (5, 43), (23, 35), (8, 41), (23, 9), (29, 36), (21, 1), (12, 43), (44, 42), (15, 14), (10, 11), (4, 6), (44, 44), (24, 0), (5, 30), (10, 33), (13, 23), (18, 43), (6, 41), (41, 23), (1, 20), (10, 17), (24, 9), (29, 14), (39, 21), (17, 19), (35, 25), (11, 27), (13, 46), (37, 31), (20, 5), (22, 11), (35, 15), (24, 8), (4, 0), (27, 44), (23, 12), (7, 36), (36, 24), (21, 23), (36, 33), (34, 41), (6, 4), (32, 5), (38, 39), (28, 37), (26, 2), (41, 32), (11, 14), (5, 44), (29, 26), (33, 31), (7, 10), (18, 35), (28, 10), (32, 12), (19, 2), (21, 28), (22, 30), (15, 4), (32, 2), (14, 37), (44, 22), (5, 47), (42, 44), (13, 24), (38, 35), (30, 34), (40, 34), (35, 26), (14, 32), (43, 0), (10, 42), (2, 6), (13, 7), (16, 34), (20, 8), (27, 38), (40, 24), (15, 7), (35, 6), (12, 21), (44, 35), (30, 2), (34, 2), (20, 13), (19, 41), (35, 0), (18, 26), (6, 30), (28, 23), (22, 35), (10, 40), (4, 43), (2, 0), (44, 37), (21, 24), (24, 13), (7, 37), (37, 11), (22, 38), (24, 47), (33, 11), (34, 4), (26, 31), (2, 41), (31, 28), (40, 30), (40, 45), (36, 11), (2, 32), (27, 0), (29, 13), (8, 24), (10, 25), (31, 42), (39, 5), (40, 15), (15, 46), (24, 21), (27, 1), (0, 24), (26, 25), (39, 31), (31, 31), (27, 23), (16, 2), (23, 4), (24, 20), (5, 37), (4, 31), (39, 22), (6, 0), (36, 12), (40, 26), (23, 34), (5, 3), (28, 47), (35, 13), (6, 40), (33, 46), (33, 25), (1, 24), (40, 2), (25, 6), (40, 43), (0, 33), (39, 29), (22, 43), (0, 9), (13, 38), (15, 15), (38, 27), (31, 20), (15, 2), (33, 23), (3, 18), (19, 45), (36, 26), (16, 41), (4, 1), (17, 22), (3, 11), (32, 30), (27, 32), (29, 37), (19, 8), (12, 41), (41, 3), (17, 14), (42, 29), (23, 32), (3, 2), (22, 24), (4, 16), (10, 37), (19, 11), (36, 15), (44, 29), (37, 47), (10, 46), (21, 34), (11, 26), (14, 21), (26, 8), (26, 21), (24, 19), (43, 12), (33, 39), (14, 14), (33, 27), (4, 15), (4, 30), (39, 7), (11, 13), (10, 8), (38, 26), (40, 23), (21, 19), (14, 38), (42, 6), (5, 15), (11, 7), (26, 7), (44, 3), (11, 38), (29, 24), (22, 18), (40, 25), (13, 6), (39, 9), (15, 42), (2, 9), (36, 22), (9, 29), (14, 46), (39, 13), (27, 33), (29, 43), (24, 35), (6, 27), (11, 32), (34, 21), (43, 46), (7, 39), (1, 10), (15, 30), (25, 8), (17, 13), (0, 32), (18, 23), (10, 19), (0, 13), (8, 12), (41, 22), (22, 34), (0, 36), (25, 28), (9, 37), (23, 21), (40, 27), (19, 6), (7, 12), (5, 21), (17, 6), (43, 40), (24, 14), (19, 40), (31, 32), (14, 22), (17, 16), (13, 30), (37, 43), (32, 4), (8, 11), (15, 18), (32, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 10), (12, 2), (3, 9), (37, 2), (32, 38), (1, 4), (3, 18), (29, 21), (13, 20), (9, 16), (31, 2), (36, 36), (7, 35), (24, 22), (39, 3), (16, 16), (34, 12), (6, 22), (12, 17), (39, 12), (7, 0), (2, 11), (28, 33), (23, 11), (0, 6), (8, 32), (37, 17), (30, 27), (0, 32), (35, 7), (16, 17), (38, 5), (17, 22), (34, 23), (24, 32), (30, 12), (1, 17), (16, 22), (6, 9), (9, 3), (14, 4), (39, 7), (26, 28), (29, 17), (15, 13), (5, 13), (39, 23), (6, 13), (19, 16), (33, 11), (16, 3), (32, 36), (30, 19), (20, 37), (0, 11), (12, 21), (8, 16), (2, 28), (28, 14), (17, 29), (35, 14), (24, 29), (12, 3), (18, 16), (13, 12), (28, 0), (7, 26), (32, 14), (11, 28), (12, 25), (34, 24), (24, 16), (0, 39), (18, 0), (8, 36), (5, 26), (23, 32), (14, 13), (0, 2), (17, 2), (13, 4), (34, 30), (5, 9), (35, 11), (21, 19), (7, 10), (18, 21), (35, 3), (11, 14), (30, 15), (13, 36), (21, 17), (11, 4), (22, 9), (27, 16), (34, 9), (17, 39), (6, 39), (6, 18), (14, 30), (34, 20), (39, 6), (2, 7), (13, 34), (22, 4), (14, 7), (0, 19), (2, 10), (3, 31), (25, 15), (36, 22), (35, 29), (36, 3), (14, 34), (30, 36), (34, 26), (9, 31), (20, 25), (20, 4), (15, 1), (22, 3), (18, 17), (9, 39), (28, 27), (31, 20), (1, 33), (32, 25), (6, 23), (11, 24), (30, 21), (19, 1), (19, 32), (5, 11), (5, 12), (36, 15), (2, 30), (19, 38), (38, 13), (17, 14), (7, 30), (10, 19), (31, 19), (33, 3), (25, 39), (20, 7), (21, 20), (24, 26), (39, 24), (4, 7), (4, 36), (31, 23), (0, 3), (3, 13), (35, 6), (3, 32), (20, 29), (32, 20), (30, 11), (12, 23), (21, 9), (17, 26), (7, 22), (4, 25), (22, 31), (10, 17), (15, 18), (21, 27), (38, 34), (2, 0), (36, 2), (14, 1), (37, 4), (2, 36), (5, 27), (31, 1), (27, 25), (2, 37), (5, 20), (39, 34), (24, 34), (39, 21), (14, 38), (21, 3), (29, 15), (28, 23), (25, 11), (7, 12), (17, 35), (23, 39), (7, 2), (35, 30), (29, 2), (15, 8), (14, 25), (5, 7), (27, 33), (11, 13), (27, 23), (7, 39), (30, 16), (14, 28), (34, 7), (6, 36), (9, 14), (13, 16), (1, 26), (36, 25), (7, 15), (1, 22), (19, 15), (21, 10), (11, 36), (33, 19), (23, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 17), (35, 20), (30, 18), (10, 7), (39, 37), (3, 31), (0, 6), (10, 6), (29, 21), (34, 17), (35, 0), (5, 10), (25, 20), (23, 31), (33, 30), (19, 8), (39, 33), (9, 9), (28, 28), (3, 12), (14, 2), (1, 14), (1, 15), (0, 2), (4, 19), (20, 18), (7, 38), (39, 8), (10, 34), (36, 4), (24, 24), (40, 21), (38, 17), (11, 20), (8, 13), (17, 29), (2, 35), (41, 5), (28, 34), (17, 33), (38, 30), (17, 28), (42, 22), (1, 11), (8, 28), (36, 24), (11, 1), (13, 11), (1, 25), (16, 13), (0, 28), (35, 5), (37, 11), (27, 3), (21, 4), (30, 8), (8, 17), (13, 34), (26, 8), (24, 39), (30, 39), (12, 11), (29, 29), (33, 8), (24, 25), (38, 36), (0, 13), (33, 4), (16, 26), (12, 14), (9, 12), (40, 23), (6, 3), (18, 5), (23, 25), (2, 26), (2, 24), (8, 34), (37, 15), (24, 16), (1, 19), (18, 28), (42, 29), (13, 18), (42, 21), (13, 6), (4, 16), (4, 33), (35, 21), (5, 29), (31, 8), (27, 12), (39, 24), (11, 22), (0, 1), (37, 34), (42, 18), (30, 7), (8, 16), (1, 38), (5, 31), (16, 39), (7, 21), (21, 7), (0, 22), (23, 2), (4, 28), (14, 10), (34, 27), (27, 38), (26, 21), (8, 1), (15, 9), (9, 31), (6, 17), (36, 30), (42, 28), (31, 37), (19, 27), (41, 34), (10, 30), (30, 12), (39, 25), (38, 31), (33, 35), (35, 23), (29, 32), (14, 34), (42, 34), (33, 18), (15, 22), (3, 0), (14, 9), (6, 21), (12, 2), (20, 22), (30, 11), (35, 35), (36, 28), (24, 31), (41, 14), (4, 0), (40, 36), (13, 5), (31, 31), (31, 39), (10, 16), (3, 21), (36, 39), (25, 39), (35, 11), (10, 23), (8, 19), (6, 33), (28, 6), (16, 12), (27, 26), (36, 37), (37, 29), (19, 31), (21, 18), (17, 12), (19, 9), (36, 27), (22, 37), (8, 37), (41, 3), (14, 14), (27, 15), (38, 20), (26, 7), (18, 20), (18, 37), (14, 31), (6, 12), (36, 21), (32, 2), (17, 25), (32, 30), (2, 17), (16, 32), (38, 8), (25, 33), (24, 19), (15, 33), (29, 26), (36, 2), (6, 32), (37, 8), (31, 3), (41, 12), (0, 20), (39, 35), (27, 13), (41, 37), (9, 11), (38, 22), (40, 2), (3, 10), (32, 6), (3, 30), (20, 32), (37, 5), (20, 30), (42, 25), (25, 14), (39, 34), (39, 30), (28, 0), (41, 17), (41, 33), (11, 33), (11, 3), (3, 18), (13, 33), (2, 25), (38, 15), (27, 19), (2, 33), (40, 3), (5, 19), (10, 5), (18, 13), (16, 28), (18, 39), (42, 0), (5, 9), (32, 25), (24, 4), (27, 4), (30, 10), (2, 0), (22, 26), (33, 34), (42, 30), (17, 13), (26, 16), (29, 11), (21, 21), (21, 30), (37, 10), (26, 12), (24, 15), (23, 19), (19, 7), (23, 37), (5, 36), (11, 16), (7, 26), (11, 31), (39, 36), (27, 14), (21, 14), (37, 17), (30, 5), (26, 28), (41, 35), (35, 22), (40, 0), (22, 9), (3, 39), (6, 16), (27, 1), (13, 29), (7, 32), (26, 9), (20, 31), (35, 36), (8, 22), (33, 10), (25, 4), (25, 18), (15, 34), (20, 9), (30, 17), (17, 0), (39, 21), (29, 37), (15, 5), (6, 27), (0, 7), (38, 0), (30, 16), (14, 24), (16, 19), (32, 9), (30, 38), (11, 0), (17, 24), (25, 5), (36, 10), (33, 25), (9, 39), (32, 20), (34, 21), (36, 26), (24, 26), (34, 14), (15, 36), (12, 15), (5, 23), (11, 7), (6, 0), (16, 20), (31, 30), (39, 10), (2, 27), (40, 30), (22, 29), (26, 33), (38, 5), (16, 31), (18, 21), (10, 9), (33, 26), (28, 29), (19, 24), (40, 1), (38, 10), (28, 30), (18, 1), (19, 29), (17, 17), (21, 10), (7, 34), (35, 37), (7, 12), (17, 2), (10, 28), (20, 8), (42, 8), (33, 17), (36, 36), (13, 7), (9, 13), (21, 5), (8, 2), (18, 17), (7, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 2), (32, 12), (13, 35), (43, 11), (9, 23), (21, 18), (20, 5), (8, 28), (3, 8), (41, 39), (34, 23), (20, 7), (27, 34), (25, 26), (2, 20), (17, 29), (12, 15), (19, 18), (27, 13), (9, 27), (2, 16), (1, 4), (37, 16), (13, 26), (19, 30), (38, 1), (8, 37), (26, 38), (6, 19), (28, 14), (15, 0), (42, 12), (22, 31), (0, 25), (29, 16), (10, 9), (2, 35), (9, 4), (13, 30), (19, 29), (0, 27), (22, 6), (42, 24), (0, 2), (11, 11), (9, 5), (24, 17), (25, 8), (11, 20), (35, 23), (25, 12), (10, 20), (4, 4), (5, 26), (22, 12), (43, 38), (33, 21), (30, 0), (6, 32), (39, 32), (11, 19), (35, 7), (33, 17), (42, 20), (25, 5), (21, 30), (17, 36), (6, 24), (9, 32), (26, 12), (23, 18), (33, 22), (5, 37), (15, 12), (32, 38), (26, 10), (42, 26), (43, 3), (22, 3), (38, 15), (21, 0), (3, 34), (23, 4), (0, 39), (19, 34), (2, 23), (5, 4), (28, 16), (3, 14), (5, 18), (5, 28), (31, 1), (2, 37), (15, 25), (2, 4), (41, 37), (18, 26), (25, 23), (36, 14), (3, 2), (25, 32), (24, 7), (40, 19), (22, 37), (43, 24), (42, 35), (29, 21), (12, 34), (16, 22), (2, 26), (38, 27), (7, 30), (16, 33), (1, 32), (35, 24), (27, 35), (38, 11), (14, 26), (30, 7), (31, 37), (28, 21), (8, 22), (4, 37), (26, 0), (38, 25), (18, 31), (43, 10), (38, 9), (9, 14), (11, 13), (3, 12), (17, 28), (7, 20), (3, 13), (35, 1), (43, 4), (4, 20), (20, 27), (5, 9), (6, 17), (20, 3), (32, 23), (22, 8), (27, 20), (28, 28), (31, 32), (23, 21), (23, 19), (14, 37), (42, 10), (21, 16), (30, 26), (13, 19), (8, 18), (3, 38), (40, 9), (31, 16), (14, 28), (1, 28), (24, 21), (7, 22), (3, 30), (43, 17), (19, 21), (27, 27), (35, 15), (15, 31), (37, 8), (6, 33), (41, 3), (0, 5), (21, 36), (27, 14), (26, 30), (7, 38), (37, 17), (24, 23), (1, 23), (41, 2), (35, 37), (23, 20), (6, 25), (5, 14), (30, 6), (38, 12), (24, 34), (42, 8), (35, 12), (13, 10), (11, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 31), (13, 18), (18, 25), (18, 29), (17, 12), (4, 10), (9, 32), (26, 17), (13, 29), (9, 39), (33, 25), (3, 10), (36, 31), (5, 32), (42, 11), (17, 34), (2, 28), (16, 36), (27, 38), (13, 14), (27, 41), (27, 39), (1, 27), (29, 45), (19, 37), (36, 32), (36, 24), (25, 38), (42, 45), (29, 17), (9, 4), (14, 21), (40, 44), (27, 15), (10, 28), (3, 6), (42, 6), (7, 22), (39, 34), (0, 38), (33, 27), (25, 43), (25, 45), (30, 28), (11, 42), (41, 2), (31, 23), (4, 39), (20, 36), (36, 0), (40, 2), (10, 44), (38, 41), (21, 20), (26, 36), (19, 43), (16, 4), (25, 25), (27, 35), (19, 33), (18, 35), (3, 25), (9, 20), (8, 32), (19, 41), (26, 37), (15, 17), (20, 39), (40, 37), (37, 12), (26, 34), (12, 36), (10, 4), (12, 22), (5, 15), (35, 15), (11, 6), (28, 3), (35, 10), (42, 21), (12, 24), (8, 16), (28, 37), (5, 19), (29, 19), (1, 38), (41, 42), (35, 20), (6, 38), (0, 23), (18, 22), (7, 43), (4, 17), (16, 32), (32, 25), (30, 10), (37, 6), (16, 41), (1, 24), (43, 13), (33, 8), (23, 9), (37, 25), (25, 41), (2, 2), (25, 34), (32, 26), (34, 30), (28, 39), (18, 18), (24, 25), (15, 41), (43, 26), (26, 21), (32, 5), (31, 32), (41, 0), (6, 25), (8, 38), (36, 17), (12, 0), (20, 29), (16, 37), (33, 7), (36, 45), (36, 19), (28, 40), (32, 24), (0, 11), (42, 27), (26, 42), (13, 30), (2, 37), (40, 38), (14, 33), (29, 0), (30, 14), (32, 33), (22, 42), (37, 23), (29, 8), (18, 31), (16, 35), (33, 31), (4, 4), (6, 33), (32, 27), (15, 38), (32, 39), (23, 11), (6, 6), (35, 12), (6, 3), (25, 12), (1, 6), (24, 10), (28, 44), (3, 18), (13, 15), (40, 25), (30, 33), (34, 44), (21, 42), (33, 41), (14, 8), (12, 38), (17, 33), (20, 27), (21, 21), (2, 16), (26, 8), (41, 20), (30, 20), (38, 5), (27, 4), (5, 20), (2, 21), (41, 11), (19, 17), (36, 15), (30, 9), (21, 40), (4, 0), (43, 23), (40, 30), (31, 13), (11, 12), (11, 39), (20, 9), (1, 29), (9, 25), (18, 44), (43, 15), (14, 6), (8, 12), (31, 5), (31, 11), (43, 18), (22, 28), (7, 44), (20, 32), (33, 12), (20, 10), (27, 14), (16, 19), (22, 22), (23, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 20), (15, 36), (30, 1), (16, 35), (28, 22), (21, 0), (23, 41), (37, 24), (9, 43), (5, 30), (15, 0), (23, 4), (37, 3), (35, 19), (30, 28), (17, 28), (4, 23), (0, 32), (39, 35), (25, 43), (22, 12), (5, 44), (16, 6), (35, 2), (21, 21), (28, 37), (10, 4), (4, 12), (32, 36), (2, 14), (33, 41), (1, 8), (36, 15), (1, 41), (16, 18), (2, 41), (36, 10), (20, 27), (12, 14), (31, 36), (17, 23), (3, 22), (11, 24), (27, 39), (8, 22), (32, 22), (27, 16), (34, 4), (25, 15), (37, 17), (11, 3), (28, 9), (20, 15), (33, 18), (22, 24), (12, 17), (13, 44), (14, 39), (20, 13), (3, 41), (20, 43), (19, 38), (36, 18), (29, 32), (24, 34), (19, 42), (7, 41), (17, 3), (3, 25), (17, 12), (15, 34), (3, 31), (38, 35), (25, 1), (32, 28), (17, 4), (2, 38), (31, 34), (2, 42), (11, 26), (26, 23), (22, 37), (10, 35), (15, 3), (10, 25), (26, 38), (25, 30), (22, 33), (10, 20), (0, 39), (24, 43), (21, 13), (15, 13), (31, 6), (14, 3), (27, 35), (2, 39), (12, 1), (38, 34), (16, 23), (34, 5), (30, 17), (26, 2), (1, 39), (21, 17), (6, 4), (6, 6), (37, 33), (2, 35), (13, 34), (39, 24), (13, 24), (1, 16), (15, 33), (38, 6), (38, 9), (13, 4), (22, 29), (30, 36), (22, 34), (1, 37), (18, 34), (23, 44), (6, 9), (31, 23), (38, 28), (13, 5), (3, 8), (39, 31), (39, 38), (16, 27), (36, 13), (2, 3), (15, 25), (23, 37), (22, 36), (6, 25), (33, 43), (8, 44), (35, 12), (21, 19), (11, 23), (11, 8), (25, 20), (32, 3), (33, 27), (16, 33), (19, 10), (4, 40), (18, 31), (9, 40), (39, 36), (12, 42), (23, 34), (2, 18), (23, 2), (4, 10), (34, 26), (19, 24), (7, 34), (37, 30), (29, 44), (16, 19), (5, 12), (26, 29), (21, 3), (9, 22), (30, 5), (18, 4), (39, 10), (30, 11), (26, 43), (26, 19), (13, 10), (27, 0), (8, 35), (28, 11), (38, 7), (29, 39), (27, 13), (11, 13), (33, 31), (36, 3), (5, 14), (0, 16), (3, 7), (29, 15), (39, 41), (14, 32), (20, 10), (34, 38), (15, 31), (35, 8), (14, 20), (11, 0), (4, 24), (22, 22), (39, 1), (19, 41), (17, 22), (20, 17), (26, 30), (11, 25), (2, 36), (11, 4), (38, 20), (31, 41), (15, 9), (36, 28), (1, 38), (39, 33), (9, 38), (21, 11), (35, 22), (38, 36), (38, 27), (22, 18), (19, 39), (23, 36), (31, 43), (18, 16), (16, 40), (28, 35), (0, 26), (37, 31), (26, 44), (7, 21), (6, 7), (28, 0), (3, 34), (20, 19), (22, 26), (39, 9), (35, 26), (36, 32), (26, 17), (30, 31), (28, 39), (30, 40), (31, 30), (9, 19), (16, 32), (4, 11), (11, 5), (36, 36), (39, 40), (29, 40), (25, 44), (12, 38), (29, 11), (8, 20), (34, 9), (30, 43), (29, 36), (26, 22), (1, 10), (9, 24), (27, 17), (28, 41), (34, 13), (13, 39), (1, 21), (5, 15), (20, 39), (20, 4), (19, 6), (23, 13), (37, 7), (17, 26), (37, 12), (39, 4), (6, 33), (15, 43), (3, 14), (18, 21), (3, 9), (20, 22), (8, 25), (2, 44), (24, 8), (1, 7), (36, 14), (23, 25), (23, 24), (35, 25), (0, 15), (37, 8), (26, 1), (19, 7), (13, 7), (10, 37), (19, 19), (24, 6), (0, 17), (26, 32), (18, 1), (30, 38), (11, 20), (22, 9), (18, 7), (22, 4), (23, 3), (36, 42), (18, 3), (37, 18), (8, 9), (28, 26), (31, 15), (3, 1), (20, 16), (32, 26), (37, 19), (6, 34), (12, 26), (33, 16), (13, 6), (7, 44), (4, 41), (9, 14), (16, 22), (18, 42), (7, 42), (12, 31), (35, 0), (33, 40), (33, 13), (31, 31), (16, 3), (34, 29), (24, 37), (14, 16), (29, 17), (6, 39), (1, 14), (21, 31), (11, 6), (16, 31), (9, 25), (11, 36), (1, 25), (28, 25), (28, 16), (9, 8), (2, 32), (8, 14), (9, 29), (22, 0), (5, 6), (37, 0), (9, 11), (21, 37), (25, 22), (1, 24), (34, 42), (16, 4), (31, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 16), (24, 34), (17, 40), (19, 42), (15, 14), (22, 13), (38, 2), (1, 36), (23, 29), (2, 4), (40, 14), (0, 20), (43, 4), (3, 36), (34, 29), (34, 19), (23, 22), (1, 18), (17, 38), (18, 28), (34, 35), (6, 30), (23, 3), (11, 2), (42, 19), (26, 0), (33, 24), (20, 16), (32, 23), (39, 8), (19, 41), (34, 31), (2, 29), (13, 0), (43, 2), (5, 8), (27, 12), (38, 6), (13, 4), (9, 1), (37, 23), (1, 19), (41, 33), (41, 28), (2, 2), (38, 33), (19, 6), (39, 41), (38, 12), (17, 3), (13, 1), (20, 17), (21, 25), (10, 0), (25, 16), (0, 12), (37, 5), (7, 4), (35, 11), (19, 21), (31, 6), (20, 38), (0, 8), (9, 33), (16, 35), (2, 15), (9, 26), (6, 15), (12, 1), (3, 22), (26, 13), (18, 16), (24, 1), (42, 38), (15, 34), (31, 18), (39, 28), (17, 2), (18, 8), (25, 10), (30, 42), (9, 24), (5, 23), (15, 22), (21, 10), (21, 3), (31, 16), (13, 37), (9, 39), (24, 23), (40, 5), (38, 20), (43, 24), (6, 41), (31, 15), (42, 16), (7, 26), (12, 13), (32, 36), (42, 29), (4, 36), (40, 43), (18, 4), (0, 14), (32, 3), (16, 3), (42, 5), (15, 26), (21, 18), (11, 40), (16, 13), (42, 25), (11, 32), (27, 2), (12, 36), (15, 2), (34, 5), (39, 33), (34, 2), (7, 6), (24, 27), (6, 3), (1, 5), (24, 42), (38, 27), (6, 4), (41, 34), (43, 35), (31, 40), (2, 21), (1, 14), (26, 29), (9, 35), (17, 37), (5, 28), (5, 12), (26, 19), (22, 31), (6, 27), (26, 20), (28, 32), (1, 24), (7, 3), (20, 32), (11, 31), (27, 42), (25, 43), (22, 27), (6, 18), (42, 37), (30, 10), (21, 8), (15, 19), (12, 28), (37, 2), (27, 20), (39, 35), (8, 0), (36, 36), (42, 9), (15, 12), (17, 24), (25, 31), (30, 8), (32, 15), (23, 36), (35, 31), (16, 2), (38, 22), (42, 35), (3, 16), (24, 36), (9, 9), (39, 17), (4, 25), (40, 40), (27, 16), (5, 30), (11, 20), (23, 33), (0, 42), (19, 40), (8, 34), (22, 35), (43, 0), (18, 2), (14, 14), (33, 10), (18, 19), (6, 19), (22, 23), (25, 25), (30, 17), (6, 22), (1, 25), (18, 35), (4, 16), (37, 12), (12, 34), (6, 11), (29, 19), (42, 7), (11, 14), (37, 28), (10, 33), (31, 8), (40, 21), (42, 6), (42, 41), (36, 26), (26, 34), (21, 4), (18, 20), (30, 0), (9, 21), (42, 15), (34, 4), (25, 4), (11, 5), (37, 19), (11, 8), (12, 11), (28, 42), (37, 22), (6, 25), (15, 15), (24, 24), (30, 22), (39, 32), (13, 12), (18, 43), (12, 40), (37, 41), (23, 43), (15, 25), (29, 35), (2, 11), (18, 40), (28, 43), (14, 43), (34, 28), (7, 32), (35, 42), (40, 41), (42, 40), (20, 40), (3, 37), (34, 12), (13, 14), (25, 19), (1, 30), (11, 25), (20, 19), (13, 13), (18, 18), (10, 32), (31, 14), (9, 18), (37, 30), (43, 12), (9, 0), (15, 21), (40, 20), (16, 6), (3, 28), (25, 26), (10, 2), (34, 36), (13, 28), (42, 3), (19, 29), (3, 12), (18, 31), (31, 26), (0, 6), (14, 16), (12, 14), (7, 13), (22, 39), (39, 37), (11, 42), (19, 14), (10, 9), (23, 4), (14, 39), (12, 20), (23, 16), (23, 1), (34, 10), (38, 15), (14, 3), (43, 5), (17, 18), (17, 30), (37, 0), (4, 42), (22, 43), (22, 32), (9, 10), (0, 3), (25, 0), (41, 43), (31, 20), (37, 18), (28, 14), (13, 17), (26, 23), (15, 11), (33, 0), (22, 17), (20, 26), (13, 23), (16, 38), (33, 26), (10, 27), (2, 16), (4, 22), (0, 5), (39, 6), (21, 28), (0, 9), (19, 11), (36, 21), (42, 10), (38, 10), (32, 38), (39, 29), (1, 39), (16, 29), (12, 15), (11, 0), (14, 11), (10, 42), (25, 11), (27, 1), (31, 33), (26, 35), (9, 4), (22, 28), (22, 14), (27, 39), (17, 9), (39, 2), (0, 25), (13, 19), (4, 19), (15, 5), (11, 24), (16, 16), (1, 15), (31, 25), (11, 12), (27, 4), (29, 37), (3, 21), (36, 6), (0, 30), (21, 34), (2, 33), (29, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 4), (43, 42), (17, 17), (28, 24), (10, 40), (9, 16), (20, 16), (33, 10), (5, 10), (42, 31), (14, 38), (23, 0), (11, 38), (9, 13), (36, 5), (42, 2), (32, 34), (47, 23), (30, 42), (18, 16), (7, 34), (6, 16), (5, 15), (7, 26), (44, 32), (0, 41), (11, 44), (41, 41), (12, 14), (6, 40), (38, 40), (2, 22), (30, 25), (31, 19), (5, 8), (33, 21), (5, 41), (24, 41), (45, 13), (36, 40), (5, 13), (42, 4), (46, 5), (20, 25), (17, 11), (37, 37), (21, 15), (5, 38), (4, 21), (23, 20), (46, 13), (36, 45), (35, 0), (32, 38), (31, 3), (32, 19), (9, 42), (29, 9), (44, 6), (21, 29), (31, 41), (44, 38), (27, 28), (16, 34), (25, 40), (47, 20), (16, 16), (38, 32), (4, 5), (35, 35), (2, 4), (21, 21), (36, 42), (24, 8), (42, 8), (10, 22), (32, 8), (20, 39), (46, 10), (47, 33), (38, 21), (10, 2), (4, 19), (21, 7), (21, 44), (28, 8), (16, 42), (29, 11), (45, 16), (5, 35), (16, 27), (42, 7), (28, 5), (42, 30), (16, 31), (23, 17), (22, 19), (38, 4), (30, 15), (22, 39), (3, 9), (40, 1), (15, 28), (39, 2), (33, 28), (15, 16), (5, 3), (19, 40), (39, 20), (34, 25), (20, 19), (43, 26), (20, 4), (35, 39), (41, 22), (12, 43), (15, 10), (27, 36), (9, 40), (3, 45), (20, 18), (10, 44), (43, 46), (7, 20), (4, 30), (10, 29), (26, 44), (13, 35), (37, 42), (14, 25), (40, 36), (6, 13), (32, 20), (31, 33), (16, 8), (26, 16), (42, 23), (3, 25), (12, 21), (42, 1), (8, 31), (26, 39), (26, 33), (30, 46), (6, 5), (37, 33), (24, 0), (33, 26), (0, 38), (20, 11), (44, 28), (32, 17), (17, 41), (25, 41), (43, 30), (4, 41), (40, 7), (15, 30), (36, 15), (26, 34), (19, 41), (22, 15), (31, 32), (47, 8), (11, 14), (34, 38), (44, 9), (4, 42), (15, 18), (23, 31), (23, 11), (17, 32), (12, 3), (19, 27), (44, 34), (45, 4), (2, 28), (42, 27), (23, 14), (18, 26), (21, 0), (41, 7), (11, 13), (15, 19), (29, 7), (18, 12), (47, 1), (3, 10), (10, 46), (11, 8), (21, 18), (18, 22), (14, 10), (10, 28), (29, 33), (33, 37), (35, 21), (34, 28), (8, 25), (17, 33), (15, 5), (44, 33), (27, 3), (6, 28), (34, 1), (22, 46), (42, 3), (14, 39), (26, 40), (0, 5), (38, 25), (20, 5), (7, 32), (29, 26), (5, 6), (22, 21), (27, 34), (29, 4), (8, 30), (35, 27), (15, 4), (18, 2), (37, 16), (18, 7), (7, 22), (31, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 36), (1, 6), (5, 26), (20, 34), (25, 14), (40, 21), (43, 10), (32, 9), (7, 42), (40, 8), (30, 36), (33, 25), (19, 29), (36, 15), (26, 30), (17, 1), (30, 17), (11, 33), (26, 13), (11, 21), (5, 7), (37, 41), (14, 18), (37, 0), (26, 5), (13, 1), (10, 41), (0, 7), (23, 43), (22, 36), (10, 31), (42, 40), (8, 15), (32, 2), (26, 12), (14, 39), (16, 9), (19, 12), (3, 39), (37, 4), (46, 21), (38, 15), (3, 23), (31, 11), (32, 40), (21, 5), (27, 43), (43, 28), (30, 18), (15, 29), (41, 4), (15, 18), (19, 45), (12, 41), (31, 1), (31, 5), (8, 24), (30, 20), (43, 29), (39, 25), (32, 39), (15, 43), (0, 17), (4, 12), (36, 20), (32, 31), (29, 38), (25, 13), (28, 25), (0, 43), (3, 22), (38, 36), (17, 27), (6, 0), (39, 31), (7, 17), (25, 8), (0, 36), (29, 40), (41, 29), (33, 24), (16, 41), (1, 28), (10, 5), (29, 14), (1, 1), (13, 22), (22, 23), (26, 26), (35, 12), (13, 14), (14, 1), (26, 17), (8, 16), (30, 21), (40, 39), (12, 40), (28, 9), (39, 38), (46, 0), (43, 30), (1, 20), (20, 28), (40, 0), (14, 21), (31, 17), (6, 29), (41, 19), (19, 4), (28, 34), (21, 44), (22, 3), (2, 23), (43, 33), (8, 30), (12, 25), (10, 18), (37, 35), (15, 3), (9, 37), (27, 36), (18, 43), (13, 15), (28, 21), (34, 15), (21, 24), (14, 10), (15, 13), (46, 6), (15, 14), (36, 27), (32, 43), (37, 20), (32, 35), (3, 40), (20, 40), (13, 36), (25, 40), (3, 36), (10, 11), (1, 17), (25, 5), (23, 4), (33, 37), (32, 16), (16, 17), (2, 31), (12, 20), (37, 15), (45, 29), (17, 4), (24, 9), (0, 31), (15, 31), (9, 26), (20, 12), (14, 35), (37, 34), (25, 12), (10, 3), (22, 20), (18, 20), (12, 38), (8, 42), (4, 35), (36, 40), (24, 31), (24, 20), (35, 42), (24, 1), (14, 6), (16, 21), (32, 23), (4, 21), (15, 8), (25, 33), (29, 37), (16, 14), (38, 1), (14, 12), (42, 7), (35, 19), (15, 4), (24, 7), (29, 19), (11, 24), (36, 31), (42, 26), (40, 36), (5, 14), (23, 22), (12, 2), (26, 8), (39, 43), (41, 43), (16, 10), (12, 37), (13, 23), (27, 33), (38, 34), (37, 3), (19, 44), (10, 0), (28, 28), (28, 8), (40, 28), (45, 13), (5, 43), (21, 38), (3, 0), (2, 45), (4, 28), (34, 13), (9, 11), (39, 8), (17, 0), (0, 30), (18, 8), (10, 21), (8, 29), (19, 10), (3, 30), (24, 10), (29, 1), (32, 19), (44, 44), (6, 38), (19, 23), (27, 13), (42, 4), (1, 22), (41, 13), (30, 27), (42, 1), (24, 24), (46, 44), (0, 22), (32, 21), (42, 10), (33, 26), (12, 4), (1, 5), (37, 23), (11, 4), (9, 31), (39, 26), (41, 25), (5, 33), (31, 16), (10, 1), (41, 42), (28, 37), (13, 21), (2, 11), (18, 2), (6, 21), (7, 22), (9, 16), (2, 14), (46, 30), (41, 30), (45, 9), (26, 4), (21, 15), (32, 22), (27, 16), (20, 45), (16, 18), (31, 19), (42, 41), (34, 41), (30, 7), (46, 3), (44, 38), (33, 20), (2, 27), (40, 17), (46, 10), (23, 0), (26, 16), (42, 30), (0, 6), (8, 21), (22, 12), (20, 1), (32, 7), (20, 16), (39, 32), (33, 43), (15, 28), (33, 0), (12, 35), (7, 3), (5, 6), (20, 31), (37, 45), (38, 2), (0, 28), (12, 9), (6, 15), (23, 27), (35, 29), (36, 1), (42, 21), (16, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 34), (20, 38), (17, 33), (22, 8), (2, 0), (16, 32), (2, 2), (31, 20), (37, 28), (3, 33), (28, 43), (24, 30), (26, 2), (22, 33), (29, 17), (19, 9), (35, 10), (32, 24), (37, 9), (35, 26), (10, 7), (23, 31), (9, 32), (6, 19), (39, 12), (31, 1), (31, 21), (14, 23), (19, 7), (14, 1), (7, 11), (16, 33), (11, 33), (37, 1), (27, 5), (2, 6), (35, 18), (27, 38), (33, 20), (5, 12), (24, 31), (6, 14), (16, 35), (6, 29), (19, 17), (18, 19), (27, 18), (18, 34), (25, 0), (31, 5), (40, 6), (25, 10), (28, 29), (23, 32), (28, 2), (13, 9), (30, 39), (38, 28), (20, 11), (23, 24), (3, 21), (3, 1), (20, 42), (39, 21), (35, 25), (20, 28), (27, 10), (17, 40), (3, 16), (40, 40), (32, 31), (2, 8), (26, 10), (27, 29), (32, 21), (34, 2), (29, 27), (2, 11), (25, 31), (39, 16), (25, 13), (32, 12), (24, 22), (38, 21), (2, 34), (34, 6), (6, 32), (10, 27), (35, 3), (24, 25), (33, 3), (10, 18), (22, 22), (24, 3), (14, 3), (8, 10), (26, 20), (19, 1), (28, 6), (7, 30), (32, 8), (16, 39), (27, 16), (8, 27), (21, 29), (30, 32), (18, 33), (3, 23), (35, 23), (26, 23), (29, 18), (27, 3), (40, 15), (37, 13), (37, 14), (0, 20), (33, 42), (0, 31), (13, 25), (29, 2), (38, 20), (9, 27), (2, 26), (22, 37), (27, 34), (24, 2), (40, 2), (18, 41), (17, 35), (34, 0), (19, 13), (11, 41), (38, 6), (37, 22), (26, 34), (12, 32), (7, 35), (36, 21), (9, 6), (16, 29), (15, 0), (1, 23), (11, 15), (19, 16), (23, 25), (21, 23), (8, 42), (7, 9), (36, 14), (27, 0), (28, 35), (4, 6), (15, 32), (35, 16), (11, 3), (29, 34), (26, 6), (21, 30), (29, 4), (26, 31), (40, 12), (20, 16), (4, 18), (39, 39), (11, 38), (24, 29), (2, 27), (26, 28), (25, 1), (22, 17), (5, 1), (11, 20), (9, 15), (1, 27), (12, 21), (10, 30), (39, 4), (7, 12), (29, 25), (27, 23), (4, 17), (21, 16), (6, 33), (20, 43), (15, 33), (11, 8), (33, 8), (39, 13), (25, 32), (5, 29), (32, 17), (22, 35), (5, 43), (29, 35), (21, 31), (31, 29), (36, 22), (36, 7), (30, 22), (25, 12), (19, 30), (26, 27), (31, 38), (13, 4), (37, 20), (6, 5), (31, 31), (27, 28), (14, 7), (9, 26), (31, 32), (16, 23), (31, 12), (13, 17), (12, 38), (10, 8), (4, 42), (33, 27), (39, 34), (9, 13), (13, 7), (32, 10), (30, 18), (38, 15), (25, 16), (26, 13), (17, 24), (40, 41), (25, 25), (25, 21), (29, 7), (2, 14), (35, 29), (21, 35), (34, 30), (31, 37), (37, 25), (11, 14), (37, 0), (19, 25), (34, 43), (6, 34), (12, 4), (14, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (27, 17), (10, 38), (28, 18), (24, 15), (36, 16), (9, 32), (36, 34), (7, 24), (30, 25), (14, 23), (13, 29), (41, 15), (14, 32), (23, 24), (40, 16), (42, 34), (37, 4), (12, 24), (0, 26), (5, 37), (14, 5), (22, 32), (1, 16), (6, 29), (8, 39), (25, 2), (39, 17), (11, 15), (3, 1), (40, 32), (8, 6), (0, 3), (35, 1), (5, 9), (16, 27), (39, 31), (34, 31), (14, 24), (23, 7), (16, 31), (7, 35), (9, 19), (30, 22), (18, 27), (20, 21), (3, 6), (10, 4), (29, 38), (19, 7), (37, 29), (35, 16), (31, 23), (29, 37), (32, 11), (3, 14), (38, 18), (6, 2), (26, 41), (7, 15), (10, 36), (31, 7), (10, 1), (38, 33), (15, 19), (27, 26), (22, 39), (5, 0), (36, 31), (17, 9), (1, 7), (25, 0), (40, 18), (19, 25), (40, 38), (37, 9), (9, 30), (17, 29), (14, 27), (8, 2), (6, 4), (33, 39), (12, 15), (12, 13), (3, 39), (7, 28), (31, 15), (13, 19), (32, 27), (37, 32), (21, 16), (9, 41), (27, 23), (20, 8), (22, 11), (8, 29), (21, 0), (42, 24), (34, 0), (4, 1), (20, 20), (26, 34), (21, 40), (26, 30), (16, 2), (33, 4), (7, 1), (17, 8), (33, 37), (31, 12), (11, 3), (17, 14), (23, 13), (36, 37), (20, 38), (6, 39), (37, 35), (11, 34), (18, 5), (37, 19), (37, 14), (20, 2), (3, 27), (35, 35), (12, 6), (33, 25), (5, 41), (28, 22), (7, 40), (1, 20), (29, 20), (17, 5), (31, 30), (24, 0), (21, 11), (27, 5), (1, 27), (33, 0), (33, 17), (15, 32), (20, 31), (24, 16), (39, 39), (6, 13), (28, 9), (10, 28), (8, 4), (4, 2), (16, 5), (42, 13), (5, 39), (36, 21), (7, 2), (30, 11), (35, 23), (22, 28), (40, 14), (17, 35), (27, 35), (33, 12), (18, 15), (14, 34), (24, 31), (25, 7), (15, 17), (6, 31), (1, 3), (18, 16), (17, 13), (7, 5), (8, 41), (17, 30), (35, 24), (32, 32), (8, 28), (11, 40), (17, 28), (18, 35), (15, 27), (11, 31), (41, 8), (2, 24), (32, 16), (22, 38), (18, 33), (9, 35), (30, 27), (18, 29), (4, 31), (23, 25), (7, 37), (40, 37), (1, 12), (33, 23), (41, 10), (30, 3), (12, 8), (25, 28), (10, 8), (10, 6), (33, 35), (4, 41), (29, 41), (18, 11), (8, 18), (18, 39), (33, 41), (6, 17), (13, 31), (15, 28), (31, 18), (37, 25), (12, 32), (39, 14), (28, 5), (38, 8), (4, 5), (17, 24), (8, 33), (17, 1), (36, 8), (12, 17), (34, 30), (14, 12), (12, 40), (0, 6), (19, 12), (36, 36), (16, 32), (39, 36), (28, 0), (32, 3), (14, 26), (38, 0), (5, 5), (0, 12), (34, 1), (39, 24), (12, 2), (8, 17), (33, 21), (9, 40), (5, 10), (26, 1), (32, 1), (30, 24), (31, 35), (19, 27), (9, 2), (2, 21), (41, 23), (3, 23), (6, 36), (42, 26), (24, 6), (36, 27), (5, 25), (11, 20), (36, 1), (36, 14), (17, 20), (7, 3), (9, 14), (38, 13), (21, 5), (25, 12), (7, 18), (40, 34), (34, 9), (34, 21), (39, 35), (28, 23), (0, 39), (37, 31), (36, 28), (27, 10), (1, 11), (0, 11), (15, 33), (33, 15), (1, 38), (12, 5), (26, 29), (12, 22), (19, 8), (20, 18), (36, 30), (42, 19), (41, 19), (29, 40), (28, 28), (1, 37), (17, 33), (3, 2), (11, 22), (20, 11), (29, 25), (41, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 10), (30, 12), (26, 6), (19, 32), (29, 41), (30, 27), (5, 0), (16, 41), (6, 36), (27, 31), (24, 37), (17, 24), (26, 25), (38, 2), (23, 22), (16, 15), (0, 13), (24, 26), (21, 17), (11, 32), (26, 41), (34, 29), (9, 34), (38, 15), (32, 28), (0, 17), (4, 39), (9, 15), (5, 11), (43, 40), (35, 30), (39, 21), (46, 23), (26, 26), (23, 39), (1, 37), (15, 38), (35, 27), (35, 20), (37, 20), (11, 37), (9, 10), (21, 32), (45, 34), (5, 9), (19, 33), (14, 38), (24, 0), (44, 6), (42, 14), (45, 7), (23, 34), (34, 14), (25, 11), (20, 16), (37, 26), (9, 4), (9, 3), (14, 18), (4, 14), (12, 9), (42, 38), (40, 18), (21, 8), (35, 3), (44, 39), (32, 26), (17, 29), (20, 17), (39, 14), (16, 6), (24, 8), (15, 17), (37, 8), (8, 28), (5, 12), (11, 41), (40, 14), (32, 14), (27, 30), (24, 17), (1, 41), (11, 33), (43, 34), (33, 6), (42, 15), (12, 24), (11, 12), (45, 19), (14, 30), (16, 13), (41, 30), (39, 30), (5, 24), (5, 32), (15, 39), (2, 20), (42, 21), (21, 27), (38, 34), (7, 20), (13, 11), (40, 26), (18, 15), (27, 4), (35, 24), (30, 28), (42, 7), (40, 34), (13, 38), (43, 25), (3, 13), (23, 37), (39, 18), (0, 29), (29, 22), (28, 29), (28, 13), (40, 8), (35, 0), (29, 14), (39, 28), (7, 29), (16, 16), (33, 31), (28, 10), (46, 39), (19, 2), (41, 27), (5, 7), (38, 8), (31, 16), (32, 8), (19, 13), (10, 40), (39, 8), (7, 26), (44, 18), (36, 26), (9, 35), (7, 11), (28, 34), (32, 38), (11, 7), (19, 7), (44, 15), (3, 32), (17, 15), (31, 3), (45, 36), (20, 14), (30, 4), (40, 41), (25, 12), (41, 8), (26, 27), (36, 2), (16, 4), (0, 25), (7, 32), (22, 27), (9, 14), (15, 4), (20, 28), (44, 2), (15, 32), (17, 17), (35, 34), (41, 40), (21, 10), (4, 41), (41, 4), (0, 2), (11, 17), (10, 33), (29, 1), (20, 5), (12, 34), (40, 33), (23, 30), (39, 12), (37, 4), (36, 32), (35, 33), (44, 33), (4, 25), (45, 6), (22, 7), (12, 7), (30, 8), (0, 31), (32, 40), (22, 15), (16, 19), (14, 22), (15, 24), (9, 26), (28, 2), (15, 19), (15, 26), (18, 7), (13, 7), (7, 19), (7, 25), (33, 5), (24, 40), (29, 20), (15, 12), (21, 26), (15, 20), (18, 16), (24, 12), (10, 9), (1, 39), (3, 26), (23, 36), (43, 9), (32, 24), (32, 25), (4, 15), (2, 22), (19, 31), (24, 33), (14, 20), (23, 38), (7, 14), (21, 11), (11, 26), (18, 0), (36, 7), (24, 27), (16, 9), (44, 17), (29, 23), (31, 26), (2, 28), (24, 1), (10, 4), (45, 37), (5, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 24), (10, 12), (33, 13), (26, 10), (29, 7), (1, 36), (19, 24), (3, 34), (10, 25), (30, 19), (38, 35), (8, 21), (1, 1), (42, 38), (39, 1), (20, 13), (20, 35), (13, 29), (23, 21), (42, 31), (18, 13), (7, 38), (45, 24), (7, 29), (23, 24), (6, 26), (32, 18), (46, 32), (2, 28), (38, 5), (27, 17), (34, 15), (4, 42), (38, 13), (13, 34), (36, 27), (31, 40), (22, 43), (35, 35), (42, 28), (45, 23), (2, 40), (11, 3), (0, 24), (35, 26), (31, 19), (17, 17), (14, 11), (2, 26), (11, 34), (39, 34), (40, 31), (9, 32), (31, 17), (13, 20), (0, 4), (43, 26), (29, 17), (18, 32), (44, 15), (5, 32), (45, 40), (48, 16), (47, 43), (9, 26), (37, 4), (29, 37), (5, 21), (18, 16), (47, 3), (10, 14), (11, 15), (34, 34), (35, 36), (6, 36), (21, 1), (30, 8), (5, 25), (15, 4), (0, 41), (12, 27), (19, 17), (40, 12), (1, 6), (1, 12), (22, 25), (7, 4), (19, 4), (44, 23), (15, 15), (24, 5), (10, 2), (12, 39), (27, 7), (28, 36), (18, 23), (11, 1), (8, 24), (11, 38), (35, 5), (15, 34), (6, 5), (34, 33), (46, 6), (15, 8), (16, 43), (28, 31), (48, 5), (19, 18), (41, 31), (27, 38), (39, 10), (38, 18), (18, 10), (5, 8), (17, 27), (10, 1), (45, 28), (33, 19), (43, 10), (20, 18), (16, 10), (14, 0), (40, 3), (48, 10), (15, 16), (6, 24), (24, 11), (0, 7), (45, 4), (10, 6), (42, 15), (44, 14), (21, 8), (4, 39), (7, 42), (48, 3), (37, 17), (43, 34), (26, 25), (9, 15), (17, 43), (41, 35), (15, 33), (4, 36), (0, 12), (30, 24), (28, 23), (14, 24), (8, 2), (24, 36), (24, 25), (46, 18), (17, 34), (34, 0), (38, 29), (26, 19), (32, 10), (7, 28), (0, 30), (28, 14), (3, 3), (22, 12), (9, 10), (27, 30), (30, 6), (9, 0), (0, 36), (23, 16), (10, 37), (29, 29), (17, 7), (39, 0), (30, 27), (31, 9), (13, 43), (8, 1), (6, 17), (16, 4), (14, 10), (33, 1), (6, 20), (19, 26), (39, 39), (15, 10), (42, 18), (24, 31), (18, 1), (41, 16), (13, 12), (33, 23), (33, 25), (38, 0), (14, 36), (42, 21), (38, 44), (41, 12), (22, 28), (15, 12), (3, 22), (6, 35), (7, 44), (34, 25), (47, 6), (17, 19), (41, 20), (39, 42), (34, 8), (21, 26), (39, 21), (5, 14), (34, 31), (45, 20), (15, 26), (42, 41), (48, 17), (5, 11), (0, 21), (43, 25), (25, 29), (16, 23), (17, 33), (1, 33), (4, 7), (19, 44), (23, 9), (36, 3), (48, 30), (31, 29), (24, 34), (43, 33), (1, 27), (28, 44), (44, 22), (12, 7), (14, 40), (47, 32), (47, 29), (5, 6), (4, 43), (42, 13), (8, 15), (25, 27), (21, 32), (6, 6), (13, 15), (14, 37), (20, 31), (37, 16), (11, 40), (10, 10), (17, 42), (12, 26), (23, 27), (1, 42), (34, 13), (28, 24), (21, 42), (7, 16), (47, 9), (0, 15), (19, 1), (36, 35), (15, 24), (46, 17), (20, 33), (18, 17), (29, 26), (43, 39), (17, 32), (14, 5), (7, 40), (10, 4), (7, 17), (10, 22), (15, 2), (15, 44), (18, 39), (40, 15), (35, 1), (46, 11), (0, 11), (20, 17), (7, 32), (37, 31), (32, 20), (39, 23), (38, 17), (4, 32), (48, 2), (20, 23), (35, 8), (16, 37), (40, 21), (33, 12), (40, 35), (40, 23), (3, 30), (31, 44), (5, 38), (29, 16), (31, 3), (27, 3), (5, 17), (37, 25), (5, 1), (36, 0), (43, 3), (0, 26), (35, 0), (20, 21), (34, 24), (31, 39), (23, 25), (3, 31), (17, 26), (48, 33), (1, 22), (6, 42), (31, 10), (33, 35), (47, 1), (18, 9), (7, 36), (16, 5), (14, 25), (2, 17), (34, 18), (14, 29), (23, 18), (5, 12), (29, 11), (5, 16), (19, 9), (5, 26), (43, 20), (17, 3), (9, 8), (32, 4), (18, 5), (43, 16), (12, 12), (32, 37), (9, 27), (48, 25), (15, 38), (33, 7), (2, 15), (29, 28), (36, 12), (3, 11), (34, 28), (36, 6), (32, 33), (41, 6), (34, 41), (16, 29), (30, 42), (14, 20), (7, 43), (12, 41), (25, 42), (3, 13), (39, 37), (1, 37), (42, 40), (16, 11), (33, 17), (22, 24), (18, 44), (0, 16), (22, 3), (10, 36), (40, 20), (25, 11), (37, 22), (47, 34), (27, 18), (35, 13), (6, 27), (0, 23), (21, 34), (47, 8), (42, 10), (43, 30), (3, 43), (26, 15), (34, 35), (22, 4), (42, 25), (17, 36), (24, 12), (9, 11), (44, 3), (24, 8), (26, 9), (20, 20), (23, 23), (47, 28), (40, 1), (17, 41), (2, 39), (37, 14), (10, 19), (32, 43), (7, 0), (13, 31), (44, 12), (45, 21), (8, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 10), (27, 9), (18, 40), (23, 9), (19, 33), (27, 17), (7, 21), (4, 19), (4, 12), (11, 40), (38, 11), (1, 3), (5, 41), (20, 17), (6, 36), (36, 12), (31, 13), (30, 4), (17, 1), (36, 29), (32, 29), (7, 8), (44, 8), (25, 9), (11, 29), (11, 27), (4, 23), (27, 39), (22, 0), (37, 37), (22, 16), (15, 1), (16, 29), (41, 3), (45, 1), (40, 26), (36, 39), (15, 39), (7, 22), (34, 3), (42, 23), (31, 29), (15, 27), (34, 8), (24, 28), (26, 30), (15, 24), (32, 20), (34, 14), (32, 13), (18, 22), (10, 34), (45, 2), (25, 0), (35, 17), (5, 3), (39, 18), (22, 40), (5, 38), (18, 12), (24, 25), (20, 31), (37, 14), (9, 31), (7, 37), (10, 17), (22, 22), (16, 18), (9, 27), (13, 27), (40, 20), (19, 36), (35, 24), (41, 15), (37, 38), (1, 6), (26, 41), (13, 37), (20, 29), (31, 28), (28, 24), (18, 2), (37, 27), (5, 5), (17, 6), (39, 35), (21, 19), (12, 19), (7, 7), (29, 39), (20, 1), (3, 4), (44, 32), (10, 27), (9, 32), (5, 12), (35, 33), (22, 23), (6, 18), (35, 27), (40, 28), (11, 28), (12, 34), (5, 32), (9, 1), (26, 6), (2, 30), (39, 26), (30, 2), (7, 5), (15, 23), (39, 27), (36, 40), (10, 25), (7, 26), (36, 28), (41, 20), (21, 12), (10, 3), (39, 29), (31, 12), (27, 19), (40, 25), (28, 11), (41, 29), (29, 19), (42, 13), (18, 1), (39, 12), (29, 40), (30, 38), (44, 39), (19, 26), (38, 23), (18, 24), (13, 39), (43, 1), (44, 38), (5, 40), (10, 21), (23, 32), (2, 19), (30, 34), (42, 28), (16, 36), (22, 24), (37, 13), (22, 17), (43, 17), (3, 17), (40, 27), (28, 16), (8, 30), (40, 35), (10, 13), (43, 2), (41, 4), (15, 33), (19, 34), (4, 40), (16, 1), (2, 18), (5, 33), (2, 3), (5, 20), (42, 3), (24, 18), (34, 36), (35, 15), (12, 15), (25, 37), (6, 15), (23, 13), (16, 12), (4, 24), (23, 24), (21, 5), (10, 14), (42, 17), (9, 12), (13, 16), (27, 27), (0, 32), (43, 35), (3, 37), (22, 25), (1, 31), (41, 6), (21, 13), (8, 27), (44, 21), (25, 29), (6, 41), (36, 19), (32, 32), (26, 39), (13, 1), (23, 2), (38, 17), (4, 37), (1, 23), (40, 40), (35, 14), (42, 2), (14, 23), (30, 14), (38, 20), (37, 12), (40, 15), (0, 34), (40, 8), (18, 7), (4, 8), (11, 33), (28, 36), (3, 41), (7, 6), (44, 26), (32, 37), (26, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 24), (27, 33), (16, 4), (9, 27), (35, 16), (7, 27), (25, 1), (15, 37), (18, 30), (25, 19), (4, 24), (31, 27), (9, 39), (5, 25), (9, 24), (19, 3), (22, 36), (7, 5), (26, 3), (32, 2), (6, 16), (37, 9), (29, 6), (40, 1), (22, 38), (32, 39), (7, 18), (31, 1), (37, 10), (6, 26), (34, 8), (22, 35), (3, 4), (24, 16), (19, 36), (13, 11), (24, 22), (5, 17), (39, 3), (32, 10), (32, 22), (29, 1), (39, 25), (30, 28), (27, 27), (1, 40), (17, 4), (6, 5), (1, 33), (24, 18), (27, 4), (34, 38), (39, 14), (15, 40), (31, 14), (23, 40), (28, 0), (40, 0), (38, 30), (21, 27), (7, 15), (25, 35), (28, 40), (36, 21), (3, 29), (21, 12), (29, 25), (7, 16), (23, 30), (18, 35), (32, 26), (3, 13), (36, 34), (16, 0), (1, 27), (6, 10), (37, 2), (19, 8), (39, 13), (12, 34), (32, 13), (19, 12), (25, 38), (40, 8), (17, 40), (36, 26), (23, 11), (35, 15), (38, 8), (39, 34), (26, 13), (25, 16), (2, 18), (28, 36), (12, 26), (33, 8), (1, 31), (39, 16), (30, 3), (28, 15), (13, 27), (0, 39), (2, 21), (37, 22), (24, 24), (1, 0), (17, 34), (40, 22), (19, 26), (21, 39), (18, 12), (37, 26), (7, 2), (12, 6), (29, 2), (2, 8), (21, 18), (32, 34), (11, 35), (18, 1), (0, 36), (0, 23), (33, 22), (11, 28), (41, 20), (3, 18), (35, 7), (14, 13), (2, 33), (37, 8), (25, 32), (24, 23), (21, 37), (26, 35), (1, 20), (30, 12), (30, 37), (26, 15), (34, 22), (39, 18), (15, 25), (33, 36), (21, 11), (21, 14), (34, 39), (22, 37), (2, 38), (23, 23), (40, 34), (8, 12), (10, 40), (29, 19), (2, 13), (27, 11), (37, 1), (31, 36), (25, 13), (41, 36), (38, 5), (2, 39), (23, 7), (36, 10), (20, 34), (10, 34), (0, 8), (32, 25), (4, 21), (23, 35), (25, 22), (5, 0), (34, 13), (15, 2), (32, 5), (14, 16), (11, 37), (22, 24), (27, 26), (3, 39), (24, 39), (13, 26), (5, 18), (7, 34), (10, 29), (2, 16), (12, 1), (28, 37), (1, 25), (29, 14), (26, 36), (39, 33), (2, 12), (7, 10), (31, 13), (32, 7), (39, 1), (3, 14), (11, 13), (12, 19), (7, 13), (12, 0), (26, 11), (12, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 7), (33, 2), (22, 33), (21, 11), (10, 0), (22, 17), (30, 38), (17, 33), (43, 15), (29, 5), (28, 13), (35, 23), (0, 23), (13, 15), (8, 8), (31, 10), (39, 27), (41, 28), (41, 40), (38, 32), (39, 29), (20, 38), (29, 7), (7, 9), (38, 30), (37, 11), (39, 19), (12, 14), (5, 25), (36, 14), (25, 16), (37, 13), (33, 15), (1, 29), (30, 22), (32, 35), (4, 7), (26, 35), (10, 11), (40, 37), (16, 21), (13, 2), (5, 35), (39, 24), (30, 39), (34, 11), (10, 17), (3, 23), (10, 3), (10, 1), (34, 38), (29, 3), (22, 25), (17, 9), (14, 19), (18, 4), (11, 22), (3, 39), (33, 33), (15, 40), (23, 12), (38, 40), (31, 8), (7, 33), (29, 17), (26, 17), (8, 33), (1, 22), (39, 10), (37, 1), (42, 5), (20, 5), (17, 20), (23, 28), (41, 1), (20, 10), (33, 19), (30, 23), (27, 3), (42, 26), (25, 27), (40, 27), (26, 22), (26, 10), (18, 18), (36, 18), (8, 18), (8, 16), (37, 21), (41, 8), (20, 16), (1, 4), (38, 39), (4, 16), (5, 21), (39, 30), (25, 37), (6, 31), (16, 2), (7, 23), (36, 6), (9, 30), (43, 3), (39, 38), (11, 28), (32, 33), (40, 0), (24, 7), (2, 25), (16, 1), (26, 39), (1, 28), (35, 27), (15, 16), (34, 17), (31, 21), (7, 24), (0, 35), (6, 33), (42, 3), (16, 7), (26, 5), (19, 14), (12, 27), (38, 24), (42, 24), (42, 13), (7, 40), (3, 37), (37, 17), (37, 22), (34, 10), (33, 26), (23, 21), (27, 25), (35, 26), (21, 26), (35, 30), (11, 38), (34, 40), (34, 39), (4, 4), (21, 23), (15, 29), (22, 2), (10, 16), (12, 39), (2, 12), (16, 31), (2, 32), (36, 33), (42, 11), (21, 40), (16, 29), (4, 12), (3, 9), (37, 15), (22, 35), (43, 9), (15, 9), (22, 11), (28, 21), (15, 34), (33, 29), (38, 29), (25, 9), (19, 1), (26, 25), (24, 4), (33, 22), (2, 3), (5, 13), (18, 9), (29, 32), (32, 1), (9, 16), (41, 15), (7, 26), (25, 20), (11, 3), (17, 37), (35, 15), (6, 10), (33, 37), (1, 3), (11, 7), (4, 36), (26, 14), (43, 13), (0, 2), (2, 10), (32, 40), (25, 32), (42, 40), (8, 2), (39, 28), (40, 30), (26, 34), (10, 38), (15, 38), (10, 28), (32, 0), (31, 39), (18, 21), (18, 17), (16, 20), (26, 27), (17, 7), (18, 31), (11, 21), (4, 24), (3, 31), (9, 39), (11, 9), (15, 14), (27, 36), (21, 13), (6, 19), (28, 22), (31, 28), (28, 37), (27, 30), (27, 12), (34, 27), (25, 14), (9, 5), (35, 9), (4, 15), (32, 22), (42, 34), (42, 17), (43, 34), (15, 33), (21, 20), (27, 31), (15, 26), (7, 28), (43, 33), (37, 18), (2, 17), (34, 31), (13, 24), (34, 12), (15, 10), (36, 25), (12, 18), (20, 1), (39, 9), (11, 32), (14, 22), (38, 34), (37, 33), (21, 29), (17, 29), (33, 0), (18, 30), (31, 3), (32, 7), (24, 0), (17, 25), (22, 4), (41, 22), (11, 6), (11, 15), (3, 10), (12, 24), (5, 29), (27, 37), (41, 34), (35, 19), (7, 15), (3, 4), (37, 25), (37, 28), (37, 23), (30, 12), (6, 15), (19, 13), (14, 37), (4, 39), (8, 24), (35, 1), (33, 27), (17, 21), (35, 39), (18, 12), (15, 11), (32, 12), (2, 6), (36, 17), (38, 20), (34, 26), (4, 34), (10, 31), (24, 2), (0, 15), (27, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 10), (8, 1), (29, 9), (3, 39), (28, 9), (37, 4), (4, 11), (34, 6), (35, 15), (36, 1), (16, 32), (15, 27), (31, 38), (19, 18), (10, 42), (9, 39), (26, 43), (33, 36), (39, 38), (20, 0), (4, 20), (36, 36), (4, 38), (17, 34), (9, 31), (2, 43), (20, 2), (18, 18), (45, 4), (37, 35), (26, 35), (27, 28), (6, 12), (39, 1), (12, 17), (42, 33), (40, 44), (38, 33), (38, 29), (12, 14), (20, 9), (2, 0), (18, 26), (5, 16), (11, 38), (7, 25), (36, 0), (44, 20), (30, 24), (11, 35), (38, 31), (0, 30), (43, 9), (36, 10), (7, 39), (29, 28), (31, 31), (43, 13), (1, 9), (5, 41), (8, 3), (36, 24), (33, 27), (11, 31), (37, 19), (30, 20), (44, 33), (30, 41), (8, 13), (17, 42), (19, 20), (5, 32), (25, 42), (5, 9), (37, 13), (19, 35), (39, 11), (2, 22), (33, 13), (9, 0), (24, 36), (5, 19), (10, 21), (42, 5), (34, 25), (10, 6), (21, 23), (41, 40), (41, 26), (21, 18), (9, 6), (29, 39), (32, 26), (45, 0), (30, 17), (29, 35), (20, 11), (13, 42), (13, 35), (45, 22), (27, 9), (29, 15), (24, 38), (12, 37), (45, 37), (14, 4), (18, 17), (10, 34), (23, 1), (22, 3), (13, 9), (23, 38), (6, 7), (4, 24), (0, 38), (38, 43), (0, 20), (22, 23), (39, 43), (38, 34), (23, 3), (0, 1), (11, 42), (16, 4), (5, 20), (33, 23), (44, 35), (12, 22), (2, 21), (43, 27), (26, 4), (18, 25), (3, 17), (31, 36), (30, 8), (45, 27), (42, 23), (9, 17), (35, 10), (9, 26), (0, 32), (22, 34), (32, 34), (45, 32), (9, 22), (13, 8), (14, 21), (39, 6), (32, 43), (29, 6), (35, 40), (2, 34), (24, 10), (2, 2), (8, 44), (5, 22), (32, 12), (33, 37), (33, 22), (43, 1), (14, 39), (21, 37), (22, 28), (21, 27), (22, 42), (14, 32), (20, 43), (25, 24), (6, 35), (5, 28), (17, 0), (30, 36), (19, 27), (23, 29), (24, 9), (35, 6), (31, 13), (36, 5), (20, 41), (34, 14), (0, 18), (44, 38), (4, 23), (6, 6), (4, 34), (42, 3), (42, 2), (32, 36), (19, 11), (3, 4), (44, 14), (36, 20), (14, 31), (36, 4), (37, 21), (19, 40), (42, 31), (11, 34), (43, 22), (22, 44), (13, 30), (6, 30), (22, 0), (40, 11), (3, 24), (34, 5), (16, 15), (4, 0), (36, 12), (45, 9), (17, 39), (3, 16), (32, 6), (20, 17), (20, 40), (23, 16), (14, 44), (30, 23), (38, 36), (19, 13), (6, 15), (30, 25), (7, 33), (25, 3), (26, 31), (10, 18), (12, 3), (45, 3), (33, 41), (29, 3), (6, 13), (7, 32), (0, 35), (8, 27), (25, 34), (20, 22), (9, 16), (38, 37), (0, 29), (45, 33), (6, 19), (11, 0), (22, 15), (32, 24), (12, 0), (30, 5), (28, 7), (26, 41), (13, 44), (13, 21), (11, 5), (37, 34), (26, 16), (27, 4), (27, 32), (20, 13), (34, 1), (10, 40), (10, 9), (28, 23), (26, 0), (37, 17), (19, 42), (26, 28), (9, 8), (0, 39), (41, 13), (22, 25), (13, 29), (35, 14), (10, 35), (25, 11), (27, 16), (45, 25), (34, 30), (9, 7), (41, 36), (29, 12), (1, 2), (12, 40), (43, 17), (42, 41), (26, 7), (21, 36), (44, 2), (45, 19), (5, 12), (26, 6), (7, 19), (9, 33), (3, 0), (23, 12), (20, 27), (17, 36), (30, 11), (24, 28), (28, 3), (43, 33), (24, 27), (13, 6), (43, 12), (12, 33), (23, 20), (36, 31), (42, 7), (24, 43), (41, 33), (25, 1), (39, 42), (12, 21), (35, 3), (18, 34), (32, 17), (35, 31), (31, 6), (31, 33), (19, 23), (8, 42), (5, 27), (3, 14), (39, 32), (2, 19), (13, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 36), (16, 10), (36, 35), (16, 11), (4, 44), (16, 1), (25, 37), (8, 28), (32, 30), (5, 31), (33, 34), (40, 33), (34, 6), (33, 11), (4, 18), (17, 22), (0, 15), (7, 31), (7, 26), (27, 8), (28, 16), (10, 25), (29, 44), (30, 18), (37, 21), (1, 30), (37, 32), (12, 7), (24, 11), (29, 21), (24, 33), (30, 19), (18, 22), (38, 27), (39, 25), (21, 40), (9, 7), (1, 29), (39, 24), (4, 25), (34, 22), (8, 19), (6, 17), (36, 2), (1, 0), (22, 22), (41, 45), (31, 10), (42, 8), (9, 3), (32, 20), (31, 6), (24, 29), (42, 37), (14, 11), (31, 8), (14, 22), (1, 10), (20, 20), (8, 29), (11, 11), (21, 8), (27, 1), (14, 35), (40, 1), (11, 34), (8, 5), (5, 9), (3, 26), (11, 14), (0, 31), (27, 39), (4, 23), (17, 11), (23, 29), (13, 13), (0, 3), (17, 37), (17, 3), (10, 21), (33, 31), (40, 11), (16, 34), (35, 16), (8, 3), (12, 41), (31, 38), (18, 29), (41, 40), (24, 21), (11, 0), (14, 13), (15, 24), (23, 13), (19, 20), (3, 14), (19, 14), (1, 11), (10, 27), (35, 21), (20, 37), (3, 0), (41, 41), (33, 29), (5, 23), (26, 24), (34, 17), (3, 21), (37, 34), (3, 34), (31, 40), (38, 43), (5, 11), (6, 20), (21, 14), (18, 21), (38, 16), (4, 28), (35, 15), (24, 35), (41, 22), (37, 0), (19, 39), (4, 0), (16, 39), (25, 10), (41, 32), (2, 3), (34, 7), (26, 6), (6, 2), (37, 20), (30, 46), (17, 13), (2, 27), (38, 17), (27, 5), (28, 1), (0, 22), (7, 40), (37, 46), (41, 16), (37, 5), (23, 30), (38, 5), (35, 11), (37, 26), (40, 42), (27, 21), (35, 34), (10, 6), (5, 27), (20, 15), (6, 28), (26, 19), (18, 33), (2, 29), (19, 31), (18, 13), (18, 20), (26, 1), (0, 32), (1, 38), (20, 25), (22, 4), (11, 2), (40, 31), (24, 24), (20, 21), (4, 29), (18, 39), (32, 9), (20, 43), (39, 6), (32, 22), (31, 15), (29, 20), (25, 7), (41, 11), (19, 16), (11, 18), (16, 16), (10, 34), (7, 5), (1, 16), (2, 11), (28, 26), (7, 0), (36, 33), (28, 3), (40, 13), (22, 17), (22, 25), (7, 17), (19, 3), (8, 35), (42, 23), (7, 27), (39, 39), (20, 46), (32, 35), (7, 35), (9, 34), (36, 5), (26, 28), (29, 12), (5, 32), (5, 34), (25, 19), (39, 23), (10, 7), (5, 18), (17, 44), (1, 37), (32, 6), (32, 40), (4, 20), (5, 43), (12, 16), (20, 5), (38, 36), (3, 46), (14, 2), (34, 30), (1, 6), (30, 35), (33, 42), (25, 1), (33, 30), (38, 26), (30, 7), (31, 31), (29, 42), (41, 10), (30, 1), (14, 38), (7, 28), (24, 39), (18, 46), (7, 24), (8, 25), (7, 39), (12, 10), (35, 40), (36, 6), (33, 14), (41, 30), (15, 3), (42, 24), (36, 15), (36, 11), (20, 3), (33, 32), (40, 29), (41, 21), (23, 19), (6, 41), (33, 43), (3, 31), (41, 12), (2, 39), (17, 18), (27, 34), (40, 20), (20, 8), (15, 16), (16, 40), (13, 32), (14, 10), (26, 3), (12, 31), (24, 17), (22, 32), (30, 28), (21, 18), (6, 33), (12, 5), (2, 1), (21, 33), (19, 27), (31, 32), (10, 42), (39, 45), (5, 28), (9, 13), (9, 5), (2, 6), (5, 35), (20, 24), (15, 32), (28, 5), (39, 35), (27, 46), (8, 27), (34, 23), (27, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 12), (11, 0), (32, 16), (19, 21), (5, 31), (6, 25), (18, 40), (35, 4), (20, 40), (12, 35), (41, 26), (8, 6), (1, 20), (19, 11), (21, 33), (25, 0), (42, 5), (42, 35), (32, 23), (1, 24), (23, 10), (16, 32), (4, 5), (26, 39), (23, 18), (0, 13), (5, 22), (37, 13), (22, 14), (22, 1), (7, 15), (15, 0), (34, 1), (45, 24), (1, 7), (24, 19), (1, 41), (19, 24), (36, 21), (12, 8), (14, 24), (34, 39), (10, 12), (39, 39), (7, 0), (9, 26), (2, 36), (10, 3), (44, 29), (17, 7), (14, 9), (33, 16), (6, 14), (40, 24), (40, 18), (35, 33), (20, 23), (11, 33), (32, 24), (17, 19), (8, 25), (44, 24), (28, 31), (45, 35), (7, 6), (36, 28), (4, 0), (22, 6), (38, 15), (11, 9), (11, 22), (0, 35), (38, 7), (19, 39), (35, 30), (33, 11), (19, 26), (11, 32), (29, 36), (38, 12), (45, 1), (16, 20), (16, 30), (27, 15), (12, 25), (12, 3), (8, 7), (31, 3), (39, 17), (3, 15), (13, 8), (23, 35), (31, 36), (4, 36), (34, 18), (2, 17), (9, 5), (37, 17), (6, 22), (4, 38), (19, 38), (30, 41), (36, 31), (0, 16), (31, 12), (14, 23), (15, 28), (28, 13), (19, 40), (39, 5), (32, 27), (36, 9), (7, 1), (3, 18), (36, 40), (24, 36), (29, 2), (16, 37), (43, 2), (10, 27), (45, 40), (9, 11), (36, 26), (28, 40), (20, 17), (20, 25), (38, 8), (32, 8), (17, 17), (17, 40), (17, 33), (1, 40), (24, 37), (25, 23), (31, 32), (21, 41), (35, 0), (12, 34), (4, 29), (19, 29), (24, 29), (40, 38), (12, 26), (6, 38), (42, 23), (17, 14), (1, 25), (16, 22), (42, 4), (26, 5), (20, 2), (10, 22), (0, 30), (38, 39), (10, 38), (16, 40), (27, 2), (8, 9), (9, 17), (38, 17), (43, 26), (16, 12), (23, 12), (1, 31), (21, 0), (40, 27), (16, 28), (21, 5), (25, 17), (27, 1), (27, 22), (6, 31), (2, 10), (23, 11), (44, 33), (37, 15), (28, 9), (39, 18), (2, 1), (13, 15), (30, 32), (37, 38), (28, 33), (1, 21), (41, 0), (10, 25), (15, 13), (10, 26), (14, 20), (40, 11), (18, 15), (32, 32), (17, 16), (22, 15), (5, 29), (45, 22), (38, 13), (12, 2), (38, 28), (26, 21), (42, 26), (40, 34), (38, 6), (9, 8), (45, 25), (45, 37), (16, 9), (43, 22), (2, 40), (45, 13), (43, 36), (36, 3), (24, 27), (6, 8), (20, 3), (30, 17), (31, 19), (1, 33), (40, 3), (21, 10), (20, 32), (25, 40), (17, 2), (34, 11), (18, 7), (33, 26), (44, 30), (26, 41), (11, 23), (33, 33), (9, 28), (8, 0), (31, 34), (21, 26), (36, 11), (7, 33), (25, 9), (32, 31), (40, 0), (28, 39), (29, 37), (2, 30), (9, 14), (25, 2), (25, 25), (5, 13), (42, 19), (18, 35), (32, 20), (24, 40), (37, 18), (27, 36), (12, 14), (16, 21), (18, 28), (41, 39), (10, 1), (31, 29), (12, 5), (32, 26), (13, 28), (8, 3), (24, 24), (5, 1), (28, 29), (33, 22), (6, 37), (45, 4), (7, 40), (11, 38), (30, 13), (1, 27), (41, 28), (12, 18), (1, 32), (41, 7), (24, 26), (27, 13), (6, 13), (0, 21), (4, 22), (15, 5), (44, 21), (44, 10), (16, 2), (35, 36), (38, 3), (16, 15), (7, 2), (25, 28), (22, 28), (42, 15), (34, 4), (39, 33), (32, 14), (21, 27), (40, 36), (15, 4), (18, 25), (25, 8), (28, 32), (35, 16), (3, 38), (37, 29), (14, 36), (10, 29), (6, 10), (40, 16), (24, 13), (18, 20), (21, 12), (42, 13), (45, 18), (17, 4), (3, 39), (42, 32), (24, 5), (29, 30), (6, 4), (34, 5), (6, 32), (41, 13), (3, 12), (3, 29), (33, 23), (8, 31), (17, 38), (38, 27), (6, 2), (7, 25), (6, 0), (23, 28), (10, 2), (28, 11), (35, 22), (1, 2), (6, 1), (10, 20), (30, 29), (20, 14), (31, 26), (8, 4), (24, 7), (36, 16), (40, 28), (0, 28), (10, 24), (39, 4), (9, 21), (17, 29), (11, 1), (11, 6), (2, 26), (35, 18), (13, 5), (29, 9), (14, 38), (13, 23), (39, 22), (10, 10), (1, 13), (17, 35), (14, 28), (15, 21), (16, 6), (32, 6), (10, 9), (43, 13), (32, 41), (15, 15), (11, 34), (37, 10), (42, 3), (12, 10), (31, 20), (36, 30), (42, 34), (27, 29), (4, 18), (7, 12), (37, 39), (0, 37), (22, 3), (4, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 27), (41, 21), (38, 41), (17, 27), (12, 5), (8, 29), (30, 28), (34, 25), (21, 12), (32, 11), (2, 8), (29, 17), (41, 30), (35, 2), (16, 4), (18, 7), (32, 16), (8, 5), (12, 9), (3, 4), (25, 27), (15, 30), (39, 28), (20, 35), (12, 20), (19, 36), (36, 9), (26, 24), (17, 35), (31, 35), (35, 1), (12, 8), (32, 41), (2, 22), (28, 21), (16, 35), (14, 5), (8, 37), (21, 3), (13, 25), (37, 19), (0, 36), (7, 37), (26, 17), (30, 9), (11, 33), (39, 22), (0, 25), (5, 32), (33, 15), (31, 11), (27, 37), (32, 26), (12, 27), (29, 2), (26, 40), (33, 8), (34, 0), (35, 12), (38, 17), (0, 40), (3, 1), (30, 10), (9, 25), (10, 27), (36, 21), (39, 14), (30, 41), (37, 24), (23, 20), (40, 7), (9, 21), (11, 34), (39, 37), (37, 35), (35, 20), (41, 23), (7, 2), (2, 19), (27, 5), (17, 20), (40, 23), (16, 28), (17, 19), (31, 38), (13, 14), (14, 12), (33, 14), (17, 33), (2, 12), (13, 27), (23, 36), (27, 17), (18, 35), (4, 31), (19, 41), (28, 9), (22, 14), (15, 19), (15, 16), (31, 18), (37, 31), (3, 22), (25, 16), (13, 42), (3, 5), (20, 27), (16, 27), (5, 19), (27, 10), (18, 6), (19, 42), (39, 3), (25, 4), (35, 15), (38, 37), (3, 41), (23, 31), (3, 6), (8, 0), (22, 39), (24, 4), (37, 13), (29, 16), (29, 42), (14, 38), (7, 6), (14, 21), (21, 37), (9, 4), (31, 5), (7, 41), (30, 21), (1, 42), (7, 40), (5, 5), (37, 8), (3, 18), (21, 20), (40, 12), (17, 41), (16, 16), (33, 3), (13, 36), (40, 42), (21, 33), (11, 30), (33, 33), (3, 42), (5, 11), (36, 29), (34, 16), (35, 21), (6, 16), (41, 15), (36, 22), (22, 6), (34, 9), (13, 8), (38, 5), (15, 37), (10, 9), (5, 9), (5, 17), (21, 31), (38, 0), (5, 34), (22, 13), (13, 32), (38, 14), (21, 27), (4, 29), (22, 18), (35, 23), (27, 34), (4, 8), (37, 25), (24, 33), (14, 7), (30, 34), (5, 4), (29, 40), (19, 25), (36, 0), (39, 4), (9, 1), (40, 9), (19, 0), (40, 29), (19, 11), (41, 25), (31, 31), (24, 2), (35, 25), (25, 5), (6, 33), (34, 33), (25, 12), (39, 12), (39, 33), (1, 41), (18, 26), (26, 0), (22, 15), (24, 21), (39, 16), (20, 5), (31, 24), (25, 32), (21, 8), (37, 15), (28, 24), (12, 6), (4, 36), (6, 42), (25, 35), (27, 29), (17, 15), (5, 2), (16, 32), (19, 16), (26, 26), (32, 14), (11, 10), (22, 22), (19, 39), (13, 11), (26, 34), (38, 31), (37, 16), (32, 36), (23, 27), (12, 31), (30, 15), (14, 15), (6, 22), (17, 37), (5, 42), (19, 27), (33, 39), (36, 12), (37, 1), (41, 4), (35, 17), (25, 34), (17, 39), (22, 41), (1, 32), (34, 22), (31, 0), (10, 31), (15, 13), (15, 38), (21, 26), (4, 28), (3, 23), (10, 15), (6, 24), (19, 22), (22, 31), (10, 13), (13, 28), (10, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 15), (18, 36), (15, 25), (21, 31), (34, 40), (3, 34), (37, 5), (42, 1), (43, 10), (6, 20), (15, 10), (25, 14), (5, 34), (37, 3), (5, 10), (44, 40), (43, 39), (23, 12), (34, 25), (1, 33), (26, 36), (41, 14), (20, 33), (13, 0), (9, 12), (1, 29), (45, 30), (43, 35), (25, 2), (3, 18), (27, 5), (1, 34), (14, 26), (0, 40), (0, 3), (6, 9), (5, 13), (25, 36), (28, 16), (40, 0), (11, 33), (20, 42), (20, 16), (42, 38), (39, 6), (13, 1), (19, 32), (36, 25), (6, 37), (28, 5), (16, 4), (43, 0), (29, 35), (30, 31), (11, 14), (42, 41), (34, 26), (2, 19), (26, 32), (20, 20), (8, 12), (4, 34), (1, 16), (44, 34), (8, 30), (17, 26), (42, 14), (29, 4), (5, 14), (39, 19), (19, 36), (42, 9), (44, 38), (14, 35), (8, 33), (4, 39), (39, 20), (30, 27), (8, 37), (5, 40), (39, 17), (42, 25), (3, 33), (41, 40), (40, 2), (13, 30), (12, 26), (31, 16), (14, 15), (18, 20), (23, 39), (7, 28), (16, 9), (43, 28), (35, 36), (28, 32), (16, 22), (5, 25), (12, 1), (26, 25), (31, 4), (1, 25), (6, 3), (21, 21), (6, 35), (37, 20), (30, 5), (44, 25), (32, 18), (14, 28), (45, 34), (1, 9), (20, 22), (39, 4), (21, 32), (12, 31), (39, 22), (39, 8), (39, 28), (8, 17), (38, 40), (17, 27), (5, 38), (25, 4), (31, 38), (27, 20), (16, 31), (33, 34), (22, 34), (24, 32), (13, 4), (16, 3), (40, 25), (42, 36), (40, 37), (1, 28), (13, 3), (11, 40), (6, 30), (15, 14), (21, 33), (39, 7), (2, 39), (10, 37), (18, 7), (33, 39), (41, 11), (28, 12), (21, 41), (13, 22), (16, 11), (40, 21), (18, 17), (39, 23), (32, 38), (33, 32), (16, 13), (40, 4), (25, 9), (38, 9), (27, 25), (18, 37), (33, 15), (38, 1), (31, 1), (8, 19), (9, 32), (44, 31), (19, 28), (32, 12), (26, 4), (35, 31), (38, 12), (12, 10), (37, 9), (0, 41), (10, 20), (28, 21), (29, 15), (38, 29), (9, 19), (28, 7), (27, 42), (7, 33), (44, 36), (31, 0), (26, 24), (5, 33), (27, 2), (31, 6), (10, 35), (30, 10), (6, 5), (6, 31), (30, 36), (7, 10), (12, 0), (39, 11), (40, 5), (26, 11), (24, 19), (17, 0), (40, 9), (40, 16), (27, 30), (18, 38), (19, 17), (7, 6), (13, 10), (13, 13), (9, 18), (7, 19), (12, 37), (33, 16), (21, 36), (34, 10), (16, 19), (45, 39), (3, 27), (27, 4), (39, 34), (37, 32), (22, 19), (16, 10), (28, 14), (27, 31), (2, 4), (5, 18), (20, 14), (22, 42), (12, 11), (15, 1), (45, 1), (23, 26), (35, 0), (26, 37), (11, 23), (36, 33), (1, 36), (21, 38), (5, 1), (35, 14), (1, 12), (29, 29), (34, 13), (5, 37), (39, 3), (24, 38), (27, 37), (34, 17), (17, 34), (23, 19), (11, 31), (21, 18), (36, 18), (41, 34), (30, 19), (18, 42), (4, 27), (21, 15), (29, 10), (9, 37), (16, 39), (2, 0), (15, 19), (45, 37), (22, 39), (0, 29), (42, 39), (28, 27), (43, 30), (14, 34), (19, 1), (38, 31), (4, 23), (32, 7), (43, 40), (37, 33), (31, 28), (23, 6), (13, 11), (30, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 36), (0, 11), (27, 27), (46, 10), (26, 40), (36, 1), (37, 5), (7, 0), (9, 28), (30, 3), (17, 26), (19, 35), (43, 14), (25, 14), (25, 16), (9, 15), (45, 18), (10, 44), (20, 30), (29, 21), (6, 32), (36, 2), (46, 36), (32, 14), (21, 28), (4, 16), (34, 23), (34, 2), (17, 27), (3, 26), (20, 18), (16, 17), (9, 34), (45, 40), (8, 30), (8, 23), (32, 6), (14, 43), (0, 19), (38, 8), (18, 14), (6, 8), (0, 43), (11, 6), (32, 13), (21, 9), (31, 36), (32, 40), (46, 12), (2, 25), (25, 22), (16, 13), (15, 9), (9, 2), (16, 34), (29, 44), (30, 45), (6, 25), (27, 21), (11, 2), (33, 44), (15, 39), (21, 4), (28, 12), (44, 28), (24, 36), (5, 7), (46, 43), (9, 3), (17, 18), (27, 25), (36, 35), (5, 20), (27, 6), (0, 44), (36, 43), (9, 6), (14, 18), (25, 26), (2, 40), (6, 16), (43, 32), (12, 5), (4, 34), (16, 26), (6, 21), (29, 32), (45, 29), (5, 23), (15, 35), (32, 21), (36, 26), (32, 29), (29, 31), (10, 35), (31, 0), (42, 18), (33, 9), (21, 23), (18, 12), (3, 21), (12, 6), (29, 1), (9, 39), (16, 27), (6, 31), (26, 20), (6, 35), (0, 24), (36, 41), (35, 6), (27, 28), (39, 13), (36, 8), (8, 6), (10, 43), (21, 27), (43, 6), (27, 2), (20, 31), (35, 9), (22, 4), (1, 6), (44, 19), (34, 34), (33, 34), (16, 24), (4, 42), (2, 38), (19, 39), (32, 41), (29, 17), (30, 33), (30, 35), (39, 15), (11, 16), (44, 41), (33, 8), (10, 6), (9, 16), (16, 4), (18, 3), (18, 28), (37, 23), (19, 6), (28, 14), (17, 32), (9, 33), (10, 27), (42, 14), (10, 3), (19, 29), (37, 15), (22, 40), (36, 23), (4, 39), (24, 27), (8, 26), (25, 23), (24, 6), (5, 12), (6, 20), (17, 41), (25, 9), (3, 15), (16, 2), (42, 27), (36, 34), (42, 3), (7, 4), (11, 34), (38, 20), (29, 12), (43, 34), (27, 4), (6, 45), (11, 27), (8, 37), (6, 36), (27, 29), (8, 0), (6, 42), (20, 3), (21, 3), (3, 36), (26, 11), (38, 16), (1, 29), (44, 5), (14, 22), (41, 6), (7, 19), (18, 45), (6, 29), (46, 21), (17, 10), (8, 15), (23, 42), (25, 7), (14, 20), (45, 39), (16, 21), (13, 9), (4, 31), (11, 29), (41, 20), (40, 36), (34, 45), (41, 17), (5, 35), (43, 45), (31, 33), (32, 44), (5, 30), (0, 40), (41, 8), (4, 45), (29, 16), (27, 33), (34, 40), (34, 27), (7, 33), (36, 25), (41, 37), (5, 44), (2, 36), (37, 1), (27, 45), (37, 14), (20, 19), (20, 42), (22, 34), (46, 7), (13, 44), (17, 44), (42, 37), (34, 11), (16, 25), (10, 23), (24, 35), (17, 17), (5, 2), (14, 9), (14, 29), (2, 39), (20, 17), (27, 37), (12, 15), (41, 27), (45, 13), (26, 9), (19, 33), (12, 31), (28, 43), (44, 30), (39, 3), (25, 40), (18, 27), (18, 11), (0, 26), (23, 36), (3, 8), (40, 32), (19, 43), (17, 24), (18, 36), (3, 9), (3, 34), (32, 45), (44, 21), (11, 42), (38, 36), (4, 14), (38, 1), (38, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 22), (4, 29), (12, 34), (36, 47), (16, 36), (43, 8), (12, 0), (9, 23), (19, 45), (37, 7), (10, 31), (44, 23), (12, 30), (14, 20), (3, 37), (20, 43), (13, 5), (45, 2), (13, 9), (30, 37), (24, 9), (38, 44), (3, 23), (27, 25), (17, 33), (14, 2), (29, 14), (45, 40), (16, 16), (29, 3), (7, 14), (16, 29), (5, 43), (38, 41), (3, 34), (42, 45), (37, 34), (37, 1), (42, 41), (17, 16), (0, 28), (18, 17), (27, 43), (32, 35), (22, 20), (25, 42), (15, 19), (30, 22), (36, 15), (15, 24), (28, 34), (36, 7), (19, 36), (40, 8), (37, 37), (23, 37), (4, 35), (10, 37), (16, 14), (35, 26), (35, 7), (42, 8), (32, 40), (34, 44), (15, 2), (19, 35), (32, 31), (3, 25), (38, 30), (11, 40), (32, 14), (9, 7), (34, 47), (31, 8), (6, 45), (20, 7), (12, 8), (44, 36), (26, 32), (41, 0), (44, 41), (2, 40), (36, 48), (4, 6), (20, 16), (5, 1), (23, 1), (12, 33), (12, 4), (37, 27), (3, 45), (12, 24), (1, 39), (43, 30), (26, 46), (18, 11), (38, 18), (13, 3), (24, 28), (38, 36), (32, 10), (2, 6), (17, 44), (32, 21), (32, 27), (26, 35), (18, 29), (6, 27), (9, 35), (13, 33), (7, 16), (37, 38), (33, 29), (43, 45), (14, 48), (1, 2), (5, 4), (31, 42), (5, 3), (17, 34), (44, 13), (4, 14), (23, 17), (15, 10), (42, 4), (16, 39), (17, 36), (45, 41), (23, 41), (11, 13), (25, 16), (1, 17), (20, 30), (21, 38), (37, 9), (13, 40), (44, 22), (29, 42), (4, 3), (28, 33), (1, 18), (30, 20), (9, 13), (34, 38), (9, 16), (2, 36), (8, 46), (11, 12), (35, 12), (23, 40), (22, 14), (35, 35), (0, 20), (36, 8), (13, 42), (33, 6), (26, 16), (21, 32), (12, 5), (4, 16), (42, 27), (6, 25), (45, 28), (12, 47), (13, 46), (7, 12), (4, 23), (17, 21), (17, 30), (4, 8), (36, 37), (6, 22), (23, 35), (6, 9), (10, 15), (5, 37), (29, 27), (14, 31), (21, 9), (34, 28), (29, 22), (14, 43), (16, 5), (34, 22), (12, 11), (29, 30), (6, 17), (36, 43), (22, 18), (38, 37), (42, 17), (26, 33), (19, 48), (35, 5), (21, 42), (31, 31), (18, 6), (30, 23), (34, 19), (2, 26), (35, 15), (1, 40), (36, 10), (8, 2), (35, 18), (14, 14), (36, 46), (34, 12), (42, 40), (38, 7), (1, 44), (25, 21), (28, 29), (31, 0), (44, 10), (39, 31), (9, 8), (38, 14), (11, 30), (11, 32), (38, 3), (8, 44), (40, 33), (21, 11), (4, 15), (29, 23), (36, 20), (42, 18), (13, 20), (22, 33), (31, 9), (10, 0), (10, 19), (22, 48), (43, 44), (27, 27), (44, 25), (3, 46), (9, 1), (22, 22), (13, 39), (22, 0), (29, 34), (22, 40), (30, 2), (29, 15), (19, 8), (22, 29), (12, 43), (13, 21), (41, 17), (12, 41), (6, 24), (37, 11), (20, 48), (9, 47), (22, 9), (22, 12), (13, 45), (27, 35), (15, 13), (18, 20), (7, 41), (21, 46), (17, 23), (3, 40), (19, 6), (33, 35), (13, 30), (9, 37), (13, 12), (10, 30), (11, 34), (6, 19), (28, 39), (37, 32), (40, 48), (29, 11), (34, 43), (28, 8), (37, 44), (40, 27), (12, 35), (6, 3), (35, 46), (45, 24), (27, 30), (5, 5), (7, 35), (42, 16), (21, 4), (14, 45), (8, 14), (42, 34), (17, 7), (11, 25), (35, 1), (21, 2), (9, 38), (42, 42), (27, 21), (0, 9), (20, 35), (29, 1), (8, 4), (14, 44), (21, 31), (25, 29), (38, 32), (27, 31), (3, 44), (2, 19), (16, 30), (17, 43), (32, 41), (34, 23), (11, 24), (7, 36), (40, 42), (2, 45), (34, 27), (10, 33), (39, 43), (39, 44), (28, 24), (0, 25), (2, 44), (32, 47), (10, 45), (11, 9), (34, 45), (45, 46), (39, 4), (39, 12), (20, 9), (13, 38), (28, 41), (11, 6), (10, 39), (38, 48), (2, 11), (8, 0), (9, 9), (30, 40), (25, 31), (18, 3), (45, 22), (5, 41), (21, 18), (16, 40), (36, 29), (38, 29), (34, 36), (24, 24), (33, 32), (4, 41), (20, 28), (19, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 15), (41, 15), (39, 36), (23, 26), (3, 43), (35, 33), (44, 23), (0, 19), (4, 11), (25, 40), (11, 15), (17, 40), (43, 42), (24, 10), (16, 8), (33, 6), (37, 5), (24, 32), (0, 14), (29, 2), (4, 29), (16, 29), (24, 44), (39, 13), (42, 13), (22, 19), (7, 39), (8, 35), (22, 30), (13, 33), (23, 27), (8, 25), (23, 1), (19, 29), (3, 31), (15, 5), (38, 33), (2, 19), (35, 29), (43, 16), (43, 29), (10, 24), (21, 15), (4, 41), (34, 28), (14, 37), (38, 27), (38, 28), (1, 10), (44, 8), (43, 39), (36, 35), (2, 42), (15, 31), (14, 10), (3, 18), (21, 35), (39, 25), (31, 30), (32, 37), (33, 37), (43, 33), (34, 24), (2, 2), (28, 28), (40, 38), (1, 18), (4, 43), (10, 34), (40, 36), (14, 27), (40, 7), (15, 14), (14, 40), (42, 3), (29, 38), (33, 9), (5, 20), (3, 19), (25, 25), (42, 17), (1, 13), (1, 44), (24, 1), (21, 26), (7, 34), (11, 32), (30, 4), (9, 1), (19, 31), (3, 23), (28, 4), (18, 32), (3, 6), (32, 34), (34, 39), (39, 24), (6, 35), (5, 37), (42, 1), (16, 42), (21, 2), (11, 10), (10, 16), (31, 28), (32, 32), (35, 14), (40, 26), (18, 12), (17, 29), (12, 6), (40, 4), (38, 15), (14, 2), (38, 31), (25, 42), (42, 28), (33, 40), (33, 13), (33, 27), (30, 6), (13, 10), (5, 31), (3, 28), (20, 39), (29, 27), (44, 28), (2, 15), (18, 34), (4, 24), (27, 33), (40, 6), (12, 22), (35, 39), (40, 29), (37, 42), (17, 27), (14, 25), (24, 28), (31, 22), (44, 2), (41, 12), (18, 36), (23, 14), (4, 40), (34, 3), (25, 13), (14, 6), (39, 6), (21, 18), (30, 27), (42, 10), (11, 17), (29, 19), (19, 32), (1, 43), (10, 29), (15, 15), (44, 16), (35, 8), (11, 39), (3, 16), (20, 4), (39, 2), (40, 12), (7, 12), (21, 41), (34, 14), (1, 1), (29, 25), (12, 32), (36, 22), (19, 12), (27, 43), (12, 18), (42, 33), (10, 22), (33, 16), (10, 31), (20, 28), (7, 7), (12, 37), (22, 14), (16, 4), (42, 35), (38, 30), (26, 22), (44, 36), (5, 32), (2, 26), (22, 44), (18, 3), (28, 2), (24, 43), (43, 19), (4, 39), (44, 13), (36, 25), (25, 9), (6, 14), (6, 42), (20, 18), (42, 32), (21, 32), (3, 0), (40, 21), (20, 40), (33, 7), (1, 7), (15, 36), (6, 30), (15, 11), (8, 36), (36, 41), (43, 14), (27, 37), (30, 9), (44, 30), (40, 28), (28, 33), (15, 41), (1, 11), (18, 38), (38, 2), (14, 9), (22, 15), (40, 43), (32, 21), (19, 11), (37, 18), (31, 38), (18, 37), (39, 5), (4, 27), (3, 30), (2, 8), (4, 13), (41, 6), (36, 15), (22, 25), (9, 26), (13, 32), (15, 2), (41, 17), (28, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 15), (15, 32), (31, 13), (14, 8), (2, 2), (36, 48), (32, 27), (29, 8), (37, 6), (37, 16), (21, 42), (3, 23), (36, 21), (12, 41), (6, 37), (6, 17), (21, 14), (25, 23), (7, 26), (18, 5), (13, 28), (12, 15), (15, 9), (31, 46), (30, 48), (25, 25), (4, 34), (20, 1), (29, 14), (38, 30), (14, 36), (7, 30), (31, 2), (39, 17), (40, 30), (26, 18), (27, 5), (30, 2), (10, 1), (8, 25), (36, 5), (17, 15), (18, 38), (29, 0), (14, 13), (38, 28), (30, 21), (25, 20), (17, 0), (31, 42), (9, 47), (20, 32), (5, 7), (10, 24), (36, 27), (15, 27), (6, 29), (21, 17), (39, 16), (1, 10), (0, 18), (1, 28), (12, 38), (15, 16), (6, 38), (24, 31), (23, 25), (7, 24), (21, 5), (22, 38), (30, 3), (3, 41), (23, 36), (38, 37), (13, 18), (27, 3), (33, 1), (19, 37), (8, 12), (16, 22), (20, 24), (26, 22), (10, 21), (27, 25), (31, 4), (34, 30), (3, 8), (8, 33), (18, 44), (29, 26), (10, 41), (39, 44), (36, 47), (28, 24), (40, 31), (16, 8), (13, 13), (33, 46), (18, 47), (2, 44), (28, 10), (32, 19), (5, 45), (15, 29), (13, 19), (26, 12), (23, 21), (29, 15), (5, 20), (37, 33), (25, 35), (37, 11), (12, 1), (25, 7), (37, 42), (6, 3), (19, 33), (28, 22), (14, 12), (32, 15), (18, 8), (10, 45), (23, 7), (28, 34), (27, 12), (9, 11), (12, 26), (26, 26), (39, 1), (20, 22), (10, 33), (32, 31), (18, 32), (35, 33), (25, 6), (35, 15), (7, 12), (19, 44), (8, 0), (5, 33), (23, 23), (20, 15), (31, 15), (14, 7), (1, 47), (24, 2), (4, 43), (15, 45), (30, 14), (12, 17), (24, 5), (29, 10), (37, 20), (21, 45), (27, 38), (26, 47), (21, 47), (12, 25), (18, 13), (27, 21), (1, 21), (37, 17), (31, 14), (8, 22), (38, 7), (14, 41), (37, 35), (17, 46), (39, 10), (24, 1), (1, 29), (11, 47), (16, 43), (15, 23), (13, 40), (2, 33), (14, 14), (26, 31), (14, 23), (36, 23), (33, 9), (19, 7), (33, 13), (16, 10), (11, 7), (37, 27), (1, 9), (11, 45), (12, 19), (11, 13), (38, 0), (1, 12), (40, 25), (6, 28), (34, 40), (25, 38), (1, 23), (3, 3), (13, 43), (15, 34), (35, 13), (28, 20), (20, 38), (21, 32), (39, 12), (4, 19), (21, 1), (22, 45), (36, 45), (23, 32), (0, 12), (36, 42), (21, 7), (36, 40), (13, 14), (0, 28), (37, 28), (28, 44), (13, 29), (2, 12), (24, 42), (0, 8), (16, 48), (12, 29), (34, 35), (40, 28), (36, 0), (21, 15), (15, 46), (37, 18), (0, 23), (7, 35), (19, 27), (16, 13), (32, 30), (14, 1), (30, 37), (40, 9), (16, 44), (1, 22), (25, 0), (31, 8), (21, 35), (7, 13), (35, 27), (14, 40), (30, 27), (6, 7), (36, 16), (37, 4), (14, 5), (39, 3), (36, 2), (17, 28), (23, 17), (11, 6), (16, 28), (2, 36), (34, 5), (8, 46), (20, 34), (15, 48), (32, 16), (37, 44), (30, 8), (29, 46), (40, 34), (38, 35), (6, 9), (18, 29), (12, 10), (0, 27), (39, 40), (7, 19), (8, 26), (9, 4), (23, 43), (27, 36), (6, 26), (27, 1), (22, 23), (39, 2), (7, 17), (10, 43), (23, 16), (21, 20), (22, 0), (5, 39), (40, 36), (28, 9), (20, 45), (38, 10), (7, 37), (6, 16), (7, 18), (25, 44), (40, 24), (20, 39), (28, 41), (22, 18), (5, 9), (2, 19), (15, 19), (21, 28), (9, 27), (35, 46), (10, 22), (0, 25), (0, 21), (11, 23), (28, 23), (17, 10), (21, 43), (28, 12), (32, 2), (28, 19), (15, 17), (33, 35), (19, 36), (38, 39), (38, 47), (20, 5), (16, 4), (12, 48), (30, 7), (18, 7), (12, 28), (1, 11), (37, 9), (15, 1), (17, 9), (38, 3), (21, 27), (36, 15), (22, 43), (24, 26), (32, 12), (12, 8), (36, 39), (5, 8), (35, 37), (22, 27), (27, 40), (21, 2), (1, 24), (37, 12), (31, 5), (38, 18), (14, 19), (26, 24), (24, 27), (35, 25), (36, 34), (24, 45), (5, 3), (38, 17), (21, 30), (18, 23), (35, 47), (10, 28), (3, 16), (5, 22), (31, 9), (25, 31), (5, 17), (20, 46)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 34), (43, 42), (16, 17), (22, 39), (2, 32), (0, 33), (9, 34), (32, 45), (43, 25), (18, 5), (13, 11), (33, 4), (11, 47), (35, 18), (11, 22), (2, 9), (14, 33), (41, 18), (31, 29), (2, 16), (37, 24), (17, 35), (42, 31), (44, 13), (40, 46), (46, 22), (38, 7), (23, 7), (1, 38), (46, 10), (46, 21), (42, 30), (35, 10), (18, 43), (30, 40), (31, 19), (25, 16), (36, 13), (4, 39), (6, 40), (46, 30), (23, 33), (21, 10), (26, 30), (12, 3), (31, 37), (8, 41), (32, 39), (3, 8), (21, 0), (9, 16), (40, 44), (43, 34), (23, 29), (3, 0), (43, 1), (15, 46), (4, 1), (24, 45), (3, 26), (2, 19), (11, 25), (1, 32), (8, 2), (45, 37), (9, 42), (5, 28), (25, 21), (37, 8), (23, 30), (35, 24), (20, 42), (18, 28), (11, 0), (4, 4), (12, 46), (35, 13), (16, 25), (31, 31), (3, 34), (41, 13), (10, 2), (1, 25), (43, 43), (19, 26), (18, 40), (46, 5), (45, 32), (40, 25), (29, 48), (39, 22), (33, 30), (14, 35), (44, 10), (18, 23), (14, 24), (45, 24), (37, 12), (34, 7), (26, 31), (16, 41), (20, 32), (18, 26), (23, 35), (36, 23), (46, 2), (8, 44), (7, 39), (31, 43), (16, 6), (23, 28), (0, 17), (24, 12), (2, 45), (18, 4), (5, 13), (0, 21), (15, 30), (20, 14), (45, 45), (14, 22), (37, 47), (15, 36), (25, 15), (24, 21), (6, 20), (29, 6), (9, 0), (19, 23), (39, 44), (1, 10), (5, 31), (0, 44), (46, 44), (24, 22), (37, 3), (28, 14), (36, 46), (26, 12), (3, 33), (36, 42), (11, 38), (38, 37), (14, 9), (16, 19), (18, 7), (25, 4), (13, 43), (27, 33), (6, 26), (43, 30), (13, 34), (25, 45), (21, 42), (3, 16), (3, 48), (3, 30), (0, 32), (8, 19), (40, 42), (1, 47), (31, 13), (14, 21), (43, 33), (18, 36), (30, 33), (33, 14), (37, 26), (0, 39), (17, 48), (6, 32), (20, 41), (24, 31), (6, 25), (22, 26), (19, 16), (36, 2), (37, 45), (17, 22), (19, 5), (24, 37), (19, 11), (14, 13), (42, 26), (39, 3), (38, 44), (14, 19), (38, 1), (9, 47), (37, 9), (18, 16), (31, 39), (28, 8), (7, 44), (35, 39), (20, 25), (42, 6), (35, 23), (9, 9), (32, 33), (13, 3), (21, 27), (36, 39), (2, 47), (27, 30), (18, 35), (19, 31), (28, 43), (19, 28), (11, 42), (15, 4), (29, 7), (43, 5), (5, 5), (11, 34), (22, 2), (33, 17), (40, 26), (21, 24), (12, 16), (3, 15), (28, 42), (37, 10), (6, 37), (27, 35), (19, 44), (42, 44), (46, 25), (44, 0), (29, 45), (43, 20), (25, 37), (46, 31), (22, 11), (24, 23), (13, 28), (12, 17), (28, 34), (9, 4), (5, 8), (16, 36), (45, 2), (6, 5), (19, 13), (9, 3), (31, 20), (34, 40), (28, 12), (25, 40), (13, 16), (3, 3), (22, 9), (41, 12), (24, 30), (21, 39), (36, 3), (12, 12), (42, 20), (13, 44), (8, 9), (45, 0), (18, 29), (14, 28), (14, 14), (31, 24), (28, 25), (12, 42), (37, 7), (16, 47), (15, 47), (31, 15), (26, 7), (1, 23), (7, 6), (10, 43), (12, 47), (34, 15), (37, 35), (35, 22), (1, 18), (29, 27), (27, 19), (2, 21), (5, 6), (8, 30), (2, 20), (5, 16), (2, 12), (41, 11), (24, 8), (29, 21), (37, 34), (28, 13), (30, 36), (34, 32), (5, 27), (21, 28), (45, 20), (35, 31), (42, 16), (0, 37), (33, 36), (20, 4), (2, 14), (23, 15), (11, 26), (15, 43), (8, 16), (42, 15), (14, 8), (43, 28), (7, 23), (6, 33), (11, 45), (14, 40), (6, 2), (11, 18), (42, 46), (10, 14), (25, 28), (10, 13), (23, 23), (26, 10), (6, 21), (39, 26), (35, 40), (16, 31), (29, 18), (42, 11), (20, 38), (7, 45), (11, 6), (3, 35), (45, 46), (12, 23), (29, 11), (13, 22), (14, 45), (0, 6), (40, 43), (8, 39), (26, 15), (11, 17), (36, 21), (3, 39), (30, 45), (5, 41), (40, 15), (0, 47), (23, 1), (24, 7), (0, 18), (21, 18), (12, 18), (7, 13), (3, 38), (20, 47), (26, 40), (8, 7), (5, 21), (35, 25), (27, 38), (44, 37), (42, 14), (32, 3), (15, 0), (28, 41), (22, 45), (33, 39), (38, 5), (44, 22), (21, 26), (28, 23), (16, 29), (19, 4), (6, 14), (12, 4), (17, 29), (6, 18), (39, 31), (11, 43), (32, 14), (37, 29), (20, 39), (8, 4), (37, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 47), (34, 42), (45, 14), (30, 5), (41, 11), (41, 43), (20, 2), (25, 19), (18, 40), (22, 30), (30, 8), (44, 30), (33, 22), (3, 11), (3, 41), (36, 28), (20, 32), (16, 24), (15, 25), (33, 43), (3, 45), (23, 23), (16, 13), (9, 47), (38, 28), (0, 40), (37, 18), (24, 28), (12, 7), (40, 21), (42, 45), (26, 22), (14, 0), (17, 2), (30, 43), (3, 36), (3, 33), (28, 17), (27, 32), (35, 26), (0, 45), (47, 1), (21, 42), (30, 39), (8, 4), (3, 21), (21, 5), (32, 1), (16, 7), (5, 0), (26, 7), (37, 20), (15, 13), (12, 10), (22, 26), (26, 10), (15, 2), (24, 24), (12, 29), (31, 34), (29, 46), (22, 16), (1, 26), (41, 1), (7, 43), (15, 10), (37, 26), (34, 17), (15, 20), (16, 3), (36, 46), (28, 10), (10, 4), (22, 32), (37, 23), (0, 5), (20, 27), (29, 31), (31, 37), (9, 31), (46, 36), (20, 21), (22, 13), (23, 17), (26, 27), (14, 45), (23, 14), (6, 20), (18, 25), (13, 47), (36, 30), (20, 36), (15, 34), (45, 42), (20, 1), (39, 46), (22, 6), (31, 15), (2, 18), (23, 24), (33, 36), (38, 46), (42, 42), (31, 30), (2, 25), (3, 1), (32, 18), (45, 32), (39, 12), (18, 42), (14, 42), (47, 43), (21, 3), (37, 42), (40, 33), (31, 5), (40, 6), (0, 41), (2, 9), (35, 21), (43, 15), (41, 36), (27, 20), (43, 13), (2, 11), (4, 46), (18, 5), (41, 18), (44, 0), (19, 39), (33, 46), (1, 41), (1, 45), (26, 47), (17, 7), (2, 29), (11, 15), (9, 24), (2, 45), (32, 36), (7, 7), (31, 32), (0, 31), (22, 17), (13, 0), (46, 16), (10, 42), (17, 8), (38, 47), (36, 18), (33, 33), (45, 38), (10, 29), (0, 11), (5, 28), (1, 21), (0, 34), (10, 20), (7, 47), (21, 26), (14, 30), (25, 31), (33, 25), (3, 2), (43, 22), (43, 23), (34, 21), (40, 3), (5, 16), (47, 42), (0, 20), (5, 21), (34, 32), (1, 44), (3, 9), (22, 12), (41, 13), (32, 4), (47, 17), (42, 6), (8, 25), (31, 47), (20, 3), (2, 26), (10, 33), (9, 46), (41, 25), (11, 37), (37, 17), (9, 9), (9, 30), (3, 34), (4, 29), (20, 10), (32, 11), (40, 16), (0, 29), (25, 24), (22, 11), (42, 46), (12, 36), (0, 25), (22, 27), (28, 27), (30, 22), (11, 27), (43, 8), (45, 20), (10, 12), (31, 1), (31, 4), (40, 36), (14, 14), (46, 7), (37, 27), (25, 8), (15, 21), (24, 34), (34, 13), (1, 25), (37, 34), (17, 39), (24, 37), (2, 43), (38, 45), (36, 9), (36, 27), (10, 26), (18, 19), (26, 32), (26, 18), (43, 9), (17, 23), (3, 47), (4, 31), (30, 46), (32, 46), (43, 16), (30, 16), (12, 16), (22, 41), (19, 18), (30, 32), (33, 9), (39, 7), (8, 35), (36, 24), (1, 13), (1, 33), (39, 25), (15, 42), (29, 3), (31, 22), (16, 8), (5, 25), (22, 9), (2, 47), (20, 12), (26, 25), (33, 12), (32, 24), (29, 23), (29, 34), (47, 5), (3, 7), (0, 27), (39, 41), (26, 34), (4, 40), (38, 32), (35, 29), (23, 12), (22, 24), (10, 24), (13, 7), (25, 46), (15, 6), (13, 34), (16, 28), (6, 24), (22, 4), (46, 33), (39, 35), (21, 7), (42, 17), (25, 22), (30, 26), (30, 21), (8, 33), (29, 14), (42, 10), (30, 33), (8, 17), (20, 46), (6, 31), (29, 17), (25, 13), (38, 44), (44, 11), (12, 15), (4, 45), (29, 8), (33, 44), (32, 30), (6, 36), (38, 18), (44, 38), (15, 47), (5, 33), (8, 26), (15, 37), (5, 43), (39, 30), (3, 15), (28, 4), (10, 43), (36, 26), (20, 31), (3, 17), (46, 39), (35, 22), (13, 37), (28, 44), (22, 18), (1, 37), (21, 16), (0, 16), (47, 10), (28, 15), (28, 2), (44, 19), (31, 19), (10, 17), (9, 28), (4, 2), (46, 5), (12, 34), (21, 12), (20, 30), (47, 15), (41, 12), (2, 5), (22, 43), (44, 18), (31, 11), (4, 11), (0, 7), (37, 1), (26, 1), (26, 2), (12, 28), (19, 45), (26, 23), (44, 26), (45, 1), (17, 44), (40, 30), (39, 8), (28, 9), (38, 27), (23, 39), (33, 34), (23, 43), (33, 20), (22, 33), (46, 11), (21, 15), (38, 16), (2, 14), (24, 8), (46, 31), (13, 9), (2, 7), (35, 47), (33, 2), (27, 10), (2, 44), (34, 12), (40, 0), (45, 22), (45, 26), (40, 29), (0, 38), (35, 15), (8, 9), (4, 42), (20, 23), (24, 15), (10, 15), (13, 46), (31, 38), (3, 42), (9, 8), (4, 12), (8, 15), (10, 23), (16, 45), (45, 13), (1, 17), (45, 6), (5, 7), (16, 37), (21, 37), (45, 33), (34, 39), (28, 24), (34, 37), (4, 16), (32, 25), (5, 20), (27, 28), (20, 28), (37, 21), (22, 31), (46, 1), (33, 7), (40, 12), (15, 8), (22, 35), (37, 36), (36, 35), (8, 21), (28, 14), (26, 26), (33, 26), (24, 29), (45, 47), (39, 26), (17, 12), (15, 31), (42, 47), (30, 38), (14, 2), (17, 32), (42, 43), (13, 17), (19, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 8), (13, 0), (34, 39), (21, 14), (20, 19), (39, 2), (39, 1), (33, 7), (43, 14), (3, 17), (23, 19), (4, 26), (9, 1), (12, 34), (8, 21), (4, 7), (15, 25), (41, 37), (41, 14), (13, 39), (9, 37), (15, 30), (0, 24), (0, 36), (19, 15), (21, 10), (11, 20), (12, 2), (42, 12), (6, 12), (17, 9), (17, 15), (38, 22), (14, 19), (29, 37), (1, 15), (0, 31), (4, 32), (18, 10), (21, 27), (12, 8), (32, 33), (29, 27), (14, 18), (22, 30), (12, 31), (23, 3), (32, 1), (38, 36), (7, 3), (36, 31), (5, 12), (33, 15), (20, 2), (34, 20), (34, 29), (19, 38), (22, 20), (25, 24), (33, 31), (0, 18), (41, 12), (24, 4), (36, 9), (12, 3), (0, 34), (25, 6), (33, 18), (43, 21), (25, 2), (14, 8), (2, 27), (33, 16), (21, 18), (26, 36), (38, 24), (9, 24), (10, 6), (20, 23), (23, 33), (34, 7), (24, 9), (15, 26), (30, 19), (37, 26), (39, 19), (26, 3), (17, 27), (8, 22), (33, 13), (38, 26), (38, 6), (1, 19), (4, 31), (35, 35), (29, 22), (14, 0), (43, 35), (32, 26), (25, 15), (7, 8), (31, 1), (21, 36), (6, 35), (23, 27), (2, 11), (13, 36), (33, 27), (27, 24), (0, 32), (2, 0), (0, 27), (2, 13), (19, 11), (34, 13), (30, 27), (20, 6), (0, 35), (8, 27), (3, 9), (0, 39), (16, 30), (40, 21), (43, 36), (30, 34), (37, 12), (6, 16), (11, 3), (1, 18), (4, 9), (18, 26), (25, 5), (33, 12), (39, 23), (22, 36), (20, 24), (13, 24), (8, 9), (22, 27), (41, 20), (26, 7), (1, 25), (12, 23), (37, 5), (43, 8), (2, 36), (32, 27), (21, 26), (27, 19), (25, 7), (10, 29), (20, 36), (22, 32), (11, 39), (42, 7), (28, 22), (20, 30), (7, 36), (35, 9), (2, 30), (4, 22), (14, 39), (24, 15), (2, 26), (34, 28), (22, 18), (1, 36), (34, 1), (29, 13), (10, 31), (24, 38), (31, 28), (33, 6), (42, 24), (18, 30), (10, 18), (1, 35), (28, 9), (4, 29), (42, 4), (13, 9), (3, 19), (41, 21), (30, 18), (30, 26), (23, 10), (13, 20), (41, 33), (11, 34), (15, 14), (23, 23), (18, 6), (5, 6), (5, 18), (22, 22), (14, 34), (0, 4), (43, 6), (31, 25), (41, 25), (23, 1), (23, 5), (43, 3), (11, 9), (35, 18), (42, 34), (28, 17), (18, 12), (41, 4), (2, 32), (40, 9), (18, 15), (14, 29), (1, 21), (38, 31), (10, 9), (24, 23), (40, 24), (43, 27), (10, 35), (41, 31), (5, 22), (13, 34), (12, 12), (19, 13), (43, 12), (43, 10), (28, 38), (6, 11), (32, 19), (35, 32), (12, 4), (11, 23), (22, 21), (37, 21), (25, 0), (37, 9), (31, 17), (6, 22), (3, 10), (22, 33), (8, 7), (43, 4), (28, 5), (2, 31), (35, 19), (4, 39), (3, 23), (18, 18), (13, 12), (31, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 5), (12, 18), (26, 18), (27, 40), (32, 34), (23, 40), (14, 46), (20, 14), (10, 43), (10, 7), (38, 14), (29, 3), (45, 37), (6, 11), (22, 26), (22, 25), (38, 11), (35, 18), (34, 29), (14, 4), (22, 42), (15, 26), (20, 30), (19, 27), (18, 40), (20, 18), (32, 42), (33, 2), (36, 13), (27, 7), (0, 26), (14, 3), (22, 13), (25, 44), (22, 12), (11, 9), (35, 6), (18, 44), (31, 2), (29, 17), (35, 9), (23, 25), (30, 15), (41, 33), (21, 35), (45, 1), (23, 11), (36, 21), (25, 7), (15, 44), (20, 19), (29, 10), (30, 31), (8, 45), (41, 11), (3, 8), (33, 34), (8, 6), (11, 6), (20, 46), (22, 45), (16, 14), (41, 15), (29, 15), (8, 14), (31, 20), (7, 4), (39, 30), (38, 30), (25, 9), (19, 46), (30, 47), (36, 39), (11, 5), (26, 45), (33, 42), (29, 0), (29, 45), (32, 39), (40, 2), (39, 38), (5, 3), (28, 20), (10, 1), (6, 26), (11, 25), (28, 39), (44, 38), (15, 46), (31, 25), (21, 41), (40, 37), (18, 22), (44, 29), (23, 15), (43, 22), (31, 33), (1, 25), (43, 19), (8, 15), (29, 30), (39, 37), (34, 33), (40, 15), (35, 0), (1, 43), (2, 11), (19, 1), (3, 35), (20, 44), (8, 3), (5, 34), (32, 0), (34, 21), (6, 45), (33, 3), (25, 33), (6, 46), (32, 29), (6, 13), (12, 21), (23, 42), (22, 38), (1, 26), (29, 7), (34, 36), (10, 21), (3, 14), (38, 8), (11, 39), (38, 2), (9, 46), (11, 36), (18, 20), (17, 5), (41, 20), (21, 21), (13, 43), (32, 6), (15, 11), (13, 1), (30, 4), (21, 8), (38, 6), (9, 47), (44, 36), (18, 45), (7, 47), (38, 3), (34, 14), (29, 37), (6, 17), (18, 4), (3, 18), (36, 1), (41, 22), (28, 31), (9, 21), (41, 42), (0, 47), (1, 28), (25, 17), (28, 35), (12, 28), (40, 35), (43, 4), (6, 47), (7, 2), (8, 7), (32, 14), (33, 1), (43, 41), (4, 17), (44, 15), (0, 21), (35, 27), (17, 24), (29, 44), (45, 39), (3, 31), (24, 0), (2, 32), (17, 21), (8, 43), (1, 18), (9, 37), (12, 27), (31, 23), (17, 15), (20, 8), (3, 0), (8, 12), (0, 31), (2, 31), (34, 15), (5, 2), (36, 17), (19, 6), (4, 34), (41, 34), (31, 30), (25, 36), (26, 23), (26, 19), (2, 47), (1, 7), (13, 16), (34, 8), (43, 15), (25, 42), (32, 15), (37, 17), (26, 43), (3, 29), (14, 11), (14, 25), (32, 20), (11, 16), (18, 32), (16, 21), (10, 24), (28, 5), (41, 28), (46, 5), (9, 4), (25, 11), (45, 32), (11, 33), (3, 16), (40, 4), (25, 0), (25, 28), (45, 42), (39, 12), (18, 33), (18, 6), (11, 21), (8, 32), (25, 26), (20, 38), (31, 29), (16, 1), (34, 39), (11, 43), (47, 25), (29, 22), (25, 41), (38, 10), (10, 44), (42, 19), (20, 1), (24, 11), (34, 19), (41, 8), (32, 41), (30, 39), (9, 16), (17, 34), (17, 38), (15, 9), (28, 45), (26, 11), (42, 9), (18, 17), (23, 46), (46, 21), (45, 15), (22, 0), (40, 5), (16, 9), (24, 23), (43, 25), (43, 12), (23, 3), (2, 33), (26, 15), (40, 31), (23, 14), (23, 7), (7, 0), (3, 39), (27, 45), (16, 4), (43, 28), (18, 31), (45, 25), (8, 11), (12, 40), (30, 43), (45, 44), (18, 36), (14, 37), (29, 38), (42, 5), (10, 34), (11, 7), (18, 25), (14, 29), (43, 6), (12, 43), (26, 5), (6, 4), (34, 27), (16, 0), (27, 43), (10, 37), (7, 22), (47, 40), (35, 5), (28, 9), (45, 16), (7, 18), (27, 10), (7, 34), (25, 23), (30, 46), (25, 47), (0, 22), (45, 24), (7, 32), (32, 22), (13, 11), (25, 20), (24, 9), (47, 44), (19, 33), (21, 12), (0, 33), (17, 36), (29, 12), (5, 45), (26, 32), (28, 43), (45, 36), (18, 34), (35, 12), (42, 36), (31, 8), (41, 43), (20, 15), (36, 34), (39, 11), (30, 7), (36, 46), (4, 41), (17, 2), (37, 19), (33, 39), (47, 13), (24, 13), (39, 23), (8, 0), (30, 44), (20, 12), (37, 15), (31, 9), (41, 40), (14, 42), (4, 44), (28, 11), (4, 16), (35, 11), (4, 42), (15, 14), (4, 9), (46, 25), (32, 2), (39, 6), (33, 12), (32, 36), (47, 27), (14, 34), (8, 37), (21, 34), (24, 7), (44, 23), (32, 7), (26, 33), (37, 14), (28, 47), (45, 30), (17, 8), (26, 47), (12, 44), (24, 41), (20, 26), (45, 17), (38, 38), (40, 7), (10, 40), (38, 20), (43, 1), (17, 4), (5, 7), (6, 35), (13, 15), (30, 45), (6, 5), (42, 15), (46, 42), (40, 6), (2, 40), (38, 24), (18, 0), (39, 46), (19, 34), (32, 17), (1, 8), (45, 5), (45, 43), (44, 6), (16, 30), (8, 20), (31, 44), (2, 45), (4, 36), (38, 12), (0, 9), (1, 10), (20, 42), (8, 36), (10, 29), (30, 8), (40, 38), (10, 36), (1, 16), (39, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 26), (20, 16), (37, 29), (37, 4), (36, 24), (3, 42), (13, 25), (24, 10), (19, 23), (16, 33), (3, 38), (30, 23), (39, 6), (3, 0), (20, 8), (27, 21), (19, 5), (19, 6), (13, 9), (31, 41), (32, 8), (10, 29), (8, 8), (31, 31), (19, 27), (21, 15), (33, 34), (3, 33), (9, 10), (1, 15), (4, 32), (35, 25), (12, 37), (19, 34), (19, 19), (20, 40), (13, 32), (5, 9), (36, 8), (36, 29), (22, 20), (3, 20), (35, 32), (1, 36), (2, 41), (1, 0), (35, 36), (8, 9), (35, 21), (31, 18), (35, 34), (1, 24), (16, 12), (33, 12), (37, 36), (14, 4), (24, 34), (39, 35), (2, 37), (32, 34), (18, 4), (15, 20), (22, 0), (24, 2), (11, 39), (34, 40), (16, 15), (19, 25), (30, 13), (14, 0), (9, 37), (12, 12), (13, 36), (20, 25), (20, 31), (38, 37), (19, 13), (35, 42), (40, 6), (8, 18), (26, 28), (4, 9), (41, 6), (22, 38), (38, 40), (34, 23), (13, 11), (28, 14), (29, 32), (33, 41), (33, 13), (25, 34), (36, 4), (38, 41), (24, 42), (4, 31), (36, 16), (13, 31), (14, 18), (3, 16), (32, 28), (18, 16), (31, 26), (11, 32), (37, 26), (17, 12), (1, 42), (30, 20), (19, 28), (28, 34), (7, 7), (17, 2), (40, 41), (2, 7), (24, 38), (2, 42), (9, 4), (15, 6), (9, 12), (37, 21), (18, 33), (4, 25), (15, 9), (39, 17), (1, 33), (27, 4), (34, 19), (8, 23), (15, 32), (23, 31), (37, 32), (16, 37), (5, 23), (33, 0), (4, 36), (17, 32), (16, 16), (9, 42), (24, 17), (2, 12), (41, 32), (17, 4), (36, 32), (30, 16), (11, 11), (23, 24), (34, 18), (4, 22), (16, 7), (4, 5), (9, 41), (21, 17), (29, 30), (23, 0), (39, 10), (23, 39), (15, 41), (35, 9), (35, 6), (40, 4), (23, 22), (7, 32), (22, 40), (37, 10), (41, 2), (24, 32), (35, 38), (33, 18), (23, 11), (27, 32), (28, 15), (32, 15), (2, 17), (39, 4), (21, 0), (24, 13), (35, 24), (29, 25), (40, 7), (18, 10), (3, 22), (41, 11), (39, 8), (16, 10), (29, 19), (38, 5), (14, 2), (27, 9), (0, 29), (34, 1), (6, 26), (34, 28), (24, 24), (7, 26), (28, 26), (40, 2), (21, 3), (25, 13), (31, 21), (12, 24), (39, 27), (4, 1), (19, 18), (3, 24), (21, 11), (40, 25), (5, 35), (5, 40), (10, 8), (20, 7), (33, 35), (25, 6), (2, 11), (13, 5), (12, 28), (9, 28), (10, 2), (25, 40), (38, 7), (10, 5), (5, 3), (6, 3), (14, 33), (9, 9), (24, 1), (15, 0), (19, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 29), (29, 25), (0, 40), (19, 10), (19, 27), (18, 48), (35, 34), (19, 7), (5, 0), (25, 44), (7, 45), (32, 39), (31, 44), (21, 47), (23, 21), (39, 39), (21, 45), (18, 11), (27, 11), (10, 38), (27, 15), (29, 9), (20, 22), (21, 1), (14, 19), (12, 41), (37, 6), (17, 28), (9, 4), (38, 2), (14, 13), (6, 12), (2, 12), (31, 19), (22, 26), (16, 24), (28, 26), (16, 20), (34, 45), (32, 21), (17, 0), (13, 47), (13, 25), (29, 48), (22, 30), (16, 48), (11, 32), (37, 33), (10, 10), (39, 6), (32, 30), (33, 10), (40, 38), (25, 46), (28, 46), (4, 39), (27, 41), (13, 19), (34, 16), (21, 27), (13, 37), (7, 25), (3, 42), (3, 8), (22, 21), (39, 8), (17, 44), (30, 4), (17, 34), (0, 32), (15, 28), (13, 23), (32, 2), (31, 34), (23, 5), (7, 40), (20, 15), (2, 8), (31, 28), (37, 8), (36, 17), (14, 9), (0, 2), (17, 20), (3, 1), (5, 40), (3, 23), (11, 47), (16, 31), (19, 23), (32, 29), (18, 46), (27, 47), (9, 47), (3, 29), (16, 0), (26, 28), (5, 3), (12, 42), (1, 14), (12, 1), (20, 41), (13, 30), (26, 3), (2, 5), (10, 29), (18, 35), (26, 12), (6, 39), (7, 0), (30, 29), (0, 5), (7, 17), (36, 21), (32, 20), (32, 35), (38, 28), (39, 29), (22, 48), (29, 29), (15, 33), (30, 3), (38, 0), (28, 38), (5, 18), (19, 45), (9, 20), (19, 34), (29, 11), (16, 28), (23, 44), (36, 24), (0, 20), (9, 40), (2, 31), (21, 36), (30, 7), (30, 10), (7, 30), (22, 7), (7, 33), (35, 5), (26, 25), (24, 46), (34, 12), (30, 8), (25, 27), (19, 12), (38, 32), (21, 21), (17, 48), (10, 16), (1, 17), (40, 25), (37, 27), (24, 5), (26, 31), (3, 10), (22, 38), (8, 38), (18, 5), (38, 35), (1, 19), (11, 15), (24, 23), (29, 40), (14, 45), (33, 23), (23, 17), (24, 37), (21, 48), (8, 11), (34, 47), (1, 32), (18, 24), (10, 15), (3, 4), (28, 35), (18, 36), (32, 16), (0, 31), (36, 13), (18, 3), (17, 16), (32, 46), (35, 42), (35, 26), (19, 35), (25, 24), (14, 47), (18, 28), (22, 37), (8, 3), (32, 38), (17, 13), (6, 3), (10, 31), (12, 6), (6, 11), (8, 29), (27, 45), (19, 1), (5, 41), (9, 18), (21, 5), (8, 17), (11, 34), (21, 44), (25, 36), (20, 2), (30, 0), (5, 5), (33, 43), (24, 0), (15, 35), (31, 11), (22, 15), (29, 14), (39, 42), (3, 26), (38, 3), (0, 37), (17, 2), (1, 28), (4, 35), (2, 18), (2, 27), (15, 19), (30, 39), (21, 9), (8, 24), (21, 23), (19, 46), (34, 13), (24, 22), (16, 44), (8, 14), (28, 42), (21, 14), (20, 4), (9, 46), (35, 3), (4, 22), (6, 6), (26, 11), (28, 39), (7, 10), (25, 43), (11, 0), (23, 45), (20, 45), (36, 5), (18, 21), (1, 11), (13, 36), (11, 41), (3, 32), (23, 12), (9, 32), (0, 19), (34, 6), (0, 15), (16, 34), (6, 8), (10, 21), (5, 43), (35, 1), (26, 29), (8, 45), (39, 15), (7, 42), (23, 38), (0, 34), (14, 14), (15, 0), (28, 34), (5, 39), (5, 33), (5, 15), (22, 36), (31, 32), (18, 6), (2, 20), (6, 31), (3, 9), (23, 16), (15, 46), (23, 6), (29, 21), (29, 15), (18, 42), (7, 36), (34, 28), (1, 18), (36, 28), (26, 47), (32, 6), (26, 22), (13, 32), (10, 20), (5, 47), (31, 20), (2, 26), (35, 8), (0, 42), (16, 23), (20, 5), (12, 44), (2, 6), (22, 16), (25, 10), (10, 17), (27, 25), (29, 1), (25, 41), (38, 24), (36, 1), (27, 20), (0, 39), (16, 4), (36, 9), (5, 16), (34, 30), (31, 31), (13, 34), (23, 19), (36, 27), (5, 29), (30, 28), (34, 4), (16, 13), (29, 13), (37, 14), (17, 10), (10, 12), (8, 43), (22, 25), (4, 19), (11, 27), (26, 9), (6, 9), (14, 11), (15, 36), (1, 46), (23, 30), (30, 31), (29, 0), (13, 5), (37, 11), (5, 20), (38, 40), (33, 32), (27, 21), (9, 39), (21, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 39), (14, 26), (33, 21), (42, 16), (24, 2), (48, 8), (13, 33), (39, 26), (36, 18), (8, 17), (2, 25), (33, 16), (36, 13), (23, 28), (42, 44), (13, 6), (19, 40), (40, 43), (2, 23), (8, 35), (41, 13), (21, 5), (44, 18), (19, 23), (41, 22), (15, 36), (47, 6), (37, 5), (25, 32), (34, 0), (32, 25), (1, 1), (46, 9), (5, 29), (31, 4), (2, 12), (8, 19), (13, 26), (8, 37), (32, 14), (47, 0), (29, 27), (27, 5), (29, 26), (24, 27), (2, 11), (36, 11), (29, 42), (45, 0), (29, 23), (9, 43), (29, 41), (39, 25), (4, 24), (33, 24), (35, 41), (3, 32), (19, 1), (41, 31), (4, 11), (25, 12), (33, 36), (22, 32), (21, 39), (39, 28), (40, 41), (16, 15), (20, 13), (13, 21), (23, 40), (41, 14), (27, 24), (11, 9), (26, 38), (26, 28), (18, 14), (20, 39), (14, 9), (24, 37), (10, 1), (23, 3), (23, 27), (17, 32), (28, 15), (1, 16), (20, 24), (47, 19), (3, 40), (15, 5), (42, 19), (24, 3), (16, 27), (30, 38), (38, 33), (23, 2), (20, 25), (13, 42), (18, 30), (14, 44), (13, 39), (34, 25), (28, 7), (43, 5), (37, 17), (16, 37), (40, 8), (14, 32), (19, 10), (9, 9), (32, 4), (16, 23), (8, 44), (22, 27), (17, 0), (16, 34), (23, 1), (30, 44), (11, 22), (17, 36), (7, 38), (9, 24), (43, 20), (0, 17), (41, 16), (38, 11), (45, 13), (21, 9), (38, 38), (9, 36), (23, 44), (39, 22), (29, 3), (1, 12), (6, 30), (48, 33), (11, 6), (38, 18), (14, 7), (16, 31), (16, 28), (23, 0), (3, 11), (13, 19), (46, 11), (13, 9), (45, 37), (40, 10), (42, 17), (32, 3), (9, 30), (10, 18), (45, 10), (28, 6), (10, 6), (0, 12), (44, 24), (14, 27), (29, 24), (47, 16), (34, 10), (36, 1), (12, 1), (19, 41), (11, 11), (2, 16), (15, 41), (1, 13), (5, 7), (4, 26), (5, 31), (34, 20), (10, 12), (4, 21), (36, 2), (27, 18), (45, 6), (24, 11), (35, 6), (30, 22), (13, 18), (4, 6), (17, 16), (35, 9), (20, 28), (44, 43), (41, 42), (44, 8), (21, 22), (18, 40), (3, 33), (28, 5), (44, 13), (45, 38), (19, 43), (40, 33), (44, 10), (30, 29), (27, 17), (3, 37), (4, 30), (46, 32), (14, 20), (39, 6), (6, 20), (37, 24), (10, 9), (21, 15), (32, 32), (25, 8), (1, 5), (33, 37), (3, 20), (30, 28), (25, 11), (30, 30), (43, 30), (19, 12), (15, 7), (13, 15), (43, 27), (36, 0), (44, 40), (27, 13), (16, 11), (11, 16), (42, 38), (4, 42), (38, 0), (9, 40), (36, 28), (12, 34), (30, 34), (7, 3), (35, 4), (10, 30), (27, 7), (29, 9), (4, 35), (34, 36), (37, 36), (47, 7), (41, 29), (2, 9), (39, 4), (6, 15), (45, 8), (2, 34), (41, 0), (0, 7), (10, 19), (15, 43), (29, 40), (46, 17), (3, 29), (9, 32), (36, 37), (34, 18), (20, 9), (33, 2), (27, 40), (33, 30), (28, 32), (37, 4), (3, 30), (2, 14), (30, 39), (15, 0), (36, 22), (47, 44), (47, 9), (31, 27), (33, 0), (41, 20), (1, 44), (20, 38), (44, 39), (45, 35), (17, 44), (10, 26), (13, 1), (1, 29), (9, 31), (6, 9), (36, 42), (36, 25), (14, 23), (7, 17), (32, 37), (42, 3), (29, 11), (12, 40), (38, 15), (43, 43), (7, 4), (34, 40), (42, 31), (41, 17), (8, 21), (42, 20), (36, 10), (19, 25), (47, 20), (2, 8), (3, 41), (15, 4), (40, 22), (14, 41), (9, 17), (32, 28), (25, 1), (43, 11), (21, 26), (13, 0), (12, 8), (12, 26), (48, 29), (18, 22), (9, 10), (24, 18), (4, 36), (17, 17), (10, 29), (35, 20), (5, 10), (43, 7), (37, 3), (34, 7), (28, 43), (19, 8), (24, 39), (28, 28), (27, 15), (44, 7), (9, 29), (15, 39), (38, 40), (12, 42), (46, 27), (48, 1), (33, 1), (11, 31), (41, 37), (46, 29), (47, 27), (24, 15), (45, 24), (17, 18), (47, 3), (36, 20), (42, 10), (33, 14), (9, 33), (24, 24), (22, 3), (7, 21), (6, 44), (21, 13), (10, 31), (31, 3), (42, 37), (43, 2), (29, 21), (34, 29), (38, 4), (45, 30), (13, 7), (0, 37), (9, 35), (18, 20), (14, 10), (30, 21), (46, 6), (5, 23), (0, 1), (33, 10), (23, 35), (0, 44), (8, 0), (44, 14), (22, 8), (35, 14), (37, 19), (4, 7), (22, 25), (31, 0), (44, 11), (45, 1), (43, 26), (23, 19), (34, 37), (2, 15), (7, 43), (3, 8), (27, 22), (44, 6), (43, 24), (21, 24), (18, 21), (41, 18), (45, 39), (23, 4), (20, 42), (19, 4), (20, 36), (4, 37), (20, 3), (28, 19), (30, 4), (18, 32), (35, 15), (6, 13), (48, 16), (38, 19), (29, 36), (35, 34), (4, 28), (32, 9), (36, 16), (3, 0), (6, 34), (29, 1), (38, 29), (45, 12), (1, 27), (37, 20), (33, 44), (23, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 22), (26, 15), (39, 42), (37, 13), (40, 27), (12, 8), (36, 31), (6, 3), (9, 14), (13, 29), (43, 43), (23, 38), (19, 32), (25, 40), (33, 25), (8, 5), (28, 6), (40, 31), (31, 12), (36, 35), (33, 43), (22, 14), (22, 22), (7, 29), (0, 23), (34, 26), (11, 28), (19, 41), (37, 31), (24, 21), (43, 17), (10, 30), (12, 39), (16, 2), (11, 12), (33, 5), (17, 24), (33, 42), (22, 20), (10, 36), (20, 10), (10, 2), (44, 18), (37, 24), (16, 20), (19, 5), (19, 17), (21, 19), (38, 7), (25, 21), (12, 22), (22, 24), (9, 0), (43, 20), (44, 37), (18, 36), (32, 4), (3, 13), (2, 39), (22, 40), (32, 15), (17, 28), (24, 19), (5, 6), (6, 40), (39, 29), (37, 11), (30, 37), (9, 12), (10, 39), (27, 31), (25, 20), (44, 30), (3, 31), (39, 24), (13, 1), (8, 13), (8, 3), (12, 3), (11, 22), (1, 29), (36, 1), (40, 33), (1, 17), (3, 12), (45, 12), (41, 26), (19, 43), (5, 14), (45, 22), (2, 21), (44, 27), (13, 40), (2, 27), (28, 30), (40, 2), (40, 20), (8, 34), (1, 20), (11, 34), (4, 14), (43, 36), (6, 23), (34, 38), (9, 35), (10, 14), (42, 29), (3, 34), (38, 30), (22, 38), (4, 37), (1, 42), (2, 28), (39, 16), (39, 5), (7, 3), (40, 10), (44, 26), (38, 22), (22, 8), (37, 21), (16, 7), (1, 22), (9, 32), (11, 5), (23, 20), (42, 12), (5, 16), (38, 3), (25, 11), (2, 12), (15, 38), (29, 5), (3, 5), (3, 39), (13, 27), (30, 43), (3, 10), (19, 13), (27, 40), (14, 28), (44, 13), (36, 4), (7, 12), (5, 38), (31, 34), (40, 38), (22, 21), (11, 21), (6, 26), (26, 0), (35, 5), (23, 30), (1, 15), (30, 15), (43, 30), (40, 0), (39, 9), (23, 5), (12, 25), (8, 42), (40, 23), (20, 39), (21, 27), (2, 37), (12, 13), (14, 10), (29, 37), (35, 34), (38, 43), (18, 20), (38, 21), (45, 4), (15, 8), (45, 25), (15, 27), (40, 14), (30, 40), (17, 21), (39, 23), (16, 16), (10, 9), (32, 12), (22, 23), (39, 30), (35, 17), (8, 21), (7, 8), (15, 24), (39, 6), (28, 39), (5, 41), (27, 41), (34, 41), (6, 43), (16, 26), (30, 3), (4, 36), (13, 0), (1, 25), (37, 9), (31, 3), (30, 4), (30, 29), (30, 6), (33, 40), (45, 19), (33, 29), (17, 5), (29, 26), (8, 11), (34, 39), (23, 32), (28, 5), (8, 30), (31, 20), (21, 28), (38, 40), (32, 40), (9, 43), (25, 10), (36, 12), (23, 7), (42, 16), (40, 35), (43, 23), (24, 29), (7, 21), (17, 16), (12, 30), (27, 27), (9, 22), (17, 41), (27, 8), (37, 28), (36, 15), (43, 3), (25, 24), (24, 25), (24, 34), (8, 24), (37, 23), (35, 26), (34, 16), (15, 14), (3, 23), (31, 18), (43, 40), (7, 39), (29, 31), (3, 7), (33, 31), (19, 16), (32, 22), (45, 11), (2, 18), (27, 42), (19, 12), (24, 37), (3, 27), (24, 12), (21, 39), (32, 31), (5, 35), (22, 3), (17, 0), (23, 21), (7, 6), (4, 35), (12, 18), (45, 8), (12, 35), (31, 9), (41, 31), (43, 12), (33, 34), (21, 9), (5, 36), (4, 10), (24, 36), (23, 33), (38, 33), (27, 21), (24, 6), (15, 7), (29, 21), (18, 35), (14, 39), (0, 24), (23, 40), (44, 19), (13, 19), (12, 1), (10, 37), (41, 11), (14, 18), (1, 35), (33, 27), (41, 43), (32, 42), (5, 7), (45, 2), (40, 16), (5, 17), (22, 2), (14, 30), (0, 13), (21, 6), (28, 19), (10, 33), (1, 1), (24, 31), (19, 8), (35, 28), (34, 25), (37, 42), (13, 13), (6, 9), (6, 32), (9, 23), (35, 31), (24, 22), (37, 37), (1, 14), (14, 20), (2, 1), (5, 3), (31, 8), (27, 9), (42, 28), (4, 38), (4, 32), (22, 37), (24, 27), (36, 28), (10, 17), (27, 23), (26, 8), (28, 22), (30, 7), (29, 4), (10, 23), (36, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 21), (11, 15), (32, 9), (9, 33), (11, 30), (13, 15), (24, 17), (20, 22), (21, 4), (40, 1), (39, 33), (8, 39), (38, 36), (35, 19), (22, 6), (30, 17), (38, 11), (21, 1), (10, 40), (4, 4), (11, 16), (40, 11), (29, 0), (11, 17), (16, 11), (22, 35), (10, 39), (29, 16), (0, 39), (33, 25), (25, 11), (11, 21), (17, 35), (9, 19), (29, 3), (28, 28), (13, 11), (24, 14), (35, 40), (20, 34), (29, 19), (10, 28), (40, 33), (13, 10), (22, 30), (13, 24), (5, 35), (33, 3), (26, 8), (28, 23), (33, 1), (0, 12), (17, 37), (0, 31), (8, 20), (6, 17), (0, 25), (23, 2), (36, 32), (4, 5), (5, 23), (25, 32), (32, 39), (19, 23), (10, 8), (23, 31), (26, 26), (11, 13), (1, 33), (2, 20), (18, 32), (37, 33), (36, 11), (15, 34), (37, 36), (21, 0), (3, 2), (32, 36), (5, 29), (28, 34), (35, 25), (23, 39), (38, 12), (8, 37), (25, 37), (37, 24), (17, 40), (24, 8), (37, 6), (24, 15), (5, 28), (25, 23), (39, 17), (39, 24), (38, 2), (14, 39), (16, 25), (28, 11), (19, 17), (15, 14), (30, 14), (27, 12), (32, 3), (12, 0), (26, 19), (11, 20), (22, 14), (39, 18), (21, 14), (17, 22), (24, 37), (24, 24), (20, 33), (12, 23), (37, 4), (7, 1), (36, 15), (10, 35), (36, 12), (31, 19), (8, 12), (15, 20), (21, 35), (28, 31), (35, 36), (25, 13), (32, 7), (37, 9), (15, 36), (3, 13), (40, 7), (2, 15), (3, 8), (36, 6), (19, 40), (21, 19), (20, 36), (11, 40), (28, 10), (31, 29), (1, 18), (23, 24), (12, 25), (32, 12), (18, 22), (19, 15), (39, 11), (30, 35), (36, 7), (8, 2), (2, 21), (32, 22), (16, 13), (40, 39), (36, 21), (30, 6), (22, 7), (39, 10), (14, 29), (1, 8), (18, 26), (7, 32), (33, 26), (9, 11), (22, 12), (35, 26), (7, 13), (0, 19), (4, 11), (3, 7), (33, 37), (8, 15), (16, 26), (31, 5), (1, 25), (39, 0), (7, 14), (24, 0), (33, 29), (11, 6), (24, 29), (1, 30), (35, 34), (26, 6), (22, 26), (4, 41), (31, 8), (29, 7), (18, 21), (7, 16), (2, 16), (21, 34), (29, 30), (24, 40), (6, 38), (32, 13), (7, 35), (27, 23), (26, 34), (24, 32), (20, 5), (18, 3), (30, 13), (0, 34), (1, 27), (10, 7), (8, 22), (9, 22), (34, 24), (29, 4), (0, 32), (32, 28), (17, 2), (0, 37), (3, 34), (28, 7), (21, 29), (25, 33), (7, 10), (13, 22), (22, 25), (33, 2), (31, 22), (10, 25), (30, 19), (18, 25), (12, 33), (35, 4), (14, 15), (17, 11), (9, 3), (34, 38), (4, 21), (31, 37), (32, 4), (37, 35), (35, 24), (26, 15), (4, 20), (4, 27), (1, 1), (15, 5), (21, 24), (40, 37), (5, 33), (33, 14), (18, 28), (18, 30), (4, 3), (23, 28), (20, 27), (20, 9), (13, 40), (25, 30), (28, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 9), (41, 6), (3, 5), (20, 36), (23, 22), (32, 6), (5, 12), (44, 12), (17, 23), (26, 15), (31, 26), (23, 19), (40, 38), (36, 31), (12, 12), (43, 41), (41, 20), (33, 37), (9, 25), (46, 28), (45, 14), (6, 5), (31, 23), (22, 26), (24, 11), (32, 34), (19, 8), (40, 44), (2, 27), (5, 27), (30, 1), (21, 5), (28, 1), (39, 8), (17, 0), (20, 1), (34, 32), (37, 9), (32, 1), (27, 29), (27, 40), (28, 11), (30, 10), (36, 5), (18, 22), (10, 34), (47, 22), (19, 14), (32, 27), (34, 45), (11, 4), (4, 0), (15, 4), (4, 35), (20, 30), (8, 27), (32, 28), (46, 3), (40, 24), (42, 11), (4, 28), (1, 11), (40, 19), (26, 34), (9, 38), (34, 9), (24, 23), (17, 15), (40, 28), (18, 38), (40, 17), (43, 43), (33, 32), (9, 40), (13, 9), (11, 12), (47, 31), (15, 25), (3, 16), (24, 7), (27, 20), (3, 44), (40, 26), (30, 19), (45, 6), (17, 16), (32, 32), (47, 14), (29, 32), (46, 38), (1, 31), (45, 0), (37, 40), (21, 36), (45, 8), (6, 40), (11, 16), (35, 7), (13, 23), (14, 35), (9, 28), (25, 10), (7, 25), (46, 39), (40, 5), (46, 23), (41, 29), (46, 24), (40, 1), (0, 35), (26, 36), (14, 18), (14, 37), (17, 25), (14, 7), (11, 6), (43, 13), (21, 35), (17, 14), (45, 23), (43, 4), (40, 29), (8, 43), (15, 36), (11, 27), (18, 18), (0, 22), (7, 17), (23, 42), (26, 9), (44, 8), (23, 3), (17, 3), (10, 11), (13, 35), (37, 39), (34, 23), (37, 16), (6, 43), (40, 22), (18, 40), (14, 36), (4, 42), (23, 25), (46, 14), (31, 35), (43, 10), (6, 31), (23, 39), (26, 22), (13, 7), (43, 12), (40, 39), (0, 9), (41, 43), (43, 42), (46, 45), (0, 38), (24, 14), (31, 27), (39, 34), (30, 7), (41, 21), (3, 40), (2, 23), (31, 13), (45, 33), (26, 26), (1, 37), (30, 36), (19, 30), (12, 23), (30, 39), (10, 27), (10, 21), (32, 31), (36, 26), (32, 42), (44, 5), (9, 7), (21, 20), (29, 43), (16, 17), (13, 18), (8, 24), (0, 20), (14, 27), (14, 13), (12, 35), (28, 36), (37, 21), (32, 40), (23, 26), (36, 44), (3, 20), (19, 22), (12, 5), (38, 41), (16, 33), (22, 24), (8, 32), (6, 28), (45, 45), (16, 12), (47, 29), (38, 2), (7, 35), (26, 8), (30, 6), (14, 8), (11, 5), (0, 45), (4, 31), (31, 32), (1, 21), (5, 5), (7, 30), (38, 36), (26, 25), (9, 12), (44, 11), (12, 17), (46, 41), (13, 0), (34, 33), (44, 43), (44, 21), (21, 30), (18, 6), (9, 0), (26, 23), (45, 39), (30, 8), (1, 33), (14, 39), (47, 39), (25, 45), (9, 30), (0, 17), (35, 9), (37, 4), (42, 44), (38, 5), (27, 10), (32, 29), (25, 41), (43, 21), (44, 16), (20, 19), (35, 45), (24, 13), (2, 2), (24, 5), (5, 36), (33, 3), (32, 2), (40, 36), (7, 28), (5, 0), (16, 22), (13, 43), (14, 16), (38, 7), (39, 41), (12, 37), (12, 21), (43, 1), (26, 7), (7, 34), (25, 37), (33, 40), (19, 43), (9, 31), (24, 29), (46, 25), (12, 39), (13, 44), (2, 28), (5, 35), (4, 39), (17, 18), (20, 16), (44, 1), (9, 34), (33, 25), (31, 12), (31, 43), (31, 30), (34, 41), (23, 21), (0, 16), (35, 4), (41, 19), (39, 39), (9, 1), (37, 45), (46, 8), (6, 32), (11, 24), (21, 42), (24, 34), (4, 29), (18, 16), (40, 14), (14, 0), (36, 13), (47, 41), (8, 2), (40, 10), (37, 28), (8, 20), (26, 24), (2, 0), (42, 4), (3, 45), (21, 22), (11, 30), (6, 45), (5, 31), (18, 11), (33, 7), (44, 37), (11, 18), (33, 1), (35, 16), (3, 7), (34, 37), (21, 7), (30, 32), (43, 25), (18, 0), (12, 33), (28, 33), (11, 35), (21, 43), (14, 10), (4, 25), (46, 30), (19, 25), (29, 23), (7, 3), (40, 7), (19, 28), (20, 13), (17, 13), (42, 41), (11, 2), (45, 29), (33, 19), (46, 21), (5, 7), (14, 41), (38, 3), (39, 32), (15, 17), (19, 34), (31, 19), (12, 45), (34, 40), (11, 32), (36, 0), (27, 1), (13, 42), (5, 2), (10, 17), (31, 40), (12, 42), (21, 18), (39, 0), (3, 41), (15, 3), (47, 33), (14, 3), (32, 7), (8, 12), (42, 33), (35, 10), (40, 25), (47, 19), (22, 14), (44, 34), (37, 18), (19, 15), (43, 8), (38, 14), (19, 42), (27, 30), (24, 22), (35, 43), (7, 29), (5, 8), (30, 42), (15, 23), (38, 27), (27, 39), (18, 42), (27, 35), (9, 23), (38, 44), (15, 41), (28, 31), (4, 19), (44, 4), (14, 14), (0, 36), (34, 27), (7, 36), (39, 4), (6, 15), (17, 41), (45, 31), (8, 26), (27, 23), (37, 41), (2, 14), (25, 7), (42, 32), (40, 41), (6, 36), (5, 40), (32, 24), (31, 24), (13, 13), (34, 38), (21, 1), (22, 10), (14, 42), (47, 4), (4, 30), (10, 23), (39, 15), (30, 35), (19, 4), (13, 5), (42, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "In a 49x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 1), (34, 24), (5, 3), (14, 28), (46, 8), (33, 2), (46, 24), (0, 29), (17, 38), (8, 16), (8, 13), (43, 16), (16, 37), (28, 21), (26, 29), (20, 21), (44, 18), (11, 31), (36, 24), (41, 6), (23, 23), (19, 29), (17, 12), (31, 6), (2, 32), (4, 30), (3, 17), (36, 11), (8, 5), (21, 11), (5, 29), (2, 1), (46, 20), (4, 31), (28, 29), (3, 7), (6, 31), (41, 1), (45, 15), (2, 38), (33, 36), (34, 22), (17, 0), (6, 10), (42, 5), (42, 3), (29, 24), (46, 27), (42, 11), (44, 39), (20, 33), (5, 15), (8, 19), (8, 20), (20, 6), (3, 12), (34, 15), (32, 0), (45, 3), (1, 34), (22, 28), (36, 32), (18, 0), (34, 3), (2, 7), (30, 7), (43, 7), (43, 15), (13, 36), (47, 2), (41, 26), (38, 30), (39, 35), (19, 3), (27, 2), (17, 27), (22, 3), (9, 29), (26, 11), (17, 19), (8, 6), (39, 16), (28, 18), (28, 4), (7, 6), (40, 15), (3, 24), (7, 5), (7, 21), (11, 29), (36, 22), (0, 36), (28, 27), (23, 31), (15, 11), (29, 8), (43, 9), (45, 35), (34, 36), (35, 3), (48, 13), (47, 37), (39, 12), (39, 38), (13, 6), (23, 28), (32, 32), (35, 8), (34, 33), (10, 11), (30, 26), (32, 4), (2, 13), (25, 31), (38, 13), (2, 19), (20, 34), (38, 14), (41, 30), (4, 12), (15, 24), (29, 37), (40, 29), (29, 10), (10, 1), (13, 11), (36, 29), (23, 3), (1, 18), (0, 35), (5, 11), (46, 16), (28, 39), (33, 39), (48, 23), (2, 28), (16, 25), (30, 0), (27, 32), (40, 5), (20, 20), (33, 29), (31, 19), (9, 13), (45, 32), (39, 29), (37, 33), (34, 8), (28, 23), (23, 15), (41, 39), (13, 8), (39, 37), (11, 19), (15, 3), (0, 10), (47, 23), (12, 37), (14, 38), (14, 11), (44, 16), (11, 25), (30, 34), (41, 24), (32, 10), (22, 37), (33, 11), (3, 29), (25, 35), (47, 20), (10, 17), (3, 1), (46, 9), (43, 22), (20, 10), (17, 16), (1, 28), (28, 36), (1, 36), (22, 27), (25, 11), (12, 20), (32, 24), (5, 34), (23, 5), (29, 20), (10, 2), (35, 33), (1, 5), (12, 3), (20, 36), (41, 37), (34, 21), (23, 14), (38, 29), (34, 0), (36, 0), (21, 17), (37, 23), (18, 21), (12, 12), (13, 1), (9, 12), (47, 13), (3, 13), (45, 20), (31, 23), (40, 4), (27, 12), (41, 32), (0, 6), (16, 8), (38, 25), (22, 22), (2, 30), (6, 38), (29, 27), (32, 19), (24, 21), (11, 32), (20, 11), (48, 22), (48, 11), (9, 35), (0, 28), (24, 11), (48, 15), (12, 33), (7, 32), (39, 17), (10, 5), (37, 16), (36, 34), (42, 38), (6, 5), (3, 27), (12, 28), (32, 39), (43, 28), (45, 7), (6, 35), (48, 2), (45, 33), (16, 14), (17, 2), (5, 2), (22, 23), (22, 38), (26, 6), (18, 7), (28, 11), (48, 12), (23, 9), (42, 26), (47, 12), (31, 35), (34, 19), (16, 39), (22, 20), (21, 2), (37, 25), (31, 2), (18, 30), (36, 33), (19, 16), (44, 17), (16, 21), (40, 19), (42, 12), (13, 19), (15, 26), (31, 21), (35, 30), (46, 30), (17, 35), (11, 18), (23, 25), (37, 6), (30, 13), (26, 31), (16, 13), (3, 31), (35, 9), (46, 39), (30, 9), (7, 22), (41, 11), (14, 9), (7, 31), (25, 37), (6, 24), (20, 8), (30, 32), (16, 1), (3, 10), (33, 38), (19, 34), (1, 8), (46, 7), (48, 37), (13, 32), (46, 4), (43, 35), (39, 3), (41, 31), (20, 28), (30, 12), (27, 11), (5, 36), (47, 24), (44, 3), (2, 11), (0, 9), (16, 15), (40, 30), (29, 9), (33, 16), (47, 21), (12, 13), (43, 18), (47, 8), (35, 39), (23, 18), (39, 2), (18, 28), (9, 4), (46, 6), (35, 38), (14, 34), (40, 12), (25, 3), (8, 36), (0, 20), (20, 9), (30, 20), (25, 17), (7, 0), (20, 29), (10, 33), (7, 35), (33, 32), (35, 19), (0, 39), (26, 28), (15, 22), (42, 1), (23, 24), (18, 13), (28, 6), (29, 30), (40, 33), (34, 28), (18, 20), (26, 21), (46, 10), (23, 37), (41, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 15), (1, 16), (4, 17), (2, 1), (17, 38), (28, 14), (33, 13), (30, 33), (20, 33), (22, 23), (34, 25), (9, 29), (19, 9), (15, 21), (25, 5), (1, 24), (10, 7), (9, 23), (12, 24), (12, 38), (15, 3), (20, 6), (0, 37), (4, 40), (37, 20), (19, 3), (0, 12), (8, 3), (0, 34), (11, 10), (43, 1), (27, 39), (29, 0), (18, 1), (41, 0), (32, 25), (12, 4), (27, 34), (13, 33), (40, 13), (5, 38), (12, 22), (5, 15), (34, 20), (7, 37), (17, 30), (13, 35), (18, 33), (1, 4), (11, 34), (4, 25), (27, 28), (31, 36), (18, 37), (42, 4), (19, 40), (33, 16), (34, 6), (16, 20), (32, 11), (42, 32), (24, 1), (27, 14), (20, 15), (11, 36), (12, 33), (29, 12), (9, 39), (27, 31), (17, 1), (3, 14), (6, 31), (23, 15), (22, 17), (25, 29), (14, 26), (14, 33), (31, 18), (37, 19), (19, 5), (19, 20), (17, 31), (0, 4), (1, 19), (20, 30), (40, 12), (19, 30), (8, 6), (30, 1), (8, 26), (44, 16), (5, 33), (29, 24), (1, 36), (4, 39), (31, 19), (26, 39), (44, 37), (5, 39), (39, 32), (29, 27), (5, 11), (35, 15), (44, 3), (4, 4), (44, 7), (9, 0), (15, 5), (31, 20), (34, 38), (41, 30), (1, 26), (9, 5), (4, 33), (26, 37), (6, 11), (5, 3), (6, 25), (16, 25), (32, 16), (28, 8), (0, 7), (32, 38), (3, 30), (40, 22), (30, 18), (15, 32), (28, 11), (4, 6), (34, 23), (0, 33), (41, 23), (8, 32), (21, 7), (41, 16), (4, 5), (21, 38), (32, 8), (37, 25), (3, 28), (38, 2), (5, 26), (23, 20), (5, 14), (3, 38), (17, 0), (17, 33), (6, 13), (7, 28), (2, 15), (7, 20), (14, 19), (4, 19), (23, 13), (18, 25), (21, 36), (31, 11), (6, 20), (23, 33), (7, 32), (38, 8), (6, 18), (7, 7), (33, 40), (3, 12), (0, 24), (11, 38), (16, 17), (43, 35), (14, 23), (44, 12), (42, 22), (23, 9), (31, 29), (28, 34), (41, 3), (38, 7), (34, 21), (28, 35), (21, 20), (44, 34), (37, 34), (37, 7), (6, 29), (20, 31), (25, 32), (20, 4), (13, 37), (44, 19), (40, 1), (12, 8), (39, 11), (18, 19), (17, 24), (1, 39), (16, 32), (18, 28), (39, 37), (34, 36), (8, 25), (41, 13), (40, 18), (16, 15), (13, 39), (36, 34), (14, 32), (9, 14), (41, 29), (30, 16), (7, 6), (43, 3), (22, 4), (32, 10), (2, 13), (39, 28), (42, 40), (27, 9), (32, 3), (7, 25), (19, 11), (34, 8), (5, 29), (13, 3), (2, 11), (37, 13), (14, 9), (40, 27), (18, 35), (28, 7), (40, 4), (7, 24), (29, 31), (26, 28), (26, 13), (8, 21), (19, 6), (8, 8), (29, 32), (5, 4), (3, 16), (6, 26), (11, 28), (26, 34), (16, 2), (32, 9), (22, 37), (40, 2), (38, 5), (9, 11), (20, 0), (8, 28), (33, 14), (13, 29), (21, 37), (14, 2), (12, 27), (37, 4), (13, 11), (29, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 27), (4, 38), (40, 8), (12, 21), (2, 16), (13, 31), (23, 4), (24, 12), (38, 23), (34, 17), (23, 33), (22, 35), (31, 6), (8, 11), (39, 31), (40, 40), (13, 10), (0, 16), (21, 17), (17, 34), (12, 22), (35, 25), (28, 24), (21, 23), (31, 7), (1, 14), (11, 2), (26, 30), (23, 13), (32, 20), (9, 13), (20, 22), (32, 27), (18, 32), (8, 28), (14, 28), (18, 20), (34, 15), (29, 1), (20, 31), (10, 2), (23, 22), (12, 31), (10, 25), (0, 41), (11, 26), (40, 18), (2, 32), (22, 40), (0, 20), (4, 7), (26, 28), (2, 29), (35, 0), (22, 8), (38, 7), (3, 23), (34, 4), (40, 26), (28, 7), (15, 4), (15, 29), (5, 37), (26, 15), (13, 15), (10, 21), (3, 39), (32, 32), (7, 10), (8, 33), (3, 8), (32, 23), (18, 41), (32, 9), (11, 21), (26, 20), (24, 20), (22, 15), (15, 23), (18, 5), (9, 40), (7, 35), (37, 5), (20, 29), (23, 3), (30, 7), (10, 29), (38, 19), (11, 5), (12, 9), (39, 18), (3, 41), (29, 10), (23, 39), (30, 37), (20, 12), (22, 41), (33, 31), (21, 35), (16, 2), (4, 20), (35, 36), (7, 12), (22, 3), (21, 15), (30, 25), (40, 11), (22, 29), (28, 23), (11, 29), (16, 38), (10, 13), (19, 15), (23, 1), (33, 23), (24, 18), (40, 24), (4, 22), (18, 15), (9, 4), (29, 33), (13, 33), (10, 17), (31, 34), (9, 36), (29, 17), (32, 16), (23, 18), (8, 10), (17, 31), (38, 3), (17, 29), (12, 15), (17, 12), (6, 9), (0, 15), (12, 1), (25, 34), (10, 5), (13, 2), (28, 26), (27, 31), (22, 25), (10, 6), (14, 17), (22, 19), (12, 4), (15, 21), (4, 10), (34, 18), (12, 36), (23, 19), (18, 18), (18, 30), (30, 2), (8, 1), (32, 4), (2, 31), (11, 27), (14, 19), (31, 13), (12, 5), (1, 2), (11, 7), (23, 37), (30, 13), (18, 21), (40, 21), (26, 21), (26, 0), (19, 16), (34, 12), (4, 11), (4, 21), (20, 5), (35, 23), (24, 7), (19, 40), (36, 0), (23, 20), (27, 35), (40, 9), (28, 34), (5, 29), (27, 4), (32, 14), (16, 28), (8, 9), (7, 15), (26, 13), (35, 40), (17, 36), (32, 34), (28, 12), (2, 5), (5, 15), (13, 23), (35, 21), (20, 10), (29, 39), (25, 36), (29, 35), (10, 19), (4, 17), (3, 38), (1, 31), (32, 0), (1, 1), (0, 19), (25, 10), (7, 29), (0, 33), (28, 13), (20, 34), (13, 1), (30, 35), (6, 31), (39, 30), (5, 3), (24, 34), (18, 10), (13, 22), (19, 30), (4, 19), (35, 30), (9, 12), (39, 14), (18, 28), (12, 0), (13, 28), (12, 27), (34, 6), (23, 38), (26, 29), (28, 1), (32, 10), (37, 6), (37, 27), (3, 25), (16, 23), (34, 26), (0, 37), (22, 30), (36, 22), (36, 11), (29, 32), (1, 0), (18, 0), (5, 13), (26, 23), (31, 41), (10, 30), (2, 38), (39, 6), (22, 4), (21, 27), (3, 18), (39, 8), (26, 35), (12, 6), (20, 3), (5, 39), (29, 0), (23, 28), (8, 0), (39, 27), (1, 22), (30, 18), (8, 12), (30, 41), (12, 20), (2, 2), (16, 12), (9, 7), (13, 7), (19, 25), (12, 34), (22, 36), (25, 6), (17, 2), (12, 29), (0, 17), (3, 3), (12, 25), (11, 41), (28, 31), (20, 39), (31, 26), (30, 22), (31, 12), (28, 40), (9, 30), (26, 4), (39, 1), (14, 11), (24, 41), (39, 12), (39, 37), (14, 39), (4, 37), (20, 35), (3, 31), (23, 23), (11, 9), (20, 18), (24, 38), (1, 35), (13, 20), (23, 34), (26, 3), (0, 8), (37, 16), (24, 5), (21, 37), (15, 31), (17, 33), (5, 36), (11, 19), (4, 39), (1, 41), (19, 6), (28, 8), (7, 33), (31, 16), (16, 31), (19, 10), (17, 15), (37, 23), (23, 14), (22, 24), (4, 34), (12, 35), (14, 4), (36, 21), (29, 37), (39, 20), (34, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 18), (17, 8), (14, 29), (18, 39), (41, 44), (7, 5), (35, 2), (41, 20), (40, 33), (12, 44), (39, 41), (20, 40), (33, 37), (18, 11), (29, 0), (11, 8), (27, 33), (4, 37), (42, 22), (43, 22), (19, 37), (0, 29), (38, 39), (30, 17), (28, 15), (37, 30), (45, 0), (17, 35), (24, 4), (0, 10), (6, 44), (23, 13), (34, 37), (20, 44), (37, 11), (0, 36), (45, 36), (44, 0), (32, 42), (10, 35), (29, 18), (7, 3), (29, 40), (34, 6), (45, 7), (7, 16), (31, 10), (8, 15), (4, 33), (41, 14), (14, 1), (26, 26), (30, 9), (3, 15), (45, 26), (4, 24), (31, 42), (16, 31), (20, 21), (24, 31), (43, 35), (2, 22), (31, 34), (27, 10), (41, 39), (0, 15), (16, 40), (34, 36), (21, 25), (40, 11), (21, 22), (10, 29), (29, 9), (10, 41), (2, 0), (3, 34), (29, 35), (40, 20), (10, 0), (24, 16), (25, 26), (39, 43), (21, 37), (44, 16), (44, 18), (13, 3), (18, 5), (42, 33), (29, 29), (21, 1), (26, 21), (5, 33), (25, 12), (22, 16), (2, 35), (14, 4), (5, 25), (46, 35), (13, 32), (43, 30), (16, 15), (12, 38), (4, 21), (21, 41), (30, 7), (18, 4), (25, 32), (4, 38), (19, 44), (39, 0), (9, 2), (0, 1), (17, 19), (37, 27), (12, 0), (3, 29), (23, 20), (28, 32), (34, 24), (46, 31), (35, 6), (12, 22), (32, 28), (18, 1), (23, 37), (39, 21), (18, 18), (20, 41), (11, 30), (23, 19), (31, 23), (33, 26), (19, 35), (0, 7), (14, 0), (46, 20), (41, 41), (13, 42), (40, 31), (41, 19), (17, 14), (46, 14), (30, 21), (16, 35), (0, 17), (30, 23), (32, 21), (42, 24), (41, 18), (20, 24), (36, 33), (39, 40), (36, 20), (44, 44), (36, 2), (23, 9), (24, 42), (35, 26), (38, 41), (38, 22), (35, 1), (20, 1), (22, 34), (5, 15), (26, 5), (46, 36), (5, 0), (1, 34), (41, 42), (19, 38), (22, 18), (31, 28), (17, 22), (11, 31), (17, 30), (37, 33), (11, 14), (9, 18), (34, 19), (36, 15), (3, 20), (10, 23), (22, 37), (8, 17), (45, 4), (28, 11), (0, 37), (30, 44), (13, 21), (18, 43), (44, 31), (6, 41), (27, 29), (14, 21), (42, 27), (18, 38), (17, 38), (19, 3), (4, 22), (31, 6), (46, 22), (8, 9), (3, 2), (1, 42), (39, 18), (24, 3), (2, 24), (26, 43), (43, 1), (17, 13), (32, 39), (12, 39), (38, 10), (28, 17), (9, 11), (9, 29), (42, 17), (20, 8), (17, 42), (31, 22), (19, 24), (22, 41), (11, 5), (6, 38), (34, 14), (17, 25), (34, 30), (15, 41), (11, 25), (12, 32), (11, 37), (37, 41), (32, 37), (21, 21), (25, 27), (43, 6), (10, 26), (45, 2), (41, 13), (30, 18), (36, 26), (35, 16), (24, 20), (23, 33), (7, 44), (29, 25), (12, 5), (8, 41), (12, 6), (4, 13), (12, 17), (34, 13), (20, 26), (34, 8), (35, 34), (39, 32), (10, 25), (3, 35), (40, 28), (38, 35), (46, 7), (25, 33), (41, 26), (38, 43), (12, 42), (32, 5), (28, 22), (15, 22), (1, 5), (26, 23), (22, 4), (27, 31), (10, 14), (27, 3), (35, 38), (43, 29), (18, 19), (24, 21), (1, 32), (18, 33), (12, 41), (46, 23), (43, 11), (45, 13), (0, 39), (18, 16), (26, 17), (31, 3), (45, 23), (2, 37), (36, 40), (24, 19), (20, 18), (33, 3), (9, 38), (23, 29), (12, 15), (4, 16), (43, 25), (4, 42), (35, 14), (13, 43), (28, 43), (13, 13), (11, 15), (24, 9), (27, 24), (31, 13), (6, 28), (20, 20), (26, 20), (17, 39), (45, 1), (13, 28), (10, 2), (3, 16), (21, 14), (35, 4), (42, 15), (8, 23), (15, 5), (10, 6), (34, 17), (40, 16), (9, 26), (19, 16), (32, 19), (16, 24), (39, 22), (5, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 17), (12, 23), (36, 31), (20, 18), (35, 14), (39, 29), (13, 26), (45, 16), (41, 17), (37, 35), (13, 19), (24, 30), (11, 5), (24, 6), (17, 39), (15, 9), (42, 24), (11, 36), (12, 39), (45, 24), (24, 40), (29, 26), (47, 18), (44, 36), (31, 8), (40, 8), (2, 13), (44, 24), (33, 40), (33, 21), (18, 39), (14, 32), (1, 1), (12, 4), (17, 0), (42, 10), (9, 4), (48, 25), (39, 8), (2, 29), (31, 22), (35, 7), (6, 9), (28, 9), (30, 42), (27, 5), (39, 33), (36, 36), (11, 17), (47, 35), (38, 25), (20, 11), (5, 35), (20, 1), (19, 11), (8, 14), (15, 22), (1, 14), (47, 21), (31, 39), (16, 11), (15, 26), (32, 33), (21, 4), (17, 20), (21, 9), (14, 21), (33, 24), (20, 13), (5, 17), (37, 16), (28, 11), (16, 17), (1, 28), (7, 10), (37, 37), (6, 24), (2, 27), (12, 26), (43, 26), (46, 1), (17, 25), (15, 29), (37, 2), (41, 12), (46, 8), (42, 9), (39, 2), (6, 5), (0, 22), (7, 18), (35, 37), (29, 36), (15, 36), (18, 0), (47, 8), (3, 28), (16, 23), (1, 12), (15, 41), (22, 19), (21, 10), (33, 34), (47, 17), (43, 4), (39, 36), (22, 34), (1, 29), (2, 35), (8, 29), (10, 28), (5, 38), (8, 4), (14, 22), (25, 16), (20, 27), (8, 37), (17, 11), (44, 6), (20, 41), (36, 26), (26, 36), (13, 17), (14, 41), (47, 12), (10, 12), (33, 16), (32, 27), (34, 3), (34, 11), (9, 9), (7, 31), (13, 2), (37, 36), (2, 42), (8, 41), (1, 25), (22, 10), (34, 0), (21, 11), (0, 33), (1, 13), (42, 39), (22, 7), (44, 7), (23, 14), (15, 1), (22, 2), (42, 17), (9, 1), (16, 8), (41, 20), (48, 34), (48, 1), (14, 4), (30, 28), (48, 40), (14, 36), (13, 39), (40, 27), (34, 29), (41, 32), (27, 4), (38, 42), (38, 18), (40, 4), (38, 6), (46, 7), (39, 24), (31, 26), (29, 25), (43, 15), (24, 22), (7, 15), (1, 24), (44, 9), (44, 3), (10, 16), (12, 3), (31, 41), (24, 31), (5, 10), (8, 22), (41, 3), (43, 3), (24, 41), (34, 34), (9, 29), (30, 21), (25, 27), (48, 26), (18, 32), (32, 28), (1, 15), (38, 21), (7, 21), (17, 40), (33, 28), (44, 27), (28, 17), (38, 32), (38, 39), (24, 15), (28, 2), (35, 9), (48, 22), (12, 10), (30, 9), (36, 13), (17, 28), (25, 11), (0, 24), (29, 9), (17, 24), (3, 16), (41, 1), (39, 20), (47, 19), (10, 25), (25, 40), (27, 37), (4, 21), (8, 11), (10, 9), (18, 10), (5, 41), (7, 32), (38, 9), (11, 30), (15, 31), (39, 19), (32, 14), (39, 11), (9, 36), (18, 28), (28, 28), (17, 16), (40, 11), (45, 10), (25, 30), (30, 13), (33, 11), (17, 2), (46, 6), (3, 41), (30, 31), (47, 23), (11, 13), (47, 31), (40, 1), (5, 16), (2, 34), (34, 27), (2, 41), (29, 29), (39, 32), (29, 3), (22, 36), (40, 3), (18, 36), (17, 41), (9, 23), (44, 5), (5, 20), (45, 25), (34, 6), (33, 35), (10, 41), (22, 21), (34, 33), (15, 12), (0, 40), (21, 14), (24, 3), (14, 39), (30, 15), (15, 42), (4, 28), (16, 27), (32, 34), (44, 2), (12, 7), (42, 15), (10, 42), (12, 42), (33, 12), (30, 30), (48, 19), (12, 6), (33, 29), (29, 11), (9, 2), (8, 3), (42, 25), (37, 4), (48, 35), (38, 16), (41, 8), (18, 9), (34, 7), (37, 13), (42, 13), (14, 15), (35, 27), (11, 9), (4, 13), (22, 0), (15, 28), (31, 30), (25, 5), (27, 26), (36, 19), (9, 14), (32, 25), (41, 18), (25, 26), (31, 7), (36, 42), (6, 32), (19, 16), (18, 27), (33, 19), (15, 2), (18, 34), (7, 40), (24, 8), (13, 41), (32, 42), (45, 33), (3, 10), (24, 16), (15, 7), (14, 20), (23, 33), (11, 24), (30, 27), (0, 13), (3, 11), (0, 25), (45, 35), (8, 36), (39, 42), (37, 12), (15, 15), (4, 2), (12, 12), (37, 41), (4, 18), (16, 33), (11, 2), (25, 41), (46, 33), (48, 4), (12, 13), (2, 37), (25, 8), (22, 29), (10, 29), (0, 16), (21, 36), (31, 19), (38, 3), (7, 16), (47, 1), (19, 33), (40, 2), (35, 10), (6, 8), (42, 38), (43, 2), (29, 34), (45, 13), (30, 35), (35, 33), (35, 12), (26, 40), (38, 10), (38, 23), (11, 3), (27, 21), (27, 29), (21, 35), (42, 40), (18, 1), (35, 24), (25, 42), (21, 29), (23, 10), (10, 6), (26, 37), (20, 31), (44, 42), (34, 12), (42, 14), (24, 10), (46, 24), (4, 9), (30, 20), (22, 11), (16, 21), (10, 7), (48, 11), (45, 1), (29, 12), (41, 5), (34, 28), (46, 32), (48, 13), (29, 19), (4, 15), (40, 26), (47, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 43), (12, 42), (27, 1), (33, 3), (16, 28), (41, 45), (43, 1), (37, 23), (21, 41), (37, 30), (28, 19), (41, 44), (44, 34), (2, 26), (9, 32), (18, 11), (45, 0), (30, 1), (26, 46), (37, 11), (11, 39), (4, 41), (3, 14), (42, 31), (43, 18), (11, 0), (27, 24), (13, 42), (13, 8), (44, 35), (27, 18), (18, 6), (8, 13), (6, 39), (25, 45), (41, 35), (21, 27), (15, 47), (15, 23), (14, 11), (39, 35), (31, 26), (24, 19), (2, 20), (0, 22), (43, 29), (28, 31), (44, 42), (35, 0), (17, 32), (31, 6), (31, 32), (19, 34), (25, 2), (4, 0), (2, 1), (31, 44), (31, 23), (37, 16), (39, 11), (35, 33), (19, 42), (28, 25), (1, 39), (32, 15), (13, 19), (14, 37), (35, 5), (4, 35), (28, 34), (16, 26), (0, 27), (41, 26), (35, 45), (39, 43), (26, 31), (29, 36), (36, 10), (5, 28), (19, 25), (17, 31), (31, 14), (5, 7), (35, 41), (20, 35), (4, 20), (31, 34), (1, 15), (13, 30), (11, 44), (11, 5), (42, 17), (10, 9), (0, 5), (22, 1), (45, 32), (4, 45), (30, 44), (13, 23), (6, 6), (30, 31), (43, 42), (42, 11), (13, 47), (9, 40), (10, 42), (23, 12), (20, 9), (6, 46), (32, 31), (9, 38), (44, 40), (20, 14), (33, 31), (18, 8), (17, 30), (41, 7), (15, 12), (41, 16), (7, 11), (42, 33), (32, 14), (31, 41), (40, 11), (19, 13), (18, 41), (5, 21), (28, 45), (7, 45), (32, 27), (12, 35), (2, 33), (21, 19), (31, 39), (45, 3), (35, 18), (2, 10), (11, 45), (18, 0), (19, 22), (21, 43), (44, 25), (8, 25), (17, 5), (11, 15), (31, 7), (29, 27), (45, 22), (11, 3), (32, 28), (40, 18), (28, 11), (41, 5), (12, 46), (19, 27), (17, 26), (42, 30), (26, 4), (9, 3), (28, 15), (8, 35), (41, 24), (18, 35), (31, 13), (15, 26), (15, 32), (16, 14), (40, 1), (9, 24), (6, 35), (11, 43), (25, 18), (25, 7), (5, 22), (29, 8), (21, 11), (42, 35), (6, 24), (26, 40), (31, 2), (20, 18), (24, 21), (16, 13), (7, 25), (9, 47), (22, 17), (23, 0), (30, 42), (39, 46), (19, 41), (22, 30), (2, 24), (43, 25), (45, 10), (44, 3), (3, 28), (14, 27), (24, 34), (13, 28), (7, 42), (45, 19), (35, 42), (22, 32), (41, 25), (32, 10), (23, 25), (3, 30), (36, 23), (33, 19), (39, 22), (7, 36), (30, 17), (21, 5), (29, 43), (29, 14), (21, 35), (38, 0), (45, 12), (5, 14), (45, 31), (32, 9), (11, 8), (30, 25), (0, 21), (27, 6), (42, 13), (19, 30), (29, 33), (21, 9), (42, 0), (30, 45), (2, 37), (35, 39), (18, 12), (38, 11), (18, 29), (30, 16), (19, 2), (41, 2), (34, 1), (23, 5), (34, 10), (24, 33), (0, 13), (27, 13), (40, 15), (9, 35), (40, 24), (21, 10), (33, 41), (41, 4), (16, 4), (34, 12), (12, 5), (19, 11), (32, 44), (23, 16), (24, 11), (28, 13), (21, 44), (38, 22), (41, 38), (30, 38), (9, 28), (6, 21), (38, 6), (24, 27), (17, 18), (36, 14), (23, 20), (45, 25), (36, 13), (9, 27), (19, 3), (40, 21), (12, 30), (24, 17), (7, 2), (22, 14), (11, 4), (36, 30), (42, 44), (44, 2), (24, 38), (35, 25), (1, 25), (15, 16), (21, 4), (16, 43), (9, 16), (15, 19), (11, 2), (38, 37), (18, 36), (10, 19), (14, 34), (24, 7), (11, 16), (13, 41), (23, 28), (6, 17), (10, 38), (3, 15), (45, 46), (26, 17), (9, 23), (45, 1), (37, 27), (38, 25), (12, 43), (4, 4), (3, 35), (4, 43), (1, 19), (6, 42), (33, 18), (37, 3), (7, 30), (38, 44), (14, 18), (39, 25), (24, 22), (10, 17), (39, 29), (13, 34), (23, 33), (19, 8), (6, 8), (45, 34), (43, 0), (24, 5), (29, 9), (41, 43), (41, 19), (13, 16), (13, 38), (34, 45), (40, 19), (18, 44), (12, 18), (29, 18), (3, 37), (9, 31), (45, 5), (6, 28), (18, 33), (22, 11), (10, 34), (25, 0), (13, 25), (39, 45), (34, 41), (16, 0), (10, 2), (17, 14), (16, 45), (20, 45), (31, 12), (4, 37), (6, 19), (42, 28), (17, 20), (17, 12), (40, 46), (9, 9), (3, 7), (19, 10), (39, 28), (45, 30), (14, 15), (10, 6), (16, 27), (16, 41), (24, 32), (28, 14), (4, 32), (16, 10), (24, 14), (32, 47), (13, 26), (3, 19), (19, 35), (21, 37), (4, 12), (3, 29), (37, 46), (0, 39), (43, 6), (38, 24), (3, 12), (15, 5), (30, 35), (0, 17), (44, 6), (7, 46), (7, 43), (30, 12), (29, 17), (1, 45), (40, 28), (18, 10), (4, 36), (14, 47), (15, 20), (8, 41), (44, 38), (32, 16), (3, 23), (44, 20), (4, 18), (8, 14), (38, 7), (25, 39), (45, 39), (38, 39), (6, 7), (37, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 3), (14, 41), (33, 12), (0, 13), (18, 31), (7, 30), (8, 6), (36, 5), (30, 25), (43, 10), (10, 37), (24, 34), (9, 34), (36, 33), (39, 31), (20, 26), (1, 37), (32, 4), (30, 31), (37, 41), (18, 36), (44, 1), (42, 1), (29, 12), (6, 37), (25, 33), (12, 14), (24, 37), (24, 40), (23, 1), (0, 32), (13, 3), (10, 33), (16, 15), (32, 43), (6, 26), (40, 24), (18, 0), (1, 35), (19, 18), (2, 15), (38, 43), (35, 23), (0, 9), (38, 41), (45, 2), (2, 13), (25, 8), (4, 21), (31, 13), (22, 31), (9, 5), (31, 21), (28, 1), (29, 15), (45, 45), (5, 44), (32, 36), (25, 2), (24, 13), (36, 7), (11, 18), (2, 6), (30, 43), (15, 23), (44, 0), (18, 5), (45, 42), (0, 41), (41, 21), (37, 3), (5, 27), (26, 17), (20, 4), (28, 11), (32, 42), (15, 2), (43, 37), (26, 12), (26, 18), (43, 31), (7, 26), (38, 15), (11, 2), (29, 2), (35, 0), (46, 21), (17, 36), (5, 45), (8, 17), (36, 10), (4, 14), (44, 39), (1, 38), (5, 37), (28, 0), (9, 10), (15, 11), (31, 35), (43, 6), (36, 27), (24, 23), (23, 22), (29, 24), (35, 3), (35, 8), (29, 14), (34, 21), (24, 21), (14, 38), (46, 37), (10, 40), (21, 12), (9, 19), (14, 9), (20, 24), (18, 18), (9, 41), (35, 16), (15, 32), (18, 23), (4, 40), (33, 44), (18, 4), (42, 15), (32, 5), (43, 22), (44, 41), (10, 3), (1, 41), (1, 7), (1, 12), (2, 12), (27, 9), (17, 45), (32, 7), (2, 31), (12, 26), (28, 21), (36, 25), (14, 8), (1, 24), (37, 24), (23, 21), (6, 15), (26, 1), (21, 20), (1, 3), (41, 11), (28, 32), (23, 8), (5, 8), (34, 44), (31, 9), (16, 14), (19, 27), (41, 36), (15, 37), (41, 41), (16, 43), (27, 33), (7, 19), (29, 10), (23, 30), (24, 7), (33, 9), (15, 22), (26, 26), (28, 33), (46, 24), (40, 42), (32, 33), (19, 21), (17, 19), (21, 0), (40, 20), (24, 29), (20, 18), (27, 27), (14, 44), (46, 11), (37, 15), (3, 40), (42, 25), (28, 28), (27, 37), (42, 24), (34, 1), (44, 30), (27, 31), (42, 6), (32, 23), (45, 27), (43, 20), (35, 43), (0, 27), (28, 3), (35, 39), (32, 39), (29, 7), (21, 28), (15, 35), (6, 8), (41, 6), (9, 14), (25, 4), (33, 17), (2, 32), (20, 5), (34, 15), (22, 42), (44, 15), (38, 36), (46, 29), (44, 6), (1, 42), (15, 17), (35, 13), (15, 43), (28, 35), (35, 12), (45, 44), (7, 28), (31, 43), (40, 8), (18, 32), (1, 34), (42, 10), (9, 12), (41, 24), (10, 41), (1, 4), (15, 9), (19, 39), (14, 19), (27, 44), (31, 10), (6, 14), (46, 19), (31, 23), (39, 39), (20, 8), (0, 44), (2, 45), (6, 2), (40, 25), (22, 37), (21, 40), (13, 21), (14, 42), (29, 40), (36, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (30, 34), (12, 10), (13, 21), (31, 15), (20, 15), (7, 29), (39, 21), (27, 17), (44, 3), (37, 17), (42, 0), (5, 34), (16, 29), (12, 34), (19, 4), (42, 28), (13, 2), (17, 32), (25, 20), (34, 38), (1, 23), (26, 25), (34, 39), (47, 15), (10, 32), (27, 0), (17, 36), (37, 38), (26, 1), (13, 15), (31, 23), (42, 34), (5, 2), (28, 36), (33, 41), (34, 20), (44, 1), (21, 19), (17, 43), (47, 6), (14, 11), (44, 10), (18, 41), (33, 19), (31, 18), (24, 22), (46, 15), (24, 14), (17, 34), (3, 29), (16, 33), (46, 37), (47, 26), (23, 39), (9, 44), (10, 26), (6, 7), (41, 20), (21, 8), (46, 12), (1, 6), (0, 3), (1, 25), (4, 33), (36, 3), (25, 10), (26, 36), (17, 19), (23, 43), (29, 0), (31, 26), (46, 23), (40, 34), (37, 6), (7, 25), (39, 41), (42, 9), (45, 9), (13, 13), (5, 18), (33, 11), (15, 12), (28, 5), (3, 35), (37, 2), (38, 44), (4, 32), (6, 39), (12, 16), (16, 38), (21, 2), (46, 13), (47, 25), (46, 27), (8, 30), (44, 19), (46, 11), (32, 8), (19, 38), (35, 11), (43, 40), (47, 13), (27, 10), (21, 29), (43, 0), (24, 35), (7, 42), (47, 9), (29, 24), (47, 18), (25, 36), (41, 10), (29, 38), (22, 12), (17, 22), (3, 40), (35, 23), (1, 1), (32, 29), (4, 21), (20, 25), (44, 35), (7, 40), (41, 19), (28, 17), (7, 39), (42, 35), (10, 43), (22, 8), (4, 36), (1, 40), (17, 8), (22, 19), (24, 6), (14, 20), (32, 4), (9, 43), (19, 0), (0, 16), (40, 12), (4, 35), (35, 37), (29, 36), (47, 23), (21, 21), (47, 12), (27, 9), (28, 38), (24, 3), (4, 39), (3, 5), (25, 22), (32, 23), (26, 18), (38, 7), (33, 4), (14, 2), (34, 31), (27, 42), (47, 35), (5, 12), (6, 33), (10, 27), (42, 38), (6, 6), (47, 41), (28, 35), (9, 11), (43, 26), (29, 35), (23, 6), (10, 9), (46, 26), (47, 29), (37, 15), (40, 7), (27, 5), (29, 19), (22, 6), (0, 21), (1, 21), (8, 24), (2, 0), (16, 17), (40, 37), (1, 14), (0, 20), (2, 23), (39, 36), (10, 17), (9, 16), (40, 22), (30, 40), (33, 39), (9, 37), (0, 13), (28, 30), (2, 43), (27, 19), (1, 15), (6, 44), (14, 37), (33, 21), (28, 21), (43, 42), (19, 22), (45, 26), (36, 39), (45, 14), (41, 43), (12, 26), (10, 1), (5, 30), (41, 23), (21, 15), (11, 38), (29, 28), (10, 31), (20, 14), (6, 37), (9, 13), (36, 13), (30, 1), (18, 32), (31, 43), (18, 12), (14, 27), (16, 12), (7, 30), (22, 30), (16, 27), (6, 1), (23, 23), (14, 0), (24, 33), (23, 10), (32, 10), (3, 31), (1, 8), (17, 39), (3, 36), (6, 24), (23, 20), (0, 32), (21, 1), (38, 43), (28, 3), (3, 4), (44, 38), (39, 3), (35, 27), (37, 13), (0, 8), (46, 25), (18, 20), (35, 21), (12, 11), (22, 32), (35, 36), (34, 16), (44, 18), (36, 6), (33, 9), (7, 41), (7, 18), (40, 25), (20, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 29), (46, 38), (7, 43), (20, 24), (43, 14), (11, 5), (12, 47), (9, 20), (5, 5), (15, 35), (10, 27), (38, 22), (30, 26), (13, 12), (35, 23), (0, 28), (27, 32), (46, 11), (5, 16), (34, 43), (12, 34), (19, 36), (21, 38), (9, 18), (3, 1), (35, 15), (31, 6), (3, 20), (11, 30), (15, 45), (31, 33), (18, 41), (16, 32), (31, 0), (31, 28), (4, 12), (7, 46), (7, 34), (15, 0), (8, 25), (40, 44), (16, 7), (33, 18), (21, 29), (38, 40), (14, 1), (5, 48), (31, 22), (42, 1), (21, 44), (45, 3), (6, 41), (42, 33), (5, 23), (34, 44), (12, 29), (17, 4), (2, 15), (21, 30), (6, 20), (31, 32), (16, 11), (27, 24), (1, 23), (38, 15), (11, 4), (1, 37), (22, 1), (35, 5), (43, 40), (6, 4), (27, 0), (19, 9), (6, 12), (25, 35), (23, 8), (26, 26), (12, 35), (6, 47), (33, 4), (16, 20), (8, 47), (28, 4), (1, 5), (10, 0), (13, 25), (34, 0), (24, 12), (30, 42), (37, 0), (1, 15), (40, 15), (36, 33), (35, 11), (16, 16), (37, 2), (22, 47), (19, 32), (11, 16), (33, 12), (15, 21), (3, 33), (27, 14), (37, 33), (1, 25), (4, 18), (24, 30), (43, 28), (39, 39), (26, 39), (40, 45), (9, 43), (3, 3), (10, 38), (10, 18), (45, 47), (34, 21), (2, 39), (30, 20), (39, 27), (28, 31), (42, 39), (45, 17), (45, 33), (11, 43), (15, 39), (13, 11), (30, 8), (3, 19), (23, 22), (22, 29), (21, 7), (15, 42), (20, 1), (36, 5), (43, 39), (42, 11), (7, 31), (22, 3), (33, 39), (45, 29), (41, 48), (3, 11), (29, 10), (19, 4), (9, 11), (6, 2), (11, 20), (32, 30), (1, 2), (45, 34), (22, 39), (34, 31), (32, 43), (4, 17), (11, 15), (4, 34), (24, 5), (36, 11), (46, 20), (7, 11), (39, 22), (30, 33), (10, 44), (22, 42), (46, 15), (6, 29), (34, 7), (24, 2), (35, 40), (30, 7), (14, 5), (38, 38), (21, 20), (22, 9), (31, 37), (38, 0), (31, 15), (38, 18), (13, 28), (27, 45), (37, 5), (38, 2), (17, 11), (24, 16), (20, 8), (25, 20), (11, 47), (33, 28), (6, 38), (4, 41), (16, 45), (36, 28), (22, 0), (12, 18), (34, 26), (14, 16), (28, 9), (23, 16), (23, 17), (4, 46), (13, 0), (17, 12), (34, 23), (3, 45), (45, 16), (15, 30), (6, 17), (13, 14), (27, 13), (41, 46), (36, 21), (12, 5), (34, 3), (17, 8), (30, 10), (21, 22), (20, 27), (11, 19), (14, 4), (10, 24), (39, 1), (5, 35), (13, 17), (13, 8), (27, 26), (6, 10), (4, 15), (36, 18), (0, 29), (23, 2), (34, 2), (11, 23), (40, 41), (37, 8), (30, 46), (46, 46), (2, 13), (3, 38), (33, 37), (24, 14), (36, 16), (2, 38), (11, 0), (24, 47), (5, 46), (12, 17), (23, 30), (31, 1), (31, 2), (20, 10), (34, 10), (36, 20), (45, 45), (32, 35), (14, 39), (39, 44), (42, 23), (2, 36), (8, 1), (31, 21), (37, 45), (16, 15), (18, 0), (34, 41), (26, 16), (16, 31), (36, 3), (4, 37), (46, 41), (16, 36), (38, 11), (41, 18), (33, 45), (35, 18), (18, 4), (38, 12), (46, 31), (39, 33), (18, 19), (7, 7), (41, 17), (6, 16), (5, 39), (33, 2), (4, 36), (41, 25), (45, 0), (19, 22), (17, 10), (32, 12), (16, 41), (23, 18), (14, 18), (45, 2), (35, 38), (24, 21), (2, 47), (1, 20), (37, 47), (30, 4), (21, 10), (2, 16), (4, 9), (44, 26), (5, 12), (1, 42), (42, 17), (10, 21), (11, 27), (11, 40), (31, 45), (22, 37), (19, 42), (40, 27), (17, 13), (29, 19), (46, 1), (33, 36), (20, 38), (12, 21), (7, 9), (43, 13), (25, 41), (15, 41), (29, 32), (24, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 14), (35, 27), (40, 29), (7, 43), (37, 44), (25, 20), (15, 37), (4, 17), (27, 1), (15, 19), (20, 18), (5, 2), (3, 0), (0, 28), (39, 32), (7, 26), (41, 13), (43, 37), (22, 31), (35, 26), (35, 5), (22, 6), (42, 34), (19, 40), (17, 6), (43, 42), (18, 14), (30, 7), (29, 43), (33, 43), (28, 36), (16, 15), (20, 44), (10, 18), (1, 16), (10, 29), (25, 34), (40, 15), (25, 13), (19, 27), (38, 45), (44, 34), (27, 22), (11, 44), (7, 11), (4, 8), (22, 10), (44, 41), (25, 45), (28, 26), (44, 37), (17, 36), (24, 15), (32, 5), (14, 42), (6, 5), (33, 7), (12, 46), (1, 1), (10, 4), (32, 16), (17, 44), (28, 3), (1, 27), (16, 34), (4, 16), (37, 40), (21, 2), (40, 6), (6, 13), (34, 48), (37, 15), (41, 18), (12, 22), (28, 19), (28, 24), (23, 7), (13, 38), (22, 30), (3, 5), (8, 44), (20, 24), (2, 12), (15, 29), (38, 15), (2, 28), (11, 27), (2, 17), (34, 5), (29, 36), (36, 41), (34, 21), (28, 14), (31, 43), (20, 34), (8, 43), (25, 11), (31, 24), (24, 43), (4, 35), (27, 27), (24, 34), (26, 40), (41, 12), (2, 46), (28, 22), (2, 40), (40, 48), (28, 44), (5, 36), (44, 20), (12, 40), (20, 30), (2, 33), (2, 31), (23, 35), (25, 8), (12, 1), (17, 0), (6, 43), (28, 42), (12, 30), (32, 23), (7, 12), (30, 23), (34, 17), (27, 45), (26, 9), (18, 23), (21, 33), (4, 13), (23, 30), (28, 10), (35, 15), (11, 5), (9, 41), (26, 13), (43, 45), (41, 8), (13, 35), (23, 41), (3, 47), (31, 12), (13, 34), (26, 6), (5, 46), (1, 9), (0, 29), (38, 29), (11, 1), (42, 32), (28, 5), (23, 1), (14, 24), (1, 34), (39, 37), (15, 46), (19, 10), (42, 41), (37, 36), (13, 5), (0, 42), (38, 18), (38, 11), (31, 23), (5, 18), (7, 22), (8, 15), (44, 24), (32, 46), (24, 36), (33, 46), (14, 40), (34, 1), (27, 34), (16, 37), (26, 0), (19, 34), (31, 34), (29, 46), (25, 46), (41, 36), (42, 6), (2, 3), (42, 30), (26, 35), (17, 37), (8, 31), (40, 31), (18, 17), (2, 6), (13, 4), (27, 42), (39, 16), (12, 8), (31, 2), (3, 20), (37, 0), (17, 1), (3, 25), (39, 10), (31, 11), (19, 46), (32, 18), (7, 23), (19, 25), (40, 4), (10, 43), (37, 21), (38, 43), (37, 4), (30, 11), (22, 41), (14, 23), (39, 44), (29, 40), (43, 6), (36, 33), (4, 28), (16, 32), (34, 4), (12, 13), (2, 23), (18, 34), (30, 5), (5, 31), (41, 31), (38, 39), (12, 27), (2, 5), (22, 0), (37, 17), (5, 44), (43, 36), (2, 7), (5, 20), (42, 12), (37, 35), (38, 31), (25, 25), (44, 6), (18, 39), (26, 41), (17, 20), (24, 4), (1, 30), (3, 1), (13, 22), (26, 30), (17, 35), (32, 36), (42, 13), (24, 20), (25, 42), (22, 45), (7, 25), (4, 9), (13, 32), (7, 20), (33, 10), (35, 22), (31, 27), (33, 38), (4, 33), (37, 34), (44, 9), (41, 35), (33, 47)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 37), (24, 21), (37, 13), (42, 11), (13, 17), (1, 26), (7, 26), (19, 14), (28, 35), (20, 0), (25, 31), (26, 31), (0, 26), (40, 2), (20, 23), (16, 37), (6, 33), (17, 28), (1, 16), (19, 29), (45, 37), (28, 11), (36, 35), (39, 25), (21, 15), (24, 7), (27, 15), (3, 11), (41, 21), (33, 4), (39, 8), (0, 33), (46, 29), (10, 15), (14, 24), (12, 8), (30, 6), (1, 35), (0, 30), (24, 39), (23, 28), (32, 39), (33, 11), (30, 36), (35, 1), (36, 22), (15, 13), (37, 1), (0, 38), (31, 12), (18, 1), (33, 28), (24, 14), (22, 1), (38, 26), (26, 35), (4, 4), (30, 10), (15, 0), (6, 40), (20, 4), (8, 17), (38, 4), (40, 20), (41, 40), (35, 36), (2, 16), (15, 34), (46, 23), (16, 22), (15, 32), (10, 12), (33, 34), (6, 19), (46, 38), (29, 15), (33, 21), (8, 14), (32, 5), (15, 38), (18, 33), (26, 8), (39, 12), (33, 17), (6, 22), (13, 0), (8, 20), (25, 39), (26, 15), (39, 7), (6, 37), (40, 15), (0, 37), (44, 12), (9, 17), (33, 33), (44, 34), (21, 32), (44, 25), (26, 29), (30, 5), (25, 25), (4, 33), (19, 27), (9, 22), (43, 21), (35, 23), (17, 39), (25, 24), (41, 8), (12, 13), (30, 9), (8, 30), (16, 7), (31, 24), (42, 15), (24, 27), (4, 1), (31, 5), (18, 9), (22, 15), (36, 6), (41, 34), (42, 3), (40, 37), (16, 12), (25, 9), (26, 17), (41, 13), (29, 24), (15, 39), (42, 21), (37, 17), (17, 20), (4, 8), (5, 20), (18, 5), (23, 20), (37, 24), (12, 5), (31, 9), (14, 2), (28, 19), (21, 39), (27, 0), (13, 11), (13, 28), (33, 10), (41, 23), (3, 22), (17, 8), (29, 37), (7, 7), (26, 12), (27, 17), (20, 37), (44, 17), (10, 6), (34, 28), (34, 38), (3, 21), (5, 12), (43, 38), (3, 8), (43, 27), (17, 36), (42, 23), (27, 6), (38, 39), (45, 17), (15, 19), (40, 29), (38, 20), (13, 39), (15, 27), (37, 38), (37, 18), (24, 1), (9, 40), (24, 6), (25, 7), (13, 1), (36, 16), (3, 32), (12, 32), (29, 5), (17, 18), (37, 39), (10, 1), (4, 9), (9, 8), (25, 16), (33, 39), (35, 7), (5, 9), (12, 1), (27, 32), (38, 25), (30, 2), (10, 0), (35, 21), (40, 17), (41, 30), (37, 10), (6, 32), (41, 22), (34, 21), (24, 4), (19, 31), (25, 11), (3, 17), (23, 13), (45, 21), (3, 30), (17, 3), (1, 40), (28, 25), (19, 20), (36, 37), (19, 13), (36, 5), (5, 22), (26, 0), (9, 15), (30, 28), (36, 19), (0, 36), (11, 21), (5, 21), (39, 36), (40, 40), (13, 27), (41, 11), (20, 9), (25, 10), (43, 6), (27, 10), (31, 16), (35, 2), (41, 9), (16, 32), (16, 9), (35, 18), (9, 19), (26, 20), (29, 39), (25, 4), (38, 13), (0, 24), (40, 12), (2, 34), (10, 13), (39, 9), (14, 9), (46, 19), (40, 14), (6, 35), (10, 5), (13, 30), (29, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 7), (22, 19), (5, 28), (5, 13), (5, 32), (33, 21), (39, 14), (32, 0), (16, 27), (26, 0), (20, 12), (17, 22), (3, 12), (9, 43), (37, 2), (16, 19), (16, 25), (43, 5), (20, 4), (21, 7), (27, 17), (34, 33), (34, 24), (36, 18), (10, 17), (42, 25), (30, 34), (19, 14), (36, 23), (29, 46), (20, 39), (36, 25), (22, 17), (21, 22), (32, 34), (3, 40), (39, 44), (1, 1), (26, 7), (40, 17), (16, 18), (16, 46), (8, 30), (2, 47), (11, 47), (30, 15), (37, 32), (31, 9), (2, 10), (28, 8), (36, 7), (9, 23), (32, 4), (3, 22), (36, 16), (10, 15), (21, 11), (3, 18), (36, 0), (9, 21), (18, 8), (15, 17), (0, 28), (1, 22), (3, 2), (8, 20), (28, 36), (41, 46), (5, 17), (10, 36), (3, 14), (26, 22), (43, 1), (30, 8), (38, 19), (42, 21), (5, 3), (1, 30), (40, 32), (23, 6), (39, 2), (7, 44), (12, 27), (39, 21), (39, 27), (35, 34), (37, 23), (37, 21), (35, 29), (0, 13), (22, 36), (39, 29), (20, 31), (37, 47), (19, 23), (19, 31), (42, 26), (23, 0), (0, 38), (31, 41), (35, 30), (6, 27), (18, 38), (11, 2), (43, 40), (9, 18), (28, 15), (34, 2), (40, 28), (7, 22), (27, 40), (22, 0), (14, 14), (37, 36), (24, 43), (29, 3), (17, 23), (43, 15), (41, 5), (36, 1), (6, 12), (41, 42), (22, 5), (12, 16), (31, 8), (28, 17), (42, 32), (31, 29), (8, 29), (25, 27), (27, 11), (30, 26), (22, 27), (36, 30), (37, 13), (8, 36), (12, 32), (23, 30), (9, 2), (29, 24), (15, 10), (18, 22), (24, 46), (37, 27), (21, 16), (33, 3), (16, 3), (10, 27), (25, 46), (30, 12), (31, 17), (37, 44), (40, 41), (30, 1), (4, 19), (23, 18), (21, 27), (39, 8), (24, 0), (6, 18), (29, 7), (1, 6), (25, 12), (27, 29), (20, 25), (13, 8), (34, 16), (7, 14), (15, 26), (32, 16), (10, 26), (8, 32), (7, 3), (34, 46), (7, 25), (7, 41), (39, 37), (29, 38), (5, 8), (41, 30), (26, 10), (28, 31), (15, 8), (26, 23), (19, 16), (37, 16), (34, 19), (24, 44), (18, 36), (20, 0), (6, 21), (27, 9), (5, 34), (4, 22), (13, 24), (42, 39), (34, 31), (21, 46), (43, 45), (36, 10), (39, 45), (18, 6), (34, 30), (19, 3), (9, 11), (8, 24), (3, 6), (31, 42), (33, 9), (9, 4), (14, 18), (24, 33), (4, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 13), (17, 36), (5, 7), (32, 43), (39, 12), (27, 38), (15, 23), (27, 12), (35, 40), (26, 32), (6, 24), (9, 44), (19, 27), (2, 34), (36, 18), (12, 16), (18, 28), (30, 18), (30, 33), (17, 7), (33, 29), (36, 5), (24, 25), (3, 3), (18, 43), (0, 5), (24, 21), (24, 3), (11, 39), (17, 34), (12, 40), (31, 35), (24, 34), (12, 20), (4, 14), (11, 30), (23, 15), (26, 42), (34, 32), (33, 38), (13, 32), (24, 12), (0, 1), (0, 41), (23, 35), (36, 36), (4, 35), (33, 5), (19, 32), (20, 0), (25, 6), (28, 10), (23, 3), (28, 44), (8, 26), (5, 36), (28, 8), (29, 7), (19, 3), (13, 18), (15, 36), (23, 11), (19, 35), (11, 10), (32, 22), (13, 40), (12, 46), (4, 39), (12, 43), (1, 7), (2, 21), (7, 36), (29, 17), (23, 29), (37, 22), (33, 0), (11, 38), (2, 19), (5, 1), (26, 15), (16, 34), (19, 48), (38, 31), (19, 40), (4, 26), (34, 35), (36, 47), (27, 41), (17, 11), (38, 27), (39, 43), (34, 5), (20, 47), (29, 21), (38, 3), (39, 23), (27, 1), (23, 12), (22, 5), (36, 20), (35, 20), (36, 28), (31, 21), (21, 43), (40, 39), (31, 2), (25, 39), (19, 30), (34, 1), (13, 43), (37, 3), (40, 9), (0, 21), (26, 38), (1, 31), (31, 27), (20, 27), (12, 19), (37, 36), (3, 45), (8, 11), (37, 48), (30, 7), (3, 22), (7, 25), (3, 34), (31, 48), (3, 11), (16, 44), (14, 41), (2, 38), (15, 43), (21, 18), (25, 3), (24, 20), (32, 47), (3, 40), (34, 40), (20, 41), (2, 20), (24, 28), (9, 29), (25, 22), (11, 6), (14, 7), (38, 41), (20, 8), (17, 27), (5, 31), (7, 16), (1, 33), (31, 42), (26, 2), (7, 39), (32, 20), (31, 37), (17, 31), (13, 38), (4, 8), (38, 13), (14, 0), (36, 35), (19, 14), (12, 2), (29, 6), (5, 14), (0, 31), (34, 26), (18, 32), (22, 42), (40, 5), (16, 37), (2, 14), (4, 5), (8, 35), (12, 18), (27, 11), (9, 48), (35, 0), (5, 17), (9, 23), (37, 31), (9, 7), (7, 37), (2, 47), (18, 41), (30, 4), (35, 6), (7, 45), (37, 14), (9, 19), (19, 29), (6, 25), (3, 24), (27, 17), (2, 12), (26, 14), (9, 12), (15, 45), (39, 7), (36, 17), (40, 34), (17, 40), (6, 21), (30, 45), (10, 48), (20, 17), (13, 15), (7, 35), (19, 34), (20, 22), (36, 19), (22, 46), (31, 34), (10, 0), (13, 31), (40, 6), (18, 23), (15, 6), (18, 25), (38, 43), (31, 45), (16, 41), (14, 2), (11, 37), (33, 39), (18, 1), (29, 0), (19, 47), (25, 30), (13, 34), (36, 2), (33, 24), (30, 42), (2, 32), (23, 21), (31, 26), (26, 28), (11, 27), (25, 31), (4, 30), (11, 3), (34, 3), (19, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (45, 14), (27, 26), (4, 22), (47, 10), (7, 11), (39, 20), (16, 26), (47, 29), (44, 3), (34, 22), (10, 39), (19, 29), (43, 8), (26, 4), (46, 32), (34, 4), (8, 12), (36, 8), (5, 39), (16, 10), (30, 23), (30, 4), (9, 1), (14, 0), (45, 31), (1, 0), (20, 4), (2, 12), (38, 26), (37, 2), (41, 33), (2, 33), (46, 27), (11, 24), (2, 34), (13, 25), (38, 19), (3, 13), (0, 15), (35, 16), (31, 37), (29, 16), (13, 4), (24, 3), (3, 27), (17, 32), (3, 12), (17, 3), (35, 8), (16, 15), (40, 13), (25, 7), (25, 19), (21, 31), (25, 39), (14, 17), (34, 34), (1, 37), (9, 5), (38, 35), (35, 28), (41, 12), (12, 4), (3, 32), (6, 23), (18, 25), (11, 10), (26, 18), (34, 9), (27, 22), (17, 18), (45, 32), (26, 11), (31, 27), (43, 27), (44, 39), (8, 17), (29, 15), (15, 13), (41, 0), (14, 13), (2, 35), (27, 11), (36, 14), (13, 0), (29, 3), (13, 17), (22, 15), (24, 23), (23, 30), (10, 35), (21, 3), (40, 35), (19, 4), (11, 13), (34, 5), (3, 39), (38, 39), (6, 6), (26, 32), (29, 20), (1, 39), (7, 10), (2, 16), (26, 9), (43, 21), (0, 32), (17, 24), (14, 27), (44, 25), (40, 2), (40, 39), (6, 28), (35, 6), (36, 2), (39, 16), (19, 23), (43, 9), (46, 20), (23, 6), (13, 13), (0, 19), (1, 17), (2, 15), (9, 35), (34, 17), (7, 23), (46, 6), (15, 17), (1, 6), (42, 19), (25, 4), (0, 10), (6, 20), (6, 31), (29, 32), (22, 21), (20, 22), (36, 29), (30, 12), (22, 16), (29, 14), (25, 28), (15, 11), (32, 23), (5, 33), (1, 34), (11, 15), (12, 7), (32, 27), (20, 25), (14, 35), (35, 13), (47, 9), (11, 38), (33, 17), (21, 1), (11, 32), (40, 6), (46, 2), (21, 29), (12, 27), (27, 4), (29, 2), (11, 7), (39, 0), (29, 25), (17, 38), (3, 11), (35, 23), (23, 37), (33, 39), (23, 0), (12, 39), (17, 12), (44, 14), (32, 26), (31, 22), (33, 18), (6, 12), (1, 10), (14, 36), (14, 31), (22, 32), (10, 17), (16, 4), (43, 2), (20, 29), (18, 33), (14, 7), (44, 4), (18, 27), (9, 26), (19, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 45x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 31), (41, 18), (12, 23), (18, 33), (39, 0), (8, 22), (19, 37), (1, 3), (12, 29), (9, 38), (28, 23), (8, 39), (4, 10), (2, 21), (31, 34), (40, 43), (10, 30), (25, 34), (39, 21), (6, 36), (20, 39), (31, 6), (35, 20), (1, 32), (17, 3), (0, 18), (21, 28), (27, 2), (0, 35), (38, 41), (24, 6), (43, 17), (20, 1), (29, 25), (17, 0), (12, 24), (35, 0), (12, 28), (3, 40), (20, 25), (2, 22), (23, 31), (8, 20), (6, 25), (29, 28), (3, 7), (21, 7), (44, 5), (26, 19), (36, 5), (19, 3), (38, 6), (19, 28), (18, 30), (42, 19), (8, 30), (32, 43), (21, 20), (10, 31), (15, 27), (37, 39), (19, 7), (8, 15), (14, 37), (14, 4), (23, 5), (15, 13), (15, 25), (22, 14), (8, 34), (36, 13), (21, 18), (27, 32), (36, 18), (4, 29), (39, 13), (24, 37), (6, 15), (21, 2), (25, 27), (22, 8), (16, 38), (41, 22), (40, 14), (37, 36), (35, 40), (33, 37), (3, 27), (16, 20), (44, 3), (19, 9), (1, 7), (27, 37), (37, 32), (36, 8), (14, 29), (22, 10), (18, 4), (25, 13), (36, 26), (39, 16), (33, 23), (28, 15), (2, 31), (4, 31), (17, 13), (21, 15), (1, 15), (21, 14), (25, 40), (5, 34), (6, 0), (40, 24), (10, 2), (25, 33), (10, 23), (35, 32), (2, 23), (40, 0), (15, 38), (23, 38), (33, 21), (11, 43), (19, 16), (5, 30), (17, 26), (36, 11), (43, 22), (15, 29), (4, 13), (19, 39), (32, 37), (13, 31), (17, 20), (29, 24), (21, 1), (9, 15), (42, 31), (20, 34), (39, 31), (15, 5), (20, 40), (37, 19), (15, 1), (36, 41), (42, 43), (17, 38), (31, 14), (22, 26), (4, 22), (3, 13), (4, 33), (38, 5), (5, 18), (29, 19), (7, 26), (35, 25), (44, 9), (5, 29), (21, 30), (4, 2), (3, 42), (41, 1), (8, 19), (39, 2), (8, 24), (23, 22), (43, 3), (26, 35), (34, 39), (27, 10), (30, 21), (38, 31), (12, 27), (43, 38), (35, 1), (20, 11), (34, 43), (38, 11), (3, 22), (35, 2), (37, 41), (41, 35), (31, 11), (13, 32), (7, 3), (30, 16), (10, 12), (3, 28), (10, 17), (10, 1), (16, 23), (23, 3), (42, 33), (8, 43), (19, 15), (7, 7), (1, 38), (8, 11), (32, 4), (41, 33), (3, 30), (0, 32), (34, 27), (4, 24), (20, 32), (30, 3), (8, 5), (26, 18), (10, 19), (44, 37), (5, 2), (43, 9), (38, 14), (35, 27), (8, 8), (43, 5), (23, 2), (33, 29), (43, 0), (33, 19), (17, 30), (26, 27), (16, 3), (15, 18), (29, 11), (42, 16), (21, 25), (14, 15), (6, 27), (3, 20), (33, 43), (26, 30), (15, 30), (28, 25), (14, 33), (3, 17), (3, 3), (41, 3), (27, 19), (44, 38), (0, 20), (34, 16), (31, 23), (29, 38), (36, 1), (19, 41), (7, 37), (41, 32), (6, 29), (21, 16), (26, 1), (21, 10), (18, 16), (30, 14), (25, 25), (26, 31), (15, 16), (27, 14), (25, 7), (16, 35), (6, 35), (10, 43), (17, 12), (5, 40), (26, 9), (7, 40), (2, 1), (2, 38), (15, 37), (25, 28), (32, 1), (42, 34), (32, 30), (16, 0), (19, 26), (15, 4), (2, 15), (16, 32), (44, 40), (26, 20), (17, 40), (30, 1), (39, 6), (3, 34), (10, 6), (5, 5), (18, 5), (25, 35), (25, 37), (22, 27), (0, 4), (6, 41), (38, 1), (25, 3), (15, 28), (37, 23), (13, 16), (28, 38), (25, 11), (42, 8), (20, 20), (16, 28), (4, 43), (32, 7), (26, 14), (28, 24), (30, 2), (30, 37), (40, 34), (35, 41), (41, 28), (33, 32), (12, 10), (24, 5), (17, 42), (40, 27), (17, 5), (43, 1), (13, 13), (40, 42), (37, 14), (42, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 36), (39, 20), (31, 13), (12, 17), (20, 35), (9, 35), (26, 15), (19, 18), (1, 12), (17, 24), (1, 8), (37, 29), (22, 17), (35, 22), (26, 18), (32, 1), (32, 28), (3, 40), (36, 39), (13, 12), (29, 17), (26, 33), (15, 12), (25, 33), (30, 35), (34, 25), (5, 22), (38, 31), (36, 9), (27, 11), (18, 24), (2, 1), (3, 30), (21, 18), (5, 27), (30, 21), (10, 39), (18, 25), (30, 33), (25, 19), (12, 34), (16, 2), (15, 5), (18, 10), (25, 29), (11, 32), (6, 6), (22, 5), (23, 28), (0, 23), (3, 1), (37, 25), (3, 12), (8, 5), (15, 10), (17, 11), (39, 33), (12, 36), (27, 33), (31, 37), (3, 26), (34, 11), (23, 10), (30, 20), (2, 14), (0, 35), (18, 38), (4, 35), (4, 13), (4, 30), (0, 17), (25, 31), (10, 33), (26, 38), (35, 7), (19, 38), (29, 7), (24, 30), (32, 12), (19, 26), (37, 31), (27, 37), (37, 3), (32, 39), (10, 17), (17, 16), (27, 2), (6, 13), (16, 9), (20, 16), (19, 1), (32, 5), (14, 8), (1, 13), (26, 3), (15, 29), (8, 18), (22, 16), (30, 10), (11, 22), (23, 25), (10, 15), (39, 28), (39, 29), (12, 31), (26, 19), (39, 18), (38, 19), (31, 9), (37, 14), (37, 6), (33, 27), (20, 1), (7, 1), (32, 26), (13, 1), (7, 17), (35, 6), (32, 3), (30, 15), (31, 39), (16, 25), (28, 24), (20, 13), (23, 27), (32, 9), (31, 15), (22, 19), (39, 37), (29, 22), (29, 37), (9, 34), (32, 16), (14, 4), (27, 36), (6, 29), (28, 12), (24, 12), (34, 15), (19, 29), (6, 33), (22, 10), (29, 13), (14, 13), (11, 40), (29, 16), (5, 26), (35, 25), (21, 21), (22, 27), (7, 16), (27, 30), (15, 6), (37, 19), (11, 34), (32, 6), (9, 22), (30, 30), (32, 20), (27, 19), (2, 16), (23, 13), (26, 13), (16, 8), (15, 0), (7, 18), (13, 31), (12, 3), (34, 18), (0, 21), (23, 4), (6, 21), (39, 2), (35, 35), (9, 18), (33, 39), (15, 28), (4, 4), (12, 12), (21, 33), (5, 17), (39, 34), (12, 16), (11, 24), (39, 10), (8, 32), (21, 4), (32, 34), (38, 3), (14, 10), (9, 10), (13, 19), (26, 28), (23, 11), (10, 32), (7, 5), (12, 22), (4, 28), (19, 19), (16, 39), (37, 20), (36, 32), (24, 22), (37, 33), (23, 33), (16, 19), (14, 40), (39, 6), (32, 8), (9, 38), (8, 29), (33, 40), (17, 19), (9, 5), (4, 20), (21, 25), (28, 8), (6, 37), (11, 15), (36, 40), (31, 38), (9, 0), (3, 15), (6, 38), (11, 21), (6, 16), (37, 24), (21, 35), (38, 26), (14, 32), (7, 0), (31, 28), (2, 9), (8, 1), (39, 26), (11, 5), (27, 34), (21, 5), (17, 9), (3, 14), (38, 20), (27, 35), (4, 26), (22, 9), (4, 31), (16, 22), (31, 4), (29, 24), (25, 8), (6, 39), (17, 13), (23, 23), (39, 3), (19, 20), (36, 4), (31, 16), (13, 2), (24, 18), (12, 35), (20, 3), (29, 10), (7, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 39), (31, 33), (9, 2), (18, 36), (41, 21), (17, 18), (36, 19), (6, 7), (25, 22), (24, 15), (36, 8), (4, 10), (6, 12), (17, 23), (22, 8), (12, 21), (40, 10), (36, 21), (26, 23), (35, 15), (27, 32), (16, 39), (25, 40), (39, 7), (7, 15), (12, 27), (33, 19), (40, 9), (5, 30), (8, 21), (0, 29), (34, 30), (0, 4), (13, 37), (8, 36), (1, 34), (19, 4), (23, 28), (35, 10), (12, 29), (17, 22), (20, 23), (33, 6), (38, 35), (13, 25), (36, 25), (11, 3), (11, 5), (35, 25), (39, 23), (6, 17), (33, 10), (23, 15), (22, 29), (31, 11), (21, 27), (28, 33), (33, 9), (20, 39), (18, 0), (37, 11), (19, 32), (5, 24), (27, 19), (3, 19), (14, 18), (32, 22), (39, 5), (8, 22), (12, 10), (11, 31), (35, 22), (29, 28), (14, 5), (18, 28), (29, 25), (0, 14), (29, 4), (16, 27), (35, 37), (3, 21), (10, 33), (23, 11), (41, 32), (21, 40), (6, 31), (21, 3), (37, 9), (35, 4), (6, 36), (26, 10), (40, 35), (18, 8), (4, 8), (0, 25), (11, 8), (29, 30), (11, 34), (25, 1), (40, 28), (5, 28), (19, 40), (40, 38), (8, 0), (42, 28), (32, 2), (37, 30), (24, 8), (22, 5), (42, 13), (26, 37), (34, 17), (37, 35), (38, 12), (9, 17), (29, 12), (5, 38), (23, 6), (1, 32), (10, 36), (42, 16), (2, 7), (14, 24), (28, 17), (29, 38), (25, 11), (15, 27), (7, 26), (33, 8), (27, 24), (3, 33), (1, 37), (2, 40), (13, 14), (40, 14), (21, 34), (3, 8), (21, 7), (1, 27), (35, 38), (3, 37), (18, 15), (4, 30), (25, 14), (15, 36), (12, 37), (23, 5), (36, 31), (39, 36), (12, 1), (10, 20), (3, 31), (23, 35), (12, 6), (11, 0), (28, 7), (20, 35), (23, 7), (39, 27), (34, 0), (37, 14), (42, 32), (1, 38), (5, 17), (19, 34), (26, 31), (1, 33), (1, 11), (18, 39), (17, 40), (34, 32), (6, 26), (9, 9), (31, 13), (6, 20), (22, 36), (2, 37), (34, 1), (22, 6), (19, 16), (18, 34), (23, 3), (36, 0), (35, 8), (17, 9), (13, 35), (41, 15), (18, 37), (8, 1), (19, 20), (25, 4), (19, 21), (19, 39), (14, 1), (22, 40), (22, 38), (40, 3), (2, 21), (28, 24), (24, 16), (3, 32), (33, 3), (29, 32), (42, 29), (18, 17), (4, 13), (1, 8), (29, 24), (30, 1), (28, 11), (23, 37), (9, 34), (23, 33), (40, 1), (6, 15), (16, 23), (20, 38), (11, 18), (4, 4), (42, 4), (6, 4), (24, 24), (6, 21), (31, 20), (23, 0), (41, 40), (12, 2), (27, 5), (10, 16), (0, 17), (35, 7), (41, 11), (30, 11), (2, 8), (11, 12), (16, 30), (41, 16), (4, 2), (24, 38), (5, 2), (19, 1), (17, 0), (7, 29), (25, 34), (0, 37), (39, 38), (37, 0), (9, 21), (30, 5), (32, 28), (18, 19), (42, 15), (16, 38), (16, 37), (12, 20), (26, 15), (5, 25), (2, 11), (39, 14), (1, 1), (15, 6), (13, 9), (30, 31), (17, 32), (24, 7), (17, 34), (0, 12), (24, 5), (30, 14), (12, 24), (11, 10), (6, 19), (22, 24), (4, 35), (27, 20), (9, 15), (34, 31), (32, 24), (20, 20), (25, 13), (34, 19), (15, 23), (18, 30), (25, 7), (26, 21), (24, 4), (21, 5), (33, 13), (23, 17), (15, 22), (42, 23), (8, 7), (6, 39), (26, 24), (6, 6), (20, 34), (24, 33), (39, 21), (37, 18), (39, 1), (14, 16), (29, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 5), (33, 29), (34, 8), (23, 24), (36, 23), (18, 23), (41, 19), (21, 31), (20, 14), (37, 12), (0, 36), (20, 30), (20, 1), (3, 38), (16, 22), (31, 3), (29, 39), (5, 5), (36, 30), (30, 41), (42, 30), (17, 27), (6, 15), (21, 7), (36, 27), (26, 10), (22, 32), (36, 26), (42, 3), (24, 23), (11, 11), (14, 32), (3, 17), (32, 43), (15, 42), (29, 30), (4, 42), (27, 46), (19, 6), (10, 21), (7, 14), (8, 33), (21, 14), (10, 38), (37, 40), (24, 20), (4, 14), (42, 39), (28, 21), (0, 5), (29, 4), (35, 1), (8, 35), (40, 41), (35, 9), (39, 30), (11, 2), (9, 46), (5, 13), (7, 6), (8, 34), (13, 46), (9, 14), (34, 12), (19, 45), (27, 22), (32, 18), (0, 15), (40, 12), (10, 39), (39, 11), (20, 20), (30, 11), (13, 43), (30, 27), (33, 33), (32, 19), (22, 37), (23, 12), (29, 16), (20, 39), (5, 20), (12, 44), (20, 33), (5, 44), (39, 16), (13, 44), (40, 8), (33, 28), (16, 32), (18, 45), (27, 2), (26, 45), (33, 24), (10, 42), (16, 38), (12, 14), (18, 24), (11, 33), (19, 21), (0, 20), (12, 28), (30, 17), (20, 24), (32, 12), (9, 34), (17, 43), (9, 15), (17, 13), (5, 8), (7, 42), (14, 23), (17, 6), (27, 40), (6, 6), (25, 2), (20, 18), (14, 6), (13, 38), (25, 22), (19, 30), (18, 31), (24, 41), (0, 27), (40, 7), (2, 17), (35, 31), (4, 6), (4, 41), (22, 6), (38, 45), (5, 26), (19, 44), (29, 34), (32, 29), (25, 39), (9, 37), (22, 10), (27, 45), (18, 36), (30, 20), (39, 33), (18, 25), (2, 23), (42, 44), (40, 9), (29, 27), (12, 45), (24, 33), (17, 8), (40, 17), (2, 41), (39, 38), (22, 14), (20, 41), (6, 33), (14, 30), (17, 39), (28, 32), (12, 19), (9, 2), (17, 37), (21, 19), (34, 39), (4, 27), (36, 10), (21, 36), (31, 26), (27, 7), (39, 8), (27, 25), (41, 10), (27, 39), (25, 0), (32, 22), (42, 32), (31, 34), (0, 21), (26, 33), (41, 32), (36, 9), (14, 37), (11, 6), (41, 26), (23, 30), (31, 35), (38, 42), (9, 27), (37, 22), (35, 29), (24, 37), (11, 25), (11, 45), (42, 37), (9, 44), (41, 24), (39, 15), (25, 10), (18, 44), (32, 11), (28, 8), (16, 42), (12, 5), (0, 6), (23, 9), (11, 42), (19, 13), (27, 44), (11, 15), (42, 41), (31, 5), (3, 44), (20, 4), (1, 14), (23, 10), (18, 15), (17, 1), (15, 34), (31, 16), (16, 27), (24, 6), (29, 10), (17, 42), (1, 42), (1, 33), (37, 9), (31, 23), (26, 13), (36, 12), (37, 27), (0, 24), (28, 6), (37, 14), (4, 18), (14, 2), (36, 24), (30, 23), (33, 7), (4, 29), (7, 34), (22, 31), (2, 16), (25, 27), (13, 28), (25, 15), (1, 45), (16, 33), (10, 29), (4, 12), (38, 11), (36, 18), (11, 27), (10, 31), (40, 4), (36, 7), (36, 29), (31, 20), (28, 44), (33, 11), (0, 23), (35, 19), (16, 28), (31, 19), (6, 13), (8, 3), (15, 14), (32, 1), (26, 5), (28, 7), (2, 12), (16, 29), (36, 31), (40, 43), (23, 11), (13, 5), (37, 21), (3, 21), (39, 24), (19, 9), (27, 5), (34, 22), (0, 41), (29, 21), (6, 0), (37, 4), (21, 26), (15, 37), (21, 4), (8, 27), (19, 18), (28, 41), (22, 7), (20, 34), (41, 36), (42, 18), (37, 43), (37, 6), (12, 23), (26, 14), (19, 29), (34, 28), (22, 38), (10, 1), (7, 36), (11, 9), (12, 39), (34, 4), (6, 36), (41, 35), (6, 20), (14, 43), (14, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 35), (22, 12), (1, 33), (33, 8), (36, 18), (28, 20), (43, 0), (19, 12), (27, 25), (24, 13), (4, 41), (17, 21), (15, 4), (33, 37), (35, 39), (1, 15), (17, 34), (11, 1), (6, 8), (41, 30), (9, 27), (4, 36), (15, 9), (29, 42), (3, 3), (3, 30), (7, 26), (11, 42), (0, 39), (23, 29), (18, 10), (38, 14), (5, 7), (17, 3), (11, 24), (42, 35), (35, 27), (13, 37), (2, 32), (16, 14), (26, 19), (10, 1), (31, 15), (43, 14), (3, 12), (4, 12), (37, 8), (28, 37), (13, 31), (30, 5), (3, 13), (20, 26), (0, 9), (27, 6), (24, 38), (10, 32), (37, 23), (41, 35), (22, 17), (5, 16), (43, 15), (24, 31), (13, 29), (4, 35), (10, 30), (12, 5), (16, 21), (4, 5), (18, 29), (7, 9), (9, 38), (29, 21), (26, 23), (34, 21), (39, 15), (14, 14), (5, 17), (31, 25), (34, 38), (9, 9), (37, 0), (33, 40), (36, 42), (35, 32), (27, 18), (32, 5), (34, 40), (3, 18), (13, 22), (18, 2), (23, 13), (16, 20), (36, 38), (17, 23), (6, 15), (6, 20), (34, 30), (32, 39), (33, 30), (42, 12), (32, 13), (39, 22), (0, 35), (15, 1), (27, 19), (32, 30), (25, 3), (9, 2), (16, 23), (29, 17), (6, 42), (21, 14), (1, 0), (9, 33), (29, 3), (16, 28), (31, 36), (37, 18), (3, 4), (17, 30), (15, 37), (36, 31), (19, 16), (37, 42), (25, 30), (23, 4), (14, 20), (0, 14), (1, 26), (29, 14), (8, 23), (4, 28), (27, 4), (40, 34), (38, 29), (21, 38), (33, 23), (11, 9), (28, 32), (37, 29), (28, 7), (0, 7), (17, 42), (13, 3), (3, 42), (15, 6), (23, 9), (40, 35), (29, 29), (32, 19), (14, 18), (9, 19), (33, 26), (0, 18), (22, 35), (37, 37), (38, 10), (26, 21), (24, 18), (14, 42), (32, 8), (35, 13), (38, 8), (0, 2), (6, 16), (20, 29), (25, 18), (41, 10), (8, 42), (33, 19), (29, 7), (2, 4), (21, 30), (30, 2), (43, 36), (19, 8), (22, 39), (25, 38), (37, 28), (29, 27), (10, 2), (0, 13), (10, 10), (9, 30), (7, 18), (23, 2), (5, 12), (9, 40), (5, 41), (7, 17), (31, 4), (35, 41), (21, 40), (32, 6), (43, 8), (19, 22), (28, 11), (24, 3), (14, 11), (3, 23), (16, 4), (6, 34), (40, 41), (2, 39), (33, 15), (11, 21), (23, 36), (36, 11), (42, 41), (33, 42), (6, 28), (31, 9), (6, 3), (43, 29), (28, 33), (10, 13), (15, 5), (33, 32), (11, 13), (1, 25), (13, 30), (31, 16), (26, 26), (33, 41), (35, 3), (16, 10), (3, 36), (10, 11), (40, 39), (12, 12), (0, 30), (24, 12), (7, 7), (38, 42), (7, 4), (43, 7), (28, 12), (36, 29), (25, 15), (16, 13), (29, 36), (10, 12), (6, 38), (16, 33), (18, 15), (36, 17), (22, 28), (36, 15), (31, 23), (25, 13), (15, 2), (15, 21), (2, 42), (13, 42), (35, 38), (22, 5), (9, 32), (16, 34), (27, 32), (13, 19), (37, 12), (8, 34), (3, 2), (21, 41), (12, 33), (26, 3), (14, 19), (17, 38), (29, 37), (8, 8), (32, 23), (12, 32), (10, 5), (0, 32), (35, 10), (7, 11), (41, 11), (19, 0), (17, 35), (13, 27), (11, 40), (6, 11), (40, 15), (36, 28), (8, 40), (11, 34), (31, 1), (18, 35), (28, 38), (18, 20), (17, 11), (8, 13), (41, 42), (31, 37), (1, 9), (34, 33), (10, 6), (36, 22), (43, 34), (5, 29), (5, 40), (20, 3), (8, 1), (10, 22), (41, 5), (0, 31), (32, 17), (7, 12), (5, 4), (36, 0), (30, 23), (3, 16), (41, 37), (9, 31), (25, 5), (2, 7), (16, 16), (39, 37), (29, 38), (25, 42), (38, 28), (19, 34), (33, 5), (35, 23), (7, 38), (25, 22), (24, 23), (22, 42), (33, 17), (30, 16), (14, 27), (33, 4), (38, 20), (21, 20), (28, 27), (27, 21), (28, 17), (29, 32), (16, 32), (2, 15), (4, 2), (33, 18), (29, 9), (17, 10), (3, 38), (28, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 4), (17, 37), (13, 18), (9, 17), (1, 25), (27, 7), (42, 8), (34, 8), (14, 31), (2, 25), (29, 26), (2, 35), (46, 11), (42, 29), (11, 24), (2, 18), (28, 15), (27, 14), (31, 28), (15, 13), (11, 11), (6, 26), (10, 24), (20, 13), (21, 8), (26, 10), (20, 16), (45, 32), (35, 8), (6, 11), (25, 6), (16, 24), (33, 17), (22, 23), (44, 9), (41, 20), (16, 37), (3, 39), (37, 27), (39, 12), (39, 29), (33, 7), (22, 1), (43, 35), (44, 20), (22, 14), (47, 13), (26, 24), (25, 25), (3, 23), (14, 17), (4, 0), (10, 33), (7, 7), (4, 21), (42, 9), (41, 0), (6, 2), (47, 18), (7, 36), (30, 32), (36, 36), (28, 24), (6, 17), (27, 11), (5, 11), (30, 17), (18, 31), (27, 27), (10, 26), (39, 27), (14, 21), (0, 27), (18, 27), (32, 32), (39, 13), (31, 13), (5, 2), (23, 4), (26, 13), (13, 39), (28, 35), (27, 33), (3, 36), (8, 12), (12, 37), (41, 10), (35, 39), (24, 17), (37, 29), (7, 39), (30, 19), (0, 5), (16, 27), (21, 35), (18, 37), (39, 34), (26, 7), (4, 30), (19, 33), (10, 3), (34, 22), (4, 4), (40, 14), (27, 19), (13, 6), (38, 14), (4, 3), (46, 33), (6, 34), (16, 32), (6, 0), (8, 2), (34, 24), (46, 14), (43, 29), (13, 20), (14, 29), (33, 4), (15, 33), (22, 0), (32, 13), (5, 25), (40, 9), (40, 13), (35, 17), (21, 6), (29, 30), (1, 26), (25, 4), (7, 22), (36, 12), (13, 23), (16, 2), (33, 39), (32, 21), (0, 11), (35, 23), (15, 23), (37, 34), (31, 6), (31, 27), (2, 15), (9, 31), (5, 22), (1, 28), (20, 29), (6, 23), (3, 32), (13, 10), (13, 3), (21, 38), (31, 20), (40, 10), (20, 9), (46, 27), (34, 39), (37, 11), (15, 31), (25, 38), (8, 31), (47, 26), (26, 18), (8, 4), (26, 28), (2, 6), (28, 2), (34, 32), (27, 22), (1, 17), (35, 6), (12, 20), (42, 20), (41, 37), (11, 12), (31, 12), (30, 29), (18, 32), (14, 2), (41, 2), (22, 16), (13, 8), (12, 36), (14, 8), (2, 4), (25, 35), (39, 19), (29, 14), (38, 1), (17, 38), (7, 24), (33, 35), (4, 35), (2, 26), (27, 26), (35, 24), (4, 39), (39, 38), (19, 2), (30, 26), (8, 10), (19, 17), (24, 12), (21, 5), (2, 30), (36, 8), (21, 30), (25, 37), (31, 8), (4, 29), (25, 5), (24, 16), (32, 34), (35, 32), (12, 38), (37, 13), (14, 24), (45, 11), (42, 23), (46, 16), (17, 25), (33, 13), (28, 21), (25, 36), (8, 29), (8, 3), (45, 21), (5, 13), (6, 16), (21, 7), (18, 17), (5, 4), (32, 22), (19, 1), (27, 6), (13, 29), (22, 2), (12, 31), (29, 37), (18, 3), (21, 25), (19, 27), (40, 4), (16, 22), (35, 34), (10, 6), (2, 9), (1, 1), (14, 28), (27, 17), (39, 32), (44, 7), (46, 29), (25, 17), (45, 3), (24, 23), (20, 18), (5, 27), (21, 17), (46, 7), (5, 15), (35, 16), (47, 19), (11, 32), (14, 13), (35, 33), (32, 30), (47, 36), (27, 30), (19, 32), (12, 15), (39, 23), (47, 31), (47, 0), (5, 23), (44, 29), (21, 29), (46, 23), (47, 33), (15, 20), (5, 16), (17, 6), (12, 13), (47, 8), (7, 35), (27, 38), (45, 30), (39, 6), (4, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 33), (31, 24), (42, 40), (31, 33), (27, 29), (47, 19), (8, 38), (28, 4), (46, 41), (32, 10), (13, 23), (1, 28), (6, 21), (32, 1), (5, 23), (1, 31), (24, 9), (11, 11), (43, 13), (22, 3), (24, 22), (6, 5), (12, 8), (20, 10), (48, 30), (32, 40), (45, 9), (14, 28), (46, 28), (19, 0), (0, 8), (14, 15), (48, 14), (30, 2), (23, 4), (5, 39), (7, 3), (43, 30), (13, 14), (45, 36), (26, 17), (46, 13), (25, 29), (27, 16), (7, 12), (6, 20), (20, 0), (6, 10), (3, 36), (4, 14), (6, 8), (43, 16), (2, 32), (39, 15), (0, 2), (21, 2), (22, 30), (29, 1), (10, 21), (6, 15), (4, 12), (0, 14), (43, 37), (38, 41), (0, 29), (36, 11), (25, 14), (17, 37), (27, 4), (2, 1), (20, 5), (18, 1), (17, 40), (44, 30), (9, 4), (36, 10), (9, 14), (46, 40), (6, 39), (27, 14), (10, 32), (45, 14), (29, 33), (20, 27), (30, 11), (18, 16), (3, 32), (25, 17), (27, 24), (39, 17), (24, 39), (46, 3), (36, 7), (40, 2), (40, 12), (0, 25), (12, 16), (15, 10), (39, 2), (44, 3), (21, 8), (21, 20), (46, 5), (47, 12), (17, 10), (16, 16), (22, 35), (33, 17), (47, 1), (24, 28), (3, 15), (23, 37), (26, 36), (8, 27), (44, 21), (8, 16), (17, 21), (34, 30), (8, 4), (4, 31), (21, 17), (40, 24), (48, 11), (21, 31), (44, 20), (3, 30), (38, 15), (44, 24), (45, 11), (13, 8), (11, 23), (22, 25), (32, 15), (16, 24), (21, 6), (28, 39), (38, 23), (31, 23), (46, 38), (21, 10), (20, 13), (4, 37), (28, 27), (36, 34), (45, 21), (17, 16), (13, 29), (15, 19), (27, 40), (17, 28), (23, 0), (48, 15), (20, 2), (22, 6), (24, 25), (18, 3), (15, 32), (19, 15), (8, 0), (16, 19), (6, 18), (15, 37), (33, 19), (8, 9), (16, 27), (5, 19), (3, 23), (6, 32), (36, 8), (2, 33), (18, 25), (23, 34), (23, 8), (30, 7), (21, 23), (35, 39), (26, 6), (3, 7), (21, 35), (24, 38), (4, 2), (38, 11), (3, 10), (38, 26), (9, 41), (12, 1), (42, 22), (17, 41), (5, 41), (10, 34), (41, 4), (7, 33), (47, 31), (33, 15), (26, 20), (32, 20), (46, 26), (17, 12), (31, 21), (43, 32), (24, 30), (10, 40), (13, 26), (29, 11), (18, 2), (4, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 32), (28, 40), (30, 11), (36, 13), (36, 19), (23, 23), (45, 28), (19, 15), (16, 9), (37, 38), (25, 13), (26, 2), (17, 15), (10, 0), (17, 5), (1, 35), (0, 42), (21, 10), (10, 6), (43, 34), (23, 42), (39, 24), (20, 1), (24, 5), (15, 7), (26, 18), (21, 3), (35, 27), (24, 35), (3, 34), (2, 22), (25, 6), (8, 17), (18, 1), (42, 32), (31, 11), (5, 9), (36, 31), (11, 26), (30, 30), (28, 27), (45, 33), (26, 20), (27, 26), (37, 42), (2, 19), (1, 7), (2, 16), (44, 9), (41, 12), (42, 14), (27, 36), (11, 14), (12, 31), (37, 4), (25, 22), (4, 10), (27, 8), (39, 8), (10, 20), (17, 41), (32, 3), (0, 21), (7, 13), (6, 0), (0, 36), (1, 33), (0, 27), (24, 24), (24, 13), (4, 37), (23, 20), (43, 5), (34, 36), (22, 37), (25, 11), (45, 2), (18, 36), (20, 5), (25, 1), (18, 14), (30, 26), (9, 41), (17, 27), (11, 40), (26, 17), (45, 25), (38, 42), (30, 29), (6, 39), (25, 8), (6, 35), (19, 4), (35, 18), (40, 40), (33, 0), (27, 9), (21, 24), (11, 37), (13, 23), (2, 28), (38, 1), (31, 39), (5, 40), (26, 24), (34, 19), (33, 41), (7, 30), (27, 2), (22, 19), (9, 33), (22, 5), (42, 20), (35, 12), (16, 5), (31, 24), (11, 38), (5, 11), (15, 9), (8, 36), (39, 18), (31, 6), (13, 36), (19, 34), (17, 17), (22, 18), (6, 17), (16, 31), (29, 27), (41, 16), (45, 8), (18, 35), (28, 8), (8, 3), (15, 27), (9, 18), (5, 3), (23, 35), (22, 22), (13, 33), (32, 29), (10, 1), (44, 25), (17, 13), (44, 6), (2, 36), (19, 24), (36, 36), (16, 16), (10, 17), (15, 22), (17, 26), (18, 24), (40, 25), (39, 41), (42, 5), (4, 36), (1, 32), (13, 27), (9, 17), (6, 21), (24, 7), (13, 9), (28, 37), (0, 15), (5, 34), (29, 42), (19, 3), (30, 12), (29, 11), (26, 15), (22, 36), (22, 33), (15, 8), (29, 5), (20, 21), (18, 26), (32, 1), (20, 15), (29, 21), (1, 30), (36, 35), (4, 1), (25, 14), (34, 35), (36, 22), (3, 21), (14, 9), (43, 13), (34, 21), (19, 23), (6, 8), (8, 23), (28, 13), (10, 23), (40, 21), (38, 37), (0, 38), (2, 8), (6, 3), (38, 14), (10, 34), (4, 16), (18, 16), (38, 24), (12, 4), (14, 42), (38, 22), (5, 7), (35, 0), (10, 38), (22, 35), (41, 26), (37, 23), (18, 21), (42, 42), (34, 16), (39, 9), (40, 37), (33, 25), (12, 36), (40, 39), (20, 40), (35, 20), (29, 24), (5, 42), (24, 36), (40, 34), (27, 14), (11, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 3), (37, 11), (34, 24), (16, 38), (34, 18), (35, 23), (42, 39), (41, 34), (33, 2), (35, 18), (7, 28), (30, 1), (33, 27), (30, 20), (27, 37), (26, 33), (15, 22), (36, 27), (41, 1), (11, 4), (8, 25), (4, 34), (35, 30), (3, 39), (36, 10), (28, 8), (11, 14), (17, 39), (30, 31), (41, 7), (35, 37), (25, 40), (30, 13), (20, 36), (32, 27), (8, 2), (9, 41), (36, 8), (42, 38), (20, 11), (33, 16), (14, 13), (32, 12), (8, 24), (13, 24), (2, 17), (24, 3), (13, 1), (28, 39), (21, 34), (0, 16), (33, 24), (37, 8), (38, 6), (14, 9), (30, 19), (5, 12), (37, 4), (13, 29), (39, 13), (7, 36), (34, 3), (28, 29), (6, 6), (37, 3), (2, 39), (25, 28), (22, 11), (9, 14), (30, 39), (39, 38), (31, 22), (36, 39), (29, 16), (12, 37), (30, 16), (29, 28), (31, 4), (12, 17), (6, 30), (13, 39), (20, 10), (25, 8), (33, 32), (31, 37), (16, 17), (3, 27), (38, 13), (14, 5), (3, 10), (39, 28), (30, 17), (20, 7), (18, 39), (40, 20), (36, 19), (12, 27), (15, 32), (2, 38), (42, 28), (16, 2), (42, 5), (1, 15), (41, 28), (25, 33), (31, 6), (43, 35), (42, 37), (34, 5), (15, 40), (38, 20), (23, 24), (20, 5), (30, 30), (21, 5), (18, 21), (43, 38), (27, 11), (34, 8), (11, 28), (9, 33), (13, 26), (26, 0), (37, 32), (39, 5), (8, 4), (38, 17), (6, 8), (25, 10), (43, 13), (4, 1), (33, 17), (29, 33), (34, 21), (43, 22), (42, 1), (32, 15), (37, 26), (32, 10), (2, 28), (19, 31), (28, 17), (24, 13), (30, 38), (15, 37), (5, 27), (31, 30), (18, 4), (32, 6), (41, 2), (28, 40), (0, 19), (8, 27), (30, 37), (38, 0), (21, 9), (36, 17), (33, 39), (9, 8), (20, 23), (27, 23), (2, 23), (9, 9), (11, 2), (36, 1), (4, 13), (25, 26), (24, 2), (1, 22), (25, 17), (41, 25), (24, 38), (37, 35), (39, 7), (5, 3), (38, 12), (23, 26), (24, 36), (20, 21), (38, 25), (36, 32), (24, 25), (33, 5), (29, 18), (0, 13), (35, 2), (43, 26), (2, 41), (21, 30), (29, 30), (9, 3), (18, 33), (41, 40), (33, 1), (33, 28), (24, 37), (18, 17), (43, 18), (34, 17), (43, 24), (37, 33), (14, 3), (43, 31), (24, 6), (37, 40), (43, 20), (11, 40), (5, 21), (6, 21), (36, 33), (12, 36), (24, 27), (11, 30), (15, 27), (22, 20), (7, 31), (31, 0), (39, 2), (18, 11), (16, 1), (15, 18), (27, 36), (2, 26), (40, 9), (8, 29), (42, 9), (40, 10), (13, 28), (41, 20), (38, 4), (19, 24), (36, 31), (14, 32), (40, 11), (9, 19), (4, 37), (23, 30), (37, 28), (23, 9), (17, 32), (3, 7), (0, 10), (10, 37), (6, 41), (29, 15), (35, 19), (5, 17), (24, 39), (1, 27), (33, 11), (2, 2), (16, 15), (19, 36), (25, 1), (5, 23), (9, 22), (20, 8), (31, 32), (27, 3), (9, 28), (4, 19), (21, 12), (15, 36), (19, 40), (37, 14), (7, 24), (21, 1), (0, 3), (1, 0), (18, 3), (23, 7), (31, 38), (12, 29), (15, 15), (3, 19), (34, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 34), (18, 20), (34, 34), (35, 7), (40, 19), (20, 38), (33, 16), (8, 38), (35, 31), (12, 21), (28, 1), (34, 12), (29, 25), (37, 20), (8, 2), (36, 12), (16, 32), (29, 1), (1, 35), (34, 30), (4, 2), (3, 24), (31, 24), (2, 26), (27, 24), (18, 23), (36, 40), (28, 31), (4, 10), (41, 14), (31, 25), (10, 22), (22, 30), (6, 9), (14, 15), (35, 16), (32, 5), (12, 1), (27, 7), (30, 19), (20, 34), (10, 10), (40, 41), (4, 39), (42, 4), (2, 7), (12, 13), (37, 26), (30, 15), (8, 20), (8, 25), (28, 36), (31, 18), (41, 36), (25, 33), (20, 8), (36, 32), (43, 27), (35, 3), (21, 28), (1, 37), (10, 6), (12, 39), (38, 15), (14, 13), (8, 27), (24, 22), (21, 22), (16, 0), (11, 11), (15, 8), (7, 5), (32, 15), (22, 2), (39, 40), (4, 37), (23, 29), (21, 4), (36, 22), (36, 30), (3, 37), (0, 7), (32, 24), (25, 3), (20, 21), (14, 41), (20, 24), (24, 34), (32, 41), (27, 33), (16, 10), (11, 18), (16, 11), (18, 8), (37, 11), (27, 16), (6, 12), (8, 36), (12, 24), (20, 33), (40, 15), (23, 30), (6, 28), (43, 30), (24, 13), (1, 2), (3, 10), (39, 25), (30, 24), (7, 18), (38, 3), (37, 39), (11, 0), (37, 13), (7, 4), (4, 1), (19, 39), (17, 9), (37, 38), (41, 35), (32, 38), (20, 39), (41, 12), (4, 31), (17, 12), (25, 14), (16, 17), (37, 22), (40, 24), (18, 22), (23, 3), (36, 16), (13, 18), (13, 22), (43, 18), (36, 0), (17, 5), (41, 34), (0, 6), (24, 12), (13, 1), (16, 36), (41, 8), (3, 2), (42, 18), (42, 33), (14, 24), (15, 39), (31, 17), (8, 37), (11, 38), (40, 20), (7, 1), (35, 27), (5, 18), (15, 3), (12, 40), (26, 24), (27, 41), (13, 8), (33, 36), (14, 5), (17, 11), (32, 39), (9, 39), (40, 17), (36, 27), (7, 21), (7, 6), (18, 2), (15, 6), (1, 8), (10, 23), (8, 14), (15, 17), (21, 0), (11, 22), (7, 23), (27, 29), (2, 19), (13, 36), (9, 10), (35, 13), (0, 40), (40, 21), (6, 39), (14, 4), (36, 25), (15, 32), (11, 35), (4, 20), (0, 13), (28, 26), (43, 39), (22, 32), (21, 29), (23, 11), (9, 6), (5, 0), (23, 20), (1, 28), (16, 6), (25, 39), (35, 34), (20, 16), (14, 35), (30, 34), (27, 36), (26, 22), (16, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 34), (15, 25), (1, 26), (13, 21), (24, 38), (16, 12), (28, 16), (43, 0), (5, 25), (6, 30), (39, 34), (42, 33), (39, 27), (36, 32), (37, 39), (21, 33), (33, 11), (18, 30), (14, 34), (18, 15), (26, 4), (13, 27), (28, 41), (43, 14), (20, 1), (3, 12), (28, 31), (12, 12), (4, 31), (22, 25), (20, 19), (22, 13), (33, 30), (8, 21), (29, 11), (20, 39), (37, 1), (43, 36), (36, 28), (31, 34), (8, 1), (21, 8), (23, 9), (2, 3), (14, 36), (4, 6), (6, 16), (1, 2), (11, 26), (15, 5), (10, 30), (21, 6), (3, 35), (12, 39), (8, 39), (20, 3), (37, 41), (37, 21), (22, 33), (5, 39), (2, 38), (15, 21), (11, 39), (22, 5), (32, 15), (30, 41), (10, 16), (8, 36), (16, 7), (40, 17), (30, 40), (14, 17), (17, 5), (26, 41), (5, 13), (36, 20), (38, 1), (40, 15), (37, 36), (20, 17), (11, 9), (37, 24), (15, 16), (7, 4), (19, 26), (6, 3), (25, 38), (1, 9), (11, 40), (1, 11), (33, 7), (43, 38), (40, 40), (22, 35), (26, 8), (2, 26), (7, 2), (27, 35), (17, 20), (14, 25), (27, 25), (40, 31), (28, 2), (23, 24), (5, 23), (38, 30), (34, 10), (14, 39), (1, 22), (42, 0), (26, 3), (32, 12), (29, 37), (21, 16), (5, 1), (17, 17), (13, 1), (42, 21), (31, 10), (1, 30), (28, 8), (11, 41), (38, 19), (18, 29), (0, 38), (29, 36), (33, 21), (30, 34), (32, 2), (13, 2), (14, 7), (2, 20), (3, 3), (42, 37), (9, 32), (13, 4), (37, 18), (5, 18), (32, 36), (41, 16), (29, 41), (9, 20), (26, 1), (23, 1), (32, 40), (22, 0), (8, 20), (38, 23), (32, 7), (26, 22), (31, 36), (6, 21), (43, 16), (33, 40), (16, 36), (36, 30), (41, 25), (22, 38), (12, 29), (1, 27), (35, 29), (36, 33), (12, 9), (27, 6), (27, 11), (19, 22), (28, 25), (30, 28), (23, 22), (41, 5), (2, 24), (36, 39), (32, 4), (43, 11), (40, 4), (38, 2), (24, 2), (33, 39), (30, 4), (41, 33), (26, 39), (33, 28), (17, 28), (3, 18), (12, 40), (0, 40), (40, 27), (15, 22), (35, 15), (3, 41), (11, 29), (23, 23), (28, 38), (12, 36), (32, 32), (25, 0), (12, 16), (39, 7), (39, 38), (41, 17), (30, 23), (17, 10), (10, 0), (21, 1), (9, 37), (24, 36), (15, 4), (43, 18), (28, 20), (18, 40), (24, 25), (37, 10), (17, 25), (5, 4), (25, 7), (12, 35), (21, 29), (12, 4), (20, 23), (39, 32), (2, 30), (7, 17), (28, 23), (14, 8), (1, 5), (12, 38), (17, 7), (15, 37), (6, 35), (33, 24), (4, 33), (42, 29), (7, 37), (25, 37), (17, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 5), (41, 2), (40, 11), (13, 3), (41, 20), (12, 23), (35, 39), (1, 34), (23, 14), (29, 29), (25, 1), (14, 5), (22, 23), (29, 9), (14, 9), (11, 37), (17, 36), (26, 32), (35, 23), (37, 1), (4, 2), (32, 27), (17, 5), (21, 4), (14, 18), (12, 36), (1, 42), (36, 43), (6, 2), (25, 18), (39, 39), (32, 9), (34, 23), (36, 38), (21, 42), (32, 40), (19, 10), (37, 4), (9, 8), (17, 42), (9, 19), (5, 25), (35, 8), (14, 28), (2, 18), (13, 31), (18, 16), (40, 38), (6, 18), (22, 14), (5, 15), (29, 20), (6, 36), (21, 33), (37, 42), (0, 6), (5, 29), (17, 29), (16, 18), (33, 34), (22, 21), (25, 31), (7, 10), (0, 38), (32, 17), (21, 41), (28, 18), (9, 34), (34, 11), (34, 36), (0, 33), (9, 18), (19, 29), (40, 42), (34, 32), (0, 2), (30, 23), (5, 28), (37, 2), (15, 35), (6, 14), (27, 2), (29, 21), (19, 41), (20, 42), (22, 7), (34, 10), (6, 38), (0, 41), (22, 8), (36, 9), (39, 38), (30, 24), (21, 30), (35, 1), (40, 14), (33, 13), (3, 38), (34, 0), (9, 14), (26, 7), (3, 17), (18, 10), (24, 21), (29, 10), (31, 38), (16, 36), (17, 18), (25, 13), (12, 37), (26, 25), (3, 39), (33, 3), (9, 3), (33, 9), (10, 34), (22, 26), (26, 2), (8, 30), (5, 9), (6, 30), (19, 33), (20, 28), (16, 41), (28, 12), (4, 16), (4, 22), (16, 43), (0, 39), (18, 34), (9, 21), (30, 16), (10, 19), (7, 18), (20, 10), (39, 17), (21, 24), (16, 3), (34, 6), (34, 30), (12, 42), (9, 10), (7, 26), (31, 24), (6, 43), (25, 36), (22, 34), (25, 35), (8, 10), (41, 23), (20, 20), (40, 31), (28, 14), (18, 32), (35, 10), (32, 33), (2, 9), (38, 35), (15, 20), (41, 8), (22, 40), (27, 7), (28, 41), (22, 36), (4, 6), (40, 41), (37, 15), (36, 10), (16, 28), (19, 24), (19, 14), (29, 33), (8, 7), (29, 12), (7, 31), (9, 31), (20, 22), (22, 6), (20, 35), (39, 24), (16, 14), (18, 40), (7, 7), (11, 3), (9, 32), (4, 39), (22, 13), (14, 0), (20, 30), (2, 23), (28, 37), (1, 15), (11, 42), (19, 9), (40, 0), (23, 35), (17, 25), (26, 27), (28, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 38), (10, 47), (9, 1), (10, 19), (24, 5), (45, 37), (26, 22), (28, 13), (20, 41), (42, 3), (43, 25), (13, 17), (10, 24), (10, 21), (44, 13), (35, 43), (13, 37), (26, 11), (37, 43), (29, 14), (42, 13), (28, 5), (13, 5), (1, 17), (7, 9), (21, 22), (36, 22), (36, 30), (12, 13), (4, 7), (5, 38), (33, 8), (9, 22), (41, 1), (4, 27), (43, 32), (45, 6), (28, 7), (23, 17), (43, 27), (45, 5), (17, 31), (46, 9), (26, 17), (29, 41), (27, 17), (41, 26), (13, 13), (19, 15), (43, 8), (24, 11), (18, 17), (11, 0), (37, 16), (21, 10), (23, 43), (35, 35), (8, 33), (37, 8), (14, 9), (17, 47), (12, 33), (1, 5), (46, 2), (18, 33), (45, 34), (30, 35), (33, 36), (15, 34), (3, 11), (15, 38), (11, 29), (31, 18), (26, 25), (11, 14), (42, 11), (26, 48), (4, 30), (4, 40), (45, 18), (21, 24), (35, 8), (21, 47), (3, 42), (22, 12), (13, 11), (40, 25), (40, 14), (41, 43), (46, 15), (33, 45), (25, 10), (3, 0), (3, 7), (13, 21), (31, 6), (39, 6), (0, 31), (31, 2), (45, 3), (7, 21), (5, 11), (3, 27), (29, 37), (43, 28), (21, 25), (32, 22), (38, 3), (2, 38), (11, 15), (14, 34), (33, 3), (8, 40), (30, 37), (11, 45), (13, 47), (8, 37), (42, 28), (6, 32), (27, 7), (4, 0), (43, 46), (20, 20), (19, 20), (16, 44), (31, 24), (30, 40), (24, 14), (10, 44), (36, 25), (5, 41), (2, 27), (45, 30), (2, 31), (7, 47), (37, 17), (35, 37), (25, 14), (21, 42), (35, 11), (34, 15), (17, 39), (22, 16), (24, 23), (37, 1), (42, 21), (18, 22), (2, 39), (40, 16), (4, 36), (39, 11), (3, 36), (17, 29), (44, 23), (11, 8), (22, 44), (19, 21), (37, 20), (28, 44), (14, 38), (11, 25), (21, 38), (8, 46), (3, 48), (41, 12), (42, 41), (25, 3), (31, 39), (27, 9), (19, 14), (42, 43), (1, 6), (14, 27), (19, 30), (2, 32), (25, 11), (22, 8), (32, 24), (32, 26), (14, 43), (20, 38), (31, 16), (25, 5), (2, 36), (46, 14), (41, 22), (9, 48), (15, 11), (16, 34), (30, 14), (6, 1), (9, 26), (1, 31), (39, 13), (40, 3), (21, 13), (16, 10), (1, 12), (10, 32), (27, 39), (2, 23), (46, 10), (4, 47), (8, 24), (32, 44), (5, 20), (15, 23), (9, 14), (27, 6), (31, 29), (28, 14), (2, 41), (26, 35), (8, 7), (20, 22), (6, 0), (4, 38), (12, 27), (11, 16), (39, 25), (32, 43), (45, 47), (21, 34), (28, 21), (25, 1), (3, 45), (32, 39), (27, 1), (34, 40), (0, 43), (31, 40), (23, 20), (23, 3), (0, 27), (39, 16), (1, 14), (43, 13), (44, 8), (11, 13), (21, 16), (23, 39), (10, 22), (22, 40), (9, 23), (7, 5), (20, 47), (12, 39), (21, 33), (16, 30), (10, 38), (28, 43), (22, 33), (24, 0), (40, 13), (40, 20), (45, 48), (39, 42), (30, 5), (19, 26), (6, 14), (6, 42), (9, 17), (2, 26), (17, 22), (13, 19), (43, 2), (15, 45), (41, 38), (6, 22), (40, 10), (41, 10), (0, 15), (13, 6), (45, 20), (35, 48), (43, 7), (3, 23), (12, 9), (7, 14), (45, 25), (26, 12), (14, 24), (24, 20), (7, 31), (23, 34), (31, 11), (26, 31), (24, 44), (11, 3), (43, 29), (5, 18), (31, 7), (27, 23), (41, 29), (35, 28), (15, 46), (20, 33), (0, 26), (9, 28), (29, 43), (24, 22), (6, 45), (41, 48), (6, 3), (45, 35), (32, 42), (3, 40), (18, 2), (22, 24), (32, 4), (43, 35), (19, 39), (28, 40), (13, 0), (5, 45), (37, 0), (43, 34), (35, 2), (14, 17), (20, 44), (46, 6), (43, 37), (7, 7), (43, 14), (26, 32), (0, 19), (37, 11), (5, 7), (24, 4), (14, 28), (32, 21), (46, 33), (19, 34), (33, 20), (3, 15), (22, 42), (17, 19), (41, 32), (9, 35), (16, 45), (11, 7), (4, 2), (46, 31), (36, 41), (30, 12), (20, 5), (7, 24), (35, 18), (44, 12), (24, 37), (35, 14), (34, 1), (11, 17), (4, 13), (39, 12), (35, 6), (20, 12), (39, 29), (9, 42), (11, 33), (31, 47), (41, 27), (46, 13), (0, 37), (35, 13), (35, 38), (26, 16), (2, 4), (23, 40), (9, 41), (13, 15), (38, 44), (36, 44), (17, 40), (46, 19), (13, 34), (12, 20), (26, 18), (36, 32), (33, 2), (16, 9), (46, 37), (0, 23), (39, 40), (42, 5), (9, 33), (29, 12), (3, 17), (28, 19), (38, 48)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 27), (39, 0), (3, 17), (10, 9), (35, 22), (48, 19), (2, 5), (1, 34), (42, 32), (37, 13), (20, 39), (6, 23), (47, 37), (9, 6), (14, 25), (25, 27), (32, 6), (21, 33), (38, 15), (44, 21), (30, 34), (11, 29), (46, 37), (4, 21), (5, 17), (11, 3), (27, 40), (15, 1), (40, 15), (34, 22), (42, 31), (39, 16), (48, 10), (35, 10), (7, 12), (9, 32), (20, 16), (35, 19), (43, 9), (44, 30), (45, 6), (20, 24), (9, 21), (43, 39), (4, 10), (4, 4), (48, 7), (31, 32), (29, 11), (10, 1), (6, 15), (41, 10), (45, 9), (31, 26), (2, 24), (12, 38), (21, 40), (32, 34), (44, 9), (34, 30), (7, 24), (11, 15), (7, 33), (17, 24), (42, 30), (42, 13), (42, 4), (21, 35), (18, 36), (2, 18), (11, 9), (14, 23), (46, 29), (19, 39), (12, 24), (33, 12), (33, 18), (26, 31), (6, 38), (24, 25), (15, 10), (13, 15), (48, 20), (0, 3), (46, 40), (21, 25), (30, 31), (5, 14), (0, 20), (31, 7), (40, 14), (38, 31), (33, 2), (41, 5), (26, 37), (1, 21), (35, 23), (35, 20), (32, 16), (12, 12), (28, 32), (10, 35), (0, 28), (12, 2), (13, 35), (27, 24), (35, 41), (34, 0), (41, 2), (24, 3), (17, 3), (24, 18), (45, 3), (23, 3), (38, 13), (10, 10), (20, 7), (12, 0), (34, 9), (16, 31), (10, 16), (44, 24), (26, 21), (13, 25), (4, 2), (41, 34), (25, 5), (21, 3), (17, 21), (14, 33), (16, 1), (41, 9), (24, 16), (6, 3), (22, 29), (44, 7), (38, 30), (31, 22), (38, 20), (22, 19), (30, 18), (5, 38), (41, 35), (4, 23), (44, 33), (33, 28), (48, 27), (42, 11), (39, 33), (8, 7), (40, 35), (35, 1), (40, 10), (6, 26), (41, 24), (23, 35), (23, 6), (10, 25), (48, 15), (4, 34), (29, 10), (13, 3), (2, 19), (3, 31), (9, 36), (37, 40), (6, 9), (23, 18), (18, 41), (26, 38), (47, 20), (26, 32), (3, 27), (40, 23), (30, 3), (33, 34), (11, 26), (1, 27), (15, 40), (38, 14), (29, 39), (23, 23), (5, 9), (29, 18), (18, 38), (35, 18), (41, 13), (7, 5), (7, 4), (13, 38), (38, 28), (15, 27), (34, 38), (41, 29), (11, 4), (2, 35), (7, 26), (8, 39), (13, 24), (1, 18), (11, 31), (20, 15), (46, 4), (29, 17), (20, 19), (46, 6), (29, 15), (9, 27), (0, 21), (31, 34), (17, 13), (24, 1), (0, 8), (19, 4), (34, 7), (30, 27), (1, 17), (1, 8), (24, 12), (27, 2), (8, 18), (12, 26), (41, 23), (8, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 31), (14, 44), (26, 8), (38, 28), (5, 19), (13, 29), (15, 29), (11, 10), (31, 1), (17, 5), (20, 11), (7, 18), (13, 37), (26, 26), (15, 48), (23, 25), (23, 4), (15, 26), (17, 31), (7, 15), (21, 2), (19, 27), (7, 20), (37, 15), (9, 36), (21, 5), (7, 29), (0, 44), (30, 41), (5, 6), (41, 40), (23, 20), (0, 16), (8, 5), (7, 14), (18, 39), (13, 3), (5, 31), (22, 41), (10, 36), (5, 33), (29, 46), (17, 39), (37, 5), (36, 6), (26, 31), (29, 2), (12, 27), (3, 18), (45, 0), (33, 26), (8, 7), (26, 14), (20, 47), (7, 19), (15, 0), (12, 25), (22, 36), (24, 38), (43, 13), (25, 26), (40, 3), (10, 20), (36, 27), (17, 0), (11, 38), (16, 48), (15, 17), (3, 47), (37, 10), (1, 42), (19, 14), (28, 7), (16, 43), (23, 44), (24, 25), (19, 24), (22, 28), (24, 0), (21, 48), (22, 33), (23, 8), (31, 33), (20, 21), (19, 41), (39, 40), (22, 16), (8, 44), (32, 12), (39, 30), (15, 15), (13, 7), (9, 22), (13, 1), (43, 37), (20, 34), (8, 47), (34, 33), (24, 6), (40, 36), (42, 30), (27, 38), (1, 31), (13, 16), (27, 0), (13, 23), (31, 39), (44, 4), (28, 39), (43, 35), (19, 39), (16, 13), (24, 31), (37, 20), (37, 30), (27, 12), (23, 30), (8, 12), (17, 37), (19, 20), (36, 16), (4, 42), (20, 29), (1, 24), (13, 40), (30, 5), (40, 28), (10, 32), (8, 9), (4, 43), (37, 26), (38, 16), (1, 48), (39, 15), (44, 40), (5, 10), (45, 36), (24, 41), (38, 7), (16, 42), (44, 35), (25, 36), (28, 18), (32, 43), (17, 46), (23, 18), (42, 16), (33, 8), (22, 4), (26, 28), (0, 37), (29, 23), (14, 35), (23, 5), (19, 23), (39, 32), (44, 8), (4, 7), (10, 44), (29, 9), (13, 25), (16, 16), (14, 6), (10, 10), (32, 45), (5, 2), (17, 3), (3, 42), (23, 9), (15, 42), (11, 42), (36, 37), (28, 21), (11, 6), (28, 46), (10, 17), (45, 14), (32, 10), (45, 43), (36, 0), (40, 20), (10, 27), (0, 12), (38, 46), (41, 7), (21, 30), (38, 14), (37, 11), (31, 43), (5, 42), (39, 6), (42, 37), (9, 43), (35, 0), (45, 32), (25, 7), (30, 8), (17, 36), (24, 2), (15, 31), (15, 41), (3, 48), (30, 33), (3, 39), (12, 14), (28, 5), (31, 46), (33, 29), (29, 4), (44, 1), (30, 42), (15, 46), (36, 10), (30, 12), (17, 13), (33, 4), (35, 2), (9, 8), (28, 0), (3, 1), (33, 43), (15, 22), (16, 41), (10, 48), (17, 22), (31, 32), (18, 45), (12, 10), (19, 25), (17, 44), (28, 40), (25, 27), (11, 35), (25, 14), (1, 6), (3, 36), (2, 41), (33, 12), (13, 41), (13, 12), (4, 41), (40, 16), (44, 39), (7, 26), (2, 18), (26, 27), (8, 31), (5, 48), (4, 39), (13, 36), (10, 5), (34, 37), (40, 19), (9, 37), (2, 16), (22, 35), (39, 43), (23, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 45), (35, 4), (31, 4), (26, 29), (2, 10), (17, 47), (16, 10), (39, 4), (0, 3), (10, 9), (20, 24), (23, 48), (9, 34), (7, 0), (25, 14), (9, 11), (29, 4), (10, 2), (8, 16), (15, 1), (30, 10), (8, 29), (19, 36), (34, 12), (5, 45), (17, 4), (24, 47), (9, 1), (7, 36), (21, 36), (33, 21), (26, 20), (36, 8), (32, 44), (11, 34), (32, 4), (20, 23), (18, 5), (4, 32), (23, 37), (32, 29), (0, 22), (16, 0), (26, 34), (16, 48), (35, 43), (5, 2), (17, 31), (26, 28), (19, 11), (36, 22), (35, 0), (26, 42), (33, 7), (31, 7), (25, 36), (29, 14), (29, 12), (7, 40), (21, 1), (6, 13), (25, 4), (26, 14), (26, 13), (18, 36), (11, 44), (19, 35), (4, 14), (21, 28), (32, 11), (0, 39), (8, 38), (13, 18), (10, 43), (33, 8), (24, 42), (9, 19), (16, 2), (8, 11), (16, 16), (23, 3), (2, 26), (23, 22), (6, 29), (12, 12), (9, 27), (29, 18), (22, 37), (28, 0), (9, 31), (8, 44), (32, 13), (6, 19), (2, 34), (5, 4), (19, 9), (7, 32), (14, 24), (25, 26), (21, 30), (31, 33), (6, 9), (28, 30), (9, 16), (24, 13), (1, 44), (34, 23), (4, 20), (24, 10), (7, 10), (1, 47), (22, 12), (7, 8), (25, 38), (21, 11), (20, 30), (1, 3), (13, 42), (34, 11), (11, 35), (31, 36), (17, 18), (20, 29), (19, 48), (23, 17), (34, 31), (15, 4), (37, 10), (36, 35), (3, 47), (1, 32), (18, 14), (33, 43), (10, 17), (2, 43), (4, 25), (3, 19), (7, 9), (25, 46), (8, 1), (34, 19), (21, 35), (39, 8), (20, 43), (9, 22), (33, 20), (17, 14), (38, 13), (30, 11), (0, 1), (36, 10), (7, 28), (35, 5), (39, 26), (34, 35), (19, 16), (39, 2), (19, 19), (32, 12), (15, 10), (35, 22), (24, 46), (9, 37), (36, 47), (38, 44), (22, 10), (17, 35), (17, 28), (19, 27), (27, 41), (22, 41), (35, 12), (14, 44), (39, 3), (5, 28), (13, 45), (13, 30), (17, 41), (25, 24), (15, 40), (11, 11), (35, 8), (34, 30), (33, 39), (10, 40), (19, 26), (39, 32), (12, 27), (4, 18), (39, 21), (7, 24), (35, 7), (28, 42), (21, 12), (11, 24), (0, 33), (34, 47), (20, 7), (35, 28), (23, 8), (15, 9), (3, 42), (38, 41), (18, 47), (23, 30), (34, 15), (30, 18), (5, 42), (0, 8), (25, 32), (39, 20), (12, 29), (0, 15), (23, 43), (3, 48), (27, 16), (36, 3), (36, 46), (39, 28), (0, 4), (23, 41), (26, 19), (21, 17), (3, 35), (7, 18), (30, 1), (25, 33), (38, 12), (22, 44), (22, 17), (13, 17), (7, 42), (24, 26), (34, 0), (21, 15), (19, 32), (11, 13), (1, 37), (6, 12), (35, 13), (25, 22), (3, 3), (5, 16), (1, 23), (35, 19), (10, 10), (12, 36), (39, 12), (22, 36), (21, 41), (13, 9), (26, 33), (7, 44), (31, 44), (14, 39), (39, 13), (11, 3), (17, 6), (2, 24), (5, 22), (14, 14), (1, 26), (23, 45), (10, 23), (1, 20), (33, 26), (6, 34), (12, 6), (17, 39), (20, 45), (12, 15), (7, 12), (26, 7), (4, 1), (33, 25), (3, 15), (36, 24), (22, 6), (25, 44), (6, 33), (17, 43), (26, 30), (37, 19), (18, 33), (10, 11), (39, 33), (24, 1), (7, 4), (19, 29), (17, 19), (3, 44), (10, 15), (6, 44), (5, 34), (39, 42), (2, 46), (25, 28), (17, 12), (37, 38), (22, 14), (5, 20), (18, 16), (12, 28), (30, 48), (29, 32), (13, 6), (12, 24), (13, 21), (26, 36), (22, 25), (14, 12), (10, 48), (30, 34), (30, 24), (0, 2), (7, 23), (26, 47), (18, 9), (31, 48), (4, 35), (38, 43), (37, 29), (28, 6), (7, 5), (22, 13), (37, 4), (15, 30), (9, 42), (1, 28), (33, 16), (14, 42), (29, 28), (29, 13), (21, 44), (34, 24), (7, 11), (0, 48), (0, 26), (31, 23), (26, 32), (28, 13), (35, 44), (38, 48), (3, 39), (39, 29), (7, 6), (17, 16), (13, 2), (3, 12), (36, 7), (16, 22), (20, 44), (38, 36), (4, 40), (21, 32), (3, 33), (6, 40), (5, 17), (15, 23), (30, 33), (18, 10), (29, 27), (6, 32), (8, 37), (8, 13), (36, 28), (25, 0), (16, 35), (23, 31), (33, 11), (20, 13), (36, 39), (17, 38), (21, 19), (10, 12), (4, 29), (26, 39), (7, 41), (11, 7), (10, 26), (36, 37), (9, 28), (29, 48), (11, 38), (17, 46), (3, 10), (14, 45), (4, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 30), (34, 32), (1, 22), (3, 12), (33, 1), (1, 33), (4, 40), (4, 16), (25, 20), (23, 6), (7, 17), (7, 5), (8, 12), (2, 28), (3, 22), (24, 2), (1, 9), (12, 37), (23, 5), (37, 0), (7, 32), (7, 34), (10, 13), (25, 40), (4, 31), (34, 15), (17, 12), (23, 18), (30, 0), (0, 11), (38, 30), (12, 15), (39, 26), (32, 40), (36, 38), (7, 2), (5, 40), (11, 30), (30, 38), (7, 27), (26, 24), (10, 40), (21, 3), (18, 24), (37, 34), (9, 22), (12, 30), (9, 36), (39, 11), (8, 40), (35, 33), (6, 29), (1, 25), (2, 9), (15, 33), (11, 20), (10, 6), (30, 29), (22, 7), (28, 25), (24, 4), (21, 0), (30, 1), (1, 1), (17, 26), (3, 4), (29, 6), (8, 9), (23, 1), (35, 9), (32, 39), (23, 9), (36, 2), (13, 35), (3, 6), (33, 32), (18, 38), (20, 14), (5, 7), (16, 20), (22, 24), (39, 35), (31, 21), (35, 17), (36, 37), (22, 8), (20, 38), (16, 8), (35, 29), (1, 8), (30, 35), (34, 19), (29, 19), (7, 30), (14, 39), (10, 24), (28, 21), (36, 34), (12, 31), (24, 36), (20, 39), (34, 7), (30, 13), (39, 10), (26, 15), (20, 22), (0, 9), (25, 33), (28, 30), (12, 27), (24, 5), (26, 1), (21, 2), (13, 33), (13, 1), (37, 31), (4, 3), (4, 34), (20, 3), (32, 20), (19, 20), (14, 5), (33, 12), (24, 40), (34, 25), (29, 30), (21, 27), (32, 32), (24, 1), (5, 2), (19, 3), (20, 15), (35, 26), (36, 9), (28, 19), (19, 22), (32, 29), (7, 22), (19, 13), (34, 33), (1, 24), (22, 34), (16, 25), (27, 10), (17, 23), (2, 5), (20, 34), (24, 23), (5, 11), (11, 1), (13, 26), (23, 17), (17, 24), (33, 28), (25, 22), (8, 31), (39, 18), (22, 17), (14, 40), (22, 20), (12, 5), (32, 36), (2, 33), (9, 4), (22, 32), (7, 35), (39, 2), (25, 25), (34, 26), (25, 7), (13, 22), (13, 6), (15, 1), (27, 4), (28, 34), (39, 32), (6, 5), (28, 10), (23, 22), (18, 28), (10, 11), (25, 24), (26, 18), (13, 31), (1, 27), (29, 22), (24, 13), (6, 19), (19, 24), (9, 9), (28, 36), (1, 2), (9, 19), (22, 27), (30, 28), (6, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 16), (0, 20), (36, 46), (43, 44), (35, 45), (36, 16), (39, 41), (15, 47), (21, 47), (25, 41), (17, 26), (16, 17), (10, 12), (34, 39), (21, 40), (21, 4), (13, 41), (25, 37), (32, 17), (19, 33), (1, 5), (23, 23), (11, 3), (12, 5), (28, 1), (34, 21), (36, 39), (36, 26), (22, 7), (18, 23), (8, 6), (16, 35), (2, 8), (31, 2), (40, 25), (23, 25), (8, 46), (42, 36), (7, 31), (41, 36), (2, 37), (12, 25), (28, 35), (43, 17), (3, 15), (40, 46), (33, 28), (16, 36), (1, 46), (38, 29), (38, 14), (1, 29), (1, 13), (24, 40), (4, 30), (20, 17), (10, 19), (7, 34), (36, 7), (42, 12), (43, 7), (11, 42), (26, 2), (33, 10), (43, 24), (32, 32), (24, 35), (6, 40), (15, 41), (19, 18), (14, 18), (5, 45), (14, 31), (27, 39), (18, 47), (8, 22), (27, 31), (13, 35), (19, 20), (5, 17), (31, 27), (12, 42), (35, 13), (10, 31), (16, 38), (29, 30), (17, 3), (34, 42), (12, 0), (32, 37), (30, 12), (37, 33), (42, 28), (3, 35), (24, 37), (26, 3), (13, 46), (11, 9), (9, 3), (27, 2), (0, 33), (1, 23), (10, 30), (22, 3), (27, 33), (16, 40), (31, 14), (29, 36), (13, 40), (34, 35), (12, 31), (23, 47), (36, 18), (25, 9), (42, 23), (8, 37), (5, 15), (37, 40), (20, 43), (19, 8), (22, 29), (23, 12), (41, 22), (22, 41), (31, 3), (32, 14), (6, 19), (19, 4), (28, 16), (10, 9), (2, 25), (4, 27), (20, 47), (37, 0), (40, 39), (14, 32), (10, 24), (38, 46), (28, 11), (14, 26), (32, 43), (4, 6), (35, 6), (2, 18), (16, 12), (41, 39), (5, 3), (4, 43), (4, 37), (37, 7), (40, 43), (33, 8), (7, 44), (20, 0), (22, 46), (17, 16), (20, 42), (10, 34), (16, 26), (20, 25), (30, 17), (11, 26), (7, 46), (30, 6), (21, 14), (12, 6), (18, 37), (6, 41), (30, 28), (42, 31), (9, 26), (15, 22), (2, 47), (28, 6), (19, 23), (35, 24), (28, 20), (32, 21), (42, 9), (39, 15), (13, 12), (11, 43), (29, 7), (8, 26), (1, 24), (40, 17), (29, 25), (21, 39), (38, 13), (40, 10), (9, 8), (35, 44), (40, 3), (6, 26), (38, 33), (0, 22), (2, 44), (14, 40), (19, 9), (15, 24), (5, 16), (13, 4), (25, 32), (5, 31), (16, 25), (39, 6), (15, 0), (14, 33), (36, 21), (23, 45), (21, 11), (30, 0), (41, 17), (34, 22), (15, 13), (37, 44), (22, 18), (23, 27), (27, 30), (16, 31), (1, 44), (38, 32), (15, 20), (16, 45), (42, 39), (30, 38), (13, 33), (12, 45), (3, 44), (17, 11), (37, 5), (31, 45), (7, 39), (24, 17), (26, 8), (30, 33), (1, 0), (11, 35), (38, 45), (10, 17), (21, 46), (43, 2), (19, 15), (41, 45), (2, 42), (36, 30), (7, 45), (32, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 15), (18, 35), (23, 14), (10, 36), (13, 40), (26, 18), (35, 48), (11, 36), (3, 24), (12, 45), (21, 19), (0, 9), (1, 48), (13, 11), (35, 42), (25, 26), (5, 8), (26, 41), (23, 24), (16, 1), (29, 29), (29, 40), (2, 26), (27, 10), (1, 29), (10, 32), (19, 9), (7, 36), (17, 39), (11, 21), (33, 20), (38, 22), (1, 1), (10, 23), (0, 28), (31, 32), (27, 48), (29, 48), (33, 15), (35, 34), (27, 9), (17, 4), (28, 26), (8, 46), (16, 0), (20, 19), (15, 36), (37, 22), (0, 39), (37, 10), (26, 28), (14, 40), (15, 2), (3, 28), (3, 14), (37, 35), (37, 11), (9, 33), (22, 34), (21, 36), (3, 29), (18, 40), (2, 25), (19, 38), (29, 31), (21, 46), (34, 47), (13, 36), (0, 40), (34, 20), (5, 5), (8, 24), (22, 5), (0, 3), (14, 3), (32, 25), (27, 47), (17, 8), (4, 16), (35, 9), (13, 13), (16, 47), (9, 14), (28, 38), (35, 29), (4, 31), (35, 22), (7, 14), (4, 42), (3, 5), (27, 36), (11, 2), (24, 20), (29, 34), (17, 27), (6, 11), (32, 10), (0, 23), (14, 10), (31, 34), (39, 47), (5, 42), (30, 16), (27, 45), (12, 8), (24, 31), (13, 41), (1, 16), (36, 47), (34, 48), (1, 30), (28, 36), (36, 16), (9, 39), (14, 32), (28, 11), (39, 26), (22, 9), (5, 40), (36, 41), (8, 44), (10, 14), (6, 12), (24, 9), (23, 35), (39, 0), (34, 32), (12, 22), (38, 38), (13, 48), (31, 7), (4, 20), (15, 20), (9, 43), (28, 0), (1, 22), (16, 30), (5, 18), (24, 6), (17, 18), (23, 28), (11, 48), (23, 33), (3, 9), (36, 34), (32, 39), (23, 27), (34, 28), (12, 24), (1, 38), (23, 38), (10, 26), (32, 16), (30, 5), (14, 15), (37, 28), (25, 7), (10, 30), (39, 12), (12, 12), (21, 8), (28, 19), (15, 10), (13, 18), (10, 6), (6, 0), (6, 18), (3, 39), (10, 5), (13, 29), (12, 33), (1, 2), (3, 37), (8, 33), (17, 33), (19, 43), (13, 24), (30, 36), (8, 3), (30, 9), (38, 30), (1, 45), (7, 31), (37, 30), (35, 19), (29, 22), (4, 45), (12, 0), (13, 28), (31, 23), (30, 44), (34, 16), (15, 44), (7, 4), (19, 23), (27, 22), (0, 13), (16, 43), (13, 6), (24, 44), (18, 9), (29, 37), (15, 27), (17, 9), (7, 25), (21, 34), (34, 24), (12, 23), (4, 36), (5, 19), (5, 45), (15, 1), (25, 36), (27, 40), (38, 43), (30, 2), (32, 41), (33, 4), (6, 27), (10, 24), (27, 32), (14, 14), (37, 46), (37, 45), (29, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 19), (31, 44), (6, 4), (28, 21), (41, 2), (45, 21), (44, 31), (11, 4), (17, 19), (33, 20), (15, 41), (21, 37), (3, 19), (29, 28), (17, 18), (12, 17), (11, 26), (30, 38), (25, 31), (39, 8), (46, 33), (8, 29), (45, 29), (26, 34), (42, 1), (37, 14), (17, 12), (44, 1), (32, 24), (16, 36), (36, 24), (27, 13), (11, 41), (34, 0), (16, 26), (2, 5), (39, 2), (36, 31), (33, 6), (41, 22), (46, 16), (20, 10), (32, 4), (37, 42), (31, 12), (5, 12), (20, 15), (19, 19), (13, 29), (43, 23), (2, 43), (38, 24), (23, 42), (29, 11), (43, 0), (8, 4), (31, 32), (40, 25), (40, 1), (8, 46), (44, 14), (29, 32), (39, 32), (22, 11), (22, 41), (30, 35), (4, 36), (45, 14), (20, 3), (36, 42), (29, 10), (15, 8), (0, 38), (23, 9), (19, 0), (34, 18), (30, 45), (8, 35), (7, 39), (44, 39), (20, 33), (15, 43), (3, 35), (43, 18), (25, 30), (5, 46), (8, 28), (27, 36), (10, 40), (36, 45), (25, 42), (34, 1), (13, 44), (26, 32), (7, 41), (25, 39), (6, 42), (4, 9), (14, 12), (38, 36), (36, 18), (39, 30), (29, 5), (26, 38), (10, 20), (44, 7), (20, 39), (30, 6), (17, 25), (5, 32), (4, 20), (29, 24), (34, 33), (29, 6), (43, 2), (46, 1), (35, 2), (22, 1), (13, 18), (29, 13), (23, 45), (9, 31), (36, 7), (45, 17), (1, 32), (42, 12), (39, 17), (29, 8), (37, 4), (38, 6), (6, 28), (20, 22), (43, 1), (11, 33), (16, 19), (42, 37), (37, 7), (10, 14), (15, 22), (29, 27), (0, 11), (2, 25), (17, 34), (2, 34), (2, 44), (34, 7), (33, 25), (0, 32), (30, 3), (36, 41), (36, 28), (3, 36), (12, 45), (44, 11), (7, 23), (6, 31), (18, 26), (15, 37), (10, 11), (15, 26), (14, 14), (42, 46), (14, 26), (44, 25), (17, 1), (0, 21), (12, 41), (24, 40), (15, 11), (22, 13), (30, 10), (41, 13), (43, 10), (45, 6), (40, 13), (5, 26), (18, 20), (11, 9), (0, 29), (21, 31), (29, 18), (30, 28), (25, 1), (31, 26), (9, 27), (21, 44), (30, 8), (25, 25), (16, 0), (21, 40), (27, 45), (15, 34), (35, 15), (42, 15), (16, 11), (23, 23), (22, 14), (46, 22), (43, 29), (14, 23), (6, 39), (19, 23), (15, 0), (32, 19), (12, 20), (30, 30), (1, 11), (43, 37), (19, 8), (6, 36), (24, 3), (26, 29), (1, 14), (38, 2), (41, 36), (19, 11), (12, 12), (21, 42), (21, 45), (44, 18), (43, 31), (42, 34), (37, 5), (44, 38), (9, 15), (29, 17), (44, 8), (33, 10), (13, 2), (23, 41), (5, 7), (19, 43), (19, 24), (44, 2), (28, 29), (20, 31), (28, 28), (46, 14), (26, 23), (7, 19), (26, 18), (24, 36), (21, 43), (45, 2), (8, 43), (20, 20), (42, 4), (2, 36), (20, 27), (11, 0), (34, 20), (20, 37), (43, 9), (24, 37), (1, 28), (34, 26), (37, 39), (20, 34), (28, 42), (33, 43), (27, 5), (5, 17), (31, 6), (0, 33), (40, 29), (37, 10), (33, 9), (12, 9), (19, 3), (43, 12), (32, 20), (37, 30), (41, 40), (35, 36), (29, 35), (17, 44), (40, 10), (6, 16), (11, 39), (17, 37), (45, 34), (40, 6), (11, 42), (1, 1), (14, 36), (22, 4), (26, 40), (34, 6), (14, 13), (15, 39), (11, 31), (41, 15), (27, 42), (3, 18), (4, 2), (3, 16), (31, 37), (11, 13), (2, 20), (46, 42), (19, 17), (11, 19), (7, 14), (11, 17), (37, 33), (15, 7), (41, 17), (38, 21), (24, 16), (10, 36), (28, 34), (28, 23), (1, 0), (37, 32), (5, 34), (12, 21), (14, 32), (1, 20), (28, 36), (37, 13), (9, 34), (39, 18), (3, 0), (42, 30), (31, 3), (16, 41), (26, 25), (2, 33), (0, 24), (19, 37), (13, 8), (44, 23), (23, 24), (20, 13), (23, 17), (7, 3), (27, 30), (15, 40), (33, 42), (42, 29), (41, 31), (41, 27), (27, 22), (30, 31), (27, 20), (44, 19), (9, 29), (0, 9), (39, 21), (27, 37), (8, 39), (42, 8), (12, 26), (21, 10), (31, 38), (46, 0), (1, 19), (26, 1), (6, 5), (28, 13), (24, 11), (10, 35), (38, 20), (13, 19), (37, 21), (4, 15), (13, 42), (39, 16), (16, 31), (38, 43), (12, 2), (8, 14), (15, 1), (9, 0), (18, 42), (32, 39), (25, 46), (44, 3), (13, 43), (7, 21), (45, 16), (9, 4), (0, 42), (17, 43), (34, 42), (17, 15), (9, 33), (22, 44), (27, 18), (46, 17), (35, 19), (25, 23), (20, 46), (40, 28), (42, 35), (2, 7), (15, 29), (34, 30), (30, 29), (10, 19), (12, 24), (7, 2), (3, 22), (40, 33), (3, 12), (11, 14), (6, 20), (36, 44), (17, 36), (43, 7), (37, 3), (32, 41), (29, 42), (24, 23), (41, 5), (23, 37), (41, 3), (35, 41), (22, 20), (17, 2), (14, 25), (30, 21), (12, 40), (32, 17), (40, 22), (38, 40), (8, 36), (11, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 21), (23, 15), (38, 31), (23, 13), (27, 8), (13, 39), (18, 9), (19, 25), (12, 9), (19, 40), (23, 8), (24, 19), (28, 6), (28, 45), (9, 18), (9, 31), (45, 8), (21, 14), (14, 17), (25, 44), (26, 38), (35, 30), (40, 9), (15, 8), (28, 0), (7, 23), (12, 35), (40, 2), (43, 3), (15, 29), (14, 36), (15, 25), (22, 12), (32, 14), (4, 30), (40, 3), (15, 10), (1, 10), (17, 24), (10, 27), (4, 18), (19, 7), (44, 12), (28, 23), (2, 15), (40, 45), (39, 36), (7, 43), (16, 23), (1, 33), (7, 2), (26, 30), (43, 44), (36, 22), (25, 30), (39, 40), (0, 3), (3, 4), (42, 42), (1, 28), (27, 21), (28, 42), (34, 43), (39, 1), (41, 15), (16, 25), (23, 25), (25, 9), (41, 3), (6, 44), (18, 11), (8, 2), (10, 10), (26, 6), (26, 42), (12, 39), (36, 3), (34, 10), (24, 34), (38, 5), (36, 26), (41, 16), (39, 13), (12, 22), (18, 30), (14, 12), (16, 38), (37, 38), (40, 40), (6, 2), (43, 7), (33, 5), (39, 17), (43, 30), (7, 19), (39, 6), (20, 23), (8, 41), (43, 13), (1, 8), (8, 34), (44, 22), (32, 33), (28, 5), (5, 4), (29, 31), (33, 41), (33, 34), (5, 18), (38, 36), (43, 5), (37, 3), (42, 28), (46, 13), (22, 36), (44, 42), (46, 7), (21, 27), (2, 28), (0, 5), (22, 10), (5, 21), (9, 45), (33, 12), (43, 14), (26, 22), (21, 5), (18, 7), (4, 43), (13, 10), (34, 13), (42, 21), (2, 17), (0, 8), (26, 2), (38, 3), (21, 19), (13, 30), (19, 35), (4, 15), (0, 18), (45, 5), (3, 23), (29, 7), (8, 23), (3, 13), (41, 44), (27, 44), (9, 27), (30, 17), (30, 7), (44, 41), (39, 31), (27, 40), (41, 13), (28, 37), (26, 27), (3, 9), (6, 17), (42, 6), (14, 44), (26, 3), (42, 34), (10, 9), (41, 7), (31, 10), (40, 29), (10, 42), (41, 9), (6, 22), (18, 13), (29, 5), (9, 41), (23, 40), (45, 6), (16, 24), (45, 12), (10, 45), (44, 1), (13, 3), (21, 28), (13, 23), (13, 35), (35, 34), (18, 44), (36, 4), (18, 2), (29, 36), (10, 8), (9, 5), (32, 16), (18, 29), (3, 28), (4, 17), (16, 7), (21, 24), (39, 39), (10, 28), (14, 7), (41, 18), (3, 25), (33, 45), (40, 4), (4, 2), (40, 43), (9, 11), (7, 8), (3, 15), (23, 41), (11, 14), (28, 22), (13, 15), (3, 2), (44, 21), (18, 42), (13, 7), (11, 8), (17, 25), (15, 30), (25, 17), (27, 19), (3, 35), (29, 17), (40, 23), (36, 33), (0, 42), (16, 45), (10, 38), (26, 45), (2, 40), (17, 13), (5, 43), (18, 35), (44, 0), (27, 13), (28, 32), (26, 12), (44, 32), (38, 21), (15, 42), (24, 27), (31, 6), (25, 36), (9, 6), (28, 17), (8, 24), (7, 14), (17, 42), (32, 45), (45, 4), (18, 26), (45, 27), (10, 18), (28, 38), (6, 11), (29, 3), (17, 27), (32, 18), (33, 15), (17, 35), (15, 15), (24, 15), (4, 13), (15, 9), (11, 35), (32, 25), (22, 17), (19, 36), (17, 21), (4, 10), (29, 42), (8, 14), (13, 24), (42, 40), (19, 24), (35, 13), (41, 32), (17, 4), (37, 25), (34, 23), (43, 11), (17, 6), (36, 15), (38, 41), (32, 13), (43, 2), (10, 5), (23, 2), (21, 1), (26, 14), (13, 27), (16, 14), (21, 15), (43, 12), (11, 16), (13, 28), (39, 27), (42, 23), (19, 45), (20, 3), (1, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 41), (26, 4), (35, 16), (8, 1), (5, 33), (12, 12), (40, 39), (16, 18), (2, 1), (38, 6), (27, 16), (34, 1), (23, 14), (19, 40), (30, 27), (14, 0), (16, 31), (31, 0), (14, 24), (30, 3), (27, 23), (10, 28), (16, 12), (41, 38), (15, 0), (23, 24), (22, 11), (37, 26), (23, 33), (33, 28), (30, 22), (16, 38), (27, 15), (17, 6), (13, 6), (35, 2), (36, 15), (13, 42), (1, 42), (30, 11), (19, 9), (25, 8), (5, 38), (13, 19), (25, 24), (14, 6), (12, 3), (3, 24), (35, 40), (13, 5), (23, 22), (25, 29), (19, 1), (1, 13), (19, 3), (31, 30), (5, 2), (34, 4), (3, 32), (35, 29), (34, 8), (31, 44), (6, 3), (33, 9), (39, 1), (6, 7), (13, 44), (1, 43), (40, 9), (1, 31), (29, 8), (17, 17), (30, 2), (6, 39), (10, 26), (13, 8), (4, 14), (25, 42), (18, 4), (6, 26), (36, 10), (1, 7), (21, 15), (4, 5), (26, 0), (39, 13), (41, 20), (13, 16), (1, 14), (17, 2), (8, 5), (16, 41), (23, 28), (34, 41), (35, 18), (10, 3), (39, 35), (30, 10), (22, 16), (39, 8), (32, 32), (1, 17), (15, 5), (19, 39), (18, 36), (41, 29), (8, 39), (26, 43), (0, 25), (38, 19), (32, 29), (38, 12), (40, 30), (26, 5), (28, 32), (39, 33), (25, 10), (20, 32), (5, 36), (12, 39), (10, 39), (21, 42), (18, 14), (22, 32), (38, 28), (30, 24), (3, 23), (34, 44), (34, 10), (39, 36), (4, 37), (16, 42), (21, 30), (8, 2), (34, 21), (30, 14), (9, 24), (40, 7), (28, 38), (18, 28), (32, 27), (8, 32), (26, 32), (0, 35), (24, 38), (26, 20), (36, 5), (3, 41), (30, 15), (10, 10), (4, 12), (6, 13), (33, 3), (31, 25), (22, 5), (27, 19), (2, 28), (0, 39), (26, 34), (4, 26), (12, 44), (40, 11), (8, 17), (21, 40), (19, 37), (8, 10), (22, 26), (39, 25), (11, 31), (6, 40), (40, 38), (24, 9), (8, 31), (4, 41), (40, 0), (33, 13), (3, 37), (16, 29), (15, 11), (7, 21), (26, 37), (39, 39), (18, 30), (29, 0), (0, 3), (10, 29), (37, 1), (20, 39), (22, 3), (26, 16), (30, 20), (2, 30), (31, 12), (8, 26), (21, 20), (11, 29), (41, 10), (21, 18), (11, 35), (5, 22), (11, 19), (41, 37), (25, 41), (3, 39), (3, 15), (9, 21), (19, 16), (8, 25), (11, 14), (12, 34), (8, 27), (27, 37), (4, 4), (11, 10), (14, 3), (20, 43), (0, 23), (12, 0), (36, 33), (2, 13), (1, 28), (26, 17), (41, 0), (26, 7), (14, 19), (3, 14), (32, 34), (7, 23), (38, 8), (1, 27), (9, 9), (27, 9), (22, 17), (20, 14), (40, 37), (2, 9), (23, 34), (19, 38), (4, 42), (31, 15), (5, 37), (10, 21), (3, 35), (15, 18), (4, 33), (11, 7), (3, 3), (27, 18), (32, 12), (27, 1), (15, 27), (1, 22), (6, 21), (3, 8), (13, 11), (0, 28), (2, 19), (35, 42), (14, 20), (12, 1), (15, 6), (7, 36), (12, 2), (14, 12), (21, 27), (0, 16), (10, 0), (2, 0), (7, 13), (31, 19), (37, 17), (3, 6), (26, 19), (19, 26), (7, 15), (18, 31), (0, 6), (5, 35), (32, 42), (32, 41), (24, 41), (14, 38), (28, 1), (34, 39), (31, 6), (24, 16), (36, 4), (7, 25), (20, 42), (37, 20), (7, 43), (32, 36), (31, 3), (39, 15), (38, 25), (12, 43), (29, 32), (26, 6), (32, 11), (33, 26), (20, 6), (33, 40), (20, 29), (35, 4), (12, 20), (40, 40), (6, 43), (41, 35), (40, 17), (27, 4), (26, 13), (7, 0), (18, 39), (11, 33), (28, 44), (12, 24), (16, 10), (34, 33), (6, 33), (38, 10), (38, 11), (36, 14), (5, 16), (26, 30), (24, 30), (36, 36), (34, 26), (41, 33), (9, 41), (12, 26), (20, 35), (7, 41), (3, 16), (24, 4), (36, 0), (22, 36), (3, 33), (41, 14), (36, 16), (39, 44), (5, 13), (19, 43), (10, 25), (18, 0), (29, 19), (32, 0), (18, 26), (11, 27), (0, 33), (17, 7), (32, 5), (17, 36), (39, 26), (2, 11), (0, 17), (3, 22), (15, 41), (37, 34), (9, 28), (31, 28), (37, 12), (15, 8), (13, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 16), (27, 5), (17, 40), (41, 11), (9, 9), (3, 13), (30, 20), (5, 39), (13, 24), (31, 19), (27, 10), (0, 37), (39, 22), (18, 13), (32, 7), (7, 40), (10, 14), (30, 12), (3, 23), (1, 36), (39, 45), (30, 16), (34, 9), (4, 39), (14, 40), (4, 15), (10, 0), (32, 36), (29, 13), (18, 21), (36, 4), (2, 10), (41, 26), (39, 20), (26, 17), (3, 45), (17, 24), (36, 14), (14, 26), (30, 43), (27, 46), (32, 0), (32, 30), (26, 14), (14, 41), (34, 23), (26, 25), (9, 38), (28, 47), (7, 21), (8, 29), (27, 32), (21, 19), (20, 41), (21, 25), (5, 14), (31, 8), (35, 37), (4, 6), (5, 35), (7, 7), (29, 37), (8, 8), (23, 29), (16, 7), (3, 30), (8, 2), (21, 10), (27, 44), (35, 28), (18, 11), (7, 32), (40, 45), (18, 39), (20, 20), (7, 16), (11, 31), (1, 11), (3, 11), (7, 25), (11, 21), (16, 35), (26, 27), (41, 4), (30, 40), (10, 5), (9, 15), (8, 9), (36, 40), (0, 26), (7, 48), (2, 22), (26, 1), (9, 12), (30, 36), (18, 2), (40, 37), (35, 47), (5, 42), (38, 9), (16, 34), (19, 44), (28, 3), (22, 1), (24, 29), (12, 17), (38, 43), (12, 20), (9, 44), (5, 44), (36, 41), (35, 6), (16, 6), (7, 18), (30, 39), (9, 36), (26, 40), (22, 32), (26, 22), (4, 2), (32, 26), (9, 17), (17, 2), (29, 30), (7, 5), (2, 30), (5, 22), (24, 34), (1, 3), (23, 1), (25, 37), (27, 43), (23, 45), (21, 3), (32, 28), (17, 29), (15, 37), (25, 12), (28, 24), (17, 35), (31, 1), (1, 32), (13, 40), (2, 40), (27, 8), (1, 25), (37, 42), (24, 17), (19, 48), (5, 24), (16, 37), (15, 12), (35, 40), (24, 11), (14, 48), (11, 37), (30, 46), (3, 20), (21, 22), (36, 37), (16, 43), (31, 41), (6, 44), (6, 17), (27, 13), (13, 25), (34, 22), (11, 36), (0, 14), (15, 45), (10, 29), (22, 3), (4, 13), (11, 17), (7, 0), (3, 15), (20, 28), (31, 10), (3, 38), (39, 48), (18, 33), (15, 8), (9, 5), (6, 22), (30, 9), (6, 29), (13, 30), (41, 19), (31, 31), (37, 12), (25, 27), (6, 4), (23, 6), (12, 9), (11, 6), (12, 42), (30, 19), (16, 47), (17, 30), (23, 32), (9, 41), (25, 10), (32, 24), (26, 30), (31, 38), (10, 32), (38, 15), (36, 44), (6, 19), (9, 2), (38, 38), (14, 29), (39, 11), (17, 13), (32, 13), (11, 45), (28, 4), (15, 25), (18, 30), (31, 3), (32, 2), (17, 25), (21, 38), (32, 20), (30, 24), (5, 20), (8, 16), (29, 0), (14, 45), (6, 0), (27, 22), (9, 1), (35, 24), (40, 28), (19, 35), (14, 44), (17, 42), (27, 0), (19, 42), (0, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 39), (33, 40), (37, 18), (17, 21), (33, 20), (9, 3), (27, 27), (10, 18), (19, 7), (30, 44), (3, 47), (33, 4), (35, 35), (29, 0), (34, 46), (6, 12), (3, 29), (44, 8), (27, 40), (30, 17), (10, 27), (33, 38), (44, 24), (26, 28), (21, 22), (44, 4), (9, 10), (34, 2), (44, 20), (27, 9), (8, 29), (5, 44), (23, 29), (34, 43), (35, 36), (20, 15), (30, 41), (34, 42), (30, 16), (23, 42), (21, 12), (40, 33), (15, 33), (18, 0), (29, 3), (36, 29), (22, 32), (4, 19), (14, 5), (0, 6), (29, 37), (34, 38), (42, 47), (20, 25), (22, 12), (31, 36), (38, 47), (37, 15), (36, 41), (2, 0), (6, 9), (35, 12), (15, 47), (22, 6), (36, 20), (23, 41), (0, 20), (9, 14), (9, 4), (2, 17), (25, 14), (24, 6), (27, 12), (7, 6), (29, 17), (27, 23), (32, 38), (1, 24), (4, 17), (36, 25), (17, 1), (36, 42), (39, 15), (1, 44), (7, 13), (40, 30), (42, 9), (30, 39), (4, 27), (32, 2), (8, 48), (42, 41), (5, 36), (9, 0), (32, 46), (14, 1), (32, 48), (16, 24), (32, 13), (44, 32), (44, 41), (0, 15), (36, 22), (20, 12), (44, 1), (22, 13), (3, 10), (5, 9), (16, 19), (40, 20), (13, 29), (26, 12), (18, 37), (15, 34), (20, 34), (0, 2), (29, 32), (0, 22), (10, 40), (7, 31), (23, 43), (39, 35), (28, 45), (32, 18), (16, 39), (0, 25), (0, 23), (11, 25), (31, 26), (33, 26), (11, 12), (34, 47), (4, 18), (25, 24), (20, 41), (26, 16), (32, 5), (41, 13), (37, 27), (28, 22), (40, 18), (38, 21), (31, 44), (10, 45), (24, 22), (37, 19), (2, 24), (29, 21), (26, 15), (41, 15), (17, 30), (19, 14), (9, 2), (8, 14), (13, 33), (10, 17), (16, 9), (43, 8), (26, 47), (28, 2), (35, 25), (15, 16), (35, 3), (32, 25), (16, 44), (33, 22), (35, 13), (36, 14), (32, 37), (41, 22), (11, 34), (9, 22), (28, 47), (10, 4), (14, 7), (8, 6), (9, 12), (6, 37), (16, 14), (2, 37), (40, 1), (28, 34), (1, 37), (5, 25), (1, 38), (19, 3), (4, 5), (18, 41), (13, 31), (23, 38), (29, 39), (35, 8), (16, 35), (23, 47), (42, 36), (25, 37), (11, 24), (15, 14), (23, 27), (37, 37), (6, 4), (4, 37), (11, 14), (5, 41), (19, 28), (23, 36), (29, 19), (40, 29), (23, 6), (25, 25), (0, 21), (10, 19), (15, 11), (37, 32), (17, 6), (0, 33), (0, 19), (25, 20), (37, 23), (21, 1), (1, 21), (34, 12), (43, 33), (23, 34), (44, 7), (29, 25), (7, 3), (21, 29), (36, 38), (43, 35), (23, 4), (16, 1), (24, 21), (34, 34), (0, 9), (43, 19), (20, 7), (4, 41), (9, 7), (18, 15), (41, 18), (8, 43), (26, 0), (9, 8), (34, 8), (37, 5), (1, 30), (19, 10), (22, 39), (1, 36), (3, 30), (36, 19), (13, 38), (5, 10), (23, 24), (12, 36), (39, 7), (36, 31), (22, 36), (30, 35), (43, 29), (13, 47), (10, 25), (20, 27), (39, 12), (39, 0), (8, 19), (37, 25), (38, 25), (12, 17), (32, 10), (42, 18), (5, 17), (24, 34), (6, 7), (4, 46), (37, 17), (31, 16), (16, 42), (33, 3), (15, 0), (39, 21), (3, 36), (26, 25), (38, 38), (0, 27), (20, 42), (19, 9), (1, 18), (40, 42), (41, 42), (8, 41), (21, 6), (23, 15), (41, 39), (34, 29), (4, 47), (42, 4), (27, 43), (11, 2), (22, 35), (29, 38), (6, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 35), (26, 6), (27, 25), (27, 34), (30, 37), (16, 22), (10, 9), (38, 38), (1, 23), (30, 7), (31, 44), (17, 33), (26, 23), (33, 33), (9, 44), (21, 0), (28, 32), (39, 9), (14, 8), (31, 27), (3, 1), (19, 19), (15, 15), (3, 21), (27, 40), (37, 36), (14, 29), (1, 19), (11, 36), (27, 36), (20, 27), (4, 10), (35, 24), (13, 6), (12, 38), (42, 13), (0, 26), (24, 14), (0, 44), (35, 30), (16, 39), (19, 35), (29, 7), (28, 21), (22, 1), (32, 44), (13, 13), (34, 32), (11, 2), (34, 6), (8, 3), (16, 8), (15, 23), (8, 23), (18, 29), (9, 34), (34, 39), (36, 1), (21, 31), (3, 7), (39, 21), (18, 19), (36, 37), (41, 39), (14, 42), (28, 33), (40, 16), (10, 41), (36, 35), (16, 10), (9, 12), (20, 19), (16, 9), (40, 33), (24, 24), (14, 23), (37, 37), (6, 31), (42, 6), (23, 13), (29, 32), (0, 42), (38, 0), (9, 8), (19, 27), (42, 3), (27, 37), (8, 29), (20, 28), (16, 7), (29, 3), (14, 36), (25, 19), (3, 4), (38, 17), (19, 29), (8, 22), (21, 42), (4, 4), (16, 16), (17, 19), (23, 20), (1, 20), (23, 5), (1, 33), (17, 42), (28, 23), (19, 40), (21, 27), (25, 15), (24, 13), (24, 23), (18, 33), (25, 40), (29, 44), (28, 29), (30, 3), (9, 1), (12, 29), (19, 22), (42, 39), (39, 14), (5, 22), (20, 36), (42, 20), (35, 4), (19, 5), (2, 25), (0, 19), (5, 27), (11, 20), (19, 23), (5, 9), (4, 11), (2, 24), (10, 30), (41, 23), (37, 19), (34, 0), (1, 2), (27, 32), (41, 9), (23, 40), (37, 8), (21, 21), (29, 17), (11, 27), (19, 24), (11, 8), (20, 25), (14, 30), (21, 26), (20, 1), (2, 36), (16, 13), (31, 41), (8, 1), (22, 22), (18, 24), (6, 25), (20, 5), (29, 27), (4, 26), (9, 26), (7, 32), (4, 21), (11, 21), (19, 11), (13, 30), (37, 39), (1, 34), (4, 1), (9, 20), (23, 36), (3, 8), (40, 10), (39, 42), (7, 7), (3, 38), (18, 27), (4, 29), (27, 23), (16, 42), (14, 33), (29, 23), (19, 17), (33, 14), (23, 4), (12, 20), (28, 30), (15, 3), (7, 42), (39, 38), (31, 34), (27, 13), (1, 30), (2, 39), (30, 21), (20, 44), (7, 0), (32, 30), (5, 12), (32, 39), (31, 29), (22, 17), (5, 0), (40, 2), (26, 24), (7, 29), (9, 13), (29, 41), (3, 22), (18, 18), (40, 43), (36, 44), (29, 5), (10, 5), (23, 21), (0, 7), (8, 44), (15, 16), (38, 41), (34, 3), (15, 33), (40, 18), (16, 24), (8, 41), (41, 16), (14, 44), (23, 9), (7, 23), (25, 17), (31, 17), (9, 16), (16, 38), (9, 10), (23, 44), (38, 20), (25, 24), (39, 7), (4, 24), (17, 34), (3, 19), (28, 5), (33, 4), (33, 42), (13, 19), (19, 34), (37, 26), (38, 10), (26, 5), (23, 31), (2, 17), (22, 7), (10, 3), (36, 30), (23, 23), (24, 10), (39, 17), (35, 16), (40, 38), (10, 36), (2, 33), (39, 18), (33, 37), (40, 14), (38, 29), (36, 18), (28, 27), (7, 33), (24, 0), (9, 40), (7, 19), (25, 42), (22, 33), (41, 0), (26, 39), (19, 0), (2, 22), (13, 31), (39, 22), (28, 24), (12, 3), (2, 12), (35, 25), (30, 36), (19, 41), (36, 11), (38, 37), (1, 37), (9, 7), (17, 4), (12, 25), (8, 20), (13, 4), (28, 41), (6, 10), (36, 38), (18, 44), (31, 36), (38, 5), (4, 6), (11, 29), (32, 32), (2, 43), (21, 3), (18, 3), (5, 40), (20, 26), (13, 14), (38, 15), (0, 38), (22, 41), (11, 42), (42, 16), (34, 41), (14, 17), (14, 34), (23, 19), (22, 21), (6, 15), (12, 7), (15, 26), (10, 44), (39, 30), (26, 25), (26, 10), (42, 31), (8, 34), (12, 4), (20, 38), (9, 11), (38, 11), (22, 18), (14, 11), (37, 22), (8, 0), (12, 39), (9, 30), (26, 20), (32, 10), (23, 17), (8, 24), (5, 24), (41, 21), (11, 37), (41, 28), (17, 20), (27, 3), (30, 35), (34, 21), (17, 35), (12, 34), (31, 10), (6, 12), (11, 14), (10, 13), (32, 25), (36, 0), (0, 35), (22, 34), (6, 28), (3, 39), (25, 37), (35, 29), (25, 21), (39, 6), (29, 16), (1, 4), (36, 26), (5, 41), (20, 41), (16, 17), (16, 0), (33, 21), (9, 0), (7, 12), (34, 9), (42, 5), (39, 12), (15, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 34), (12, 6), (1, 30), (1, 5), (28, 17), (23, 3), (45, 15), (44, 26), (45, 0), (17, 3), (34, 18), (1, 37), (41, 26), (25, 20), (7, 2), (10, 9), (17, 13), (44, 4), (47, 5), (35, 9), (34, 20), (1, 18), (43, 8), (39, 2), (47, 36), (9, 8), (24, 9), (10, 5), (4, 25), (6, 2), (33, 5), (0, 13), (7, 29), (41, 37), (13, 11), (44, 0), (0, 33), (20, 11), (2, 32), (10, 19), (25, 15), (23, 34), (19, 4), (29, 12), (7, 15), (22, 39), (19, 35), (32, 38), (3, 36), (34, 31), (16, 8), (8, 11), (15, 6), (22, 16), (22, 22), (38, 27), (21, 13), (42, 27), (16, 23), (45, 13), (15, 5), (29, 3), (42, 16), (31, 10), (26, 22), (4, 16), (38, 17), (27, 6), (46, 19), (19, 2), (4, 24), (26, 33), (2, 11), (40, 11), (25, 26), (33, 35), (15, 17), (15, 37), (28, 15), (3, 31), (29, 32), (4, 7), (40, 4), (34, 8), (20, 3), (23, 33), (2, 29), (39, 35), (31, 29), (17, 35), (14, 28), (21, 16), (43, 13), (0, 5), (18, 27), (1, 32), (27, 0), (11, 6), (18, 36), (1, 33), (25, 30), (7, 19), (31, 28), (0, 26), (15, 32), (13, 13), (14, 20), (29, 19), (9, 9), (15, 2), (24, 34), (5, 26), (29, 20), (18, 21), (28, 6), (8, 29), (31, 11), (38, 1), (12, 20), (24, 35), (22, 20), (0, 35), (35, 36), (10, 11), (6, 28), (9, 28), (34, 25), (34, 30), (9, 24), (27, 38), (46, 12), (27, 12), (47, 35), (35, 0), (4, 12), (40, 38), (33, 28), (46, 21), (5, 22), (10, 6), (46, 38), (6, 34), (27, 25), (22, 3), (33, 0), (7, 26), (14, 31), (9, 20), (12, 30), (34, 28), (17, 7), (4, 14), (10, 4), (11, 1), (42, 21), (40, 27), (23, 15), (28, 0), (32, 4), (39, 34), (39, 5), (18, 14), (43, 7), (13, 22), (19, 33), (4, 17), (42, 34), (31, 35), (22, 19), (8, 39), (4, 10), (42, 2), (33, 34), (4, 23), (17, 22), (13, 34), (7, 14), (35, 22), (38, 15), (33, 29), (47, 25), (15, 11), (5, 36), (47, 20), (43, 28), (23, 8), (3, 4), (17, 30), (37, 34), (34, 4), (2, 9), (43, 26), (12, 38), (41, 8), (17, 8), (21, 18), (12, 39), (18, 3), (8, 20), (46, 10), (45, 8), (5, 10), (11, 31), (7, 39), (27, 11), (38, 19), (45, 37), (47, 19), (14, 22), (30, 19), (16, 37), (37, 22), (24, 22), (36, 18), (46, 26), (43, 22), (19, 39), (12, 12), (45, 21), (36, 29), (35, 10), (23, 26), (42, 0), (7, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 4), (23, 37), (33, 17), (37, 39), (10, 23), (6, 5), (13, 11), (41, 30), (27, 10), (18, 27), (30, 29), (39, 28), (37, 13), (7, 38), (24, 40), (16, 3), (36, 14), (35, 27), (0, 33), (17, 35), (24, 4), (5, 29), (39, 34), (2, 4), (38, 30), (2, 39), (21, 23), (3, 10), (26, 19), (17, 7), (19, 20), (27, 23), (37, 9), (15, 31), (31, 32), (17, 31), (13, 7), (26, 2), (2, 16), (13, 18), (32, 18), (23, 25), (35, 2), (2, 13), (40, 11), (29, 28), (3, 35), (18, 19), (17, 1), (38, 15), (14, 24), (3, 13), (14, 5), (31, 35), (27, 29), (23, 21), (30, 9), (39, 13), (6, 33), (24, 36), (0, 5), (8, 41), (11, 35), (36, 25), (9, 6), (38, 10), (5, 24), (41, 11), (34, 24), (18, 41), (3, 33), (10, 32), (5, 32), (4, 15), (36, 18), (11, 1), (20, 3), (41, 33), (28, 40), (30, 26), (26, 5), (21, 38), (37, 14), (28, 5), (36, 3), (22, 33), (24, 35), (27, 30), (15, 25), (33, 31), (35, 3), (35, 0), (40, 35), (22, 23), (17, 11), (0, 38), (18, 31), (28, 11), (23, 16), (38, 27), (16, 29), (31, 36), (14, 20), (0, 39), (17, 5), (36, 4), (14, 33), (12, 23), (9, 11), (31, 3), (31, 30), (40, 12), (27, 13), (35, 25), (39, 23), (15, 36), (36, 6), (20, 4), (39, 40), (15, 23), (40, 9), (41, 22), (32, 24), (9, 15), (7, 6), (30, 5), (20, 9), (7, 4), (12, 33), (28, 12), (34, 35), (31, 16), (35, 4), (12, 24), (4, 11), (18, 28), (1, 35), (39, 37), (6, 16), (24, 28), (8, 38), (31, 2), (14, 13), (29, 36), (28, 27), (19, 33), (19, 7), (9, 41), (25, 24), (38, 35), (29, 3), (26, 12), (7, 33), (12, 7), (2, 8), (16, 34), (10, 20), (32, 22), (28, 30), (4, 3), (41, 31), (41, 21), (15, 27), (21, 40), (10, 14), (7, 5), (16, 2), (4, 19), (28, 21), (28, 35), (1, 16), (12, 1), (37, 8), (6, 19), (1, 6), (3, 11), (18, 40), (39, 24), (31, 39), (30, 38), (4, 14), (16, 5), (19, 37), (17, 4), (2, 33), (16, 28), (23, 35), (12, 20), (34, 38), (15, 11), (41, 40), (30, 12), (7, 20), (14, 6), (25, 15), (22, 5), (3, 25), (34, 13), (32, 7), (14, 7), (3, 22), (6, 0), (39, 18), (26, 41), (31, 23), (27, 33), (37, 15), (18, 0), (33, 38), (17, 23), (17, 28), (13, 29), (33, 2), (8, 19), (26, 16), (24, 7), (24, 9), (8, 30), (20, 1), (20, 31), (35, 36), (24, 3), (34, 8), (11, 16), (26, 22), (20, 20), (10, 26), (4, 27), (2, 35), (25, 30), (2, 6), (22, 41), (7, 26), (14, 15), (11, 9), (26, 31), (6, 32), (37, 2), (25, 36), (5, 27), (2, 19), (35, 16), (34, 4), (4, 35), (29, 22), (35, 31), (32, 16), (10, 40), (9, 22), (22, 14), (32, 9), (9, 3), (28, 29), (21, 15), (32, 38), (38, 34), (29, 35), (12, 10), (12, 30), (13, 26), (34, 27), (14, 40), (40, 1), (11, 8), (18, 38), (35, 37), (25, 34), (17, 29), (28, 7), (16, 22), (9, 30), (16, 18), (21, 41), (35, 26), (4, 34), (35, 41), (30, 27), (11, 33), (12, 0), (28, 8), (18, 29), (13, 30), (32, 39), (13, 5), (24, 38), (2, 28), (28, 41), (9, 14), (25, 33), (18, 9), (19, 11), (35, 19), (21, 17), (21, 18), (25, 32), (21, 32), (13, 16), (1, 14), (14, 21), (17, 0), (6, 35), (29, 7), (20, 15), (23, 33), (32, 10), (16, 0), (40, 39), (28, 17), (10, 10), (39, 27), (37, 33), (3, 24), (0, 28), (5, 34), (0, 30), (24, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 44), (1, 5), (2, 2), (37, 45), (37, 22), (13, 41), (3, 37), (38, 1), (8, 3), (11, 34), (35, 43), (8, 0), (32, 30), (43, 34), (44, 30), (2, 11), (36, 1), (28, 37), (30, 21), (27, 22), (30, 38), (14, 12), (1, 30), (37, 36), (0, 39), (20, 3), (30, 39), (33, 0), (43, 9), (1, 8), (36, 14), (21, 34), (23, 6), (31, 35), (39, 7), (12, 46), (34, 23), (29, 12), (45, 38), (18, 37), (2, 22), (1, 35), (41, 38), (14, 11), (15, 32), (31, 29), (24, 27), (2, 0), (34, 26), (12, 34), (16, 7), (1, 36), (47, 13), (13, 23), (36, 12), (3, 2), (16, 39), (21, 21), (47, 4), (19, 42), (34, 6), (23, 16), (13, 28), (15, 24), (6, 44), (32, 9), (41, 5), (28, 28), (21, 45), (35, 38), (33, 30), (8, 18), (37, 25), (41, 19), (29, 3), (17, 14), (15, 21), (31, 1), (34, 42), (8, 29), (21, 26), (9, 36), (46, 4), (17, 28), (9, 24), (4, 13), (16, 18), (44, 44), (4, 17), (22, 36), (29, 39), (40, 18), (46, 13), (25, 26), (43, 13), (25, 12), (0, 41), (9, 4), (23, 3), (44, 29), (22, 25), (35, 45), (26, 12), (31, 20), (26, 20), (19, 15), (44, 1), (39, 2), (31, 2), (2, 7), (7, 36), (37, 44), (30, 34), (11, 46), (27, 18), (8, 21), (9, 2), (3, 23), (15, 38), (35, 40), (9, 8), (19, 39), (46, 42), (20, 12), (1, 25), (32, 32), (11, 17), (25, 44), (14, 20), (13, 31), (29, 8), (23, 14), (28, 3), (23, 7), (36, 26), (42, 28), (16, 9), (21, 27), (22, 8), (4, 12), (43, 23), (15, 37), (21, 14), (40, 2), (14, 37), (7, 43), (18, 34), (2, 37), (1, 38), (19, 27), (18, 7), (29, 42), (25, 18), (20, 42), (9, 15), (27, 6), (36, 9), (11, 19), (35, 41), (36, 7), (44, 46), (12, 23), (16, 17), (33, 36), (24, 20), (31, 27), (30, 12), (26, 27), (28, 36), (26, 18), (2, 43), (31, 16), (23, 8), (23, 2), (18, 4), (30, 13), (42, 16), (44, 23), (23, 37), (38, 29), (33, 37), (14, 5), (7, 22), (39, 33), (1, 41), (3, 35), (39, 27), (19, 44), (34, 43), (24, 39), (0, 38), (43, 29), (47, 41), (46, 11), (29, 28), (27, 8), (25, 1), (19, 45), (44, 43), (20, 10), (5, 31), (14, 27), (42, 39), (4, 19), (5, 20), (25, 46), (24, 23), (20, 7), (10, 28), (31, 19), (23, 13), (15, 39), (38, 21), (24, 44), (40, 6), (9, 26), (33, 19), (5, 8), (25, 35), (8, 32), (32, 25), (40, 23), (9, 39), (0, 15), (31, 34), (27, 37), (16, 41), (36, 27), (24, 0), (26, 39), (12, 5), (12, 11), (8, 24), (5, 36), (1, 24), (33, 27), (31, 45), (0, 37), (17, 26), (33, 46), (37, 0), (6, 42), (38, 20), (24, 35), (28, 10), (4, 2), (6, 13), (13, 43), (14, 45), (39, 28), (47, 40), (38, 9), (22, 40), (3, 18), (2, 8), (28, 46), (20, 20), (39, 39), (37, 17), (11, 20), (22, 7), (12, 13), (38, 17), (39, 43), (4, 33), (37, 3), (25, 33), (39, 16), (11, 40), (12, 39), (3, 7), (12, 45), (44, 25), (29, 25), (11, 28), (30, 33), (17, 2), (32, 12), (32, 15), (40, 1), (0, 14), (27, 43), (35, 42), (35, 12), (15, 19), (10, 44), (18, 33), (13, 4), (34, 2), (45, 12), (34, 1), (24, 7), (44, 31), (17, 42), (31, 13), (42, 40), (28, 35), (9, 7), (5, 14), (11, 13), (19, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 39), (34, 2), (0, 8), (29, 12), (29, 37), (17, 39), (38, 21), (30, 27), (22, 22), (1, 33), (27, 47), (25, 31), (20, 39), (11, 25), (28, 23), (9, 43), (33, 39), (15, 10), (0, 41), (33, 40), (22, 13), (30, 31), (6, 46), (11, 16), (10, 31), (13, 25), (7, 17), (28, 7), (29, 29), (35, 18), (35, 36), (6, 2), (27, 41), (24, 2), (17, 18), (7, 13), (5, 1), (7, 16), (22, 34), (10, 29), (6, 29), (22, 48), (15, 39), (32, 34), (2, 13), (30, 39), (0, 25), (28, 11), (20, 19), (5, 28), (39, 30), (39, 39), (9, 12), (24, 19), (14, 48), (33, 31), (11, 6), (3, 28), (33, 0), (17, 47), (24, 1), (4, 27), (2, 21), (22, 20), (22, 24), (4, 6), (38, 27), (10, 46), (0, 33), (34, 5), (11, 4), (2, 12), (18, 39), (26, 25), (0, 37), (0, 39), (11, 23), (8, 33), (6, 23), (13, 17), (9, 40), (30, 2), (35, 20), (22, 30), (38, 39), (39, 1), (27, 6), (23, 32), (28, 28), (4, 37), (0, 18), (36, 36), (7, 5), (11, 22), (25, 14), (39, 21), (24, 37), (7, 22), (32, 6), (30, 3), (27, 28), (13, 0), (1, 47), (7, 23), (33, 3), (22, 25), (32, 25), (20, 10), (1, 10), (35, 5), (14, 5), (2, 28), (26, 21), (2, 40), (19, 28), (33, 2), (25, 35), (35, 33), (16, 26), (29, 27), (23, 20), (15, 45), (11, 48), (12, 22), (26, 22), (11, 42), (3, 6), (6, 41), (11, 44), (38, 12), (27, 15), (4, 0), (17, 41), (21, 44), (38, 36), (16, 22), (37, 0), (9, 48), (38, 9), (10, 1), (30, 34), (14, 2), (37, 40), (17, 36), (33, 25), (7, 40), (30, 40), (29, 3), (14, 18), (0, 28), (3, 7), (13, 8), (19, 22), (16, 2), (28, 48), (9, 7), (38, 25), (35, 0), (5, 2), (38, 0), (18, 7), (18, 38), (37, 34), (11, 7), (16, 43), (14, 19), (8, 0), (12, 40), (10, 12), (35, 40), (12, 39), (24, 10), (39, 34), (24, 48), (11, 35), (17, 31), (34, 31), (26, 39), (20, 15), (8, 4), (1, 36), (25, 7), (32, 16), (26, 2), (2, 24), (29, 43), (18, 23), (23, 6), (1, 13), (4, 14), (39, 25), (11, 0), (35, 44), (35, 3), (12, 16), (34, 13), (26, 38), (2, 35), (3, 45), (15, 0), (8, 36), (4, 41), (33, 24), (25, 22), (34, 14), (1, 9), (17, 37), (19, 29), (15, 22), (37, 30), (0, 34), (1, 22), (19, 40), (11, 30), (13, 29), (1, 23), (17, 22), (9, 27), (28, 34), (37, 48), (15, 33), (22, 44), (30, 32), (4, 42), (1, 25), (16, 41), (22, 11), (31, 25), (31, 14), (13, 6), (2, 16), (38, 15), (12, 7), (12, 15), (14, 17), (11, 2), (32, 7), (5, 7), (1, 5), (4, 43), (28, 5), (15, 2), (1, 8), (28, 13), (36, 25), (26, 11), (34, 45), (16, 27), (37, 19), (12, 8), (37, 9), (33, 23), (3, 1), (30, 33), (18, 12), (2, 20), (19, 30), (8, 19), (38, 26), (10, 43), (22, 40), (35, 39), (26, 45), (3, 19), (19, 42), (13, 46), (32, 30), (3, 30), (38, 7), (10, 11), (28, 46), (38, 4), (33, 14), (29, 2), (1, 15), (33, 15), (37, 1), (3, 10), (1, 48), (28, 10), (38, 30), (18, 40), (19, 5), (2, 38), (38, 33), (28, 32), (3, 32), (10, 5), (13, 22), (29, 0), (6, 36), (22, 36), (15, 25), (29, 6), (18, 24), (6, 4), (19, 27), (23, 26), (22, 46), (17, 32), (2, 4), (35, 17), (14, 36), (4, 46), (19, 14), (30, 36), (36, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 12), (27, 20), (14, 9), (36, 16), (42, 42), (12, 6), (24, 12), (7, 19), (15, 26), (17, 20), (19, 22), (42, 27), (9, 41), (31, 40), (47, 34), (36, 21), (42, 28), (18, 19), (24, 8), (25, 44), (35, 22), (35, 41), (6, 25), (39, 4), (16, 0), (43, 41), (21, 27), (0, 7), (2, 30), (38, 47), (18, 16), (41, 36), (1, 18), (41, 17), (40, 32), (22, 11), (13, 12), (27, 42), (43, 4), (23, 32), (24, 38), (25, 12), (31, 20), (3, 4), (18, 3), (32, 47), (14, 1), (5, 28), (39, 28), (32, 6), (16, 22), (28, 40), (35, 25), (6, 19), (4, 34), (23, 22), (33, 31), (31, 8), (32, 31), (8, 18), (26, 17), (32, 23), (23, 13), (9, 37), (4, 44), (6, 38), (9, 20), (10, 47), (4, 41), (16, 40), (26, 35), (31, 11), (5, 6), (8, 39), (5, 16), (25, 39), (47, 36), (39, 0), (15, 24), (27, 35), (34, 21), (36, 6), (47, 31), (47, 40), (9, 19), (23, 37), (27, 4), (5, 24), (45, 29), (1, 23), (34, 38), (18, 18), (14, 40), (18, 6), (45, 7), (37, 44), (11, 14), (28, 16), (22, 25), (37, 43), (23, 23), (38, 40), (12, 20), (32, 7), (46, 45), (2, 44), (41, 18), (6, 10), (6, 6), (33, 25), (29, 41), (42, 7), (13, 22), (34, 0), (24, 32), (22, 42), (10, 26), (17, 10), (34, 9), (14, 2), (2, 19), (3, 8), (42, 0), (43, 28), (26, 23), (28, 12), (20, 33), (5, 35), (9, 33), (7, 12), (25, 29), (47, 13), (10, 37), (9, 15), (33, 43), (46, 21), (46, 36), (23, 6), (31, 23), (19, 30), (24, 35), (15, 42), (26, 40), (21, 47), (9, 5), (7, 23), (4, 1), (6, 1), (16, 37), (27, 32), (29, 7), (41, 42), (3, 14), (5, 27), (3, 35), (33, 42), (44, 6), (42, 34), (31, 27), (39, 42), (27, 11), (21, 21), (46, 24), (9, 23), (32, 25), (1, 45), (2, 32), (17, 16), (34, 39), (18, 46), (42, 23), (13, 27), (29, 22), (1, 40), (36, 1), (1, 17), (22, 34), (34, 41), (45, 42), (1, 21), (22, 19), (37, 35), (10, 4), (3, 39), (25, 2), (36, 25), (28, 32), (26, 19), (2, 39), (30, 40), (13, 37), (40, 27), (22, 38), (2, 5), (33, 0), (46, 22), (19, 5), (15, 29), (7, 20), (18, 38), (27, 10), (21, 41), (33, 26), (15, 3), (3, 19), (18, 47), (29, 10), (33, 11), (34, 2), (31, 35), (37, 40), (7, 44), (11, 11), (11, 29), (20, 22), (43, 34), (6, 20), (28, 22), (42, 21), (25, 1), (12, 16), (39, 18), (26, 47), (0, 46), (15, 40), (44, 15), (25, 16), (13, 6), (47, 27), (35, 42), (2, 37), (30, 47), (2, 24), (20, 36), (23, 4), (10, 46), (4, 3), (35, 47), (3, 41), (46, 20), (28, 34), (0, 21), (35, 37), (9, 22), (4, 32), (8, 24), (14, 0), (3, 46), (18, 10), (14, 28), (30, 27), (22, 18), (14, 6), (21, 30), (13, 35), (5, 17), (8, 6), (28, 39), (44, 42), (21, 40), (14, 11), (43, 36), (41, 47), (17, 30), (31, 41), (41, 8), (25, 24), (30, 41), (38, 41), (11, 28), (33, 13), (12, 12), (37, 17), (7, 14), (4, 26), (21, 3), (38, 22), (42, 2), (14, 8), (4, 15), (19, 10), (30, 35), (45, 27), (46, 39), (19, 36), (1, 37), (43, 37), (33, 10), (38, 20), (6, 17), (31, 16), (24, 37), (20, 6), (18, 11), (22, 35), (23, 9), (38, 13), (3, 21), (26, 45), (10, 9), (13, 41), (38, 21), (21, 7), (43, 32), (34, 34), (41, 21), (47, 19), (19, 31), (29, 38), (15, 18), (8, 11), (29, 31), (17, 46), (1, 24), (6, 7), (19, 2), (40, 43), (32, 35), (21, 0), (29, 17), (8, 41), (35, 29), (5, 7), (21, 28), (35, 3), (2, 1), (31, 43), (23, 11), (44, 7), (42, 15), (46, 9), (13, 4), (16, 11), (40, 17), (10, 45)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 26), (28, 22), (17, 29), (44, 1), (9, 21), (23, 1), (22, 28), (31, 9), (27, 21), (33, 12), (29, 33), (40, 7), (14, 42), (37, 40), (28, 13), (6, 19), (12, 10), (9, 33), (20, 5), (9, 19), (3, 15), (26, 39), (16, 38), (34, 38), (8, 41), (17, 26), (41, 1), (26, 24), (42, 8), (43, 31), (26, 29), (1, 35), (16, 2), (20, 17), (23, 3), (1, 29), (10, 25), (2, 37), (25, 41), (4, 33), (16, 24), (25, 17), (29, 30), (34, 40), (18, 5), (1, 16), (34, 17), (43, 18), (15, 32), (3, 32), (19, 19), (3, 12), (37, 35), (25, 1), (21, 21), (7, 5), (17, 2), (21, 8), (45, 3), (30, 2), (12, 25), (34, 34), (3, 20), (39, 22), (45, 22), (15, 17), (24, 25), (12, 42), (34, 41), (42, 19), (15, 35), (1, 28), (39, 34), (5, 36), (42, 18), (13, 26), (0, 12), (6, 37), (43, 13), (25, 16), (20, 18), (6, 17), (25, 32), (37, 11), (22, 14), (29, 31), (26, 14), (19, 1), (41, 26), (14, 37), (42, 17), (42, 42), (16, 7), (15, 36), (12, 26), (45, 40), (22, 38), (45, 34), (13, 14), (21, 41), (27, 9), (25, 21), (19, 36), (9, 35), (13, 4), (20, 33), (34, 3), (5, 3), (31, 38), (4, 7), (1, 9), (28, 32), (39, 31), (30, 21), (38, 41), (18, 37), (32, 18), (12, 17), (40, 31), (5, 24), (7, 14), (24, 6), (14, 12), (19, 38), (25, 14), (30, 10), (21, 14), (7, 1), (11, 28), (36, 3), (22, 39), (0, 32), (14, 0), (36, 22), (11, 0), (23, 28), (40, 38), (16, 33), (18, 14), (15, 7), (25, 29), (36, 8), (28, 25), (26, 36), (45, 24), (22, 0), (0, 30), (27, 36), (44, 20), (4, 1), (36, 29), (24, 1), (25, 13), (29, 14), (33, 7), (33, 15), (1, 32), (33, 18), (31, 7), (42, 10), (10, 24), (45, 31), (35, 14), (3, 22), (0, 38), (44, 15), (1, 17), (15, 37), (39, 24), (8, 14), (12, 24), (31, 6), (40, 23), (26, 30), (39, 3), (22, 16), (9, 4), (34, 21), (41, 25), (45, 5), (28, 1), (7, 12), (24, 10), (41, 34), (5, 38), (10, 3), (37, 0), (7, 34), (36, 2), (15, 30), (3, 34), (23, 5), (4, 17), (35, 23), (28, 37), (25, 15), (12, 36), (17, 0), (9, 7), (40, 28), (31, 19), (1, 27), (1, 20), (37, 32), (35, 2), (17, 33), (45, 17), (9, 15), (9, 18), (10, 42), (31, 10), (43, 42), (32, 23), (30, 4), (2, 9), (34, 8), (24, 16), (22, 22), (33, 41), (39, 41), (36, 41), (27, 35), (39, 15), (15, 13), (27, 41), (4, 3), (26, 9), (3, 13), (33, 42), (2, 8), (36, 16), (28, 7), (36, 5), (7, 4), (25, 34), (22, 31), (19, 26), (41, 19), (32, 5), (13, 3), (10, 29), (5, 35), (29, 32), (45, 10), (45, 35), (11, 18), (41, 38), (14, 3), (22, 27), (10, 19), (33, 1), (13, 18), (40, 22), (2, 24), (21, 6), (43, 27), (36, 6), (31, 23), (18, 13), (22, 19), (12, 8), (36, 11), (44, 29), (6, 42), (45, 41), (20, 42), (7, 13), (17, 5), (26, 26), (2, 30), (3, 31), (13, 8), (14, 27), (33, 2), (8, 23), (38, 42), (22, 21), (11, 26), (0, 1), (17, 31), (32, 33), (23, 16), (26, 0), (38, 2), (12, 27), (29, 38), (27, 2), (6, 9), (16, 36), (34, 6), (21, 15), (40, 19), (26, 35), (18, 15), (21, 19), (26, 7), (28, 36), (36, 10), (38, 10), (16, 32), (35, 31), (32, 30), (23, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 1), (25, 5), (0, 28), (27, 22), (13, 8), (32, 12), (32, 7), (28, 1), (38, 13), (31, 37), (13, 33), (41, 9), (35, 6), (10, 19), (38, 27), (24, 41), (32, 38), (43, 15), (2, 37), (36, 3), (37, 22), (12, 23), (16, 21), (15, 9), (31, 4), (4, 29), (42, 32), (0, 26), (40, 6), (9, 21), (20, 21), (27, 41), (39, 19), (12, 25), (26, 7), (23, 18), (36, 42), (32, 5), (0, 33), (24, 27), (20, 9), (1, 2), (13, 37), (27, 34), (21, 29), (38, 42), (16, 7), (18, 41), (20, 7), (0, 1), (22, 33), (25, 24), (15, 26), (28, 2), (24, 37), (40, 21), (18, 28), (10, 35), (19, 11), (6, 27), (1, 42), (35, 18), (21, 8), (22, 36), (19, 33), (23, 11), (9, 24), (9, 7), (41, 30), (30, 39), (23, 24), (0, 12), (34, 0), (35, 26), (24, 11), (28, 0), (3, 1), (44, 10), (42, 31), (12, 8), (22, 42), (8, 24), (44, 12), (34, 42), (4, 4), (42, 8), (1, 20), (14, 21), (17, 20), (15, 17), (27, 2), (12, 11), (18, 24), (24, 2), (24, 36), (21, 19), (33, 33), (22, 39), (29, 10), (27, 6), (33, 4), (21, 9), (29, 2), (1, 35), (19, 0), (9, 4), (4, 28), (17, 5), (11, 14), (36, 7), (19, 34), (8, 21), (14, 22), (26, 31), (8, 7), (8, 39), (35, 27), (26, 14), (38, 38), (30, 23), (6, 18), (21, 30), (9, 15), (2, 20), (33, 38), (9, 30), (5, 22), (3, 6), (8, 36), (22, 7), (10, 23), (33, 6), (4, 16), (2, 33), (2, 26), (16, 40), (33, 20), (14, 34), (31, 18), (2, 16), (2, 9), (26, 29), (27, 35), (41, 4), (33, 10), (25, 28), (25, 15), (26, 35), (19, 40), (24, 16), (9, 8), (11, 23), (42, 40), (27, 17), (11, 29), (20, 29), (37, 26), (41, 0), (2, 42), (7, 10), (1, 33), (43, 23), (6, 24), (33, 35), (6, 10), (5, 23), (4, 24), (25, 21), (43, 14), (27, 19), (16, 23), (41, 14), (11, 36), (12, 18), (20, 24), (12, 14), (29, 31), (18, 21), (11, 18), (24, 33), (36, 6), (2, 5), (31, 32), (44, 7), (38, 32), (37, 39), (19, 32), (13, 9), (1, 29), (7, 3), (33, 27), (0, 2), (3, 28), (34, 35), (1, 39), (40, 35), (11, 11), (44, 26), (26, 0), (30, 38), (4, 10), (6, 19), (30, 24), (33, 18), (30, 40), (15, 16), (26, 13), (35, 5), (17, 17), (41, 5), (36, 37), (3, 40), (5, 27), (24, 29), (38, 10), (23, 29), (41, 21), (12, 29), (17, 3), (36, 20), (1, 12), (44, 8), (23, 17), (23, 25), (28, 38), (14, 37), (33, 19), (6, 20), (31, 5), (11, 7), (35, 25), (11, 32), (41, 26), (33, 13), (22, 8), (32, 21), (15, 13), (41, 8), (16, 15), (17, 9), (12, 41), (30, 9), (30, 8), (34, 19), (37, 37), (39, 36), (37, 30), (23, 6), (22, 20), (12, 0), (9, 34), (5, 26), (41, 1), (19, 23), (3, 17), (36, 28), (39, 20), (9, 29), (4, 31), (9, 40), (35, 22), (27, 7), (31, 9), (26, 20), (2, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 4), (36, 29), (11, 13), (3, 29), (8, 7), (34, 34), (10, 26), (14, 30), (7, 1), (28, 42), (8, 5), (22, 9), (30, 18), (13, 27), (10, 39), (39, 20), (14, 31), (22, 13), (4, 27), (25, 11), (7, 30), (2, 7), (14, 37), (0, 30), (19, 43), (18, 23), (26, 44), (8, 9), (2, 16), (32, 22), (11, 34), (30, 20), (13, 26), (8, 31), (14, 28), (14, 36), (2, 6), (21, 30), (0, 7), (39, 13), (3, 37), (8, 11), (8, 28), (0, 10), (5, 33), (16, 37), (19, 10), (33, 33), (12, 43), (39, 30), (31, 7), (5, 9), (11, 14), (7, 38), (3, 26), (21, 6), (0, 2), (17, 41), (39, 9), (19, 15), (21, 36), (2, 37), (10, 36), (25, 25), (30, 35), (25, 43), (23, 28), (22, 43), (24, 16), (15, 28), (16, 1), (8, 13), (6, 16), (37, 32), (33, 17), (35, 32), (18, 44), (13, 13), (36, 12), (35, 3), (17, 0), (3, 18), (4, 2), (21, 27), (4, 9), (24, 26), (10, 33), (20, 24), (29, 0), (1, 11), (15, 34), (22, 23), (7, 5), (28, 25), (13, 38), (0, 23), (6, 1), (34, 1), (7, 24), (8, 2), (6, 17), (30, 44), (28, 5), (4, 22), (0, 25), (1, 5), (5, 13), (16, 38), (6, 11), (16, 6), (17, 23), (18, 29), (27, 42), (35, 35), (28, 32), (23, 39), (27, 19), (19, 17), (22, 8), (0, 22), (9, 25), (18, 42), (3, 27), (12, 1), (10, 12), (17, 13), (38, 15), (35, 8), (25, 2), (39, 35), (39, 24), (4, 38), (32, 29), (24, 36), (18, 2), (31, 30), (24, 4), (5, 20), (29, 29), (13, 14), (0, 27), (1, 34), (2, 28), (1, 16), (33, 1), (29, 22), (13, 36), (38, 37), (13, 0), (29, 44), (16, 25), (8, 10), (20, 7), (16, 15), (37, 10), (1, 10), (3, 42), (24, 43), (26, 40), (0, 34), (25, 18), (17, 44), (10, 31), (38, 4), (34, 41), (27, 31), (30, 17), (27, 27), (24, 39), (15, 5), (23, 17), (28, 0), (4, 31), (5, 31), (21, 42), (24, 32), (36, 0), (5, 42), (28, 24), (39, 2), (22, 28), (25, 28), (20, 14), (11, 37), (4, 7), (33, 18), (35, 16), (26, 17), (30, 19), (9, 29), (35, 23), (2, 15), (12, 11), (33, 2), (11, 23), (31, 9), (26, 37), (12, 33), (20, 2), (32, 33), (37, 37), (19, 35), (23, 26), (27, 23), (32, 7), (5, 27), (22, 5), (16, 12), (14, 0), (9, 36), (20, 4), (39, 29), (6, 42), (31, 29), (26, 1), (16, 9), (11, 43), (27, 25), (37, 3), (22, 1), (35, 14), (31, 32), (14, 18), (27, 36), (7, 44), (0, 42), (31, 15), (5, 25), (9, 18), (17, 39), (38, 44), (31, 12), (1, 9), (3, 5), (22, 39), (38, 25), (1, 25), (4, 41), (17, 9), (24, 42), (0, 44), (21, 18), (34, 7), (21, 38), (16, 10), (0, 18), (1, 30), (20, 42), (17, 15), (30, 22), (13, 18), (18, 14), (0, 26), (37, 0), (8, 32), (35, 7), (32, 41), (30, 12), (38, 24), (21, 1), (33, 3), (25, 26), (26, 12), (32, 24), (18, 30), (23, 11), (20, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 25), (4, 34), (3, 37), (32, 7), (29, 18), (2, 29), (27, 17), (9, 13), (8, 45), (34, 27), (31, 9), (35, 11), (2, 38), (8, 25), (8, 14), (2, 45), (40, 43), (42, 30), (12, 8), (2, 6), (14, 2), (30, 35), (40, 18), (33, 36), (4, 1), (37, 23), (20, 7), (24, 42), (2, 9), (11, 44), (21, 8), (23, 37), (38, 3), (8, 20), (31, 31), (5, 22), (41, 38), (33, 34), (13, 37), (23, 36), (4, 8), (24, 45), (11, 35), (0, 8), (20, 5), (3, 0), (34, 0), (6, 34), (23, 2), (1, 31), (16, 28), (28, 32), (38, 31), (30, 9), (17, 21), (17, 41), (35, 25), (3, 35), (6, 2), (36, 39), (15, 8), (21, 2), (29, 3), (19, 39), (20, 25), (35, 6), (13, 4), (13, 34), (0, 21), (26, 40), (39, 9), (15, 36), (20, 45), (1, 8), (30, 23), (37, 11), (6, 0), (42, 26), (27, 45), (41, 9), (7, 33), (41, 30), (38, 38), (4, 13), (30, 26), (5, 38), (42, 11), (41, 25), (38, 26), (12, 26), (12, 23), (32, 45), (14, 11), (0, 32), (27, 5), (30, 12), (37, 31), (14, 35), (7, 25), (17, 35), (10, 39), (10, 42), (24, 4), (6, 23), (3, 7), (0, 36), (16, 36), (13, 27), (25, 29), (40, 16), (8, 41), (29, 26), (26, 42), (39, 40), (31, 15), (12, 16), (39, 20), (23, 4), (16, 35), (2, 2), (3, 14), (22, 16), (27, 12), (0, 6), (5, 37), (31, 20), (26, 13), (36, 17), (20, 32), (42, 0), (16, 5), (23, 27), (37, 43), (0, 34), (9, 17), (13, 22), (9, 40), (23, 20), (22, 27), (0, 40), (25, 14), (13, 38), (23, 13), (30, 8), (15, 26), (19, 34), (34, 12), (40, 17), (10, 45), (20, 17), (0, 35), (36, 1), (29, 45), (3, 2), (15, 18), (27, 15), (35, 3), (30, 22), (2, 44), (15, 19), (8, 13), (6, 3), (23, 14), (23, 35), (5, 30), (39, 28), (3, 18), (32, 18), (1, 41), (42, 29), (26, 39), (30, 33), (30, 38), (8, 4), (34, 33), (28, 27), (11, 32), (32, 39), (1, 1), (22, 15), (3, 36), (42, 35), (12, 0), (8, 5), (40, 14), (29, 0), (18, 2), (40, 23), (12, 10), (21, 3), (36, 0), (27, 42), (14, 16), (14, 36), (15, 45), (22, 45), (14, 6), (23, 15), (27, 31), (25, 7), (3, 42), (16, 12), (14, 37), (25, 0), (23, 11), (10, 25), (29, 13), (28, 31), (38, 29), (4, 20), (24, 28), (38, 40), (30, 36), (9, 34), (5, 45), (11, 24), (6, 45), (17, 17), (31, 34), (0, 45), (1, 2), (38, 10), (38, 5), (22, 10), (32, 43), (16, 20), (40, 31), (24, 32), (42, 33), (7, 30), (19, 14), (9, 31), (20, 38), (7, 32), (26, 10), (19, 16), (12, 27), (16, 27), (12, 7), (39, 21), (41, 26), (28, 29), (17, 29), (8, 9), (27, 43), (41, 10), (23, 33), (36, 6), (21, 25), (11, 30), (34, 19), (10, 14), (11, 39), (8, 23), (28, 20), (6, 25), (36, 40), (17, 14), (5, 12), (33, 40), (31, 36), (28, 1), (25, 3), (16, 14), (27, 36), (42, 37), (37, 22), (3, 1), (32, 23), (31, 16), (26, 16), (31, 0), (5, 17), (17, 37), (10, 17), (33, 1), (27, 39), (28, 36), (3, 12), (19, 37), (4, 22), (40, 29), (28, 2), (41, 31), (36, 22), (28, 3), (15, 29), (29, 31), (39, 2), (4, 41), (25, 35), (22, 21), (19, 12), (10, 29), (27, 4), (25, 30), (36, 28), (21, 0), (42, 42), (25, 12), (7, 34), (38, 15), (33, 43), (23, 21), (5, 6), (22, 0), (36, 37), (11, 15), (41, 29), (35, 16), (20, 16), (3, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 5), (27, 16), (15, 17), (0, 22), (2, 18), (17, 6), (8, 29), (44, 4), (34, 0), (13, 35), (30, 39), (35, 27), (6, 40), (5, 4), (17, 30), (25, 20), (42, 30), (0, 39), (3, 45), (14, 9), (20, 43), (42, 25), (17, 19), (12, 17), (42, 22), (35, 0), (23, 32), (7, 39), (6, 31), (44, 3), (41, 45), (43, 6), (10, 7), (2, 20), (11, 12), (45, 6), (39, 23), (6, 7), (10, 39), (37, 18), (43, 11), (44, 38), (32, 13), (2, 7), (37, 26), (21, 9), (44, 32), (19, 35), (33, 7), (15, 39), (15, 0), (16, 1), (16, 8), (7, 17), (28, 39), (43, 28), (42, 27), (4, 2), (18, 11), (30, 12), (30, 1), (7, 26), (32, 26), (29, 39), (22, 18), (46, 24), (5, 30), (15, 20), (43, 9), (18, 13), (38, 18), (8, 6), (9, 35), (32, 22), (2, 30), (12, 18), (30, 21), (46, 23), (33, 12), (0, 19), (46, 43), (32, 9), (3, 37), (34, 2), (15, 36), (21, 2), (19, 43), (1, 32), (9, 36), (22, 41), (4, 8), (29, 41), (28, 13), (43, 43), (26, 32), (41, 33), (26, 33), (23, 21), (18, 39), (41, 22), (32, 8), (33, 26), (23, 6), (43, 14), (24, 14), (27, 7), (19, 34), (18, 20), (6, 32), (10, 38), (28, 6), (22, 16), (19, 30), (39, 32), (0, 35), (42, 40), (39, 28), (13, 13), (30, 27), (31, 19), (39, 38), (43, 45), (40, 38), (3, 6), (34, 9), (45, 27), (4, 19), (35, 28), (21, 35), (30, 34), (24, 12), (42, 3), (26, 5), (27, 18), (37, 4), (23, 16), (7, 34), (14, 5), (15, 16), (14, 34), (19, 44), (12, 12), (17, 15), (25, 34), (20, 45), (26, 38), (26, 8), (26, 43), (43, 13), (26, 22), (25, 36), (2, 0), (44, 17), (24, 31), (3, 29), (26, 41), (32, 44), (31, 5), (12, 36), (15, 1), (4, 39), (33, 27), (38, 44), (23, 14), (42, 45), (40, 20), (26, 20), (40, 10), (17, 14), (30, 5), (38, 30), (45, 43), (21, 8), (44, 36), (15, 29), (27, 6), (35, 31), (11, 25), (45, 26), (45, 7), (26, 19), (18, 38), (7, 42), (39, 17), (23, 37), (43, 25), (18, 30), (3, 44), (2, 35), (12, 38), (35, 15), (35, 17), (21, 7), (31, 17), (27, 19), (6, 19), (44, 0), (19, 14), (18, 14), (41, 36), (32, 35), (24, 20), (27, 35), (0, 31), (21, 1), (46, 31), (46, 27), (3, 38), (27, 25), (9, 43), (2, 22), (28, 38), (44, 10), (11, 11), (46, 14), (19, 27), (25, 37), (1, 27), (15, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 26), (41, 7), (22, 31), (34, 16), (21, 5), (42, 44), (43, 8), (24, 9), (18, 25), (27, 18), (18, 15), (36, 37), (16, 4), (48, 41), (19, 20), (29, 4), (9, 41), (47, 16), (9, 17), (14, 18), (37, 24), (24, 38), (39, 17), (32, 15), (39, 32), (17, 1), (4, 1), (9, 1), (8, 36), (10, 39), (3, 8), (41, 32), (48, 37), (12, 34), (33, 10), (3, 11), (36, 39), (43, 22), (30, 20), (39, 13), (48, 25), (39, 33), (48, 2), (46, 12), (42, 37), (47, 41), (2, 40), (4, 41), (48, 15), (28, 35), (20, 44), (1, 41), (28, 3), (44, 45), (27, 35), (32, 27), (7, 24), (20, 19), (27, 39), (17, 9), (24, 13), (46, 20), (11, 45), (4, 28), (5, 29), (5, 22), (23, 9), (11, 32), (16, 16), (17, 8), (28, 30), (30, 43), (38, 14), (23, 27), (34, 27), (17, 17), (47, 7), (45, 45), (33, 2), (45, 12), (33, 25), (9, 14), (22, 11), (37, 36), (20, 15), (22, 32), (47, 29), (15, 5), (28, 23), (12, 42), (12, 35), (44, 39), (20, 14), (2, 16), (0, 18), (0, 17), (14, 22), (11, 3), (24, 21), (27, 21), (12, 6), (31, 45), (18, 22), (20, 22), (21, 30), (37, 25), (4, 6), (26, 34), (12, 14), (15, 35), (5, 10), (40, 18), (18, 16), (44, 41), (38, 7), (29, 6), (28, 13), (31, 1), (6, 42), (21, 10), (17, 29), (36, 5), (10, 9), (3, 38), (48, 33), (7, 31), (24, 34), (19, 44), (24, 1), (37, 18), (12, 43), (5, 28), (40, 26), (17, 11), (38, 13), (37, 27), (27, 45), (33, 3), (6, 16), (10, 33), (27, 0), (0, 7), (24, 23), (2, 5), (7, 13), (32, 28), (2, 14), (30, 45), (42, 15), (26, 8), (46, 6), (16, 31), (34, 23), (20, 36), (45, 35), (5, 36), (32, 26), (14, 36), (2, 9), (6, 34), (11, 19), (38, 24), (16, 27), (4, 38), (41, 40), (16, 21), (41, 14), (33, 4), (43, 24), (11, 15), (39, 6), (12, 41), (31, 9), (40, 11), (29, 43), (12, 21), (19, 31), (44, 23), (13, 29), (9, 34), (3, 0), (33, 20), (7, 40), (4, 31), (3, 9), (14, 24), (29, 23), (41, 4), (33, 14), (31, 17), (15, 44), (43, 43), (1, 29), (29, 13), (33, 12), (13, 26), (8, 25), (19, 10), (30, 6), (45, 43), (31, 25), (42, 17), (14, 14), (24, 15), (16, 18), (43, 37), (30, 8), (31, 13), (33, 34), (11, 30), (4, 23), (25, 30), (30, 9), (13, 28), (36, 6), (10, 45), (15, 24), (39, 7), (31, 19), (18, 37), (17, 13), (7, 35), (36, 44), (45, 36), (27, 23), (46, 26), (45, 7), (11, 35), (20, 16), (45, 14), (22, 20), (19, 38), (11, 37), (24, 28), (3, 10), (15, 12), (30, 1), (20, 21), (20, 20), (2, 23), (23, 34), (47, 26), (42, 30), (29, 24), (14, 10), (27, 6), (28, 34), (1, 37), (13, 44), (32, 4), (35, 24), (23, 13), (35, 38), (29, 2), (0, 8), (39, 12), (25, 13), (36, 38), (33, 15), (6, 23), (36, 27), (39, 41), (12, 31), (11, 28), (33, 6), (40, 1), (9, 40), (5, 18), (34, 13), (22, 27), (15, 22), (28, 39), (8, 13), (17, 0), (22, 9), (23, 11), (2, 10), (22, 36), (44, 5), (48, 17), (26, 23), (34, 12), (10, 42), (10, 23), (42, 5), (37, 39), (46, 2), (33, 42), (7, 37), (13, 34), (38, 28), (21, 1), (7, 43), (13, 10), (0, 40), (15, 26), (34, 4), (6, 41), (17, 20), (16, 1), (34, 22), (20, 32), (37, 33), (11, 9), (43, 21), (7, 42), (2, 27), (5, 25), (31, 44), (30, 19), (45, 4), (10, 8), (42, 14), (0, 4), (45, 10), (20, 9), (48, 27), (21, 11), (16, 28), (5, 21), (18, 29), (39, 27), (24, 3), (30, 37), (44, 34), (40, 40), (24, 43), (48, 20), (11, 5), (6, 18), (26, 3), (30, 3), (1, 23), (24, 10), (7, 8), (4, 7), (5, 41), (46, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 13), (36, 31), (44, 9), (23, 44), (45, 46), (20, 36), (18, 6), (5, 36), (33, 29), (15, 33), (16, 21), (9, 21), (6, 43), (12, 26), (46, 20), (13, 42), (32, 18), (29, 28), (36, 23), (21, 6), (37, 16), (11, 18), (30, 29), (37, 2), (29, 0), (14, 2), (42, 12), (9, 4), (36, 5), (44, 42), (0, 11), (7, 34), (23, 37), (9, 35), (21, 23), (38, 20), (9, 10), (2, 35), (9, 37), (39, 16), (38, 10), (28, 26), (33, 8), (12, 40), (46, 11), (7, 13), (25, 0), (36, 20), (26, 24), (41, 1), (38, 3), (28, 1), (10, 14), (25, 18), (27, 36), (34, 16), (19, 39), (3, 4), (13, 34), (0, 23), (35, 22), (3, 16), (18, 28), (34, 14), (37, 22), (45, 25), (23, 8), (8, 40), (39, 12), (24, 41), (15, 28), (8, 13), (28, 9), (44, 36), (38, 5), (5, 26), (13, 12), (46, 10), (30, 42), (40, 42), (29, 16), (25, 12), (44, 4), (35, 45), (3, 39), (25, 40), (8, 14), (25, 27), (31, 34), (23, 17), (27, 41), (46, 26), (43, 21), (33, 15), (20, 25), (34, 33), (1, 37), (37, 14), (30, 32), (6, 2), (37, 19), (10, 9), (22, 27), (29, 23), (6, 23), (33, 22), (17, 39), (11, 46), (31, 0), (21, 9), (14, 29), (12, 46), (5, 43), (18, 45), (27, 2), (36, 36), (22, 0), (5, 18), (35, 36), (44, 37), (36, 46), (21, 8), (19, 32), (39, 23), (12, 27), (3, 17), (31, 39), (34, 21), (21, 29), (31, 3), (24, 26), (18, 23), (42, 10), (1, 18), (21, 27), (42, 35), (33, 20), (44, 41), (16, 34), (10, 1), (36, 34), (29, 44), (9, 14), (13, 28), (16, 38), (13, 20), (16, 40), (31, 38), (4, 15), (40, 33), (9, 45), (19, 37), (44, 31), (20, 20), (39, 43), (11, 22), (24, 6), (18, 16), (31, 46), (23, 38), (19, 19), (27, 20), (21, 32), (37, 7), (36, 45), (17, 34), (4, 6), (3, 14), (20, 11), (25, 33), (0, 31), (5, 1), (21, 39), (22, 38), (36, 1), (2, 31), (42, 24), (0, 26), (37, 24), (27, 23), (14, 0), (8, 20), (38, 12), (0, 13), (4, 3), (27, 43), (7, 32), (23, 41), (39, 7), (43, 19), (20, 41), (42, 26), (14, 31), (3, 20), (19, 34), (24, 20), (9, 0), (36, 22), (15, 12), (28, 27), (37, 28), (8, 2), (9, 32), (28, 29), (29, 22), (24, 43), (25, 46), (3, 26), (44, 35), (5, 35), (19, 6), (44, 20), (41, 32), (8, 41), (37, 31), (17, 26), (27, 18), (30, 44), (20, 30), (35, 12), (26, 22), (34, 10), (19, 33), (34, 26), (33, 28), (21, 42), (39, 40), (2, 5), (42, 17), (23, 32), (29, 36), (24, 18), (42, 11), (5, 37), (42, 4), (34, 44), (13, 15), (43, 28), (2, 19), (38, 18), (8, 38), (0, 24), (15, 41), (13, 5), (7, 21), (39, 13), (45, 37), (30, 41), (41, 17), (25, 16), (28, 2), (16, 13), (22, 7), (42, 31), (46, 43), (40, 8), (15, 45), (8, 18), (9, 11), (41, 28), (26, 7), (0, 16), (38, 38), (3, 6), (34, 2), (10, 0), (17, 23), (39, 37), (11, 28), (8, 16), (25, 23), (25, 21), (14, 44), (45, 33), (6, 44), (3, 2), (0, 19), (6, 22), (6, 24), (43, 0), (31, 5), (22, 19), (20, 7), (21, 34), (38, 17), (15, 2), (19, 41), (35, 11), (32, 22), (32, 10), (25, 11), (43, 23), (1, 5), (26, 20), (30, 34), (4, 19), (30, 43), (10, 2), (24, 32), (30, 23), (27, 35), (26, 8), (46, 4), (13, 17), (32, 41), (13, 35), (32, 37), (34, 9), (34, 20), (14, 24), (43, 3), (23, 5), (32, 14), (16, 15), (21, 43), (30, 3), (21, 21), (41, 30), (27, 14), (32, 6), (2, 8), (4, 41), (14, 4), (19, 8), (24, 2), (40, 15), (20, 1), (6, 15), (45, 40), (44, 13), (43, 1), (9, 40), (15, 0), (39, 35), (9, 2), (41, 3), (8, 36), (18, 13), (8, 37), (7, 29), (2, 36), (46, 23), (32, 44), (19, 31), (33, 25), (45, 11), (27, 24), (44, 3), (2, 14), (28, 16), (30, 38), (40, 29), (42, 1), (42, 6), (10, 34), (2, 25), (20, 12), (9, 34), (20, 22), (18, 12), (21, 17), (23, 29), (7, 24), (9, 16), (10, 45), (29, 46), (29, 35), (34, 3), (37, 42), (25, 6), (20, 14), (23, 10), (44, 34), (14, 3), (35, 29), (19, 13), (36, 41), (41, 35), (11, 17), (18, 2), (33, 44), (35, 5), (21, 41), (11, 31), (40, 30), (30, 14), (43, 33), (34, 11), (6, 29), (46, 37), (13, 45), (27, 16), (11, 38), (32, 34), (31, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 8), (26, 30), (30, 30), (14, 27), (27, 33), (30, 11), (31, 17), (37, 9), (5, 12), (19, 28), (36, 39), (25, 24), (19, 36), (7, 0), (36, 2), (23, 33), (40, 5), (15, 32), (1, 24), (40, 35), (35, 5), (14, 24), (31, 16), (26, 39), (18, 27), (10, 38), (44, 19), (20, 21), (17, 19), (39, 0), (36, 28), (21, 28), (32, 4), (43, 12), (9, 37), (43, 29), (27, 26), (17, 25), (1, 29), (42, 35), (18, 5), (17, 24), (1, 6), (46, 33), (23, 15), (36, 26), (44, 28), (31, 25), (28, 38), (16, 39), (12, 0), (10, 26), (17, 11), (30, 14), (35, 21), (35, 1), (10, 4), (17, 7), (1, 27), (24, 6), (22, 33), (10, 6), (33, 30), (44, 35), (35, 4), (16, 29), (28, 21), (37, 32), (24, 11), (27, 40), (21, 8), (6, 6), (46, 38), (19, 7), (43, 14), (20, 25), (14, 32), (39, 12), (22, 16), (34, 16), (26, 11), (43, 38), (3, 13), (0, 22), (43, 21), (9, 38), (31, 8), (25, 8), (8, 34), (29, 15), (25, 3), (34, 40), (26, 20), (5, 1), (45, 1), (2, 3), (29, 7), (4, 24), (41, 20), (38, 27), (2, 7), (44, 23), (11, 21), (10, 16), (41, 39), (20, 12), (46, 13), (46, 25), (17, 38), (16, 10), (33, 4), (24, 8), (43, 10), (30, 12), (26, 0), (20, 8), (23, 37), (8, 35), (2, 34), (7, 19), (37, 12), (3, 0), (39, 23), (3, 11), (5, 38), (39, 16), (15, 26), (30, 8), (32, 19), (31, 28), (44, 7), (3, 40), (14, 30), (34, 33), (44, 15), (20, 13), (37, 29), (43, 23), (19, 32), (29, 25), (15, 14), (21, 16), (15, 5), (17, 9), (15, 27), (39, 26), (8, 33), (26, 14), (40, 14), (36, 1), (9, 20), (32, 1), (20, 29), (19, 5), (24, 27), (0, 24), (17, 16), (12, 34), (16, 16), (19, 9), (26, 2), (41, 32), (38, 20), (22, 31), (38, 8), (7, 23), (25, 12), (24, 25), (35, 15), (37, 26), (35, 39), (11, 38), (13, 30), (9, 36), (34, 11), (18, 9), (26, 3), (7, 11), (41, 29), (19, 25), (38, 1), (37, 30), (43, 26), (42, 27), (33, 34), (21, 20), (20, 14), (46, 23), (12, 10), (18, 29), (0, 2), (9, 7), (12, 1), (18, 6), (33, 22), (2, 9), (26, 5), (38, 0), (34, 15), (29, 35), (45, 33), (28, 1), (45, 13), (41, 40), (1, 35), (15, 0), (39, 14), (44, 33), (7, 28), (41, 9), (9, 2), (29, 11), (14, 26), (27, 11), (36, 12), (43, 6), (32, 33), (24, 39), (46, 34), (2, 38), (13, 7), (12, 27), (43, 27), (8, 16), (29, 21), (10, 13), (45, 0), (34, 32), (42, 37), (31, 3), (32, 17), (30, 0), (35, 19), (0, 3), (29, 1), (31, 9), (34, 24), (25, 39), (44, 16), (32, 30), (22, 38), (26, 13), (28, 23), (3, 4), (25, 21), (23, 1), (46, 28), (10, 8), (12, 33), (42, 33), (20, 9), (20, 0), (37, 1), (39, 27), (24, 15), (9, 8), (26, 6), (41, 17), (39, 28), (2, 27), (34, 4), (18, 33), (45, 25), (21, 32), (36, 9), (11, 0), (25, 18), (15, 3), (4, 8), (25, 28), (19, 12), (18, 10), (10, 9), (26, 26), (43, 34), (18, 19), (0, 9), (3, 23), (15, 23), (34, 28), (16, 26), (23, 11), (7, 39), (19, 15), (30, 33), (42, 6), (6, 21), (39, 1), (15, 37), (30, 17), (26, 15), (44, 10), (34, 8), (19, 2), (8, 14), (28, 36), (9, 31), (33, 23), (6, 27), (25, 16), (1, 12), (19, 14), (0, 6), (9, 16), (22, 27), (31, 2), (5, 11), (16, 38), (41, 13), (36, 0), (7, 16), (38, 13), (2, 23), (36, 7), (46, 15), (26, 16), (6, 22), (11, 11), (22, 1), (35, 0), (21, 18), (15, 13), (2, 4), (24, 18), (15, 34), (18, 18), (38, 18), (36, 16), (14, 5), (46, 20), (12, 13), (30, 22), (46, 21), (34, 26), (4, 14), (15, 8), (23, 16), (45, 39), (23, 25), (5, 17), (22, 11), (39, 33), (14, 19), (2, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 40), (22, 15), (31, 18), (31, 0), (39, 15), (32, 38), (25, 27), (6, 4), (1, 25), (5, 3), (26, 34), (21, 18), (12, 36), (38, 4), (40, 29), (36, 38), (37, 24), (35, 7), (14, 9), (26, 14), (23, 38), (38, 0), (31, 13), (43, 26), (21, 14), (32, 3), (2, 38), (22, 32), (18, 5), (15, 3), (31, 27), (4, 35), (41, 12), (10, 35), (6, 12), (24, 18), (3, 18), (34, 38), (35, 36), (36, 33), (6, 6), (5, 27), (18, 41), (21, 8), (5, 35), (33, 26), (11, 37), (1, 17), (41, 38), (39, 14), (25, 15), (26, 24), (11, 28), (22, 41), (16, 5), (20, 29), (2, 12), (39, 32), (12, 19), (41, 9), (29, 17), (12, 18), (32, 28), (25, 7), (32, 1), (9, 14), (31, 26), (5, 13), (14, 32), (35, 23), (0, 36), (0, 32), (23, 8), (0, 30), (15, 0), (34, 2), (29, 41), (39, 5), (27, 38), (33, 7), (41, 37), (36, 4), (43, 14), (27, 4), (25, 22), (4, 28), (40, 32), (13, 22), (23, 29), (25, 32), (33, 32), (34, 10), (26, 38), (4, 20), (16, 37), (41, 41), (34, 3), (12, 33), (38, 39), (24, 35), (12, 8), (1, 6), (5, 29), (3, 8), (32, 4), (18, 30), (40, 13), (7, 33), (17, 2), (2, 20), (26, 12), (7, 10), (18, 0), (10, 2), (4, 4), (24, 24), (31, 5), (2, 28), (1, 20), (27, 37), (38, 23), (20, 19), (12, 10), (24, 30), (12, 6), (34, 9), (9, 41), (35, 14), (21, 36), (13, 16), (7, 2), (43, 30), (14, 20), (0, 12), (4, 39), (39, 23), (11, 8), (34, 4), (38, 1), (28, 3), (2, 26), (1, 9), (5, 10), (10, 21), (13, 8), (10, 38), (34, 31), (5, 41), (22, 19), (26, 5), (4, 1), (5, 16), (30, 40), (15, 31), (41, 24), (33, 1), (41, 33), (11, 34), (14, 22), (38, 13), (40, 5), (43, 37), (23, 18), (36, 3), (4, 38), (15, 32), (13, 3), (5, 7), (11, 32), (35, 26), (39, 28), (36, 13), (2, 14), (41, 19), (22, 17), (15, 26), (16, 23), (37, 4), (7, 36), (42, 4), (27, 23), (9, 31), (18, 19), (33, 3), (22, 2), (40, 28), (2, 6), (8, 28), (2, 41), (1, 31), (13, 0), (2, 18), (4, 18), (26, 28), (17, 38), (27, 40), (31, 28), (9, 2), (19, 15), (7, 20), (26, 41), (6, 34), (11, 40), (10, 9), (14, 24), (31, 31), (35, 25), (10, 19), (25, 10), (19, 19), (0, 1), (31, 2), (5, 0), (28, 29), (14, 38), (31, 9), (19, 31), (40, 4), (38, 8), (35, 37), (28, 38), (42, 35), (41, 3), (12, 29), (36, 22), (23, 11), (17, 9), (31, 3), (39, 22), (17, 35), (31, 4), (40, 8), (6, 16), (9, 39), (26, 16), (11, 10), (41, 15), (29, 29), (13, 39), (30, 24), (18, 4), (28, 6), (40, 20), (26, 13), (2, 37), (16, 13), (23, 14), (35, 33), (1, 11), (25, 4), (39, 3), (11, 13), (19, 13), (5, 38), (42, 11), (23, 3), (28, 34), (25, 37), (27, 7), (9, 38), (37, 39), (10, 8), (20, 2), (8, 33), (38, 31), (22, 29), (5, 5), (10, 41), (10, 39), (32, 15), (8, 2), (18, 16), (23, 17), (10, 7), (4, 31), (40, 41), (8, 38), (20, 16), (10, 6), (12, 17), (42, 1), (3, 12), (35, 39), (38, 21), (41, 10), (26, 8), (13, 41), (29, 0), (13, 7), (10, 26), (6, 32), (3, 31), (42, 6), (8, 6), (42, 12), (30, 1), (30, 4), (21, 30), (42, 39), (24, 4), (5, 18), (21, 27), (7, 24), (6, 27), (29, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 27), (46, 26), (35, 13), (34, 34), (21, 25), (25, 34), (40, 37), (29, 30), (10, 31), (2, 38), (46, 27), (3, 21), (33, 28), (5, 2), (7, 19), (12, 1), (10, 24), (4, 15), (15, 29), (23, 24), (48, 15), (43, 11), (8, 19), (6, 41), (29, 27), (31, 30), (32, 10), (28, 13), (36, 9), (46, 34), (7, 4), (30, 19), (2, 0), (40, 21), (41, 29), (6, 34), (18, 27), (32, 20), (36, 32), (14, 22), (4, 18), (41, 39), (37, 40), (45, 3), (16, 42), (4, 5), (43, 10), (7, 35), (14, 33), (7, 20), (23, 2), (4, 39), (23, 26), (9, 27), (1, 41), (47, 11), (31, 29), (41, 31), (38, 32), (7, 27), (23, 42), (25, 16), (6, 1), (37, 11), (10, 15), (18, 6), (11, 39), (34, 14), (4, 34), (2, 14), (24, 36), (34, 6), (45, 26), (44, 30), (31, 23), (27, 37), (32, 25), (17, 3), (19, 13), (24, 13), (10, 25), (16, 11), (10, 36), (26, 0), (1, 14), (2, 25), (19, 24), (21, 1), (38, 6), (8, 15), (10, 30), (2, 23), (14, 3), (30, 38), (25, 37), (17, 9), (12, 10), (4, 11), (25, 31), (1, 38), (5, 4), (48, 28), (43, 17), (36, 14), (28, 38), (12, 32), (3, 17), (28, 2), (7, 30), (7, 23), (35, 7), (24, 4), (1, 9), (34, 25), (43, 19), (34, 26), (5, 20), (31, 31), (2, 8), (23, 39), (29, 38), (18, 1), (6, 9), (18, 32), (19, 12), (12, 0), (25, 42), (21, 8), (14, 0), (38, 37), (0, 36), (48, 36), (20, 40), (6, 31), (21, 29), (8, 1), (4, 29), (41, 32), (13, 38), (28, 28), (12, 38), (0, 18), (11, 4), (12, 31), (41, 37), (31, 39), (23, 1), (22, 15), (34, 28), (35, 6), (14, 1), (7, 9), (24, 0), (26, 21), (48, 29), (19, 32), (13, 23), (23, 4), (40, 34), (22, 11), (35, 29), (45, 37), (16, 6), (22, 16), (43, 20), (23, 15), (22, 6), (39, 1), (26, 24), (11, 16), (32, 16), (29, 0), (36, 7), (28, 1), (23, 38), (37, 0), (41, 14), (39, 8), (20, 12), (35, 40), (2, 32), (5, 24), (3, 25), (12, 37), (5, 34), (4, 42), (39, 0), (27, 34), (15, 38), (24, 28), (43, 4), (23, 20), (30, 18), (39, 16), (43, 31), (8, 42), (44, 35), (22, 19), (5, 12), (3, 1), (44, 37), (36, 43), (4, 30), (23, 5), (34, 27), (27, 15), (0, 14), (8, 30), (13, 16), (21, 35), (20, 17), (38, 25), (30, 17), (33, 38), (41, 20), (33, 37), (42, 19), (44, 15), (0, 33), (28, 33), (34, 32), (19, 25), (5, 23), (28, 3), (48, 16), (21, 43), (38, 15), (30, 24), (26, 29), (35, 17), (35, 16), (2, 1), (1, 6), (7, 33), (14, 21), (43, 13), (1, 22), (39, 17), (47, 39), (48, 17), (26, 14), (33, 33), (13, 25), (17, 7), (20, 21), (10, 35), (32, 19), (8, 20), (37, 32), (21, 23), (39, 40), (29, 13), (7, 5), (48, 7), (13, 31), (48, 9), (29, 8), (9, 21), (24, 26), (9, 20), (43, 6), (46, 18), (27, 42), (12, 30), (47, 8), (13, 39), (24, 12), (1, 28), (34, 37), (32, 38), (44, 4), (2, 24), (39, 3), (47, 5), (36, 2), (47, 2), (9, 9), (20, 20), (35, 10), (27, 1), (9, 37), (0, 41), (26, 19), (7, 12), (10, 37), (24, 5), (35, 34), (13, 32), (41, 12), (5, 14), (44, 25), (42, 5), (33, 7), (3, 3), (25, 1), (29, 1), (4, 4), (1, 5), (5, 33), (37, 7), (29, 11), (29, 24), (23, 31), (8, 29), (29, 42), (22, 22), (25, 0), (42, 16), (47, 42), (7, 8), (33, 21), (3, 36), (47, 36), (42, 33), (2, 3), (31, 36), (31, 16), (23, 33), (7, 16), (28, 0), (29, 6), (31, 24), (7, 18), (38, 19), (46, 1), (25, 39), (26, 11), (15, 22), (1, 16), (29, 26), (15, 27), (7, 6), (22, 9), (11, 25), (23, 9), (9, 8), (46, 16), (10, 1), (35, 14), (28, 41), (42, 14), (38, 4), (37, 37), (48, 37), (9, 26), (30, 15), (4, 22), (39, 26), (28, 30), (14, 23), (8, 43), (43, 35), (30, 31), (30, 27), (21, 27), (36, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 15), (22, 21), (36, 29), (24, 27), (40, 29), (7, 12), (12, 29), (27, 18), (32, 4), (27, 5), (16, 4), (20, 21), (43, 41), (46, 25), (8, 12), (40, 34), (31, 3), (2, 41), (31, 34), (38, 45), (17, 40), (10, 4), (6, 5), (42, 12), (15, 0), (34, 34), (23, 27), (19, 27), (6, 12), (46, 41), (2, 23), (17, 25), (28, 11), (3, 40), (19, 38), (4, 35), (46, 45), (44, 40), (18, 12), (13, 14), (23, 11), (15, 5), (18, 30), (6, 7), (31, 7), (34, 1), (45, 11), (44, 1), (30, 26), (31, 30), (34, 19), (5, 1), (36, 37), (2, 37), (29, 11), (22, 17), (0, 39), (38, 19), (9, 29), (33, 23), (28, 23), (17, 42), (18, 18), (6, 15), (48, 42), (23, 18), (39, 2), (14, 3), (40, 4), (39, 8), (20, 24), (35, 12), (29, 40), (32, 23), (25, 36), (24, 32), (20, 38), (23, 31), (48, 12), (37, 2), (22, 3), (7, 3), (43, 28), (4, 34), (7, 16), (25, 5), (28, 35), (28, 15), (5, 10), (42, 40), (27, 43), (26, 6), (21, 26), (33, 44), (46, 31), (29, 42), (1, 32), (27, 21), (27, 29), (44, 31), (3, 30), (43, 0), (22, 37), (43, 3), (37, 35), (26, 19), (36, 2), (1, 16), (14, 9), (46, 27), (48, 13), (46, 14), (29, 20), (22, 4), (13, 6), (31, 43), (33, 6), (1, 37), (8, 9), (35, 28), (19, 42), (5, 12), (21, 31), (16, 43), (22, 24), (34, 3), (23, 19), (5, 17), (13, 1), (25, 29), (40, 17), (34, 16), (30, 34), (17, 0), (38, 11), (35, 19), (19, 4), (23, 1), (23, 23), (13, 35), (42, 13), (43, 35), (36, 20), (3, 16), (38, 6), (39, 21), (21, 18), (48, 23), (15, 27), (26, 39), (37, 26), (27, 8), (16, 9), (47, 31), (3, 15), (11, 23), (7, 20), (26, 4), (38, 32), (23, 25), (11, 41), (24, 19), (29, 28), (3, 21), (33, 22), (25, 9), (41, 42), (32, 17), (31, 4), (28, 41), (20, 10), (24, 31), (31, 39), (44, 26), (40, 27), (22, 16), (45, 25), (6, 39), (16, 11), (6, 27), (27, 45), (16, 33), (30, 22), (42, 21), (20, 6), (12, 2), (38, 3), (14, 39), (31, 41), (26, 45), (15, 32), (17, 4), (7, 19), (22, 6), (16, 24), (36, 18), (21, 4), (35, 0), (34, 39), (14, 26), (15, 1), (23, 21), (3, 20), (43, 27), (15, 33), (15, 28), (21, 22), (13, 43), (11, 17), (46, 26), (45, 31), (6, 9), (46, 42), (28, 37), (48, 18), (21, 20), (26, 43), (18, 39), (46, 21), (8, 38), (13, 45), (37, 34), (29, 31), (37, 23), (13, 15), (11, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 2), (24, 27), (38, 19), (42, 9), (35, 11), (16, 7), (27, 25), (30, 25), (38, 13), (16, 13), (30, 24), (40, 10), (44, 6), (28, 30), (14, 22), (18, 6), (35, 23), (7, 29), (34, 43), (16, 21), (3, 26), (20, 13), (10, 42), (27, 6), (14, 29), (21, 5), (39, 37), (43, 24), (35, 29), (23, 30), (3, 25), (19, 12), (33, 21), (27, 34), (1, 31), (41, 43), (37, 36), (36, 11), (29, 25), (23, 39), (9, 34), (14, 23), (27, 2), (34, 4), (36, 22), (29, 43), (12, 34), (23, 35), (32, 11), (0, 17), (8, 4), (27, 35), (14, 8), (41, 10), (32, 1), (3, 32), (15, 36), (23, 16), (17, 19), (7, 35), (40, 18), (19, 7), (14, 0), (42, 22), (14, 13), (30, 34), (38, 36), (14, 25), (15, 1), (42, 29), (21, 27), (20, 30), (18, 1), (8, 25), (40, 15), (8, 16), (4, 30), (10, 25), (37, 41), (43, 16), (23, 8), (2, 12), (28, 35), (19, 41), (18, 43), (28, 14), (32, 29), (43, 42), (2, 11), (39, 43), (3, 10), (25, 23), (3, 42), (24, 14), (17, 24), (28, 23), (5, 7), (28, 44), (15, 17), (8, 9), (23, 34), (30, 21), (13, 42), (40, 17), (16, 28), (9, 36), (42, 6), (6, 38), (28, 18), (34, 41), (0, 26), (19, 35), (11, 34), (23, 41), (21, 18), (0, 7), (9, 14), (1, 30), (15, 25), (20, 1), (11, 14), (18, 20), (42, 36), (0, 36), (42, 7), (2, 43), (8, 27), (12, 3), (8, 19), (39, 12), (17, 2), (7, 0), (18, 7), (35, 26), (10, 29), (40, 3), (33, 19), (14, 42), (23, 36), (24, 23), (28, 22), (8, 8), (42, 2), (29, 33), (13, 18), (40, 2), (26, 21), (5, 34), (11, 5), (36, 39), (9, 20), (34, 8), (1, 18), (36, 41), (29, 23), (15, 2), (16, 43), (10, 32), (12, 25), (3, 28), (15, 7), (38, 35), (16, 15), (14, 26), (5, 12), (36, 12), (30, 2), (11, 24), (31, 44), (11, 11), (17, 25), (34, 40), (25, 27), (22, 40), (16, 24), (36, 2), (7, 30), (42, 5), (42, 26), (13, 22), (30, 30), (10, 12), (24, 39), (41, 44), (27, 4), (21, 28), (17, 6), (25, 28), (19, 18), (29, 9), (0, 29), (18, 15), (6, 33), (20, 4), (5, 44), (42, 17), (17, 20), (18, 30), (30, 12), (24, 38), (17, 4), (42, 30), (2, 37), (13, 8), (20, 44), (15, 42), (30, 40), (28, 32), (43, 3), (35, 20), (9, 44), (17, 16), (14, 43), (37, 11), (41, 4), (31, 29), (10, 15), (41, 24), (35, 21), (10, 4), (33, 5), (37, 39), (11, 0), (40, 0), (31, 20), (17, 10), (6, 10), (30, 33), (17, 26), (37, 33), (25, 9), (8, 1), (44, 36), (3, 6), (16, 32), (38, 37), (29, 18), (32, 27), (1, 38), (42, 25), (20, 3), (38, 27), (10, 20), (35, 32), (30, 6), (40, 9), (1, 42), (29, 26), (26, 11), (37, 14), (39, 6), (18, 2), (19, 8), (44, 37), (8, 38), (2, 18), (10, 21), (27, 32), (12, 2), (28, 31), (16, 18), (23, 4), (1, 37), (29, 6), (36, 20), (41, 1), (40, 31), (3, 19), (1, 0), (18, 9), (6, 29), (41, 8), (3, 7), (42, 11), (17, 40), (39, 23), (13, 41), (22, 20), (16, 38), (23, 2), (31, 15), (36, 24), (42, 35), (26, 28), (13, 24), (20, 38), (36, 9), (18, 26), (14, 16), (29, 4), (3, 8), (30, 19), (7, 13), (20, 29), (23, 12), (7, 5), (27, 16), (40, 39), (15, 33), (39, 21), (1, 15), (9, 7), (23, 28), (15, 32), (21, 2), (3, 31), (41, 5), (2, 9), (27, 3), (29, 42), (20, 43), (14, 21), (21, 44), (12, 40), (38, 7), (17, 12), (6, 25), (7, 11), (37, 15), (37, 38), (28, 29), (19, 28), (37, 26), (7, 23), (13, 38), (15, 15), (26, 15), (0, 24), (25, 18), (43, 30), (7, 15), (5, 32), (17, 41), (29, 31), (43, 0), (36, 5), (31, 17), (35, 1), (36, 35), (14, 15), (31, 23), (17, 18), (37, 43), (20, 22), (0, 11), (6, 0), (9, 19), (9, 42), (31, 18), (43, 15), (27, 29), (30, 7), (28, 2), (4, 17), (41, 11), (39, 0), (26, 9), (11, 21), (2, 27), (41, 7), (29, 28), (23, 13), (19, 4), (9, 9), (13, 37), (5, 36), (43, 17), (4, 10), (9, 3), (25, 29), (26, 36), (39, 24), (43, 6), (2, 15), (41, 36), (2, 32), (35, 16), (42, 23), (42, 13), (22, 19), (27, 42), (22, 1), (31, 10), (40, 28), (8, 10), (2, 13), (1, 33), (32, 19), (22, 24), (42, 15), (12, 0), (2, 40), (43, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 12), (38, 42), (32, 36), (5, 16), (41, 44), (10, 6), (37, 19), (25, 44), (25, 27), (32, 41), (8, 24), (5, 18), (6, 37), (21, 2), (3, 34), (14, 1), (43, 28), (32, 5), (3, 45), (38, 40), (14, 32), (36, 10), (29, 9), (20, 22), (23, 16), (8, 37), (43, 36), (17, 42), (34, 7), (9, 45), (15, 42), (36, 5), (21, 30), (8, 46), (4, 38), (8, 43), (28, 5), (1, 40), (25, 7), (37, 12), (41, 22), (40, 41), (44, 36), (22, 19), (36, 14), (31, 39), (44, 24), (21, 10), (28, 25), (26, 17), (35, 32), (37, 2), (43, 29), (39, 17), (16, 18), (0, 10), (34, 37), (26, 13), (32, 43), (39, 39), (2, 7), (1, 41), (4, 15), (1, 44), (6, 21), (35, 33), (38, 37), (25, 21), (14, 33), (26, 45), (2, 23), (29, 17), (6, 40), (9, 11), (5, 0), (43, 13), (36, 11), (12, 24), (32, 33), (5, 37), (30, 21), (1, 43), (11, 14), (20, 11), (39, 9), (16, 12), (28, 1), (34, 0), (0, 35), (5, 46), (6, 38), (9, 13), (23, 25), (29, 27), (21, 31), (38, 38), (1, 26), (20, 40), (9, 41), (30, 4), (28, 2), (24, 1), (12, 2), (22, 8), (6, 6), (3, 9), (37, 31), (15, 9), (23, 41), (3, 32), (38, 15), (7, 21), (3, 8), (11, 7), (11, 15), (33, 20), (5, 24), (34, 39), (27, 46), (23, 10), (21, 21), (42, 4), (10, 26), (17, 37), (40, 17), (34, 25), (11, 31), (16, 41), (8, 6), (29, 35), (33, 46), (12, 18), (21, 44), (30, 23), (2, 9), (43, 46), (2, 14), (22, 20), (26, 21), (1, 19), (9, 6), (13, 37), (28, 0), (25, 18), (6, 18), (2, 4), (11, 1), (16, 45), (0, 20), (0, 24), (15, 33), (15, 0), (15, 29), (12, 27), (1, 11), (24, 26), (20, 0), (13, 10), (17, 34), (1, 30), (43, 3), (12, 10), (21, 16), (40, 0), (22, 30), (10, 30), (21, 18), (8, 23), (21, 4), (10, 4), (41, 9), (8, 36), (38, 2), (34, 17), (16, 10), (7, 27), (3, 0), (9, 15), (21, 11), (44, 37), (34, 40), (19, 18), (27, 29), (42, 19), (37, 45), (24, 31), (36, 39), (7, 0), (29, 23), (10, 3), (32, 20), (28, 23), (27, 24), (18, 22), (29, 11), (13, 29), (33, 8), (34, 36), (20, 28), (22, 42), (28, 41), (8, 31), (2, 8), (3, 42), (3, 33), (36, 44), (30, 12), (13, 18), (18, 43), (34, 15), (4, 17), (6, 33), (34, 18), (13, 43), (34, 13), (8, 21), (29, 3), (37, 38), (29, 38), (38, 34), (35, 8), (13, 44), (37, 9), (26, 46), (34, 6), (1, 46), (0, 44), (41, 30), (24, 40), (31, 44), (34, 4), (10, 16), (18, 29), (16, 28), (26, 27), (38, 32), (39, 0), (4, 5), (32, 1), (34, 3), (25, 10), (3, 12), (32, 14), (27, 35), (6, 23), (20, 16), (17, 44), (17, 7), (5, 11), (3, 19), (36, 30), (35, 13), (42, 28), (40, 12), (6, 32), (24, 9), (27, 44), (10, 32), (15, 32), (41, 18), (5, 32), (19, 34), (4, 20), (21, 24), (5, 12), (39, 44), (7, 3), (30, 16), (28, 43), (34, 44), (10, 37), (3, 4), (36, 19), (44, 40), (41, 28), (27, 42), (12, 44), (28, 9), (12, 42), (13, 35), (19, 43), (42, 22), (21, 25), (42, 14), (43, 45), (36, 37), (31, 5), (37, 21), (4, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 36), (13, 10), (18, 13), (41, 11), (8, 34), (36, 27), (31, 11), (24, 24), (17, 14), (41, 0), (26, 7), (41, 27), (30, 22), (19, 31), (10, 19), (35, 2), (11, 10), (14, 20), (9, 22), (39, 6), (24, 16), (10, 10), (34, 11), (6, 33), (4, 38), (1, 33), (6, 31), (7, 31), (17, 6), (39, 22), (41, 28), (22, 32), (18, 5), (24, 18), (19, 16), (11, 37), (33, 21), (13, 24), (29, 25), (11, 19), (16, 34), (33, 19), (23, 12), (34, 4), (9, 1), (5, 12), (15, 11), (1, 34), (42, 13), (35, 32), (7, 36), (34, 24), (34, 9), (21, 14), (0, 30), (16, 38), (39, 16), (32, 9), (18, 31), (37, 9), (9, 32), (30, 9), (29, 37), (10, 39), (35, 17), (18, 21), (26, 30), (33, 23), (8, 12), (1, 27), (16, 0), (38, 22), (21, 22), (5, 7), (38, 24), (34, 17), (39, 18), (36, 30), (44, 7), (17, 10), (9, 21), (13, 11), (29, 9), (40, 29), (9, 33), (0, 21), (20, 36), (1, 20), (22, 27), (35, 36), (35, 15), (23, 31), (18, 10), (31, 16), (26, 13), (40, 24), (3, 39), (19, 6), (41, 21), (2, 31), (13, 27), (1, 26), (9, 0), (0, 27), (15, 14), (41, 19), (17, 21), (8, 35), (22, 12), (31, 33), (9, 11), (7, 12), (10, 17), (24, 1), (29, 34), (10, 25), (15, 22), (2, 13), (7, 3), (18, 24), (39, 2), (1, 9), (14, 28), (12, 38), (28, 18), (16, 9), (13, 23), (42, 23), (44, 24), (0, 18), (1, 5), (12, 18), (0, 37), (38, 4), (18, 14), (27, 5), (7, 9), (12, 36), (37, 24), (1, 29), (36, 17), (21, 38), (1, 21), (0, 5), (32, 1), (37, 38), (37, 3), (32, 29), (41, 39), (23, 15), (10, 9), (3, 10), (8, 16), (32, 37), (25, 39), (39, 25), (43, 14), (2, 2), (21, 36), (31, 31), (2, 27), (18, 27), (17, 11), (9, 12), (15, 38), (35, 25), (27, 7), (39, 7), (38, 23), (43, 35), (28, 11), (13, 39), (4, 27), (28, 22), (14, 27), (19, 18), (40, 38), (24, 35), (19, 29), (6, 32), (36, 24), (21, 10), (29, 39), (7, 32), (2, 14), (6, 8), (20, 29), (4, 15), (17, 32), (15, 16), (4, 31), (10, 24), (29, 38), (40, 39), (29, 28), (43, 3), (33, 9), (35, 29), (35, 22), (42, 5), (24, 29), (2, 25), (18, 18), (17, 25), (20, 17), (42, 3), (20, 12), (37, 34), (30, 8), (27, 6), (39, 15), (37, 26), (26, 15), (11, 5), (10, 0), (15, 4), (25, 2), (20, 34), (18, 33), (26, 5), (30, 12), (19, 12), (44, 12), (6, 13), (30, 20), (30, 21), (37, 27), (14, 24), (6, 0), (6, 9), (34, 3), (33, 39), (0, 4), (11, 13), (18, 35), (11, 22), (9, 20), (41, 8), (12, 31), (43, 0), (25, 24), (26, 20), (5, 25), (33, 18), (12, 12), (31, 20), (23, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 4), (33, 34), (1, 31), (37, 38), (43, 21), (24, 15), (42, 10), (44, 35), (24, 9), (33, 38), (4, 41), (13, 12), (18, 9), (44, 4), (10, 38), (11, 36), (42, 47), (44, 1), (19, 8), (28, 24), (16, 35), (31, 26), (18, 24), (44, 7), (44, 44), (20, 2), (16, 6), (34, 6), (16, 25), (19, 3), (1, 42), (43, 38), (31, 7), (39, 7), (38, 45), (13, 31), (32, 0), (13, 25), (30, 18), (42, 0), (39, 32), (33, 12), (6, 40), (39, 18), (11, 45), (34, 44), (30, 2), (23, 0), (30, 30), (17, 29), (25, 34), (5, 4), (1, 2), (39, 30), (15, 14), (5, 9), (30, 7), (28, 32), (44, 14), (22, 17), (34, 43), (30, 5), (26, 36), (31, 42), (36, 20), (15, 45), (45, 33), (42, 38), (18, 48), (22, 45), (24, 0), (18, 4), (19, 32), (15, 27), (40, 10), (30, 13), (27, 26), (42, 32), (37, 3), (18, 42), (16, 14), (14, 15), (7, 41), (14, 37), (12, 23), (28, 11), (13, 33), (16, 42), (5, 43), (30, 1), (7, 39), (37, 16), (32, 38), (21, 28), (42, 7), (12, 26), (5, 1), (24, 23), (1, 36), (25, 45), (9, 23), (24, 33), (27, 7), (27, 3), (2, 40), (34, 31), (15, 38), (44, 23), (13, 24), (39, 20), (26, 28), (16, 23), (8, 29), (0, 3), (25, 27), (14, 4), (22, 11), (44, 29), (31, 20), (33, 36), (27, 41), (28, 7), (35, 32), (4, 42), (40, 13), (4, 7), (2, 13), (12, 42), (21, 46), (11, 14), (33, 13), (11, 18), (33, 47), (31, 11), (15, 11), (5, 14), (21, 41), (31, 40), (21, 32), (43, 45), (17, 2), (18, 47), (44, 48), (14, 20), (32, 18), (13, 46), (22, 33), (41, 40), (20, 40), (39, 3), (32, 26), (24, 35), (0, 26), (9, 41), (25, 4), (23, 21), (19, 30), (14, 33), (33, 21), (22, 3), (1, 11), (35, 14), (26, 32), (31, 5), (41, 0), (45, 48), (9, 46), (40, 9), (46, 20), (40, 43), (39, 45), (38, 4), (22, 27), (3, 13), (29, 48), (46, 22), (13, 45), (32, 9), (18, 31), (19, 42), (12, 27), (33, 46), (0, 21), (8, 11), (30, 46), (18, 13), (20, 0), (36, 35), (42, 11), (4, 38), (44, 22), (34, 24), (46, 43), (26, 30), (42, 5), (34, 2), (16, 34), (39, 41), (9, 14), (22, 46), (13, 11), (43, 48), (45, 16), (38, 38), (19, 31), (15, 8), (10, 42), (5, 6), (30, 14), (6, 15), (3, 48), (27, 6), (13, 34), (32, 30), (44, 36), (4, 4), (38, 33), (14, 23), (5, 45), (10, 37), (29, 22), (25, 33), (43, 27), (19, 7), (21, 31), (35, 13), (0, 35), (9, 9), (36, 13), (40, 45), (24, 48), (12, 1), (16, 45), (9, 18), (8, 30), (41, 14), (26, 0), (20, 24), (45, 1), (7, 13), (40, 6), (21, 15), (28, 47), (1, 41), (39, 47), (29, 44), (0, 36), (6, 10), (27, 22), (38, 11), (25, 1), (34, 13), (25, 30), (6, 3), (11, 41), (19, 35), (25, 21), (42, 43), (28, 16), (4, 21), (1, 27), (46, 40), (38, 35), (37, 27), (38, 22), (36, 37), (11, 39), (17, 37), (37, 0), (41, 43), (34, 23), (2, 1), (1, 3), (20, 33), (44, 41), (11, 26), (8, 45), (23, 16), (45, 34), (25, 18), (18, 17), (9, 17), (3, 35), (11, 2), (41, 15), (45, 10), (18, 38), (33, 17), (0, 28), (15, 41), (31, 25), (25, 41), (9, 2), (21, 36), (14, 25), (13, 16), (26, 31), (31, 46), (29, 17), (5, 2), (39, 9), (43, 4), (28, 19), (0, 2), (3, 7), (17, 30), (22, 16), (34, 48), (23, 41), (5, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 18), (41, 17), (4, 13), (16, 37), (1, 36), (36, 4), (45, 22), (3, 4), (46, 23), (2, 0), (21, 22), (42, 15), (5, 11), (0, 25), (47, 14), (32, 11), (28, 14), (17, 34), (43, 13), (34, 9), (38, 10), (0, 4), (19, 12), (8, 36), (38, 18), (2, 22), (35, 18), (44, 21), (27, 28), (33, 16), (44, 23), (41, 30), (27, 26), (7, 17), (12, 35), (38, 32), (6, 8), (8, 31), (13, 11), (12, 19), (47, 32), (28, 17), (17, 36), (7, 15), (30, 6), (34, 30), (35, 39), (11, 16), (5, 0), (26, 24), (15, 37), (12, 14), (27, 23), (14, 27), (28, 7), (38, 8), (30, 26), (20, 7), (32, 19), (19, 31), (33, 36), (30, 5), (9, 39), (32, 35), (43, 4), (16, 34), (1, 27), (6, 35), (41, 18), (45, 9), (13, 31), (41, 27), (42, 24), (27, 37), (18, 11), (22, 26), (21, 28), (47, 22), (24, 22), (22, 36), (29, 17), (35, 36), (6, 23), (4, 14), (4, 30), (29, 2), (22, 22), (11, 3), (4, 1), (38, 25), (19, 1), (30, 19), (26, 37), (27, 12), (19, 16), (18, 0), (39, 23), (37, 14), (34, 3), (7, 12), (24, 16), (10, 14), (29, 19), (0, 36), (26, 10), (1, 32), (38, 23), (36, 27), (2, 18), (5, 17), (5, 10), (4, 36), (33, 17), (26, 6), (43, 2), (8, 11), (13, 15), (30, 0), (47, 24), (17, 5), (3, 34), (7, 30), (28, 2), (32, 30), (10, 22), (8, 39), (40, 22), (0, 9), (31, 32), (36, 6), (29, 14), (35, 25), (41, 23), (14, 31), (17, 1), (35, 6), (13, 30), (30, 8), (21, 17), (5, 25), (3, 20), (38, 11), (40, 31), (25, 34), (10, 9), (29, 20), (11, 22), (20, 26), (21, 26), (32, 27), (10, 34), (2, 9), (16, 36), (37, 29), (46, 9), (25, 10), (3, 9), (12, 12), (38, 3), (25, 3), (18, 3), (28, 36), (12, 21), (47, 35), (32, 31), (4, 27), (10, 18), (14, 35), (17, 29), (39, 34), (26, 8), (47, 19), (16, 13), (27, 11), (29, 29), (30, 32), (3, 25), (44, 39), (11, 35), (5, 37), (19, 0), (13, 39), (7, 22), (26, 20), (20, 15), (18, 10), (3, 14), (12, 9), (25, 15), (30, 39), (37, 31), (17, 27), (23, 24), (41, 11), (14, 9), (17, 6), (24, 25), (24, 5), (23, 14), (30, 30), (3, 12), (8, 4), (9, 29), (0, 11), (18, 16), (41, 12), (12, 8), (45, 23), (0, 32), (46, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 29), (23, 21), (21, 38), (9, 45), (15, 22), (25, 43), (25, 3), (33, 8), (16, 46), (39, 0), (15, 1), (15, 15), (29, 40), (37, 37), (6, 11), (22, 12), (24, 8), (30, 14), (14, 10), (13, 24), (34, 14), (38, 9), (24, 25), (9, 4), (39, 16), (16, 24), (21, 39), (15, 14), (17, 2), (11, 16), (36, 15), (7, 1), (23, 48), (6, 28), (37, 20), (18, 34), (9, 42), (22, 11), (11, 12), (16, 22), (21, 28), (26, 47), (32, 48), (28, 1), (19, 28), (38, 17), (24, 41), (34, 15), (34, 0), (28, 2), (22, 17), (28, 21), (32, 45), (17, 48), (23, 41), (6, 21), (31, 43), (6, 39), (11, 25), (9, 21), (34, 5), (38, 28), (4, 30), (3, 5), (15, 34), (18, 18), (9, 40), (30, 9), (21, 13), (26, 41), (37, 3), (37, 16), (3, 34), (2, 14), (21, 19), (5, 44), (3, 12), (34, 8), (23, 40), (36, 34), (31, 32), (12, 4), (15, 9), (0, 36), (26, 29), (0, 37), (5, 43), (7, 3), (11, 40), (9, 10), (8, 17), (34, 12), (20, 21), (33, 2), (10, 7), (37, 43), (13, 11), (34, 35), (19, 31), (31, 40), (10, 4), (22, 9), (19, 48), (2, 35), (18, 42), (39, 21), (16, 12), (13, 0), (35, 23), (15, 24), (30, 36), (24, 38), (27, 2), (8, 29), (30, 38), (37, 36), (31, 35), (37, 39), (25, 23), (12, 2), (28, 17), (22, 31), (22, 47), (11, 13), (20, 13), (31, 36), (8, 26), (20, 40), (26, 14), (33, 21), (1, 35), (13, 4), (23, 10), (37, 42), (27, 5), (26, 40), (12, 25), (5, 4), (25, 44), (23, 39), (35, 29), (4, 35), (32, 8), (1, 1), (36, 9), (0, 2), (31, 13), (31, 46), (23, 28), (39, 45), (5, 45), (7, 14), (0, 33), (24, 32), (39, 22), (16, 32), (14, 16), (32, 35), (35, 9), (17, 42), (14, 6), (5, 0), (28, 31), (3, 41), (6, 34), (28, 3), (5, 17), (9, 22), (31, 33), (16, 25), (24, 40), (23, 29), (5, 11), (11, 7), (20, 16), (25, 48), (18, 47), (23, 7), (25, 2), (27, 23), (10, 19), (2, 22), (2, 44), (6, 26), (0, 28), (24, 39), (3, 17), (13, 45), (11, 0), (13, 30), (21, 16), (4, 14), (28, 42), (8, 13), (30, 16), (32, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 8), (13, 36), (28, 32), (6, 28), (13, 40), (9, 14), (11, 26), (7, 25), (17, 39), (2, 37), (33, 22), (4, 10), (24, 1), (33, 20), (18, 15), (37, 34), (28, 36), (28, 5), (8, 3), (37, 13), (39, 12), (30, 32), (19, 35), (34, 24), (22, 8), (4, 36), (18, 26), (37, 16), (35, 36), (37, 18), (26, 1), (36, 32), (0, 1), (8, 19), (5, 7), (29, 3), (13, 11), (8, 32), (34, 18), (27, 5), (14, 28), (2, 30), (2, 22), (0, 8), (23, 35), (5, 18), (30, 5), (6, 17), (11, 13), (38, 27), (11, 33), (31, 30), (28, 18), (39, 27), (30, 36), (19, 21), (8, 16), (7, 18), (0, 33), (18, 31), (28, 38), (0, 6), (40, 37), (5, 2), (4, 40), (37, 8), (18, 32), (39, 23), (29, 1), (15, 35), (31, 0), (11, 8), (33, 16), (23, 7), (23, 21), (9, 37), (36, 13), (10, 22), (4, 35), (16, 16), (17, 18), (28, 37), (19, 33), (0, 27), (38, 26), (13, 1), (11, 27), (31, 27), (20, 30), (22, 4), (38, 37), (20, 31), (25, 20), (31, 34), (20, 40), (35, 33), (20, 4), (39, 24), (10, 39), (23, 11), (30, 23), (26, 31), (8, 9), (3, 20), (28, 4), (30, 40), (2, 8), (38, 2), (36, 34), (36, 31), (36, 36), (40, 28), (26, 25), (9, 31), (11, 1), (27, 15), (12, 15), (31, 25), (7, 3), (10, 26), (12, 8), (33, 4), (5, 33), (25, 32), (34, 8), (34, 40), (14, 27), (20, 27), (17, 17), (39, 19), (26, 4), (4, 4), (36, 26), (24, 38), (9, 10), (2, 0), (25, 10), (19, 11), (4, 7), (28, 16), (25, 5), (21, 37), (32, 36), (40, 36), (40, 16), (17, 16), (39, 1), (9, 26), (13, 33), (12, 16), (10, 33), (1, 31), (26, 15), (32, 5), (1, 6), (11, 7), (22, 14), (22, 36), (6, 20), (34, 4), (10, 7), (21, 26), (7, 36), (8, 38), (20, 23), (24, 26), (23, 4), (22, 23), (24, 5), (7, 40), (8, 33), (23, 33), (4, 20), (36, 0), (21, 17), (29, 12), (10, 34), (10, 10), (27, 33), (4, 38), (16, 25), (15, 19), (3, 35), (20, 8), (35, 4), (36, 12), (35, 18), (32, 33), (16, 33), (0, 28), (30, 30), (1, 34), (2, 10), (12, 20), (40, 33), (18, 33), (19, 32), (6, 18), (3, 5), (30, 0), (25, 24), (6, 34), (30, 3), (3, 27), (27, 6), (16, 19), (31, 9), (26, 37), (9, 4), (38, 40), (18, 11), (11, 29), (30, 4), (24, 36), (37, 23), (26, 20), (22, 28), (27, 38), (32, 32), (22, 19), (31, 33), (35, 15), (10, 4), (32, 30), (19, 17), (33, 38), (10, 23), (18, 38), (22, 21), (15, 12), (22, 33), (33, 32), (27, 7), (30, 38), (40, 22), (14, 6), (33, 23), (24, 9), (5, 6), (10, 15), (32, 37), (1, 21), (26, 17), (8, 11), (34, 6), (14, 33), (6, 14), (0, 7), (5, 28), (7, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 28), (7, 28), (40, 28), (45, 13), (35, 34), (30, 43), (7, 21), (5, 27), (28, 24), (35, 0), (8, 31), (31, 12), (28, 3), (38, 29), (22, 13), (2, 26), (38, 33), (44, 34), (18, 8), (34, 41), (6, 29), (17, 41), (36, 1), (16, 33), (14, 8), (34, 12), (19, 28), (11, 6), (45, 21), (15, 37), (40, 14), (11, 34), (32, 37), (42, 31), (22, 26), (34, 13), (16, 11), (42, 41), (11, 20), (36, 6), (24, 5), (46, 9), (11, 7), (24, 23), (15, 39), (33, 0), (9, 4), (31, 13), (12, 38), (0, 8), (44, 12), (8, 20), (41, 26), (20, 20), (3, 4), (18, 31), (23, 31), (29, 32), (26, 20), (24, 25), (0, 27), (46, 34), (46, 28), (14, 4), (23, 9), (20, 43), (40, 11), (42, 7), (26, 4), (28, 41), (26, 43), (17, 18), (5, 23), (15, 38), (42, 16), (21, 6), (17, 27), (27, 27), (33, 18), (29, 13), (4, 25), (27, 22), (41, 15), (4, 5), (6, 6), (0, 23), (35, 19), (34, 16), (38, 40), (44, 2), (38, 20), (4, 6), (43, 2), (20, 24), (27, 2), (25, 8), (39, 4), (44, 36), (22, 2), (16, 38), (13, 10), (27, 11), (36, 29), (36, 37), (2, 37), (43, 38), (42, 39), (43, 17), (41, 37), (25, 43), (17, 7), (18, 0), (28, 29), (20, 14), (9, 20), (16, 21), (12, 23), (8, 27), (38, 39), (10, 12), (30, 8), (35, 6), (31, 38), (3, 24), (43, 25), (46, 42), (23, 43), (27, 15), (10, 21), (6, 0), (33, 16), (16, 16), (35, 7), (10, 22), (31, 40), (32, 29), (30, 38), (9, 1), (8, 11), (45, 38), (46, 31), (15, 17), (37, 37), (46, 16), (31, 2), (3, 38), (27, 4), (38, 6), (7, 34), (4, 19), (5, 22), (32, 7), (19, 21), (7, 31), (1, 27), (35, 14), (32, 18), (3, 8), (36, 38), (46, 1), (44, 21), (33, 7), (35, 12), (6, 11), (44, 18), (45, 2), (35, 21), (36, 20), (37, 40), (34, 31), (19, 19), (32, 35), (36, 42), (39, 13), (17, 15), (24, 20), (29, 28), (28, 20), (3, 40), (5, 24), (35, 17), (33, 1), (8, 18), (41, 1), (26, 39), (23, 16), (21, 12), (24, 34), (7, 43), (0, 16), (22, 24), (17, 21), (1, 29), (2, 21), (34, 40), (46, 4), (29, 5), (6, 28), (14, 13), (11, 1), (17, 19), (39, 36), (24, 36), (37, 20), (38, 24), (41, 22), (28, 13), (28, 0), (2, 9), (45, 7), (26, 2), (9, 25), (33, 9), (23, 18), (13, 5), (5, 0), (23, 14), (41, 43), (11, 44), (4, 38), (31, 27), (29, 10), (45, 24), (22, 5), (4, 11), (43, 36), (25, 16), (20, 23), (4, 24), (27, 37), (43, 33), (36, 30), (14, 33), (25, 30), (20, 18), (43, 40), (2, 18), (10, 44), (33, 39), (22, 27), (11, 13), (5, 32), (2, 11), (40, 30), (19, 31), (5, 15), (20, 38), (41, 6), (33, 23), (16, 25), (8, 22), (11, 23), (23, 44), (7, 10), (25, 12), (44, 9), (44, 35), (27, 0), (2, 33), (5, 41), (2, 38), (1, 11), (8, 9), (14, 25), (14, 5), (43, 16), (32, 28), (15, 28), (10, 35), (46, 5), (12, 15), (33, 28), (20, 26), (43, 19), (38, 25), (19, 1), (42, 10), (35, 27), (16, 35), (17, 11), (19, 12), (9, 8), (45, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 37), (16, 2), (14, 27), (13, 36), (33, 24), (31, 23), (10, 18), (42, 27), (36, 13), (18, 12), (39, 11), (36, 35), (23, 22), (13, 27), (24, 29), (2, 30), (1, 0), (1, 5), (29, 16), (22, 13), (21, 40), (3, 39), (10, 3), (28, 2), (25, 2), (19, 27), (34, 7), (32, 30), (0, 39), (6, 22), (26, 22), (34, 15), (21, 37), (26, 2), (28, 23), (28, 26), (24, 40), (5, 24), (31, 14), (5, 19), (4, 10), (39, 0), (12, 20), (27, 11), (31, 22), (12, 30), (3, 9), (26, 4), (42, 2), (19, 9), (35, 0), (36, 32), (3, 0), (15, 19), (6, 30), (35, 13), (11, 10), (21, 35), (35, 25), (8, 24), (14, 32), (29, 34), (38, 3), (17, 29), (34, 22), (3, 5), (17, 35), (19, 32), (38, 2), (7, 17), (30, 16), (2, 20), (21, 4), (40, 17), (20, 40), (39, 8), (8, 22), (9, 30), (35, 8), (32, 0), (29, 27), (23, 26), (6, 28), (25, 18), (1, 10), (30, 26), (19, 7), (9, 12), (14, 37), (10, 29), (22, 4), (16, 9), (32, 4), (32, 22), (2, 37), (38, 4), (27, 41), (37, 35), (8, 26), (9, 18), (14, 34), (23, 31), (2, 14), (20, 21), (26, 10), (14, 1), (19, 35), (38, 8), (21, 24), (1, 16), (8, 11), (35, 36), (12, 18), (6, 4), (0, 31), (14, 39), (28, 41), (5, 25), (39, 18), (6, 40), (25, 32), (22, 38), (42, 17), (32, 38), (7, 31), (8, 27), (8, 37), (38, 20), (2, 2), (44, 39), (3, 26), (17, 39), (12, 7), (39, 1), (12, 22), (7, 22), (44, 28), (24, 7), (26, 28), (7, 28), (27, 31), (26, 6), (5, 6), (41, 8), (33, 32), (1, 13), (19, 34), (38, 17), (7, 14), (41, 15), (22, 27), (34, 17), (31, 27), (4, 41), (22, 32), (40, 1), (41, 18), (21, 41), (40, 5), (41, 37), (27, 6), (41, 23), (44, 12), (40, 21), (32, 35), (0, 29), (12, 25), (11, 5), (13, 7), (41, 22), (36, 29), (32, 20), (32, 26), (42, 41), (10, 8), (24, 41), (25, 5), (28, 16), (22, 8), (26, 18), (1, 6), (13, 16), (40, 12), (11, 26), (4, 35), (33, 38), (5, 8), (44, 15), (40, 16), (32, 21), (7, 32), (21, 1), (17, 24), (12, 19), (27, 29), (32, 12), (7, 41), (27, 36), (25, 41), (27, 1), (9, 16), (9, 29), (23, 37), (37, 7), (13, 23), (29, 38), (24, 34), (18, 29), (0, 33), (23, 38), (24, 17), (35, 24), (33, 19), (42, 24), (31, 6), (21, 33), (35, 40), (26, 19), (22, 16), (14, 20), (12, 26), (41, 33), (28, 8), (7, 30), (25, 34), (32, 19), (20, 35), (28, 11), (31, 33), (39, 3), (33, 25), (8, 18), (25, 27), (38, 32), (16, 32), (29, 6), (14, 28), (24, 27), (37, 32), (28, 3), (44, 32), (6, 21), (4, 40), (16, 0), (40, 41), (29, 0), (0, 25), (11, 28), (6, 20), (9, 13), (1, 38), (1, 41), (33, 3), (11, 37), (14, 13), (22, 35), (30, 41), (9, 32), (38, 24), (25, 0), (18, 35), (4, 21), (6, 29), (23, 23), (18, 6), (43, 23), (14, 22), (5, 7), (43, 33), (20, 25), (21, 9), (20, 18), (5, 31), (33, 36), (27, 23), (12, 29), (39, 23), (4, 14), (16, 8), (6, 19), (13, 9), (20, 36), (6, 9), (31, 36), (39, 33), (23, 19), (11, 34), (16, 20), (36, 38), (33, 30), (35, 35), (15, 15), (16, 7), (22, 31), (3, 13), (40, 2), (31, 31), (34, 19), (19, 10), (29, 39), (37, 10), (21, 0), (39, 14), (41, 34), (9, 34), (20, 13), (18, 1), (3, 31), (4, 25), (11, 25), (26, 33), (34, 1), (42, 29), (32, 16), (22, 30), (31, 37), (25, 9), (36, 25), (35, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 18), (32, 16), (14, 2), (24, 23), (1, 36), (8, 43), (45, 28), (31, 20), (43, 11), (28, 36), (32, 6), (14, 26), (20, 27), (31, 44), (3, 23), (33, 10), (34, 36), (16, 7), (22, 42), (33, 27), (33, 46), (16, 26), (2, 40), (15, 22), (31, 21), (0, 11), (24, 30), (35, 23), (21, 28), (34, 24), (31, 16), (19, 32), (1, 42), (10, 45), (30, 28), (33, 47), (5, 35), (46, 37), (10, 36), (19, 19), (34, 26), (1, 23), (45, 11), (20, 36), (33, 8), (23, 41), (7, 1), (25, 13), (25, 32), (3, 44), (7, 35), (36, 28), (37, 43), (40, 14), (40, 12), (46, 24), (25, 12), (32, 23), (38, 1), (17, 27), (28, 19), (8, 41), (35, 15), (33, 13), (37, 17), (1, 47), (32, 35), (17, 39), (3, 30), (16, 25), (33, 0), (9, 13), (12, 17), (37, 25), (8, 1), (40, 20), (32, 7), (1, 26), (1, 21), (40, 5), (7, 4), (35, 44), (15, 44), (3, 46), (10, 25), (17, 41), (2, 26), (27, 1), (36, 31), (42, 23), (42, 34), (40, 30), (0, 31), (6, 30), (38, 39), (20, 16), (38, 33), (12, 0), (34, 3), (25, 37), (9, 15), (23, 22), (40, 3), (11, 10), (8, 47), (5, 42), (46, 1), (41, 39), (45, 12), (8, 37), (1, 4), (35, 6), (41, 42), (46, 18), (29, 14), (46, 13), (23, 27), (20, 37), (15, 31), (22, 5), (21, 6), (31, 36), (13, 4), (29, 16), (37, 26), (41, 4), (8, 24), (1, 33), (38, 44), (29, 8), (24, 20), (21, 37), (17, 3), (16, 15), (6, 11), (28, 32), (27, 40), (7, 20), (18, 37), (36, 2), (17, 30), (38, 29), (27, 22), (17, 46), (21, 41), (22, 24), (4, 37), (15, 35), (44, 15), (5, 47), (40, 17), (12, 36), (28, 15), (2, 5), (24, 40), (41, 15), (11, 47), (0, 20), (32, 43), (28, 29), (42, 43), (11, 11), (14, 23), (40, 8), (6, 3), (0, 36), (18, 32), (28, 47), (10, 39), (22, 15), (16, 43), (46, 20), (27, 25), (3, 43), (45, 7), (28, 7), (22, 38), (26, 38), (4, 7), (25, 26), (34, 23), (15, 27), (32, 38), (26, 20), (12, 20), (21, 39), (4, 15), (31, 47), (7, 36), (9, 43), (42, 27), (39, 31), (37, 5), (44, 26), (38, 5), (40, 45), (43, 25), (4, 32), (31, 42), (28, 45), (40, 18), (42, 38), (39, 35), (3, 21), (45, 20), (29, 5), (12, 21), (25, 40), (32, 44), (6, 27), (0, 2), (27, 44), (5, 19), (0, 29), (27, 0), (34, 14), (33, 6), (13, 22), (13, 37), (6, 1), (18, 33), (13, 26), (42, 42), (16, 10), (21, 35), (20, 3), (4, 4), (10, 11), (16, 34), (4, 44), (42, 32), (23, 7), (17, 33), (3, 16), (39, 24), (40, 7), (28, 37), (10, 13), (44, 12), (12, 27), (5, 44), (24, 26), (24, 14), (11, 39), (26, 13), (26, 41), (32, 17), (44, 9), (46, 19), (37, 45), (39, 13), (14, 9), (13, 32), (17, 12), (36, 7), (38, 38), (37, 35), (45, 5), (45, 9), (27, 39), (19, 22), (2, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 48), (40, 37), (20, 12), (31, 32), (36, 16), (23, 10), (10, 29), (39, 1), (33, 28), (15, 11), (3, 0), (39, 29), (14, 35), (16, 28), (39, 18), (5, 25), (29, 31), (29, 45), (31, 7), (6, 36), (15, 8), (5, 30), (7, 30), (4, 21), (15, 6), (1, 37), (17, 35), (3, 5), (30, 35), (7, 17), (18, 14), (43, 13), (16, 5), (26, 0), (21, 28), (3, 8), (6, 30), (36, 22), (25, 14), (9, 37), (0, 19), (32, 34), (38, 22), (33, 48), (42, 42), (41, 15), (1, 39), (15, 13), (43, 10), (10, 10), (43, 43), (37, 44), (13, 3), (30, 15), (38, 26), (8, 10), (42, 29), (4, 15), (25, 6), (40, 41), (40, 8), (34, 6), (37, 1), (15, 47), (8, 45), (36, 11), (25, 8), (8, 18), (40, 3), (30, 4), (13, 31), (28, 23), (43, 41), (41, 44), (27, 47), (33, 40), (11, 22), (37, 42), (41, 31), (36, 5), (4, 38), (33, 11), (41, 42), (19, 23), (19, 26), (9, 17), (18, 45), (9, 23), (14, 18), (40, 20), (42, 28), (17, 7), (30, 14), (8, 16), (34, 22), (18, 4), (28, 26), (14, 30), (7, 6), (12, 14), (26, 36), (33, 9), (10, 30), (25, 22), (13, 27), (35, 42), (32, 17), (11, 11), (38, 14), (42, 23), (33, 18), (20, 23), (8, 2), (12, 6), (29, 1), (19, 30), (12, 33), (20, 9), (23, 20), (37, 21), (17, 15), (36, 9), (26, 1), (16, 15), (27, 16), (25, 42), (3, 2), (7, 9), (20, 39), (37, 17), (22, 11), (14, 11), (17, 31), (9, 20), (27, 46), (26, 24), (9, 10), (5, 45), (43, 45), (37, 10), (8, 44), (41, 13), (6, 20), (14, 12), (3, 43), (23, 41), (16, 26), (20, 7), (0, 33), (18, 32), (26, 27), (24, 4), (12, 3), (9, 2), (4, 39), (2, 18), (30, 6), (22, 7), (28, 2), (13, 28), (23, 46), (39, 27), (30, 24), (5, 40), (9, 21), (27, 14), (38, 25), (6, 2), (29, 33), (16, 17), (30, 0), (30, 47), (0, 14), (42, 34), (33, 0), (40, 27), (13, 19), (39, 0), (36, 38), (25, 11), (33, 47), (0, 42), (21, 30), (12, 26), (7, 39), (39, 5), (39, 3), (35, 13), (8, 47), (3, 11), (35, 22), (1, 42), (12, 46), (22, 4), (17, 16), (9, 38), (21, 14), (43, 35), (21, 40), (34, 45), (14, 20), (22, 25), (35, 47), (8, 24), (36, 41), (2, 6), (6, 22), (38, 45), (20, 19), (28, 34), (28, 35), (30, 20), (2, 35), (36, 17), (12, 20), (9, 22), (32, 7), (3, 36), (20, 1), (25, 47), (11, 15), (28, 20), (40, 21), (36, 30), (32, 9), (4, 9), (7, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 26), (9, 22), (10, 17), (35, 13), (38, 11), (14, 4), (11, 0), (23, 42), (1, 19), (36, 7), (24, 14), (39, 41), (38, 16), (33, 10), (2, 38), (20, 42), (36, 17), (39, 29), (21, 36), (7, 10), (36, 34), (34, 37), (11, 42), (0, 10), (6, 44), (15, 22), (21, 22), (11, 40), (23, 1), (18, 20), (25, 34), (22, 24), (31, 29), (12, 20), (11, 27), (31, 38), (10, 12), (1, 17), (36, 42), (37, 34), (12, 41), (7, 29), (24, 46), (8, 3), (31, 36), (36, 44), (38, 3), (31, 5), (24, 29), (28, 42), (37, 30), (25, 9), (28, 26), (21, 13), (14, 22), (7, 1), (9, 1), (15, 42), (18, 27), (15, 23), (26, 43), (23, 19), (30, 19), (18, 37), (8, 21), (23, 36), (16, 6), (18, 12), (6, 9), (12, 30), (3, 25), (2, 43), (7, 32), (15, 9), (16, 4), (7, 6), (12, 12), (13, 11), (22, 46), (18, 23), (23, 34), (28, 38), (23, 7), (15, 24), (39, 16), (35, 21), (5, 39), (16, 28), (32, 12), (22, 32), (6, 1), (39, 43), (14, 28), (28, 27), (17, 5), (24, 42), (5, 22), (7, 40), (9, 11), (33, 40), (8, 25), (7, 39), (30, 33), (31, 4), (31, 19), (6, 23), (1, 7), (3, 20), (27, 18), (17, 30), (21, 10), (19, 41), (26, 2), (28, 2), (4, 38), (37, 25), (5, 10), (13, 16), (28, 19), (6, 26), (34, 11), (15, 44), (13, 33), (24, 41), (16, 7), (4, 28), (36, 3), (27, 11), (20, 24), (14, 14), (37, 35), (5, 21), (0, 34), (38, 29), (2, 19), (33, 21), (12, 4), (38, 31), (4, 30), (39, 27), (6, 19), (14, 35), (6, 21), (36, 46), (13, 0), (7, 45), (12, 29), (22, 34), (28, 11), (16, 21), (4, 22), (31, 41), (29, 7), (15, 32), (23, 22), (18, 45), (11, 6), (39, 34), (17, 37), (26, 25), (8, 7), (29, 18), (34, 4), (25, 12), (39, 32), (7, 30), (23, 21), (8, 23), (23, 16), (12, 43), (33, 5), (38, 10), (9, 13), (12, 27), (38, 43), (34, 30), (34, 17), (31, 16), (14, 40), (30, 46), (8, 29), (9, 15), (22, 2), (31, 32), (26, 17), (20, 2), (39, 6), (26, 20), (5, 28), (14, 7), (24, 34), (10, 1), (28, 24), (12, 5), (17, 28), (8, 16), (2, 27), (19, 13), (15, 38), (16, 44), (0, 8), (12, 28), (10, 42), (18, 28), (37, 44), (9, 39), (1, 3), (3, 17), (13, 26), (26, 37), (7, 24), (22, 33), (32, 33), (5, 34), (31, 40), (39, 15), (26, 12), (17, 16), (27, 26), (33, 41), (38, 7), (24, 3), (12, 42), (13, 30), (32, 37), (27, 2), (3, 40), (17, 44), (36, 31), (33, 24), (8, 15), (30, 38), (22, 9), (37, 40), (34, 24), (6, 33), (5, 9), (12, 3), (20, 46), (2, 17), (0, 43), (13, 17), (15, 15), (18, 40), (35, 11), (19, 5), (12, 37), (28, 36), (37, 29), (16, 18), (34, 12), (24, 30), (32, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 31), (11, 29), (45, 8), (24, 39), (5, 21), (17, 22), (38, 0), (7, 0), (16, 14), (35, 27), (13, 44), (35, 34), (11, 14), (26, 20), (14, 39), (39, 1), (45, 36), (22, 24), (42, 46), (2, 33), (14, 29), (36, 12), (20, 43), (34, 33), (44, 13), (38, 24), (5, 36), (38, 18), (15, 27), (30, 45), (7, 28), (43, 45), (30, 10), (9, 12), (27, 5), (46, 23), (22, 20), (26, 22), (35, 42), (36, 31), (4, 42), (32, 14), (42, 30), (44, 36), (23, 44), (5, 45), (24, 12), (17, 46), (8, 32), (17, 34), (32, 21), (30, 37), (4, 21), (33, 9), (34, 39), (19, 45), (1, 14), (9, 22), (35, 32), (7, 17), (17, 15), (15, 20), (44, 25), (32, 35), (9, 10), (42, 25), (31, 40), (31, 10), (36, 19), (14, 0), (34, 37), (36, 34), (1, 39), (40, 32), (30, 2), (8, 12), (3, 18), (34, 25), (33, 16), (12, 27), (15, 34), (10, 22), (36, 4), (20, 46), (43, 26), (14, 21), (38, 3), (6, 37), (5, 30), (26, 5), (26, 47), (0, 12), (7, 19), (35, 15), (4, 19), (0, 36), (6, 32), (20, 22), (5, 9), (44, 28), (38, 33), (9, 13), (15, 1), (29, 40), (41, 9), (2, 9), (3, 16), (39, 33), (4, 14), (46, 6), (33, 28), (19, 2), (30, 6), (46, 34), (36, 38), (28, 10), (0, 16), (26, 38), (28, 48), (13, 47), (31, 42), (45, 38), (5, 5), (46, 36), (33, 44), (20, 47), (46, 44), (44, 2), (40, 39), (19, 28), (7, 9), (5, 19), (17, 32), (44, 16), (45, 18), (26, 9), (23, 20), (34, 35), (23, 9), (21, 23), (34, 20), (25, 12), (22, 15), (41, 25), (41, 10), (0, 45), (6, 47), (25, 30), (37, 45), (39, 32), (25, 41), (8, 14), (47, 35), (20, 21), (13, 23), (5, 17), (10, 3), (32, 9), (38, 28), (28, 34), (16, 32), (15, 32), (2, 3), (29, 2), (45, 44), (18, 4), (42, 17), (26, 36), (24, 33), (15, 40), (34, 47), (42, 22), (9, 19), (8, 16), (30, 0), (19, 27), (25, 48), (22, 25), (38, 46), (5, 35), (43, 46), (13, 20), (7, 38), (1, 27), (41, 44), (14, 17), (25, 1), (42, 43), (1, 30), (13, 4), (41, 12), (37, 35), (43, 20), (45, 47), (35, 2), (46, 18), (22, 27), (1, 3), (5, 6), (13, 30), (47, 41), (20, 31), (39, 48), (11, 13), (43, 7), (11, 10), (3, 48), (1, 8), (28, 28), (28, 15), (11, 41), (26, 28), (4, 2), (26, 8), (23, 37), (38, 5), (43, 36), (10, 18), (22, 0), (27, 0), (15, 0), (40, 3), (38, 29), (8, 2), (0, 35), (45, 14), (9, 41), (36, 16), (7, 32), (41, 23), (32, 28), (33, 36), (14, 4), (34, 31), (40, 17), (4, 40), (9, 35), (18, 44), (35, 12), (2, 41), (16, 37), (2, 44), (20, 24), (0, 14), (0, 40), (18, 0), (20, 14), (31, 6), (6, 44), (39, 20), (27, 28), (28, 43), (2, 2), (35, 31), (15, 19), (28, 18), (11, 32), (41, 2), (36, 39), (45, 19), (43, 14), (8, 19), (20, 16), (28, 33), (35, 43), (29, 30), (10, 20), (31, 18), (25, 35), (41, 17), (18, 27), (38, 37), (46, 4), (17, 37), (24, 21), (45, 31), (5, 14), (46, 41), (3, 33), (11, 45), (14, 28), (2, 47), (42, 35), (23, 5), (29, 19), (45, 2), (1, 1), (26, 33), (39, 36), (23, 34), (43, 34), (27, 4), (16, 20), (35, 6), (39, 44), (34, 6), (41, 21), (30, 34), (1, 29), (35, 36), (27, 35), (23, 35), (11, 1), (29, 33), (17, 5), (6, 36), (6, 43), (47, 28), (6, 41), (37, 43), (18, 17), (45, 40), (3, 24), (24, 46), (30, 42), (40, 18), (40, 19), (31, 22), (39, 40), (39, 27), (19, 46), (36, 2), (19, 18), (7, 39), (32, 47), (29, 18), (10, 8), (38, 39), (28, 9), (43, 29), (46, 11), (38, 2), (30, 33), (4, 9), (40, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 37), (10, 1), (21, 38), (36, 13), (27, 17), (39, 31), (14, 6), (14, 23), (41, 29), (29, 8), (14, 9), (33, 4), (26, 22), (37, 13), (4, 26), (31, 22), (32, 33), (25, 7), (24, 28), (18, 33), (32, 38), (29, 10), (2, 39), (17, 16), (30, 5), (45, 37), (11, 0), (12, 34), (35, 40), (26, 11), (28, 5), (8, 39), (3, 25), (4, 23), (8, 9), (4, 29), (15, 4), (13, 36), (47, 34), (4, 14), (9, 7), (34, 4), (28, 2), (23, 14), (9, 9), (8, 40), (47, 29), (3, 13), (13, 10), (21, 1), (14, 37), (39, 28), (41, 30), (6, 12), (15, 31), (38, 32), (9, 5), (14, 40), (35, 33), (38, 28), (38, 33), (44, 23), (13, 28), (20, 34), (36, 7), (41, 15), (5, 38), (22, 37), (2, 22), (21, 13), (20, 17), (0, 6), (44, 5), (1, 21), (11, 5), (33, 1), (39, 0), (28, 30), (36, 20), (10, 29), (2, 19), (21, 11), (39, 8), (7, 8), (35, 17), (4, 13), (4, 31), (20, 5), (42, 25), (11, 33), (28, 26), (24, 32), (41, 19), (33, 17), (18, 29), (13, 40), (33, 20), (26, 24), (5, 26), (26, 3), (40, 37), (6, 1), (11, 29), (33, 26), (19, 27), (42, 34), (13, 8), (2, 10), (42, 27), (36, 34), (6, 21), (28, 18), (33, 15), (19, 30), (39, 23), (8, 17), (20, 36), (9, 17), (37, 39), (46, 9), (25, 36), (26, 37), (20, 6), (21, 27), (20, 29), (6, 19), (30, 3), (21, 33), (44, 28), (28, 28), (39, 19), (34, 10), (21, 12), (6, 8), (47, 8), (25, 0), (24, 18), (33, 10), (28, 10), (34, 21), (9, 1), (10, 25), (1, 27), (33, 35), (17, 39), (34, 34), (45, 31), (23, 18), (36, 37), (28, 32), (38, 18), (44, 9), (38, 17), (17, 28), (32, 12), (43, 13), (6, 30), (15, 12), (28, 17), (46, 36), (19, 25), (47, 33), (24, 35), (40, 36), (18, 20), (31, 40), (17, 21), (12, 33), (27, 11), (12, 6), (33, 38), (24, 38), (22, 21), (24, 26), (47, 24), (25, 25), (37, 30), (44, 39), (31, 5), (8, 29), (19, 15), (8, 10), (44, 8), (26, 31), (18, 8), (43, 31), (41, 0), (14, 4), (3, 31), (8, 23), (44, 10), (8, 1), (7, 7), (7, 12), (34, 22), (3, 0), (32, 14), (17, 15), (21, 21), (23, 2), (4, 4), (33, 19), (36, 14), (1, 15), (0, 5), (22, 3), (35, 5), (20, 13), (25, 8), (28, 9), (17, 4), (34, 31), (21, 8), (5, 7), (35, 4), (4, 30), (45, 11), (2, 5), (7, 25), (26, 35), (36, 15), (39, 36), (24, 37), (44, 24), (37, 22), (20, 16), (36, 39), (12, 23), (24, 7), (1, 24), (31, 3), (34, 2), (44, 27), (26, 38), (20, 8), (42, 20), (42, 3), (27, 33), (35, 10), (40, 12), (25, 26), (41, 14), (28, 19), (41, 33), (7, 29), (3, 32), (33, 34), (46, 2), (27, 14), (42, 8), (20, 31), (15, 3), (39, 6), (12, 21), (42, 12), (2, 13), (23, 19), (44, 1), (45, 16), (27, 18), (46, 7), (33, 8), (26, 21), (5, 5), (40, 19), (39, 20), (31, 4), (26, 4), (9, 11), (40, 8), (22, 14), (7, 13), (31, 27), (30, 36), (44, 32), (21, 30), (7, 28), (2, 31), (28, 4), (25, 1), (15, 18), (3, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 29), (25, 12), (19, 6), (12, 14), (38, 37), (11, 4), (6, 30), (41, 43), (3, 34), (1, 36), (9, 38), (1, 28), (2, 5), (22, 15), (38, 8), (5, 17), (13, 37), (36, 17), (43, 34), (22, 9), (40, 8), (39, 3), (36, 11), (6, 7), (36, 26), (32, 18), (45, 2), (38, 36), (18, 27), (36, 40), (6, 10), (17, 35), (36, 8), (16, 11), (26, 35), (33, 38), (28, 38), (14, 26), (20, 34), (28, 14), (36, 13), (14, 30), (26, 1), (30, 18), (33, 8), (45, 42), (27, 37), (23, 42), (16, 3), (14, 16), (29, 2), (34, 27), (37, 33), (45, 14), (34, 3), (15, 23), (30, 5), (16, 31), (41, 2), (31, 6), (45, 32), (22, 14), (2, 18), (43, 3), (9, 28), (14, 35), (27, 18), (26, 8), (21, 31), (34, 8), (38, 30), (26, 16), (11, 31), (12, 15), (39, 6), (28, 13), (4, 6), (30, 35), (14, 25), (7, 30), (4, 20), (33, 6), (28, 6), (31, 27), (32, 31), (10, 38), (21, 18), (23, 32), (19, 38), (32, 19), (15, 39), (36, 32), (8, 37), (13, 13), (36, 4), (25, 9), (28, 37), (16, 32), (34, 17), (39, 11), (15, 22), (29, 34), (23, 29), (43, 10), (25, 42), (36, 38), (38, 43), (42, 3), (26, 39), (12, 24), (19, 10), (28, 32), (12, 28), (45, 27), (25, 20), (38, 3), (36, 0), (9, 35), (27, 7), (40, 31), (21, 40), (13, 33), (44, 19), (35, 34), (16, 42), (30, 13), (31, 20), (45, 11), (40, 24), (37, 2), (4, 42), (15, 41), (38, 33), (8, 22), (4, 9), (0, 30), (13, 40), (19, 40), (23, 4), (37, 11), (38, 35), (27, 10), (38, 10), (34, 1), (13, 5), (10, 6), (16, 40), (38, 5), (29, 24), (45, 23), (15, 40), (4, 41), (29, 19), (26, 33), (6, 33), (19, 27), (35, 37), (5, 22), (16, 5), (30, 31), (26, 11), (9, 31), (45, 34), (5, 30), (20, 14), (42, 10), (1, 35), (38, 1), (7, 18), (9, 40), (21, 6), (24, 15), (31, 39), (36, 3), (32, 27), (45, 39), (2, 23), (32, 37), (36, 10), (12, 26), (8, 11), (4, 18), (6, 11), (6, 31), (2, 29), (10, 11), (1, 27), (41, 24), (24, 26), (4, 10), (1, 8), (18, 41), (37, 9), (29, 6), (3, 26), (44, 12), (14, 22), (0, 40), (33, 15), (28, 1), (24, 22), (19, 1), (7, 8), (32, 0), (15, 1), (42, 31), (4, 39), (11, 19), (29, 37), (24, 8), (35, 16), (40, 32), (11, 43), (43, 38), (4, 19), (29, 25), (23, 40), (39, 40), (34, 6), (39, 30), (34, 19), (45, 1), (33, 18), (16, 27), (17, 18), (37, 4), (20, 33), (42, 23), (24, 33), (37, 0), (44, 4), (3, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 20), (9, 29), (45, 13), (7, 19), (30, 18), (8, 13), (43, 31), (39, 35), (30, 29), (16, 44), (32, 42), (36, 11), (29, 13), (19, 14), (26, 24), (29, 40), (10, 4), (39, 6), (13, 46), (12, 22), (27, 21), (25, 21), (8, 18), (17, 9), (40, 29), (33, 18), (12, 45), (12, 30), (32, 9), (0, 11), (35, 33), (45, 46), (45, 26), (42, 9), (17, 23), (3, 11), (5, 6), (3, 39), (36, 25), (8, 7), (13, 47), (1, 45), (38, 8), (43, 17), (17, 31), (34, 32), (5, 33), (24, 21), (0, 30), (8, 46), (7, 30), (8, 35), (36, 21), (39, 33), (16, 35), (29, 19), (36, 34), (38, 21), (1, 20), (42, 48), (44, 33), (19, 32), (22, 38), (25, 8), (37, 34), (22, 6), (34, 20), (28, 11), (2, 40), (24, 40), (34, 39), (2, 10), (33, 44), (14, 31), (0, 44), (24, 35), (7, 24), (38, 28), (8, 39), (29, 48), (21, 5), (32, 26), (0, 27), (16, 47), (13, 48), (0, 6), (15, 33), (12, 0), (12, 34), (13, 26), (15, 15), (1, 24), (44, 16), (34, 11), (6, 6), (14, 32), (25, 19), (39, 1), (44, 48), (31, 5), (4, 30), (20, 2), (32, 22), (38, 13), (9, 43), (33, 28), (20, 46), (11, 43), (26, 9), (8, 41), (14, 43), (30, 21), (11, 13), (9, 45), (8, 42), (4, 7), (37, 2), (2, 8), (3, 35), (40, 20), (11, 7), (40, 5), (13, 29), (14, 7), (45, 25), (16, 7), (14, 21), (38, 15), (21, 33), (43, 0), (45, 42), (24, 14), (28, 5), (3, 22), (4, 38), (19, 35), (27, 44), (15, 8), (17, 14), (5, 28), (34, 19), (33, 30), (45, 12), (16, 12), (8, 37), (2, 31), (33, 40), (11, 14), (1, 0), (43, 37), (30, 48), (18, 45), (9, 21), (21, 9), (16, 31), (23, 7), (7, 0), (18, 42), (41, 7), (3, 31), (11, 39), (42, 42), (41, 3), (5, 18), (15, 38), (26, 2), (36, 39), (9, 33), (25, 36), (42, 11), (41, 47), (44, 36), (43, 35), (30, 32), (29, 25), (37, 35), (33, 23), (28, 32), (4, 39), (23, 10), (22, 30), (30, 39), (45, 2), (37, 32), (7, 22), (5, 1), (7, 36), (31, 9), (24, 30), (15, 37), (0, 21), (40, 39), (41, 29), (32, 2), (18, 48), (1, 30), (7, 13), (4, 18), (18, 46), (1, 46), (43, 39), (12, 7), (36, 6), (10, 21), (4, 47), (0, 4), (40, 28), (35, 24), (37, 17), (26, 39), (43, 43), (42, 41), (15, 1), (31, 21), (2, 43), (21, 15), (15, 28), (32, 1), (11, 3), (42, 47), (27, 47), (42, 13), (9, 40), (26, 32), (33, 33), (36, 24), (31, 23), (6, 3), (20, 38), (22, 34), (29, 16), (3, 41), (13, 4), (19, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 3), (42, 19), (3, 39), (43, 40), (20, 31), (38, 44), (30, 15), (23, 45), (42, 13), (43, 42), (40, 36), (18, 38), (32, 44), (34, 36), (19, 16), (7, 11), (12, 44), (17, 4), (19, 12), (16, 2), (7, 32), (20, 10), (42, 20), (27, 18), (24, 46), (12, 40), (14, 15), (6, 43), (39, 38), (25, 37), (9, 45), (1, 45), (39, 28), (15, 45), (40, 32), (25, 1), (14, 28), (16, 34), (5, 44), (15, 14), (0, 27), (1, 34), (17, 47), (11, 11), (16, 17), (29, 12), (1, 5), (37, 2), (21, 45), (37, 34), (28, 46), (43, 27), (23, 8), (33, 14), (28, 22), (9, 36), (10, 13), (12, 38), (9, 37), (5, 1), (31, 37), (18, 22), (40, 31), (12, 26), (18, 46), (40, 26), (9, 44), (36, 15), (20, 26), (5, 35), (2, 39), (29, 31), (32, 14), (30, 26), (28, 0), (41, 19), (30, 35), (38, 19), (2, 14), (12, 8), (16, 44), (42, 21), (37, 37), (35, 22), (1, 38), (4, 18), (14, 39), (40, 22), (36, 39), (19, 47), (39, 0), (36, 26), (2, 35), (28, 47), (32, 34), (4, 20), (21, 22), (36, 13), (30, 29), (28, 27), (22, 24), (9, 24), (35, 5), (3, 11), (9, 2), (6, 27), (33, 16), (0, 12), (30, 4), (17, 16), (31, 16), (36, 28), (22, 30), (38, 7), (11, 32), (3, 23), (38, 32), (19, 27), (3, 22), (6, 31), (20, 8), (21, 40), (28, 31), (13, 10), (36, 29), (17, 22), (41, 41), (32, 38), (28, 28), (39, 7), (19, 0), (40, 1), (12, 28), (23, 40), (32, 43), (33, 4), (29, 46), (24, 41), (2, 26), (14, 8), (3, 0), (13, 34), (25, 23), (10, 18), (15, 47), (18, 8), (29, 29), (19, 6), (31, 44), (35, 45), (4, 12), (21, 37), (26, 8), (26, 32), (39, 1), (32, 3), (33, 28), (34, 41), (34, 1), (21, 15), (34, 39), (15, 12), (17, 0), (12, 29), (30, 13), (7, 29), (23, 9), (5, 18), (35, 33), (26, 20), (14, 14), (43, 33), (33, 39), (30, 30), (25, 13), (34, 9), (33, 2), (11, 20), (40, 13), (6, 6), (24, 42), (18, 2), (9, 22), (35, 41), (1, 29), (28, 20), (26, 14), (9, 10), (34, 12), (38, 30), (18, 13), (10, 22), (37, 41), (1, 25), (16, 23), (25, 16), (22, 27), (16, 39), (36, 23), (20, 11), (43, 6), (26, 21), (4, 38), (5, 7), (3, 10), (15, 19), (5, 3), (19, 20), (30, 34), (25, 0), (43, 15), (19, 41), (28, 12), (16, 8), (23, 47), (41, 22), (7, 13), (24, 2), (1, 15), (26, 30), (3, 29), (38, 10), (34, 19), (43, 12), (10, 4), (38, 27), (33, 45), (23, 24), (43, 25), (40, 34), (7, 34), (43, 3), (20, 42), (31, 39), (32, 11), (23, 36), (12, 0), (28, 23), (38, 23), (31, 41), (11, 12), (21, 42), (10, 45), (30, 20), (28, 41), (24, 26), (3, 18), (32, 47), (9, 19), (16, 47), (32, 10), (15, 0), (0, 20), (38, 13), (28, 4), (3, 12), (6, 29), (21, 3), (31, 24), (20, 9), (8, 24), (26, 46), (30, 33), (31, 25), (36, 3), (0, 34), (0, 40), (38, 5), (7, 18), (41, 3), (7, 17), (12, 22), (43, 29), (37, 38), (14, 44), (27, 1), (35, 11), (30, 39), (39, 46), (21, 19), (11, 46), (19, 21), (25, 46), (10, 47), (38, 25), (29, 38), (0, 22), (29, 13), (2, 17), (29, 24), (32, 0), (39, 40), (38, 22), (36, 47), (0, 29), (10, 7), (7, 3), (23, 0), (33, 35), (1, 2), (13, 42), (32, 17), (32, 26), (31, 8), (24, 13), (37, 27), (42, 26), (26, 23), (3, 27), (0, 44), (0, 10), (23, 43), (0, 46), (36, 5), (16, 0), (37, 36), (10, 32), (24, 47), (8, 27), (9, 41), (6, 9), (31, 28), (37, 17), (39, 14), (28, 26), (38, 43), (9, 1), (33, 11), (20, 0), (2, 34), (42, 47), (36, 31), (20, 23), (43, 17), (22, 40), (32, 46), (28, 42), (9, 20), (43, 23), (35, 0), (14, 4), (3, 42), (10, 31), (40, 46), (17, 35), (19, 30), (12, 6), (11, 17), (11, 7), (11, 6), (21, 38), (25, 9), (19, 1), (0, 3), (31, 36), (24, 40), (13, 33), (39, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 21), (22, 12), (0, 1), (21, 33), (28, 2), (33, 6), (35, 9), (1, 21), (34, 2), (14, 25), (6, 30), (6, 26), (12, 10), (38, 1), (19, 44), (35, 43), (34, 42), (33, 27), (15, 42), (30, 40), (1, 2), (31, 16), (28, 18), (32, 11), (33, 34), (12, 21), (37, 18), (10, 22), (4, 16), (32, 10), (37, 8), (18, 16), (18, 2), (27, 34), (8, 8), (1, 18), (4, 18), (2, 40), (10, 8), (14, 5), (15, 1), (21, 23), (26, 9), (6, 22), (13, 17), (8, 13), (2, 43), (38, 10), (30, 29), (35, 24), (38, 14), (4, 17), (28, 25), (37, 6), (3, 29), (23, 7), (23, 30), (16, 16), (34, 8), (35, 22), (31, 44), (14, 2), (8, 30), (33, 32), (13, 29), (18, 6), (33, 23), (11, 17), (29, 37), (30, 35), (29, 24), (12, 19), (27, 0), (14, 6), (12, 31), (23, 20), (15, 6), (36, 9), (31, 10), (28, 5), (3, 15), (12, 4), (19, 8), (22, 25), (21, 9), (2, 13), (7, 24), (4, 20), (39, 21), (6, 16), (5, 8), (24, 36), (23, 15), (20, 5), (34, 35), (24, 5), (36, 44), (33, 19), (22, 43), (18, 38), (7, 42), (15, 33), (20, 6), (3, 8), (4, 25), (0, 20), (29, 33), (3, 17), (24, 44), (1, 32), (0, 22), (7, 12), (36, 11), (3, 27), (25, 41), (13, 16), (35, 3), (14, 11), (19, 22), (32, 22), (5, 43), (22, 19), (2, 1), (18, 31), (35, 40), (29, 31), (2, 9), (2, 28), (15, 3), (37, 35), (2, 26), (12, 44), (20, 14), (2, 11), (20, 35), (22, 35), (15, 43), (4, 22), (0, 18), (13, 6), (34, 4), (25, 0), (31, 34), (2, 16), (16, 9), (3, 9), (14, 8), (26, 36), (11, 10), (20, 19), (20, 38), (39, 38), (27, 21), (23, 16), (9, 38), (6, 24), (30, 32), (10, 26), (32, 41), (31, 12), (14, 33), (35, 20), (9, 23), (38, 18), (15, 23), (20, 37), (25, 1), (8, 38), (2, 33), (35, 4), (25, 23), (20, 41), (19, 33), (11, 2), (28, 0), (18, 4), (31, 28), (5, 9), (25, 16), (26, 14), (31, 31), (33, 36), (34, 15), (19, 37), (37, 37), (22, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 13), (6, 36), (30, 40), (40, 10), (33, 11), (29, 17), (0, 9), (3, 15), (7, 19), (38, 18), (24, 40), (28, 20), (41, 5), (17, 41), (7, 22), (24, 31), (30, 26), (17, 18), (43, 13), (15, 6), (47, 5), (2, 24), (44, 41), (32, 30), (26, 18), (10, 33), (24, 18), (39, 0), (0, 29), (23, 37), (12, 13), (14, 27), (6, 12), (30, 4), (19, 16), (41, 23), (7, 37), (9, 9), (1, 23), (25, 43), (32, 41), (12, 11), (45, 1), (8, 3), (39, 38), (18, 4), (27, 1), (13, 32), (2, 3), (40, 0), (31, 38), (33, 34), (37, 21), (6, 4), (38, 35), (2, 17), (25, 4), (28, 22), (29, 4), (18, 15), (40, 29), (31, 26), (37, 7), (18, 13), (24, 17), (12, 37), (0, 5), (22, 43), (2, 1), (20, 5), (36, 27), (15, 8), (12, 8), (20, 37), (14, 14), (38, 4), (6, 17), (0, 2), (36, 0), (1, 40), (8, 34), (44, 5), (39, 16), (38, 31), (18, 5), (10, 29), (33, 8), (12, 14), (44, 22), (7, 10), (5, 24), (18, 28), (11, 20), (7, 26), (16, 34), (9, 24), (24, 2), (44, 8), (38, 17), (13, 21), (34, 36), (20, 35), (8, 15), (12, 1), (26, 38), (1, 19), (12, 30), (29, 32), (0, 23), (29, 23), (5, 39), (4, 0), (46, 26), (8, 31), (32, 16), (24, 35), (32, 36), (19, 17), (41, 6), (7, 18), (17, 16), (39, 33), (8, 9), (34, 25), (13, 25), (45, 41), (47, 24), (5, 32), (15, 12), (6, 1), (12, 27), (15, 3), (44, 27), (41, 10), (45, 23), (7, 8), (10, 2), (35, 39), (6, 11), (17, 26), (29, 29), (31, 1), (26, 28), (24, 10), (35, 24), (20, 24), (27, 24), (46, 33), (8, 10), (36, 4), (7, 7), (25, 27), (12, 42), (23, 0), (11, 7), (5, 40), (17, 36), (16, 42), (29, 7), (34, 17), (4, 9), (11, 18), (24, 39), (23, 10), (2, 27), (8, 35), (47, 33), (42, 10), (25, 10), (22, 4), (16, 4), (27, 26), (27, 29), (4, 4), (19, 1), (26, 14), (9, 3), (37, 25), (7, 36), (41, 42), (34, 8), (30, 38), (32, 19), (14, 35), (2, 8), (12, 40), (11, 1), (14, 22), (37, 8), (43, 37), (11, 26), (14, 8), (20, 33), (24, 28), (42, 3), (11, 17), (47, 31), (43, 32), (43, 20), (24, 4), (40, 28), (11, 41), (5, 37), (0, 22), (10, 1), (35, 14), (3, 22), (33, 33), (16, 2), (7, 16), (20, 20), (4, 14), (39, 34), (43, 6), (0, 6), (27, 37), (25, 8), (27, 39), (37, 28), (40, 2), (41, 39), (39, 40), (46, 8), (29, 34), (11, 14), (3, 6), (32, 33), (7, 11), (40, 5), (28, 26), (12, 10), (28, 33), (11, 16), (38, 33), (9, 10), (40, 11), (25, 5), (5, 7), (35, 23), (19, 4), (47, 2), (25, 24), (29, 38), (32, 20), (16, 26), (37, 5), (46, 39), (27, 42), (22, 18), (39, 17), (32, 9), (4, 38), (14, 17), (6, 16), (5, 30), (17, 34), (46, 27), (6, 2), (30, 5), (1, 4), (36, 18), (9, 37), (47, 16), (12, 36), (34, 30), (8, 20), (20, 21), (28, 34), (33, 28), (37, 42), (6, 32), (23, 24), (27, 15), (34, 14), (29, 5), (44, 24), (20, 11), (31, 21), (8, 23), (39, 28), (20, 27), (46, 17), (28, 13), (14, 34), (4, 16), (26, 25), (39, 29), (1, 18), (1, 11), (15, 9), (35, 11), (20, 31), (1, 31), (10, 25), (41, 4), (10, 13), (8, 28), (5, 19), (0, 19), (5, 15), (14, 43), (12, 23), (9, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 9), (34, 29), (34, 20), (37, 44), (3, 7), (2, 17), (29, 20), (2, 29), (38, 30), (5, 14), (0, 2), (6, 1), (2, 26), (15, 26), (24, 44), (31, 39), (15, 30), (30, 17), (36, 11), (20, 31), (14, 11), (25, 34), (37, 37), (42, 16), (21, 37), (26, 1), (26, 41), (20, 21), (8, 14), (13, 34), (26, 8), (41, 2), (31, 25), (15, 43), (39, 17), (9, 36), (14, 0), (43, 34), (40, 23), (39, 24), (6, 22), (24, 36), (30, 11), (34, 27), (22, 20), (6, 13), (16, 22), (37, 15), (4, 25), (30, 8), (36, 37), (18, 39), (28, 33), (13, 23), (23, 27), (24, 26), (9, 15), (6, 0), (9, 11), (18, 40), (8, 37), (8, 21), (31, 12), (1, 28), (42, 24), (25, 40), (27, 39), (9, 23), (5, 31), (28, 21), (26, 12), (16, 43), (9, 7), (9, 34), (15, 25), (11, 6), (39, 26), (7, 21), (22, 17), (5, 1), (1, 7), (6, 40), (10, 25), (29, 40), (3, 23), (10, 0), (13, 1), (9, 44), (15, 45), (0, 19), (12, 34), (35, 24), (2, 33), (27, 44), (42, 2), (17, 36), (42, 4), (32, 12), (32, 6), (42, 11), (30, 13), (41, 16), (33, 40), (18, 44), (30, 34), (28, 25), (11, 30), (21, 12), (42, 29), (14, 26), (37, 7), (43, 17), (15, 28), (40, 35), (36, 19), (29, 4), (2, 43), (41, 1), (13, 11), (42, 0), (7, 25), (3, 44), (22, 32), (35, 14), (11, 31), (38, 35), (40, 38), (28, 43), (42, 36), (23, 35), (20, 23), (21, 20), (6, 35), (16, 26), (41, 39), (32, 39), (37, 4), (35, 45), (10, 17), (30, 45), (33, 21), (1, 5), (23, 0), (0, 7), (16, 30), (5, 3), (35, 30), (36, 9), (0, 9), (28, 4), (9, 25), (19, 6), (14, 3), (22, 21), (31, 0), (8, 1), (17, 39), (28, 3), (22, 3), (12, 2), (39, 38), (25, 27), (17, 34), (38, 16), (17, 21), (1, 4), (2, 27), (16, 37), (36, 6), (35, 20), (29, 23), (16, 35), (31, 11), (37, 45), (13, 4), (13, 8), (0, 36), (42, 22), (42, 9), (8, 41), (4, 22), (23, 1), (16, 31), (14, 37), (34, 31), (35, 13), (17, 16), (21, 2), (40, 45), (12, 1), (0, 39), (36, 31), (21, 1), (36, 26), (20, 38), (6, 4), (43, 18), (25, 8), (3, 14), (16, 36), (4, 42), (28, 14), (38, 32), (14, 17), (9, 43), (1, 38), (20, 39), (30, 3), (9, 32), (2, 32), (32, 24), (34, 39), (4, 20), (0, 34), (3, 39), (21, 35), (29, 45), (42, 42), (18, 7), (37, 8), (33, 7), (21, 5), (2, 34), (8, 39), (10, 33), (41, 29), (26, 18), (12, 36), (27, 26), (16, 33), (24, 41), (7, 39), (15, 13), (32, 1), (20, 44), (35, 40), (40, 37), (19, 32), (27, 38), (16, 18), (10, 27), (27, 8), (32, 20), (11, 36), (30, 16), (23, 16), (11, 34), (19, 41), (28, 31), (42, 18), (23, 41), (6, 38), (22, 42), (11, 41), (2, 21), (23, 15), (33, 39), (31, 24), (10, 26), (25, 15), (20, 18), (28, 16), (28, 37), (15, 1), (24, 15), (33, 33), (8, 10), (0, 32), (35, 29), (12, 29), (33, 26), (19, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 16), (40, 8), (21, 17), (0, 18), (15, 31), (27, 14), (2, 25), (31, 7), (31, 18), (10, 34), (8, 7), (13, 7), (25, 22), (18, 32), (13, 19), (27, 39), (38, 25), (6, 13), (37, 0), (6, 36), (21, 34), (29, 21), (30, 7), (32, 21), (27, 20), (0, 8), (43, 9), (13, 35), (35, 9), (14, 31), (38, 16), (31, 0), (31, 26), (34, 12), (1, 26), (22, 39), (37, 38), (14, 35), (20, 29), (15, 6), (24, 9), (18, 31), (32, 3), (7, 27), (14, 29), (12, 25), (9, 36), (5, 8), (6, 25), (18, 4), (3, 21), (41, 21), (4, 7), (2, 27), (28, 35), (40, 28), (30, 32), (33, 1), (14, 26), (35, 8), (31, 23), (20, 0), (19, 11), (29, 34), (23, 20), (12, 31), (40, 35), (25, 20), (19, 35), (33, 18), (31, 40), (12, 15), (33, 37), (28, 24), (25, 14), (23, 25), (14, 28), (27, 28), (28, 12), (23, 39), (39, 28), (13, 26), (0, 39), (37, 34), (32, 10), (8, 32), (16, 0), (14, 10), (36, 30), (5, 5), (16, 20), (5, 11), (34, 28), (20, 27), (33, 40), (9, 19), (32, 16), (27, 33), (14, 25), (16, 26), (18, 22), (25, 40), (39, 12), (23, 12), (22, 11), (25, 13), (26, 23), (2, 4), (15, 16), (34, 11), (23, 6), (43, 11), (33, 34), (38, 20), (1, 15), (11, 9), (21, 30), (14, 24), (41, 6), (33, 22), (34, 37), (29, 38), (0, 9), (11, 6), (12, 38), (14, 0), (15, 21), (19, 38), (23, 1), (23, 9), (4, 8), (22, 28), (14, 39), (21, 22), (36, 33), (24, 29), (29, 27), (34, 9), (16, 17), (38, 35), (38, 8), (2, 37), (37, 30), (16, 19), (25, 26), (25, 33), (29, 13), (9, 18), (30, 37), (11, 28), (13, 11), (18, 29), (31, 12), (11, 24), (6, 0), (17, 13), (21, 20), (35, 29), (37, 33), (40, 24), (18, 5), (38, 34), (12, 21), (34, 13), (17, 14), (16, 24), (28, 26), (19, 18), (25, 29), (38, 28), (40, 25), (28, 7), (15, 25), (42, 2), (9, 11), (32, 39), (37, 4), (21, 13), (9, 20), (35, 37), (10, 27), (30, 17), (36, 4), (12, 20), (33, 6), (33, 36), (3, 5), (38, 3), (8, 9), (43, 32), (37, 9), (37, 29), (0, 30), (36, 20), (3, 1), (38, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 9), (0, 20), (16, 36), (10, 27), (0, 37), (28, 8), (22, 41), (22, 28), (29, 48), (47, 42), (17, 6), (39, 16), (34, 23), (26, 46), (6, 41), (4, 41), (30, 34), (40, 6), (17, 36), (13, 27), (19, 44), (31, 36), (37, 33), (36, 48), (23, 36), (23, 43), (9, 1), (27, 6), (29, 20), (38, 20), (1, 8), (37, 36), (30, 12), (1, 37), (43, 37), (2, 9), (47, 15), (11, 9), (13, 15), (34, 24), (1, 42), (41, 14), (23, 18), (36, 25), (32, 26), (38, 3), (15, 21), (30, 4), (15, 32), (28, 7), (2, 37), (22, 37), (43, 28), (41, 31), (38, 42), (26, 19), (9, 13), (6, 16), (37, 17), (19, 39), (34, 43), (38, 12), (7, 20), (0, 11), (36, 30), (41, 35), (8, 40), (42, 31), (37, 8), (7, 42), (28, 10), (35, 18), (11, 35), (42, 5), (47, 39), (17, 37), (12, 48), (14, 48), (12, 6), (11, 24), (5, 45), (23, 15), (34, 11), (15, 13), (12, 43), (43, 36), (15, 8), (44, 23), (30, 11), (15, 35), (26, 4), (29, 3), (6, 26), (5, 36), (11, 28), (32, 3), (12, 39), (21, 11), (37, 29), (35, 20), (36, 43), (35, 46), (36, 38), (47, 23), (21, 14), (39, 20), (16, 30), (46, 18), (30, 16), (21, 39), (36, 0), (25, 14), (34, 20), (11, 43), (37, 19), (15, 40), (46, 27), (28, 42), (40, 4), (36, 35), (10, 13), (21, 1), (4, 10), (11, 18), (37, 24), (40, 35), (33, 19), (27, 2), (10, 24), (3, 35), (3, 9), (39, 43), (39, 32), (25, 1), (13, 18), (2, 48), (15, 3), (43, 35), (14, 9), (40, 19), (24, 39), (42, 0), (15, 27), (21, 5), (27, 32), (24, 6), (47, 22), (21, 6), (45, 6), (39, 46), (28, 29), (20, 9), (29, 17), (15, 26), (21, 46), (21, 7), (33, 39), (30, 28), (5, 5), (48, 23), (41, 11), (6, 46), (25, 21), (48, 28), (11, 31), (37, 16), (8, 17), (2, 10), (45, 19), (33, 17), (26, 47), (39, 10), (22, 0), (30, 29), (4, 6), (40, 38), (0, 13), (24, 9), (5, 4), (36, 20), (22, 11), (8, 32), (46, 19), (40, 46), (42, 6), (29, 23), (35, 10), (26, 25), (39, 4), (34, 35), (29, 39), (46, 0), (45, 20), (15, 1), (18, 35), (26, 9), (41, 41), (2, 47), (27, 10), (46, 34), (4, 45), (39, 26), (12, 26), (18, 23), (6, 39), (41, 13), (38, 2), (31, 7), (47, 17), (22, 36), (20, 1), (42, 38), (13, 30), (12, 25), (32, 32), (32, 47), (40, 3), (9, 0), (47, 32), (0, 38), (44, 4), (14, 36), (44, 17), (9, 23), (19, 33), (24, 47), (9, 20), (13, 22), (1, 45), (20, 14), (8, 15), (8, 24), (18, 7), (46, 23), (41, 15), (19, 12), (25, 7), (18, 21), (30, 47), (1, 30), (21, 33), (25, 19), (41, 16), (16, 0), (9, 33), (38, 35), (18, 44), (24, 7), (36, 6), (4, 16), (33, 46), (9, 45), (9, 16), (40, 20), (3, 34), (33, 38), (25, 44), (24, 34), (33, 13), (31, 38), (48, 21), (35, 47), (33, 8), (16, 24), (11, 16), (20, 42), (22, 32), (31, 19), (35, 30), (11, 47), (19, 45), (18, 4), (21, 37), (28, 38), (30, 42), (35, 5), (10, 0), (10, 6), (3, 19), (14, 45), (21, 42), (6, 10), (38, 36), (31, 18), (28, 30), (22, 6), (7, 24), (17, 42), (33, 43), (1, 48), (46, 17), (22, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 15), (37, 14), (28, 21), (1, 26), (24, 1), (33, 16), (14, 20), (11, 14), (19, 23), (34, 33), (22, 8), (1, 33), (3, 19), (6, 2), (38, 18), (2, 5), (19, 18), (16, 35), (13, 14), (31, 3), (39, 27), (9, 23), (30, 22), (34, 24), (32, 30), (28, 23), (14, 34), (9, 14), (12, 38), (15, 21), (17, 36), (32, 1), (19, 37), (35, 35), (23, 13), (19, 28), (36, 16), (22, 11), (15, 12), (23, 29), (4, 17), (26, 5), (19, 17), (10, 22), (30, 1), (34, 25), (28, 24), (9, 8), (38, 19), (10, 24), (9, 4), (36, 26), (32, 5), (17, 7), (17, 11), (0, 39), (6, 40), (19, 27), (2, 29), (21, 34), (0, 18), (36, 34), (6, 30), (16, 29), (20, 40), (1, 5), (1, 22), (4, 8), (17, 1), (0, 19), (5, 33), (14, 29), (0, 14), (37, 1), (4, 40), (6, 20), (39, 3), (22, 2), (37, 39), (2, 31), (24, 23), (28, 27), (27, 12), (25, 3), (39, 28), (22, 33), (33, 36), (15, 19), (7, 9), (35, 28), (2, 12), (26, 32), (21, 18), (39, 15), (35, 33), (33, 23), (27, 21), (30, 20), (37, 11), (26, 11), (20, 12), (24, 8), (34, 11), (14, 15), (15, 8), (34, 37), (0, 23), (38, 8), (24, 9), (23, 20), (28, 14), (23, 37), (30, 26), (26, 38), (4, 24), (27, 25), (4, 33), (35, 18), (24, 39), (31, 24), (15, 27), (15, 23), (36, 35), (31, 33), (28, 35), (22, 18), (17, 27), (12, 21), (6, 14), (6, 15), (17, 25), (29, 36), (9, 39), (24, 15), (5, 3), (17, 10), (34, 7), (4, 25), (4, 0), (37, 35), (39, 32), (29, 10), (9, 25), (9, 15), (1, 31), (35, 21), (6, 16), (35, 14), (2, 10), (28, 8), (0, 37), (25, 7), (10, 13), (36, 29), (26, 28), (38, 39), (11, 4), (3, 8), (20, 2), (31, 6), (14, 27), (38, 38), (6, 4), (31, 27), (37, 19), (35, 30), (13, 5), (39, 21), (30, 21), (24, 40), (35, 38), (9, 27), (3, 37), (1, 19), (16, 16), (39, 19), (31, 35), (31, 36), (11, 12), (5, 17), (32, 7), (21, 21), (18, 17), (10, 4), (26, 12), (33, 5), (21, 30), (3, 26), (2, 27), (8, 33), (35, 0), (22, 24), (27, 29), (5, 38), (11, 7), (0, 33), (2, 35), (4, 7), (20, 20), (32, 0), (0, 16), (35, 7), (20, 5), (16, 7), (26, 19), (10, 10), (33, 0), (37, 36), (13, 1), (11, 25), (37, 26), (6, 19), (1, 8), (6, 36), (35, 25), (7, 24), (6, 8), (10, 34), (36, 5), (19, 29), (14, 4), (14, 33), (10, 19), (31, 1), (9, 10), (24, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 23), (14, 42), (19, 5), (17, 39), (6, 3), (9, 18), (2, 16), (15, 39), (32, 15), (27, 14), (24, 46), (27, 28), (3, 44), (17, 44), (35, 14), (16, 30), (24, 21), (13, 41), (41, 3), (27, 12), (9, 45), (0, 38), (3, 40), (8, 21), (32, 0), (30, 28), (13, 40), (10, 3), (40, 43), (24, 31), (2, 21), (6, 37), (7, 37), (10, 25), (23, 45), (38, 15), (36, 36), (38, 38), (19, 40), (29, 9), (37, 4), (19, 3), (1, 47), (1, 32), (25, 6), (3, 2), (28, 22), (18, 1), (26, 9), (3, 29), (9, 43), (24, 41), (13, 42), (20, 2), (20, 14), (27, 33), (15, 47), (20, 18), (15, 4), (2, 44), (32, 31), (24, 15), (22, 30), (40, 31), (28, 25), (34, 45), (16, 38), (39, 35), (12, 32), (23, 28), (8, 25), (36, 2), (0, 15), (23, 36), (14, 27), (17, 20), (1, 14), (11, 15), (34, 6), (36, 9), (23, 9), (11, 35), (33, 37), (26, 33), (31, 32), (12, 40), (30, 15), (8, 38), (22, 28), (24, 20), (32, 22), (38, 46), (4, 40), (36, 33), (19, 11), (15, 10), (41, 5), (15, 20), (4, 28), (38, 11), (24, 29), (14, 6), (6, 16), (28, 35), (11, 23), (36, 19), (34, 26), (1, 21), (33, 4), (28, 2), (38, 44), (2, 17), (17, 35), (0, 36), (3, 46), (19, 37), (14, 23), (1, 25), (5, 2), (41, 12), (6, 24), (16, 41), (11, 38), (36, 45), (13, 0), (41, 15), (13, 46), (5, 36), (19, 10), (36, 16), (5, 25), (22, 12), (14, 5), (2, 39), (35, 26), (40, 12), (29, 10), (32, 10), (4, 38), (15, 6), (6, 44), (39, 29), (9, 28), (35, 12), (2, 32), (10, 43), (28, 21), (29, 36), (20, 9), (28, 27), (0, 40), (11, 1), (18, 31), (27, 10), (20, 17), (26, 26), (7, 36), (24, 43), (19, 45), (7, 45), (26, 28), (38, 41), (28, 34), (31, 16), (34, 46), (1, 28), (20, 39), (29, 46), (38, 16), (4, 46), (11, 25), (38, 28), (25, 26), (10, 30), (37, 27), (7, 25), (12, 19), (10, 0), (38, 12), (2, 45), (12, 9), (4, 5), (4, 37), (12, 42), (25, 21), (33, 9), (22, 11), (16, 0), (22, 20), (19, 18), (34, 15), (19, 0), (23, 16), (23, 46), (31, 20), (10, 10), (20, 43), (5, 37), (41, 27), (35, 9), (3, 0), (7, 40), (10, 12), (32, 43), (34, 31), (31, 31), (22, 25), (5, 13), (7, 44), (32, 27), (7, 20), (8, 9), (27, 15), (25, 40), (14, 36), (39, 46), (35, 39), (33, 38), (21, 4), (6, 17), (3, 13), (28, 37), (5, 41), (37, 0), (34, 4), (35, 13), (15, 22), (35, 46), (26, 13), (38, 14), (33, 13), (25, 41), (39, 26), (32, 35), (13, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 31), (13, 19), (6, 14), (24, 46), (20, 37), (14, 38), (2, 22), (17, 27), (12, 21), (21, 46), (2, 24), (42, 32), (11, 13), (11, 7), (41, 25), (0, 42), (27, 21), (8, 44), (28, 4), (45, 18), (26, 28), (16, 0), (34, 3), (17, 22), (25, 0), (29, 30), (42, 16), (26, 12), (6, 28), (12, 40), (21, 37), (17, 9), (12, 44), (10, 21), (18, 2), (42, 14), (31, 44), (5, 44), (5, 1), (6, 36), (12, 35), (35, 6), (33, 30), (44, 4), (19, 38), (38, 20), (22, 11), (12, 8), (39, 6), (25, 41), (20, 20), (16, 5), (36, 16), (28, 39), (14, 8), (44, 3), (43, 18), (17, 14), (11, 34), (4, 5), (11, 28), (12, 5), (45, 23), (35, 18), (40, 32), (20, 19), (37, 44), (40, 25), (32, 10), (35, 2), (22, 10), (18, 45), (22, 42), (42, 36), (34, 14), (45, 36), (17, 13), (20, 9), (25, 21), (1, 10), (16, 3), (7, 16), (5, 45), (44, 46), (39, 0), (27, 46), (12, 3), (22, 44), (0, 46), (3, 43), (41, 2), (11, 24), (36, 46), (8, 4), (30, 35), (13, 12), (37, 40), (23, 30), (32, 16), (5, 19), (15, 35), (29, 44), (38, 26), (3, 30), (45, 39), (31, 17), (16, 42), (16, 13), (34, 11), (37, 9), (7, 38), (22, 38), (22, 18), (24, 42), (13, 23), (28, 31), (4, 4), (4, 2), (23, 3), (42, 40), (12, 17), (19, 18), (17, 0), (25, 17), (29, 13), (44, 7), (3, 34), (40, 23), (42, 31), (33, 21), (27, 30), (19, 31), (45, 0), (1, 13), (21, 28), (36, 38), (33, 38), (32, 47), (12, 27), (9, 35), (45, 43), (27, 27), (29, 17), (43, 35), (25, 12), (37, 45), (18, 27), (39, 29), (18, 21), (20, 34), (40, 17), (46, 35), (41, 37), (14, 18), (2, 45), (44, 1), (22, 5), (24, 4), (23, 10), (26, 32), (41, 16), (31, 0), (15, 12), (9, 41), (2, 28), (0, 35), (1, 39), (21, 1), (43, 21), (10, 39), (40, 5), (31, 26), (20, 11), (0, 6), (23, 8), (22, 2), (12, 29), (39, 21), (31, 6), (37, 26), (4, 13), (10, 17), (42, 5), (15, 9), (13, 15), (39, 11), (38, 30), (30, 12), (46, 36), (43, 41), (40, 47), (32, 36), (29, 14), (26, 7), (37, 24), (19, 44), (46, 6), (5, 5), (5, 40), (22, 9), (41, 40), (17, 19), (43, 7), (14, 28), (43, 16), (43, 47), (39, 10), (43, 26), (2, 15), (18, 35), (22, 17), (7, 36), (39, 39), (5, 14), (20, 0), (34, 26), (8, 16), (18, 1), (18, 29), (13, 33), (18, 24), (11, 16), (29, 10), (16, 28), (33, 39), (25, 1), (18, 19), (42, 28), (33, 17), (28, 9), (28, 22), (35, 16), (43, 20), (24, 28), (45, 30), (31, 33), (44, 44), (41, 22), (8, 22), (11, 25), (23, 2), (37, 43), (0, 3), (42, 46), (36, 6), (40, 35), (45, 38), (1, 9), (41, 9), (31, 13), (8, 43), (34, 8), (36, 13), (7, 41), (36, 31), (31, 29), (31, 11), (21, 16), (11, 41), (9, 47), (41, 42), (38, 19), (35, 9), (0, 11), (10, 42), (31, 25), (27, 34), (31, 16), (29, 47), (29, 18), (1, 18), (1, 30), (15, 38), (4, 21), (43, 44), (7, 5), (45, 8), (23, 46), (39, 17), (3, 1), (46, 26), (34, 10), (7, 17), (7, 43), (17, 15), (30, 32), (14, 47), (2, 19), (28, 20), (25, 8), (5, 16), (5, 26), (15, 6), (44, 12), (18, 38), (27, 4), (10, 7), (35, 21), (14, 33), (25, 7), (14, 14), (33, 11), (16, 31), (10, 28), (39, 18), (37, 20), (35, 3), (33, 0), (9, 21), (40, 29), (22, 12), (10, 36), (35, 30), (31, 4), (25, 27), (37, 14), (15, 39), (3, 37), (3, 40), (42, 35), (44, 5), (40, 1), (30, 15), (46, 41), (40, 27), (19, 45), (44, 9), (39, 31), (21, 11), (35, 22), (17, 10), (7, 37), (16, 44), (45, 27), (3, 31), (41, 26), (29, 12), (44, 13), (7, 0), (35, 4), (36, 14), (20, 12), (17, 28), (14, 7), (29, 40), (38, 11), (15, 13), (34, 34), (34, 21), (1, 43), (30, 37), (29, 4), (10, 45), (19, 1), (28, 29), (23, 22), (46, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 2), (21, 18), (30, 19), (13, 8), (22, 26), (18, 11), (18, 24), (36, 1), (36, 19), (20, 3), (25, 34), (38, 4), (14, 33), (12, 16), (23, 7), (36, 0), (32, 30), (2, 38), (39, 6), (16, 32), (15, 27), (39, 3), (17, 23), (12, 7), (23, 35), (35, 36), (0, 36), (14, 38), (42, 35), (7, 14), (4, 6), (2, 34), (7, 10), (14, 0), (6, 1), (15, 35), (32, 25), (4, 8), (41, 27), (24, 30), (32, 35), (15, 39), (26, 38), (15, 34), (38, 26), (6, 31), (17, 8), (13, 6), (29, 26), (8, 8), (31, 22), (39, 12), (5, 3), (12, 36), (33, 17), (42, 30), (26, 32), (24, 22), (15, 21), (40, 17), (0, 13), (9, 2), (10, 22), (37, 20), (34, 11), (30, 8), (33, 5), (4, 13), (20, 17), (20, 13), (14, 6), (40, 1), (31, 21), (26, 17), (19, 9), (10, 11), (27, 19), (10, 37), (40, 12), (43, 19), (22, 17), (19, 10), (16, 35), (42, 24), (42, 1), (24, 27), (40, 25), (29, 29), (20, 36), (42, 23), (8, 2), (12, 3), (14, 34), (29, 19), (43, 15), (17, 15), (26, 15), (16, 22), (9, 4), (17, 21), (10, 20), (41, 2), (23, 29), (41, 9), (8, 38), (28, 21), (29, 3), (26, 23), (30, 22), (5, 27), (18, 20), (38, 15), (12, 4), (30, 32), (17, 22), (12, 14), (13, 15), (30, 39), (3, 36), (23, 19), (12, 26), (42, 29), (8, 36), (38, 23), (3, 22), (43, 39), (16, 30), (9, 15), (13, 0), (24, 39), (8, 33), (36, 31), (39, 39), (42, 7), (24, 12), (28, 29), (40, 30), (4, 15), (23, 24), (12, 39), (21, 17), (34, 26), (13, 29), (38, 10), (35, 6), (6, 37), (12, 5), (2, 1), (9, 30), (16, 17), (2, 28), (35, 9), (33, 32), (14, 37), (43, 34), (5, 36), (35, 4), (12, 0), (18, 18), (42, 5), (27, 38), (2, 10), (8, 27), (20, 18), (4, 12), (25, 14), (38, 8), (43, 14), (15, 19), (33, 1), (41, 38), (35, 20), (24, 25), (22, 16), (13, 23), (31, 16), (9, 16), (20, 19), (30, 27), (33, 29), (9, 6), (29, 18), (9, 17), (4, 21), (27, 39), (0, 3), (18, 4), (14, 14), (13, 10), (35, 29), (8, 14), (26, 8), (17, 40), (31, 35), (18, 21), (39, 10), (41, 10), (36, 40), (13, 18), (26, 2), (34, 39), (18, 12), (20, 15), (13, 9), (6, 34), (5, 10), (32, 11), (24, 4), (33, 23), (30, 11), (28, 20), (5, 2), (13, 24), (43, 36), (7, 5), (12, 13), (11, 14), (42, 18), (1, 5), (14, 2), (18, 7), (42, 12), (28, 13), (36, 7), (11, 27), (4, 11), (22, 12), (27, 18), (20, 6), (35, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 23), (0, 20), (27, 37), (40, 35), (17, 41), (35, 28), (4, 10), (11, 20), (16, 25), (15, 25), (20, 7), (19, 23), (19, 28), (7, 25), (39, 16), (5, 39), (4, 28), (41, 6), (34, 12), (5, 21), (16, 16), (27, 0), (23, 39), (31, 6), (3, 28), (19, 4), (37, 4), (30, 5), (8, 41), (7, 35), (34, 38), (6, 0), (25, 35), (23, 13), (37, 35), (42, 22), (36, 34), (25, 11), (39, 37), (19, 17), (29, 29), (32, 34), (33, 5), (33, 30), (10, 10), (14, 14), (5, 41), (31, 30), (6, 10), (27, 21), (38, 25), (39, 13), (8, 35), (37, 30), (22, 17), (34, 27), (41, 7), (5, 32), (13, 18), (23, 19), (42, 0), (33, 25), (3, 10), (24, 39), (36, 22), (8, 34), (27, 2), (11, 32), (0, 39), (25, 29), (14, 13), (4, 35), (23, 31), (7, 38), (25, 26), (37, 40), (26, 41), (31, 31), (34, 40), (6, 25), (1, 13), (0, 27), (1, 19), (25, 13), (8, 4), (15, 18), (37, 27), (24, 28), (5, 9), (5, 22), (25, 36), (1, 34), (6, 8), (31, 5), (41, 8), (3, 41), (17, 4), (2, 39), (32, 32), (34, 42), (38, 21), (34, 26), (6, 21), (0, 10), (10, 13), (18, 3), (15, 4), (12, 37), (30, 23), (34, 17), (31, 12), (6, 29), (15, 29), (30, 13), (14, 34), (13, 24), (28, 15), (30, 24), (1, 16), (7, 5), (27, 11), (42, 24), (2, 31), (42, 15), (24, 14), (21, 21), (17, 1), (13, 9), (39, 14), (23, 22), (23, 14), (25, 19), (5, 40), (32, 13), (0, 35), (2, 18), (8, 30), (22, 30), (4, 5), (35, 6), (38, 22), (29, 20), (14, 22), (29, 13), (30, 15), (33, 9), (22, 1), (6, 2), (29, 28), (11, 15), (16, 31), (34, 18), (5, 29), (33, 37), (2, 10), (17, 42), (9, 24), (36, 0), (1, 9), (20, 42), (24, 34), (11, 19), (22, 36), (27, 19), (20, 30), (36, 25), (38, 39), (34, 36), (38, 38), (18, 19), (28, 1), (10, 1), (22, 3), (24, 31), (14, 24), (7, 41), (1, 5), (24, 41), (39, 39), (4, 9), (21, 12), (33, 34), (28, 21), (1, 7), (22, 37), (10, 30), (34, 28), (1, 36), (25, 10), (38, 2), (11, 11), (2, 32), (25, 42), (32, 9), (23, 4), (3, 16), (23, 0), (21, 41), (0, 13), (37, 6), (10, 16), (27, 32), (16, 30), (11, 34), (27, 17), (10, 33), (6, 1), (39, 32), (29, 34), (29, 7), (1, 0), (23, 40), (27, 3), (32, 10), (15, 20), (32, 2), (28, 11), (15, 2), (21, 20), (20, 3), (15, 36), (22, 6), (39, 31), (18, 7), (31, 4), (18, 26), (4, 30), (7, 33), (10, 18), (0, 32), (5, 27), (24, 29), (6, 20), (22, 4), (17, 16), (6, 14), (6, 4), (12, 18), (28, 26), (16, 36), (2, 19), (4, 0), (38, 32), (26, 26), (40, 27), (33, 7), (21, 10), (23, 17), (41, 41), (20, 27), (3, 40), (5, 38), (16, 42), (27, 1), (15, 12), (29, 27), (11, 28), (41, 28), (23, 38), (2, 9), (2, 23), (11, 33), (22, 32), (7, 27), (16, 40), (23, 27), (1, 17), (30, 39), (16, 1), (17, 11), (17, 38), (3, 18), (15, 13), (17, 17), (15, 15), (19, 34), (17, 13), (3, 1), (5, 8), (23, 3), (15, 24), (5, 13), (28, 13), (5, 3), (13, 3), (9, 10), (35, 21), (20, 38), (8, 31), (22, 38), (39, 4), (10, 39), (8, 0), (3, 20), (4, 17), (2, 8), (8, 28), (27, 22), (11, 41), (2, 7), (31, 40), (26, 27), (18, 29), (7, 39), (12, 28), (34, 32), (1, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 28), (16, 16), (28, 14), (4, 12), (44, 19), (2, 14), (40, 34), (46, 2), (24, 35), (0, 20), (41, 23), (14, 12), (21, 31), (46, 10), (35, 28), (42, 21), (26, 33), (40, 33), (33, 35), (11, 14), (13, 13), (33, 28), (46, 19), (17, 5), (25, 23), (44, 17), (8, 21), (39, 42), (10, 38), (38, 35), (34, 27), (25, 20), (40, 12), (30, 26), (40, 1), (6, 19), (23, 11), (24, 14), (32, 22), (18, 43), (4, 33), (44, 22), (43, 43), (40, 32), (17, 2), (24, 1), (0, 42), (41, 24), (25, 5), (9, 38), (17, 3), (6, 22), (36, 34), (44, 21), (4, 0), (45, 0), (14, 27), (19, 6), (23, 10), (44, 24), (38, 6), (25, 17), (36, 32), (20, 23), (34, 23), (19, 37), (2, 23), (34, 43), (0, 7), (36, 10), (19, 8), (21, 9), (44, 16), (16, 28), (8, 31), (35, 27), (22, 11), (23, 40), (13, 4), (35, 15), (26, 35), (42, 34), (40, 28), (25, 6), (13, 32), (30, 15), (10, 10), (17, 23), (24, 34), (45, 43), (31, 16), (45, 6), (29, 20), (11, 16), (19, 34), (40, 20), (22, 24), (4, 35), (33, 29), (9, 0), (18, 1), (15, 25), (17, 42), (45, 13), (28, 1), (29, 21), (9, 9), (32, 36), (42, 6), (3, 26), (8, 32), (44, 30), (8, 20), (3, 11), (29, 23), (3, 40), (4, 41), (0, 11), (21, 25), (43, 6), (3, 27), (16, 9), (12, 1), (27, 26), (5, 29), (9, 8), (41, 29), (0, 28), (32, 5), (3, 34), (25, 2), (44, 13), (14, 30), (42, 42), (39, 18), (4, 24), (5, 25), (26, 7), (32, 26), (5, 21), (41, 6), (32, 6), (23, 30), (20, 12), (32, 2), (35, 5), (36, 15), (37, 36), (20, 9), (10, 42), (12, 29), (8, 39), (45, 32), (21, 15), (42, 12), (34, 33), (8, 38), (1, 21), (26, 41), (40, 38), (3, 16), (8, 34), (46, 16), (34, 37), (6, 10), (11, 39), (28, 37), (15, 35), (26, 22), (14, 8), (43, 26), (15, 16), (41, 8), (30, 21), (28, 15), (39, 13), (3, 39), (29, 39), (16, 20), (18, 10), (22, 21), (33, 13), (41, 37), (20, 30), (11, 19), (2, 36), (31, 5), (34, 32), (22, 2), (21, 2), (21, 14), (19, 12), (31, 14), (19, 0), (25, 35), (31, 4), (8, 29), (31, 28), (16, 39), (7, 6), (42, 16), (8, 13), (33, 3), (37, 2), (10, 20), (30, 22), (44, 43), (39, 6), (33, 21), (34, 29), (41, 40), (27, 37), (37, 12), (25, 32), (7, 31), (11, 26), (30, 27), (37, 27), (9, 35), (22, 15), (4, 30), (5, 17), (38, 34), (6, 20), (43, 15), (36, 33), (15, 4), (35, 42), (39, 9), (42, 2), (2, 3), (31, 8), (41, 18), (32, 7), (7, 4), (8, 18), (24, 38), (22, 43), (21, 28), (6, 26), (19, 3), (33, 23), (17, 34), (1, 3), (1, 23), (45, 27), (43, 17), (27, 22), (24, 28), (30, 1), (19, 43), (16, 26), (29, 41), (6, 11), (22, 14), (1, 15), (33, 22), (35, 32), (43, 21), (14, 38), (13, 7), (4, 27), (27, 2), (25, 29), (38, 19), (31, 38), (46, 4), (2, 4), (41, 17), (32, 8), (21, 34), (18, 36), (40, 29), (24, 11), (46, 30), (9, 29), (36, 35), (8, 6), (31, 20), (34, 11), (13, 41), (10, 6), (44, 32), (1, 6), (28, 9), (20, 21), (8, 9), (32, 10), (39, 12), (12, 42), (41, 42), (32, 23), (35, 36), (10, 40), (38, 25), (23, 8), (28, 8), (43, 9), (20, 11), (7, 11), (39, 0), (19, 33), (31, 41), (1, 38), (36, 9), (1, 11), (36, 13), (38, 20), (5, 9), (18, 26), (11, 9), (11, 42), (12, 28), (3, 23), (6, 4), (37, 30), (21, 12), (24, 19), (36, 18), (39, 15), (18, 38), (11, 24), (37, 26), (41, 1), (21, 19), (22, 37), (31, 40), (0, 25), (7, 8), (4, 32), (29, 0), (20, 4), (11, 2), (5, 0), (4, 42), (17, 7), (27, 17), (23, 7), (15, 15), (22, 39), (2, 32), (22, 7), (18, 15), (11, 11), (13, 11), (35, 23), (30, 0), (4, 20), (12, 25), (37, 3), (10, 21), (37, 28), (19, 36), (42, 19), (25, 21), (4, 1), (38, 38), (38, 33), (12, 13), (24, 7), (4, 2), (34, 26), (2, 25), (25, 8), (9, 31), (35, 12), (42, 23), (25, 42), (24, 16), (44, 5), (29, 2), (29, 3), (8, 24), (3, 24), (23, 35), (5, 16), (44, 35), (31, 32), (33, 25), (10, 37), (29, 42), (37, 14), (5, 39), (29, 14), (27, 21), (7, 39), (27, 19), (35, 2), (3, 12), (16, 17), (21, 6), (16, 37), (44, 42), (0, 43), (31, 10), (35, 17), (41, 30), (45, 40), (5, 40), (4, 23), (10, 31), (8, 43), (6, 31), (9, 17), (32, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 16), (45, 40), (7, 30), (31, 2), (20, 8), (17, 40), (46, 22), (41, 32), (28, 3), (35, 21), (2, 8), (8, 42), (39, 35), (21, 22), (17, 12), (11, 16), (5, 25), (46, 33), (25, 31), (24, 39), (5, 42), (43, 9), (31, 0), (31, 43), (45, 31), (4, 44), (33, 8), (29, 34), (4, 14), (22, 6), (9, 44), (33, 29), (31, 39), (23, 26), (4, 1), (42, 26), (43, 10), (30, 11), (37, 27), (13, 19), (39, 9), (17, 13), (14, 43), (16, 0), (43, 5), (14, 42), (11, 3), (32, 15), (6, 45), (25, 30), (30, 10), (41, 38), (2, 27), (29, 27), (2, 1), (34, 7), (35, 41), (30, 42), (38, 42), (17, 26), (44, 1), (29, 15), (22, 35), (18, 8), (19, 1), (1, 16), (39, 18), (32, 6), (7, 24), (22, 44), (10, 14), (31, 9), (17, 44), (32, 26), (19, 8), (37, 44), (5, 35), (25, 40), (14, 13), (41, 5), (12, 7), (20, 11), (46, 2), (38, 8), (44, 32), (24, 7), (37, 25), (30, 23), (1, 17), (28, 2), (20, 45), (3, 2), (4, 19), (35, 38), (15, 14), (42, 17), (30, 9), (5, 6), (9, 38), (32, 28), (32, 13), (44, 29), (43, 14), (3, 11), (19, 17), (8, 36), (14, 24), (8, 29), (37, 42), (23, 1), (14, 38), (13, 37), (32, 3), (44, 10), (22, 14), (28, 14), (15, 30), (42, 13), (9, 8), (40, 21), (19, 5), (27, 2), (13, 43), (18, 6), (38, 40), (18, 36), (14, 45), (0, 8), (29, 8), (25, 45), (46, 28), (30, 8), (41, 29), (5, 38), (30, 15), (0, 35), (4, 18), (20, 19), (12, 22), (37, 4), (7, 17), (17, 8), (45, 11), (36, 40), (45, 34), (38, 37), (25, 4), (43, 25), (3, 21), (14, 3), (7, 31), (1, 13), (13, 29), (2, 35), (25, 17), (36, 37), (26, 3), (35, 25), (11, 40), (25, 41), (22, 7), (41, 41), (4, 0), (23, 22), (28, 7), (30, 24), (42, 22), (4, 25), (15, 23), (23, 10), (4, 4), (2, 11), (30, 37), (45, 5), (16, 7), (30, 13), (7, 0), (35, 15), (25, 0), (39, 31), (37, 20), (30, 26), (44, 20), (21, 34), (28, 11), (27, 44), (24, 12), (6, 29), (6, 9), (33, 19), (43, 21), (42, 12), (4, 5), (40, 39), (7, 32), (28, 37), (45, 10), (36, 7), (13, 44), (34, 3), (39, 22), (26, 16), (4, 40), (42, 31), (2, 20), (17, 1), (4, 3), (22, 39), (13, 20), (28, 19), (11, 37), (15, 3), (43, 36), (36, 12), (35, 31), (5, 9), (32, 9), (6, 8), (29, 26), (11, 11), (13, 30), (26, 24), (42, 1), (29, 29), (42, 6), (32, 7), (0, 7), (24, 10), (2, 44), (1, 40), (44, 0), (6, 37), (27, 19), (37, 3), (30, 7), (30, 22), (13, 39), (4, 32), (8, 11), (27, 15), (33, 11), (3, 16), (8, 17), (1, 7), (34, 29), (35, 0), (21, 28), (19, 18), (12, 44), (10, 29), (21, 17), (12, 21), (2, 7), (38, 12), (34, 2), (9, 35), (3, 13), (40, 26), (30, 21), (34, 21), (34, 0), (10, 0), (16, 20), (26, 11), (36, 6), (11, 33), (9, 37), (20, 14), (41, 31), (46, 4), (11, 30), (12, 40), (43, 45), (5, 1), (40, 6), (7, 44), (17, 37), (16, 22), (43, 0), (31, 10), (23, 25), (36, 13), (31, 24), (13, 26), (45, 41), (23, 8), (6, 3), (6, 33), (7, 4), (12, 5), (38, 7), (16, 45), (9, 3), (44, 26), (31, 38), (44, 30), (17, 22), (21, 9), (19, 9), (19, 21), (27, 6), (36, 1), (46, 12), (22, 1), (19, 2), (10, 27), (39, 40), (0, 4), (13, 15), (0, 36), (7, 41), (39, 27), (45, 0), (40, 25), (0, 28), (33, 3), (20, 4), (16, 6), (31, 33), (15, 40), (1, 32), (16, 43), (35, 28), (14, 25), (14, 26), (24, 33), (25, 6), (26, 2), (44, 39), (16, 30), (9, 41), (2, 10), (38, 39), (1, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 8), (13, 28), (40, 34), (38, 33), (5, 1), (41, 32), (38, 30), (34, 12), (39, 25), (6, 16), (29, 16), (33, 20), (3, 30), (22, 14), (19, 36), (27, 37), (8, 2), (1, 21), (13, 8), (26, 3), (12, 11), (5, 38), (16, 13), (30, 7), (25, 39), (6, 22), (33, 24), (37, 35), (10, 3), (9, 16), (14, 13), (34, 23), (14, 19), (26, 10), (33, 26), (7, 35), (10, 29), (13, 9), (33, 0), (25, 21), (1, 23), (5, 36), (18, 31), (19, 23), (39, 22), (29, 25), (35, 15), (16, 2), (0, 10), (31, 37), (40, 39), (24, 17), (35, 36), (40, 26), (21, 38), (8, 34), (23, 36), (1, 7), (11, 3), (3, 14), (16, 5), (4, 38), (24, 16), (20, 32), (27, 8), (40, 12), (33, 28), (24, 34), (16, 6), (36, 29), (6, 18), (11, 32), (31, 9), (41, 20), (34, 34), (30, 16), (14, 25), (34, 31), (0, 20), (39, 28), (31, 19), (23, 12), (20, 23), (40, 0), (9, 9), (41, 29), (29, 21), (31, 0), (8, 27), (3, 20), (24, 36), (15, 22), (7, 30), (9, 35), (27, 18), (21, 11), (19, 11), (15, 34), (40, 38), (41, 10), (15, 38), (6, 36), (2, 12), (19, 35), (21, 27), (38, 0), (8, 5), (32, 31), (24, 2), (6, 24), (15, 32), (0, 27), (1, 33), (18, 5), (12, 19), (40, 24), (8, 4), (39, 12), (30, 19), (35, 33), (9, 10), (8, 8), (25, 33), (20, 36), (29, 3), (9, 32), (33, 33), (12, 3), (11, 19), (8, 33), (18, 38), (10, 8), (34, 28), (6, 14), (3, 15), (9, 1), (8, 20), (1, 29), (2, 1), (6, 6), (10, 20), (34, 24), (14, 35), (2, 25), (28, 3), (28, 15), (39, 13), (10, 5), (3, 16), (25, 26), (7, 9), (36, 22), (20, 35), (30, 24), (22, 34), (8, 36), (23, 11), (39, 4), (35, 30), (36, 39), (11, 9), (7, 34), (4, 13), (9, 14), (7, 39), (9, 37), (16, 25), (33, 36), (21, 33), (27, 28), (22, 25), (36, 18), (7, 29), (11, 30), (2, 36), (40, 6), (15, 3), (1, 10), (41, 13), (29, 38), (29, 36), (29, 17), (4, 31), (28, 6), (16, 21), (38, 19), (12, 9), (15, 8), (23, 4), (22, 18), (6, 3), (31, 16), (16, 9), (20, 16), (18, 30), (10, 38), (11, 16), (14, 14), (35, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 33), (23, 23), (12, 41), (40, 7), (44, 31), (6, 27), (30, 35), (41, 3), (16, 20), (28, 24), (2, 11), (24, 37), (26, 9), (26, 37), (22, 1), (26, 5), (36, 38), (41, 19), (36, 31), (13, 3), (31, 22), (16, 32), (33, 3), (26, 28), (14, 13), (28, 1), (32, 3), (10, 41), (12, 32), (8, 16), (0, 14), (31, 0), (0, 35), (31, 27), (2, 6), (13, 28), (23, 29), (33, 28), (24, 12), (5, 24), (19, 33), (29, 4), (28, 8), (35, 6), (32, 21), (15, 32), (41, 15), (25, 4), (25, 20), (10, 18), (44, 35), (6, 0), (44, 38), (16, 7), (38, 20), (41, 40), (43, 1), (23, 21), (4, 20), (4, 15), (39, 1), (11, 27), (14, 41), (34, 5), (35, 21), (42, 11), (37, 35), (38, 32), (33, 23), (3, 23), (38, 39), (19, 7), (17, 27), (29, 17), (8, 35), (29, 5), (11, 15), (32, 7), (38, 12), (23, 1), (9, 4), (12, 35), (25, 36), (18, 18), (32, 11), (25, 39), (40, 23), (28, 40), (34, 1), (31, 24), (33, 26), (40, 5), (32, 36), (34, 31), (27, 29), (8, 5), (22, 36), (12, 27), (1, 41), (32, 25), (30, 24), (15, 31), (9, 14), (37, 23), (21, 5), (13, 36), (7, 3), (6, 9), (22, 22), (0, 25), (35, 41), (11, 2), (3, 4), (36, 1), (30, 10), (22, 40), (29, 22), (33, 22), (43, 19), (3, 30), (13, 31), (14, 4), (34, 35), (5, 40), (22, 2), (5, 32), (14, 34), (41, 9), (23, 3), (27, 11), (42, 17), (34, 38), (44, 15), (38, 34), (42, 37), (32, 5), (28, 32), (18, 5), (11, 39), (33, 9), (30, 1), (27, 39), (7, 6), (24, 31), (16, 2), (8, 4), (6, 7), (36, 19), (26, 25), (33, 29), (41, 12), (9, 41), (6, 3), (19, 34), (1, 32), (43, 8), (14, 36), (36, 37), (9, 12), (0, 19), (7, 11), (42, 30), (23, 38), (33, 11), (34, 10), (25, 19), (30, 12), (44, 13), (6, 10), (42, 13), (43, 17), (3, 10), (1, 33), (16, 22), (25, 34), (35, 36), (10, 10), (27, 20), (28, 12), (37, 41), (5, 2), (18, 16), (39, 39), (39, 40), (14, 21), (32, 12), (1, 19), (35, 3), (18, 27), (27, 1), (25, 32), (28, 20), (36, 34), (0, 24), (10, 35), (22, 12), (14, 39), (36, 13), (30, 21), (17, 35), (26, 7), (1, 2), (4, 39), (0, 27), (20, 33), (28, 26), (29, 41), (11, 23), (22, 20), (19, 3), (3, 11), (1, 31), (12, 10), (6, 32), (35, 9), (31, 28), (35, 13), (30, 22), (12, 9), (20, 35), (10, 2), (37, 9), (30, 32), (27, 12), (44, 1), (16, 13), (30, 34), (31, 39), (44, 0), (30, 16), (9, 21), (13, 39), (31, 30), (40, 31), (3, 34), (39, 28), (16, 1), (1, 35), (37, 24), (17, 31), (0, 28), (43, 12), (26, 36), (9, 2), (32, 0), (40, 30), (7, 32), (2, 33), (43, 18), (37, 17), (34, 7), (20, 10), (24, 29), (19, 35), (2, 27), (22, 38), (8, 6), (1, 36), (14, 7), (7, 14), (21, 11), (39, 22), (14, 3), (34, 41), (0, 36), (4, 23), (9, 30), (32, 19), (37, 30), (25, 14), (39, 38), (16, 15), (19, 32), (4, 8), (44, 24), (34, 25), (14, 22), (27, 8), (4, 28), (42, 34), (3, 17), (42, 7), (40, 2), (3, 7), (1, 5), (40, 8), (26, 19), (7, 25), (11, 33), (19, 26), (22, 41), (5, 8), (11, 31), (21, 24), (25, 26), (0, 2), (26, 12), (39, 8), (23, 39), (8, 29), (22, 16), (16, 24), (43, 31), (1, 22), (42, 9), (12, 20), (6, 5), (15, 11), (27, 23), (16, 28), (32, 31), (28, 4), (33, 24), (26, 31), (35, 15), (24, 24), (40, 26), (15, 7), (32, 8), (17, 24), (4, 29), (2, 15), (18, 22), (31, 9), (36, 15), (25, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 40), (31, 10), (3, 19), (36, 15), (19, 31), (7, 14), (30, 9), (40, 19), (4, 34), (33, 17), (27, 19), (41, 21), (3, 39), (33, 19), (32, 40), (25, 33), (41, 13), (3, 28), (25, 26), (9, 35), (7, 10), (31, 5), (12, 2), (3, 1), (17, 31), (3, 6), (37, 42), (33, 40), (9, 3), (7, 25), (18, 22), (27, 9), (22, 36), (38, 40), (32, 1), (1, 5), (24, 36), (5, 8), (23, 40), (11, 30), (31, 15), (12, 26), (41, 40), (8, 24), (17, 27), (33, 16), (28, 8), (35, 18), (32, 4), (23, 3), (34, 30), (8, 31), (36, 9), (17, 29), (1, 0), (32, 24), (0, 19), (23, 0), (7, 17), (16, 19), (37, 26), (21, 41), (15, 21), (15, 13), (16, 32), (4, 4), (6, 33), (16, 37), (33, 33), (18, 26), (25, 30), (33, 38), (25, 2), (7, 13), (38, 19), (6, 11), (13, 35), (17, 4), (38, 3), (28, 42), (36, 41), (34, 20), (37, 5), (32, 19), (19, 39), (3, 32), (7, 33), (29, 20), (8, 22), (14, 37), (29, 5), (6, 41), (27, 40), (10, 21), (18, 0), (16, 26), (0, 4), (4, 41), (7, 1), (13, 2), (19, 8), (10, 6), (15, 42), (41, 1), (32, 31), (15, 28), (20, 32), (38, 32), (37, 37), (4, 42), (21, 12), (33, 3), (33, 36), (2, 24), (5, 17), (2, 16), (34, 3), (12, 5), (30, 4), (2, 3), (20, 39), (30, 23), (28, 3), (10, 11), (5, 15), (6, 25), (9, 23), (38, 6), (3, 18), (4, 9), (22, 29), (4, 31), (40, 25), (36, 31), (36, 22), (39, 22), (7, 20), (3, 7), (9, 31), (27, 14), (8, 4), (38, 25), (6, 15), (33, 2), (7, 26), (20, 25), (37, 30), (41, 12), (26, 7), (37, 39), (24, 4), (8, 5), (27, 42), (16, 1), (35, 26), (0, 29), (34, 31), (29, 35), (26, 15), (18, 8), (37, 38), (13, 23), (35, 13), (35, 42), (39, 30), (33, 28), (9, 30), (27, 22), (14, 10), (14, 39), (4, 11), (34, 2), (30, 41), (13, 7), (19, 36), (26, 28), (19, 34), (15, 32), (32, 38), (18, 25), (19, 7), (22, 13), (5, 11), (17, 7), (4, 36), (7, 42), (4, 6), (21, 6), (16, 13), (7, 12), (3, 31), (21, 0), (28, 7), (36, 35), (11, 23), (0, 17), (1, 13), (6, 34), (7, 22), (6, 29), (20, 28), (1, 10), (31, 21), (27, 26), (18, 36), (35, 19), (11, 1), (25, 39), (1, 6), (17, 36), (28, 5), (1, 7), (37, 33), (5, 34), (34, 1), (34, 6), (22, 2), (24, 6), (9, 24), (0, 11), (2, 20), (22, 8), (32, 33), (22, 34), (34, 11), (19, 15), (1, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 4), (31, 41), (30, 0), (33, 41), (18, 19), (41, 41), (34, 33), (3, 33), (18, 9), (32, 13), (19, 0), (7, 1), (16, 22), (24, 39), (23, 6), (31, 23), (16, 6), (21, 30), (9, 46), (32, 16), (25, 44), (11, 2), (18, 13), (26, 28), (26, 44), (37, 19), (36, 29), (29, 12), (18, 42), (20, 37), (18, 23), (31, 17), (32, 27), (14, 33), (6, 1), (19, 18), (15, 7), (23, 17), (4, 41), (28, 9), (23, 33), (34, 1), (28, 41), (4, 10), (40, 18), (33, 30), (41, 34), (22, 37), (12, 34), (0, 37), (15, 35), (38, 5), (5, 39), (41, 30), (11, 20), (27, 14), (11, 13), (21, 14), (22, 22), (35, 35), (5, 27), (40, 42), (13, 0), (17, 13), (42, 40), (35, 2), (12, 43), (8, 9), (23, 25), (14, 22), (42, 3), (22, 2), (19, 16), (17, 37), (34, 41), (26, 26), (28, 7), (28, 4), (35, 36), (21, 17), (42, 33), (1, 9), (15, 16), (35, 12), (25, 20), (37, 9), (42, 38), (16, 25), (25, 34), (15, 4), (38, 4), (30, 2), (29, 11), (32, 23), (8, 12), (24, 30), (22, 13), (7, 17), (24, 27), (16, 15), (35, 23), (41, 43), (1, 40), (15, 6), (9, 16), (21, 35), (9, 37), (10, 41), (34, 22), (36, 41), (31, 30), (7, 15), (18, 3), (40, 31), (14, 0), (18, 18), (3, 31), (22, 33), (21, 20), (2, 23), (33, 2), (24, 34), (4, 29), (16, 14), (41, 16), (9, 6), (20, 26), (42, 10), (24, 35), (2, 8), (33, 35), (34, 40), (28, 3), (5, 9), (27, 27), (41, 22), (1, 16), (26, 38), (2, 13), (8, 41), (20, 17), (8, 3), (23, 8), (19, 32), (38, 7), (6, 34), (7, 10), (38, 3), (21, 4), (25, 22), (14, 36), (25, 23), (22, 17), (42, 29), (30, 20), (32, 34), (4, 23), (15, 33), (18, 2), (27, 25), (3, 11), (21, 26), (36, 19), (37, 43), (16, 31), (26, 24), (10, 38), (0, 36), (24, 37), (28, 43), (9, 31), (22, 30), (10, 31), (5, 35), (0, 10), (8, 32), (27, 23), (41, 33), (11, 31), (1, 31), (6, 24), (26, 21), (4, 44), (14, 42), (13, 11), (42, 41), (35, 19), (29, 6), (7, 18), (26, 46), (33, 46), (8, 38), (33, 5), (26, 37), (36, 34), (40, 14), (30, 7), (13, 46), (2, 18), (24, 9), (34, 29), (32, 0), (19, 20), (15, 32), (33, 44), (38, 38), (28, 40), (39, 15), (15, 14), (19, 46), (26, 2), (35, 1), (5, 36), (29, 22), (38, 27), (20, 45), (3, 34), (39, 11), (29, 39), (0, 42), (4, 31), (15, 39), (7, 39), (6, 8), (36, 7), (8, 35), (32, 6), (26, 9), (15, 24), (17, 36), (9, 5), (38, 29), (18, 1), (23, 19), (28, 12), (2, 12), (3, 36), (42, 39), (7, 34), (4, 9), (41, 45), (6, 30), (33, 15), (20, 0), (32, 42), (9, 10), (4, 3), (31, 13), (6, 2), (42, 1), (36, 10), (31, 1), (21, 23), (15, 34), (34, 31), (38, 41), (4, 21), (21, 13), (39, 16), (30, 12), (19, 30), (20, 9), (22, 23), (10, 5), (8, 13), (37, 5), (38, 0), (14, 41), (13, 6), (10, 36), (36, 30), (42, 17), (25, 31), (29, 23), (18, 26), (11, 11), (28, 25), (10, 40), (16, 10), (40, 4), (35, 4), (12, 32), (19, 9), (7, 5), (23, 40), (5, 25), (17, 0), (39, 29), (19, 42), (3, 5), (42, 23), (34, 16), (20, 13), (4, 0), (7, 38), (23, 2), (1, 27), (41, 19), (22, 6), (12, 42), (25, 36), (35, 20), (21, 32), (22, 36), (6, 36), (24, 3), (17, 25), (20, 16), (42, 14), (9, 14), (39, 26), (2, 25), (29, 32), (34, 39), (25, 26), (22, 31), (20, 12), (25, 19), (16, 38), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 37), (29, 7), (30, 34), (42, 4), (27, 34), (28, 7), (24, 7), (35, 35), (5, 4), (1, 4), (38, 21), (16, 1), (0, 6), (8, 26), (26, 28), (19, 28), (8, 36), (8, 14), (33, 0), (25, 3), (40, 35), (16, 3), (41, 26), (25, 15), (28, 26), (8, 28), (16, 40), (9, 21), (12, 16), (14, 36), (7, 5), (23, 34), (42, 25), (39, 40), (34, 27), (7, 0), (5, 31), (21, 4), (4, 17), (37, 36), (19, 26), (23, 22), (19, 2), (7, 33), (3, 24), (25, 27), (22, 36), (7, 1), (26, 26), (22, 6), (29, 16), (17, 9), (23, 16), (5, 28), (6, 36), (17, 4), (32, 19), (7, 11), (24, 0), (17, 14), (18, 7), (28, 5), (18, 19), (6, 29), (37, 26), (36, 8), (5, 38), (9, 36), (36, 19), (9, 7), (30, 9), (3, 5), (26, 33), (10, 38), (30, 11), (23, 21), (10, 35), (4, 24), (3, 10), (11, 20), (36, 26), (18, 40), (27, 8), (40, 40), (41, 37), (20, 29), (28, 25), (33, 25), (6, 31), (20, 34), (22, 22), (28, 36), (7, 18), (27, 33), (32, 27), (3, 36), (42, 28), (41, 38), (5, 1), (26, 18), (29, 5), (12, 40), (38, 33), (19, 14), (8, 20), (27, 3), (2, 38), (1, 39), (31, 12), (16, 26), (27, 37), (34, 29), (13, 40), (24, 32), (12, 28), (2, 32), (39, 33), (24, 20), (11, 23), (3, 1), (30, 19), (1, 15), (30, 1), (4, 37), (6, 22), (27, 7), (21, 16), (9, 38), (17, 11), (9, 10), (7, 32), (21, 19), (33, 32), (29, 15), (3, 0), (32, 14), (4, 10), (2, 37), (13, 36), (33, 37), (40, 18), (11, 32), (21, 10), (22, 38), (29, 11), (35, 17), (3, 2), (28, 40), (0, 21), (28, 22), (10, 6), (32, 24), (13, 39), (37, 30), (22, 13), (13, 6), (10, 24), (14, 34), (12, 29), (28, 38), (39, 0), (8, 11), (23, 23), (16, 9), (18, 15), (23, 2), (28, 20), (7, 40), (0, 20), (9, 2), (40, 23), (17, 5), (22, 8), (40, 21), (36, 5), (15, 3), (16, 31), (27, 26), (42, 11), (31, 27), (8, 22), (26, 13), (30, 25), (1, 7), (34, 2), (32, 21), (6, 11), (2, 3), (29, 1), (17, 20), (42, 5), (13, 20), (24, 6), (42, 20), (14, 29), (26, 38), (29, 24), (5, 35), (13, 16), (37, 8), (12, 39), (34, 15), (23, 37), (24, 25), (21, 28), (42, 21), (18, 10), (15, 27), (32, 1), (24, 13), (4, 5), (17, 0), (37, 13), (18, 9), (31, 13), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 42), (27, 39), (11, 42), (24, 38), (23, 19), (17, 16), (15, 22), (31, 11), (21, 10), (21, 3), (10, 31), (1, 29), (1, 43), (7, 41), (16, 9), (13, 40), (11, 39), (0, 6), (41, 33), (4, 32), (40, 9), (23, 29), (15, 12), (1, 46), (28, 24), (21, 7), (15, 23), (3, 15), (43, 39), (22, 14), (36, 47), (8, 30), (26, 21), (39, 30), (7, 45), (15, 11), (23, 36), (43, 3), (44, 21), (6, 4), (35, 17), (7, 3), (38, 6), (6, 41), (41, 41), (1, 36), (10, 13), (36, 35), (32, 3), (20, 4), (16, 42), (14, 19), (8, 2), (34, 0), (12, 1), (16, 13), (19, 34), (37, 26), (1, 19), (45, 43), (21, 2), (30, 42), (24, 33), (16, 4), (8, 27), (26, 14), (7, 20), (35, 28), (9, 42), (22, 8), (15, 4), (3, 10), (32, 19), (1, 9), (10, 42), (32, 43), (18, 39), (43, 43), (31, 29), (27, 38), (32, 38), (37, 29), (16, 8), (9, 35), (31, 24), (37, 36), (40, 39), (5, 4), (29, 29), (20, 33), (16, 37), (40, 44), (43, 19), (20, 3), (3, 14), (22, 47), (25, 0), (11, 45), (15, 15), (0, 28), (27, 0), (33, 12), (29, 10), (32, 25), (26, 36), (42, 14), (17, 9), (40, 30), (1, 20), (3, 22), (29, 46), (45, 34), (45, 38), (34, 8), (30, 13), (18, 12), (27, 15), (41, 26), (26, 33), (24, 2), (15, 25), (4, 47), (27, 2), (3, 45), (34, 27), (23, 0), (2, 19), (43, 29), (20, 32), (19, 18), (5, 40), (17, 27), (14, 28), (35, 5), (32, 10), (33, 46), (45, 11), (25, 27), (27, 42), (29, 24), (25, 16), (24, 37), (25, 32), (36, 6), (28, 6), (1, 14), (11, 23), (8, 1), (33, 38), (45, 13), (32, 23), (18, 1), (2, 41), (30, 47), (44, 13), (36, 20), (8, 31), (35, 39), (42, 11), (32, 20), (12, 21), (18, 11), (6, 30), (44, 44), (10, 38), (15, 7), (0, 24), (34, 40), (11, 16), (4, 8), (20, 14), (24, 7), (29, 34), (29, 44), (24, 11), (4, 25), (20, 19), (43, 1), (9, 3), (22, 30), (6, 46), (25, 24), (39, 29), (35, 47), (29, 27), (24, 14), (39, 19), (25, 41), (43, 23), (35, 3), (18, 46), (20, 13), (18, 21), (3, 16), (17, 1), (29, 26), (5, 37), (3, 25), (29, 35), (17, 28), (8, 9), (17, 14), (11, 27), (44, 37), (34, 2), (35, 7), (20, 40), (36, 22), (23, 46), (18, 10), (45, 17), (1, 11), (18, 23), (22, 21), (37, 31), (9, 5), (36, 29), (34, 28), (23, 35), (16, 45), (11, 43), (17, 21), (19, 36), (40, 27), (6, 27), (36, 14), (1, 22), (28, 42), (43, 15), (31, 26), (4, 36), (26, 38), (35, 18), (0, 38), (37, 35), (26, 6), (27, 20), (6, 1), (33, 34), (36, 2), (11, 1), (11, 15), (45, 1), (30, 0), (10, 25), (29, 47), (23, 26), (42, 15), (6, 43), (22, 39), (44, 24), (22, 18), (39, 31), (3, 27), (36, 4), (34, 6), (43, 14), (25, 3), (12, 9), (23, 22), (27, 45), (28, 29), (42, 35), (43, 46), (7, 46), (24, 22), (2, 23), (23, 17), (4, 6), (11, 44), (24, 5), (36, 44), (22, 41), (31, 3), (20, 21), (31, 0), (41, 17), (38, 35), (4, 7), (12, 27), (36, 37), (37, 6), (41, 46), (23, 39), (45, 9), (12, 47), (41, 4), (9, 7), (17, 41), (36, 33), (16, 19), (34, 39), (6, 5), (6, 15), (15, 13), (8, 44), (1, 42), (10, 44), (30, 19), (34, 13), (19, 47), (42, 28), (7, 22), (12, 43), (18, 25), (40, 5), (3, 24), (42, 37), (37, 17), (45, 22), (38, 46), (4, 43), (18, 42), (6, 42), (0, 33), (19, 20), (5, 16), (11, 47), (18, 29), (14, 14), (33, 9), (24, 8), (38, 31), (12, 29), (14, 6), (8, 17), (9, 22), (29, 17), (16, 32), (43, 26), (10, 6), (32, 47), (32, 32), (25, 37), (39, 15), (7, 2), (16, 20), (36, 7), (33, 23), (8, 42), (3, 36), (28, 41), (45, 33), (1, 0), (44, 12), (42, 39), (22, 22), (34, 4), (19, 42), (42, 43), (4, 35), (10, 21), (15, 6), (29, 31), (21, 45), (10, 33), (2, 16), (37, 32), (45, 8), (0, 31), (34, 44), (35, 13), (19, 26), (22, 19), (43, 42), (0, 47), (43, 7), (45, 31), (17, 6), (44, 35), (30, 16), (44, 36), (23, 42), (25, 39), (2, 6), (11, 14), (37, 20), (32, 29), (25, 9), (44, 45), (8, 45), (10, 41), (45, 24), (28, 15), (4, 4), (32, 30), (16, 5), (24, 29), (38, 40), (20, 12), (15, 2), (5, 33), (16, 3), (35, 36), (30, 39), (30, 34), (15, 34), (40, 22), (21, 41), (28, 1), (12, 32), (9, 46), (45, 25), (41, 44), (42, 31), (45, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 6), (14, 20), (17, 37), (38, 17), (29, 18), (16, 43), (29, 16), (0, 8), (27, 23), (16, 8), (5, 40), (37, 12), (11, 42), (11, 12), (38, 24), (25, 44), (32, 41), (15, 31), (28, 17), (26, 13), (1, 14), (28, 32), (14, 44), (24, 40), (45, 5), (26, 34), (20, 22), (23, 44), (14, 15), (17, 14), (29, 24), (1, 17), (41, 30), (15, 12), (19, 33), (10, 30), (18, 18), (34, 33), (8, 13), (11, 30), (10, 14), (12, 6), (0, 16), (30, 11), (38, 1), (26, 7), (44, 23), (7, 16), (1, 20), (6, 28), (31, 12), (0, 13), (23, 7), (42, 38), (16, 36), (6, 13), (3, 1), (2, 34), (43, 40), (24, 26), (27, 28), (18, 31), (14, 28), (3, 36), (27, 3), (34, 10), (25, 9), (7, 39), (37, 35), (34, 21), (12, 33), (24, 42), (42, 44), (25, 39), (12, 27), (1, 19), (15, 3), (12, 9), (34, 20), (15, 25), (14, 30), (1, 29), (39, 26), (0, 37), (23, 25), (5, 8), (31, 22), (4, 19), (9, 21), (35, 44), (40, 41), (47, 28), (2, 22), (36, 23), (13, 3), (20, 37), (47, 0), (1, 3), (39, 37), (14, 38), (1, 36), (23, 2), (38, 0), (35, 15), (13, 38), (8, 26), (46, 1), (39, 7), (34, 15), (15, 32), (41, 11), (18, 24), (7, 25), (3, 21), (10, 2), (38, 32), (8, 22), (1, 30), (25, 4), (24, 2), (38, 5), (17, 32), (36, 13), (38, 13), (14, 41), (17, 15), (18, 41), (39, 2), (17, 1), (0, 3), (36, 41), (0, 34), (30, 37), (3, 13), (5, 33), (42, 19), (39, 3), (6, 5), (13, 35), (44, 10), (32, 10), (18, 33), (44, 9), (16, 20), (29, 6), (39, 41), (2, 13), (24, 34), (16, 34), (27, 39), (32, 15), (36, 25), (29, 20), (41, 10), (2, 41), (30, 21), (27, 10), (14, 26), (33, 40), (4, 34), (35, 41), (0, 31), (33, 24), (5, 10), (26, 29), (16, 1), (3, 19), (11, 22), (30, 1), (20, 6), (0, 12), (27, 13), (7, 26), (11, 16), (34, 6), (17, 29), (8, 24), (19, 29), (9, 18), (28, 23), (38, 9), (45, 40), (10, 40), (26, 5), (7, 12), (36, 42), (32, 40), (8, 28), (36, 19), (7, 21), (6, 9), (9, 11), (35, 34), (29, 21), (28, 22), (3, 33), (27, 26), (28, 12), (38, 40), (27, 41), (7, 1), (19, 10), (23, 21), (15, 28), (47, 13), (29, 1), (22, 2), (35, 3), (18, 39), (21, 10), (3, 10), (8, 3), (4, 39), (28, 44), (32, 2), (32, 42), (33, 22), (12, 3), (12, 12), (42, 4), (38, 42), (8, 39), (27, 25), (14, 0), (17, 17), (18, 43), (47, 10), (29, 5), (22, 12), (36, 30), (18, 4), (22, 19), (29, 4), (41, 42), (39, 28), (18, 6), (2, 38), (14, 19), (26, 23), (30, 30), (37, 41), (47, 40), (25, 5), (4, 35), (43, 5), (14, 43), (20, 19), (34, 28), (32, 29), (28, 13), (18, 15), (17, 3), (9, 30), (18, 10), (43, 6), (6, 30), (35, 18), (47, 29), (6, 24), (33, 43), (33, 27), (44, 19), (10, 33), (45, 10), (42, 41), (30, 6), (1, 21), (15, 23), (38, 18), (36, 26), (9, 20), (15, 42), (3, 5), (20, 24), (14, 33), (27, 9), (35, 26), (38, 35), (18, 42), (5, 6), (17, 20), (45, 24), (27, 19), (31, 16), (37, 26), (26, 37), (5, 15), (44, 22), (37, 22), (18, 3), (31, 26), (19, 20), (31, 32), (43, 29), (15, 7), (26, 6), (44, 35), (26, 28), (31, 14), (0, 11), (32, 5), (33, 25), (34, 2), (18, 44), (18, 22), (13, 29), (2, 18), (21, 35), (43, 37), (14, 17), (31, 38), (19, 15), (43, 17), (20, 33), (35, 0), (40, 21), (42, 30), (4, 15), (13, 30), (17, 40), (30, 18), (2, 32), (25, 43), (13, 6), (12, 41), (23, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 42), (19, 3), (20, 7), (2, 26), (4, 15), (45, 26), (36, 41), (26, 38), (19, 14), (38, 17), (0, 39), (19, 13), (24, 39), (37, 35), (16, 8), (14, 27), (46, 3), (42, 31), (23, 35), (6, 7), (22, 20), (40, 37), (38, 40), (39, 37), (28, 13), (3, 16), (23, 12), (16, 10), (38, 18), (24, 30), (9, 25), (7, 21), (23, 16), (35, 22), (3, 33), (38, 5), (36, 25), (41, 6), (33, 12), (47, 4), (34, 14), (32, 13), (38, 23), (18, 33), (2, 32), (26, 37), (29, 35), (33, 26), (5, 32), (33, 2), (43, 1), (47, 8), (1, 27), (40, 8), (39, 17), (5, 10), (33, 16), (36, 42), (6, 0), (18, 17), (32, 42), (33, 33), (18, 4), (13, 41), (28, 7), (24, 37), (30, 13), (15, 14), (17, 23), (10, 8), (42, 29), (47, 10), (7, 1), (46, 10), (26, 7), (12, 15), (29, 24), (30, 36), (7, 30), (38, 20), (18, 11), (28, 21), (20, 35), (30, 18), (6, 20), (44, 26), (18, 16), (41, 9), (40, 21), (23, 14), (43, 18), (6, 18), (45, 41), (4, 25), (20, 25), (6, 33), (12, 19), (46, 12), (8, 9), (4, 40), (37, 15), (25, 35), (4, 19), (15, 22), (40, 6), (40, 42), (2, 28), (23, 11), (10, 34), (43, 29), (15, 16), (1, 9), (43, 39), (3, 14), (4, 17), (18, 18), (2, 21), (40, 0), (21, 4), (4, 9), (2, 17), (28, 30), (48, 16), (42, 35), (23, 42), (9, 30), (26, 13), (0, 41), (35, 20), (37, 22), (20, 23), (17, 21), (7, 25), (27, 12), (35, 10), (27, 2), (29, 15), (17, 19), (12, 12), (39, 20), (5, 30), (14, 9), (21, 19), (24, 32), (0, 25), (1, 39), (18, 8), (25, 36), (35, 1), (44, 1), (8, 36), (48, 26), (7, 12), (20, 29), (18, 28), (7, 17), (17, 12), (47, 28), (47, 33), (46, 2), (6, 16), (10, 18), (13, 31), (36, 24), (19, 22), (14, 41), (41, 11), (19, 26), (37, 5), (45, 19), (10, 0), (32, 24), (43, 12), (10, 12), (16, 39), (43, 35), (29, 41), (1, 13), (16, 13), (28, 28), (29, 23), (16, 34), (35, 35), (16, 12), (31, 21), (21, 14), (4, 18), (37, 40), (33, 1), (47, 18), (48, 37), (41, 42), (12, 13), (39, 32), (42, 32), (27, 15), (14, 20), (14, 31), (27, 32), (35, 2), (43, 9), (24, 16), (4, 16), (47, 38), (12, 20), (8, 16), (47, 35), (5, 36), (28, 22), (27, 9), (29, 42), (5, 20), (4, 2), (7, 20), (42, 22), (29, 17), (27, 39), (24, 12), (7, 16), (38, 32), (33, 5), (18, 20), (37, 19), (31, 16), (19, 12), (39, 38), (1, 29), (44, 13), (33, 4), (16, 6), (12, 42), (2, 16), (3, 0), (6, 38), (20, 34), (47, 36), (34, 16), (30, 25), (4, 7), (3, 38), (8, 8), (31, 23), (10, 1), (32, 8), (18, 35), (20, 33), (2, 27), (3, 22), (9, 1), (3, 8), (0, 9), (0, 35), (38, 35), (37, 24), (48, 23), (37, 10), (4, 10), (42, 8), (27, 18), (20, 19), (1, 19), (9, 3), (36, 30), (23, 5), (32, 22), (45, 38), (3, 18), (33, 10), (43, 13), (0, 23), (24, 41), (18, 26), (1, 42), (41, 31), (20, 17), (40, 14), (6, 11), (6, 30), (22, 30), (21, 34), (2, 24), (43, 21), (37, 6), (7, 40), (9, 12), (4, 27), (16, 18), (25, 15), (23, 8), (18, 14), (2, 2), (14, 19), (0, 16), (44, 21), (32, 3), (15, 25), (37, 16), (2, 15), (1, 30), (45, 31), (42, 23), (6, 23), (21, 37), (12, 17), (41, 20), (48, 38), (46, 5), (31, 22), (9, 15), (21, 24), (28, 24), (45, 14), (47, 3), (40, 33), (21, 17), (43, 15), (8, 11), (13, 1), (24, 22), (3, 21), (45, 22), (30, 1), (26, 2), (40, 38), (5, 22), (15, 21), (35, 26), (40, 2), (36, 29), (12, 1), (43, 6), (31, 0), (36, 33), (11, 2), (8, 40), (34, 15), (39, 25), (44, 15), (10, 41), (14, 26), (42, 16), (37, 27), (38, 19), (47, 20), (20, 13), (31, 17), (42, 24), (47, 27), (12, 7), (26, 17), (16, 35), (3, 32), (38, 25), (26, 27), (1, 32), (10, 42), (36, 9), (36, 16), (43, 30), (20, 2), (5, 14), (29, 5), (0, 14), (35, 14), (41, 13), (35, 34), (46, 27), (38, 39), (21, 33), (15, 5), (4, 41), (4, 12), (43, 36), (11, 39), (9, 14), (30, 2), (41, 17), (34, 35), (20, 32), (38, 12), (8, 1), (32, 11), (16, 25), (26, 14), (47, 5), (32, 36), (19, 10), (35, 30), (36, 4), (24, 17), (39, 6), (1, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (48, 10), (9, 4), (25, 3), (8, 1), (12, 21), (24, 46), (22, 16), (23, 0), (27, 19), (41, 32), (27, 18), (19, 10), (40, 33), (6, 18), (34, 34), (9, 29), (19, 4), (46, 21), (1, 32), (36, 3), (9, 11), (31, 3), (44, 15), (43, 38), (42, 25), (6, 44), (46, 43), (18, 15), (21, 6), (29, 38), (5, 25), (3, 5), (48, 35), (13, 21), (12, 34), (8, 45), (26, 38), (4, 23), (42, 30), (4, 0), (12, 17), (37, 37), (23, 4), (17, 33), (7, 33), (26, 47), (40, 4), (37, 9), (29, 7), (23, 42), (25, 9), (5, 45), (32, 46), (34, 28), (20, 27), (33, 13), (25, 4), (35, 44), (34, 43), (11, 40), (7, 0), (24, 42), (29, 28), (2, 44), (21, 18), (32, 28), (2, 10), (18, 40), (11, 12), (30, 2), (8, 4), (19, 13), (13, 30), (33, 34), (17, 2), (22, 45), (0, 10), (12, 1), (27, 29), (24, 3), (7, 2), (43, 20), (41, 5), (29, 39), (7, 30), (6, 41), (0, 34), (16, 47), (30, 3), (11, 35), (7, 29), (3, 40), (47, 1), (6, 5), (46, 34), (31, 31), (39, 47), (35, 5), (28, 43), (33, 37), (16, 25), (7, 46), (10, 47), (35, 39), (33, 4), (31, 20), (36, 30), (16, 28), (44, 34), (45, 45), (2, 7), (27, 12), (4, 20), (47, 14), (34, 9), (0, 25), (16, 5), (11, 17), (39, 32), (8, 34), (41, 22), (19, 16), (34, 4), (0, 18), (43, 21), (47, 33), (35, 31), (26, 7), (23, 25), (11, 36), (42, 38), (12, 44), (14, 13), (47, 23), (0, 8), (0, 27), (15, 35), (41, 45), (42, 13), (27, 23), (17, 24), (33, 8), (14, 43), (21, 27), (17, 8), (43, 46), (39, 15), (35, 22), (24, 10), (18, 17), (29, 14), (42, 31), (27, 42), (8, 27), (36, 31), (46, 25), (12, 46), (43, 39), (15, 44), (43, 41), (16, 11), (30, 7), (45, 14), (10, 39), (41, 1), (5, 14), (37, 8), (40, 17), (0, 20), (14, 35), (31, 45), (8, 20), (47, 10), (14, 42), (43, 30), (44, 1), (3, 35), (17, 44), (37, 4), (38, 3), (48, 14), (14, 44), (31, 16), (18, 35), (14, 26), (0, 3), (3, 23), (18, 44), (48, 18), (29, 9), (34, 7), (9, 39), (0, 21), (40, 29), (27, 30), (46, 40), (36, 28), (10, 34), (17, 7), (12, 36), (35, 20), (43, 19), (37, 17), (48, 1), (35, 21), (11, 33), (33, 14), (0, 33), (30, 6), (13, 41), (5, 39), (25, 47), (23, 41), (10, 6), (29, 32), (2, 13), (38, 4), (33, 9), (38, 16), (43, 4), (32, 31), (3, 33), (20, 40), (20, 33), (17, 45), (19, 46), (10, 12), (6, 46), (18, 41), (38, 26), (43, 18), (34, 15), (32, 19), (10, 18), (10, 13), (47, 16), (44, 33), (34, 29), (30, 12), (19, 24), (12, 4), (17, 29), (16, 15), (19, 25), (21, 32), (4, 47), (43, 45), (37, 22), (33, 32), (12, 31), (29, 33), (14, 17), (23, 32), (17, 0), (47, 34), (2, 2), (47, 37), (37, 42), (11, 2), (2, 19), (8, 33), (29, 2), (24, 38), (42, 23), (39, 24), (7, 43), (29, 17), (6, 3), (24, 9), (0, 28), (44, 18), (41, 0), (29, 45), (45, 3), (15, 8), (2, 5), (32, 17), (0, 23), (0, 19), (44, 13), (3, 13), (29, 19), (21, 2), (47, 24), (31, 18), (40, 26), (31, 10), (48, 25), (40, 6), (22, 11), (22, 19), (32, 12), (15, 24), (40, 0), (1, 20), (35, 2), (7, 5), (26, 25), (32, 16), (45, 34), (36, 43), (23, 35), (11, 45), (48, 23), (27, 1), (40, 31), (32, 45), (4, 18), (15, 21), (26, 24), (24, 32), (15, 32), (17, 1), (44, 3), (45, 39), (41, 40), (34, 13), (30, 1), (6, 26), (44, 29), (30, 43), (20, 34), (20, 36), (22, 47), (40, 13), (11, 10), (28, 20), (22, 15), (32, 18), (47, 28), (24, 5), (40, 11), (17, 39), (45, 42), (44, 6), (9, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 44), (6, 28), (15, 12), (33, 46), (27, 14), (22, 8), (32, 6), (4, 30), (36, 33), (27, 30), (28, 5), (26, 28), (6, 12), (37, 18), (18, 31), (38, 26), (27, 39), (29, 9), (0, 18), (26, 6), (33, 1), (14, 24), (8, 7), (26, 46), (2, 35), (30, 16), (12, 14), (4, 24), (17, 23), (29, 22), (40, 21), (12, 0), (30, 32), (17, 28), (14, 30), (36, 38), (34, 6), (18, 26), (22, 13), (17, 40), (16, 13), (16, 2), (34, 12), (39, 41), (4, 38), (31, 0), (3, 13), (26, 3), (26, 43), (20, 37), (5, 10), (41, 29), (22, 34), (10, 23), (28, 10), (25, 20), (14, 16), (2, 45), (23, 40), (4, 9), (26, 8), (22, 45), (9, 35), (38, 21), (31, 19), (22, 37), (7, 24), (33, 45), (28, 3), (38, 28), (16, 23), (1, 47), (38, 1), (6, 42), (0, 39), (8, 17), (2, 22), (40, 40), (15, 37), (35, 22), (19, 29), (10, 26), (28, 8), (10, 1), (6, 2), (0, 21), (16, 0), (14, 6), (28, 32), (27, 44), (8, 8), (1, 33), (15, 41), (7, 30), (35, 30), (34, 38), (31, 30), (39, 10), (39, 22), (2, 15), (20, 28), (11, 13), (27, 18), (26, 37), (27, 25), (37, 34), (11, 19), (37, 7), (17, 36), (24, 35), (2, 32), (0, 42), (34, 43), (18, 40), (31, 26), (33, 2), (16, 36), (19, 11), (16, 42), (21, 33), (12, 28), (9, 7), (10, 14), (18, 10), (17, 5), (12, 2), (27, 5), (37, 22), (21, 22), (12, 16), (22, 22), (2, 18), (40, 6), (29, 26), (15, 10), (0, 32), (28, 11), (19, 40), (37, 25), (3, 23), (30, 44), (28, 44), (4, 40), (6, 47), (22, 44), (1, 39), (37, 13), (32, 44), (34, 30), (20, 32), (29, 2), (32, 31), (14, 32), (15, 29), (20, 9), (0, 16), (5, 28), (28, 34), (17, 43), (17, 27), (6, 16), (29, 1), (29, 36), (15, 22), (37, 38), (13, 0), (23, 17), (25, 10), (2, 3), (12, 43), (39, 8), (7, 41), (39, 23), (24, 23), (37, 28), (40, 11), (23, 38), (32, 14), (6, 1), (9, 25), (36, 23), (29, 43), (11, 27), (2, 23), (27, 42), (18, 32), (8, 31), (9, 33), (34, 18), (11, 35), (25, 3), (26, 7), (19, 1), (34, 29), (0, 17), (13, 10), (1, 25), (16, 12), (5, 33), (35, 6), (34, 40), (24, 21), (31, 37), (21, 15), (41, 31), (4, 12), (33, 42), (22, 19), (25, 37), (12, 42), (40, 36), (37, 4), (6, 19), (26, 35), (18, 11), (33, 7), (22, 16), (27, 33), (20, 14), (25, 0), (16, 35), (29, 46), (21, 30), (21, 5), (6, 9), (12, 4), (41, 16), (16, 4), (19, 47), (26, 45), (11, 11), (14, 41), (1, 40), (17, 22), (33, 13), (27, 11), (32, 12), (22, 43), (12, 15), (28, 33), (5, 2), (12, 32), (3, 43), (36, 12), (14, 0), (0, 28), (4, 7), (27, 17), (0, 30), (7, 37), (1, 37), (9, 12), (36, 6), (19, 23), (34, 31), (2, 42), (10, 32), (21, 18), (7, 17), (36, 34), (34, 3), (3, 35), (7, 46), (36, 29), (0, 3), (31, 41), (21, 32), (0, 46), (38, 20), (37, 47), (35, 47), (30, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 37), (25, 36), (32, 41), (6, 3), (30, 5), (14, 35), (1, 30), (26, 1), (35, 7), (42, 38), (8, 35), (34, 15), (22, 19), (37, 9), (32, 35), (36, 16), (41, 24), (43, 20), (9, 34), (31, 5), (2, 28), (31, 19), (16, 6), (25, 37), (29, 44), (28, 3), (42, 27), (28, 13), (17, 7), (13, 28), (45, 12), (10, 11), (26, 19), (16, 0), (14, 4), (19, 38), (41, 2), (4, 22), (23, 24), (27, 25), (24, 8), (3, 29), (23, 40), (30, 33), (42, 43), (3, 43), (5, 44), (8, 2), (5, 37), (15, 6), (42, 14), (28, 27), (22, 25), (12, 41), (2, 43), (14, 39), (9, 1), (14, 14), (16, 15), (28, 5), (42, 7), (36, 30), (22, 39), (28, 35), (20, 30), (38, 16), (20, 14), (31, 28), (1, 34), (6, 37), (33, 30), (3, 36), (27, 34), (2, 23), (33, 40), (33, 4), (23, 13), (23, 4), (1, 25), (30, 42), (7, 28), (15, 1), (44, 14), (23, 43), (39, 14), (3, 25), (8, 22), (9, 2), (13, 4), (11, 19), (5, 26), (35, 35), (15, 32), (23, 41), (6, 22), (34, 17), (5, 12), (28, 17), (40, 41), (26, 29), (39, 34), (35, 43), (25, 27), (45, 35), (9, 31), (23, 19), (12, 8), (26, 15), (20, 12), (11, 23), (36, 8), (22, 42), (27, 44), (42, 28), (4, 4), (5, 17), (19, 25), (1, 11), (7, 41), (37, 41), (26, 33), (8, 29), (5, 8), (41, 19), (34, 32), (15, 5), (22, 24), (7, 22), (13, 31), (20, 41), (8, 37), (29, 4), (2, 22), (3, 8), (2, 9), (15, 42), (7, 30), (33, 34), (6, 27), (31, 21), (40, 7), (42, 8), (18, 28), (2, 13), (24, 0), (44, 16), (20, 1), (6, 1), (19, 19), (12, 4), (11, 10), (15, 33), (38, 40), (9, 32), (34, 40), (42, 3), (29, 11), (32, 23), (23, 3), (7, 25), (35, 22), (2, 33), (10, 30), (35, 17), (21, 15), (43, 18), (38, 43), (7, 12), (1, 10), (12, 39), (6, 14), (24, 12), (31, 22), (7, 18), (41, 8), (29, 1), (45, 13), (35, 9), (19, 11), (42, 34), (15, 14), (17, 4), (18, 24), (14, 25), (37, 43), (36, 15), (18, 18), (32, 26), (33, 2), (43, 35), (26, 11), (39, 3), (35, 36), (39, 11), (10, 5), (15, 25), (34, 34), (36, 34), (32, 12), (25, 3), (29, 19), (6, 10), (1, 16), (34, 24), (24, 10), (33, 38), (6, 13), (41, 5), (44, 35), (1, 29), (38, 36), (14, 13), (20, 34), (5, 30), (23, 8), (37, 4), (40, 13), (37, 12), (43, 8), (37, 17), (45, 19), (43, 28), (36, 42), (7, 44), (35, 41), (10, 18), (41, 0), (8, 12), (33, 22), (38, 12), (24, 38), (12, 12), (3, 17), (24, 16), (5, 13), (29, 28), (24, 14), (31, 10), (0, 23), (2, 11), (0, 33), (34, 35), (35, 24), (23, 29), (34, 6), (21, 22), (43, 34), (36, 28), (5, 15), (27, 24), (14, 28), (11, 27), (7, 21), (25, 33), (20, 32), (36, 25), (10, 6), (8, 7), (18, 0), (34, 4), (14, 33), (25, 22), (37, 14), (16, 10), (42, 22), (15, 17), (31, 7), (5, 34), (42, 1), (44, 27), (22, 44), (0, 35), (27, 35), (42, 17), (12, 40), (27, 15), (30, 26), (11, 14), (18, 42), (44, 43), (13, 22), (16, 8), (20, 38), (14, 24), (10, 44), (15, 22), (17, 38), (14, 0), (38, 4), (43, 11), (7, 27), (4, 40), (22, 4), (29, 18), (32, 3), (36, 17), (28, 26), (41, 10), (27, 41), (23, 35), (7, 3), (23, 21), (28, 29), (34, 8), (24, 20), (12, 29), (44, 3), (36, 2), (35, 3), (8, 3), (41, 12), (2, 38), (10, 34), (1, 27), (21, 1), (12, 31), (31, 42), (20, 39), (13, 19), (3, 33), (9, 27), (37, 29), (37, 5), (0, 21), (30, 35), (42, 36), (10, 9), (2, 16), (10, 10), (26, 41), (28, 41), (44, 4), (3, 19), (36, 44), (36, 36), (20, 16), (42, 20), (12, 15), (3, 16), (34, 11), (3, 6), (7, 31), (27, 0), (35, 33), (6, 2), (32, 17), (16, 42), (13, 14), (22, 30), (38, 11), (40, 0), (30, 4), (5, 11), (39, 28), (12, 6), (36, 41), (44, 37), (8, 20), (10, 40), (25, 39), (1, 9), (19, 18), (31, 40), (40, 27), (43, 0), (27, 7), (6, 11), (33, 16), (40, 28), (13, 41), (22, 0), (5, 23), (39, 2), (28, 44), (29, 22), (9, 29), (16, 14), (20, 21), (12, 16), (25, 24), (13, 13), (4, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 8), (40, 45), (1, 13), (19, 10), (7, 33), (12, 38), (9, 31), (6, 10), (34, 7), (15, 19), (40, 17), (19, 13), (13, 38), (4, 3), (24, 36), (11, 15), (39, 16), (8, 3), (6, 22), (3, 24), (38, 30), (27, 1), (19, 8), (0, 3), (30, 39), (37, 3), (35, 21), (22, 39), (31, 8), (27, 16), (34, 21), (17, 22), (15, 16), (34, 42), (30, 20), (11, 9), (31, 45), (34, 30), (15, 38), (32, 20), (29, 46), (32, 10), (38, 20), (20, 46), (33, 36), (0, 11), (17, 27), (13, 5), (6, 26), (14, 4), (28, 24), (37, 6), (3, 9), (27, 38), (23, 10), (40, 2), (38, 26), (21, 9), (39, 30), (40, 35), (34, 35), (40, 19), (23, 45), (6, 14), (25, 11), (30, 23), (17, 24), (36, 30), (20, 43), (32, 42), (19, 32), (31, 30), (18, 28), (21, 12), (38, 19), (8, 7), (5, 0), (14, 7), (22, 7), (36, 19), (27, 25), (5, 15), (18, 44), (0, 38), (5, 42), (34, 24), (18, 37), (32, 34), (28, 27), (8, 43), (3, 25), (13, 4), (7, 27), (35, 10), (30, 5), (32, 1), (21, 27), (7, 45), (17, 6), (36, 4), (32, 28), (36, 15), (14, 19), (38, 3), (20, 44), (0, 6), (17, 7), (7, 37), (33, 43), (9, 7), (6, 9), (24, 31), (7, 38), (35, 44), (0, 40), (25, 17), (36, 2), (24, 26), (0, 23), (18, 11), (33, 24), (10, 18), (16, 17), (20, 6), (16, 46), (5, 38), (23, 14), (19, 27), (13, 18), (32, 24), (6, 2), (6, 33), (11, 8), (13, 45), (15, 5), (32, 38), (33, 28), (31, 1), (27, 31), (40, 32), (9, 9), (2, 1), (36, 22), (25, 4), (11, 6), (16, 5), (2, 11), (25, 18), (34, 34), (8, 24), (1, 9), (38, 14), (30, 46), (26, 17), (13, 8), (27, 28), (30, 9), (12, 25), (10, 5), (37, 34), (30, 17), (7, 42), (35, 17), (14, 3), (14, 9), (31, 22), (1, 8), (1, 42), (38, 31), (22, 23), (10, 26), (37, 38), (23, 25), (14, 11), (39, 24), (16, 27), (24, 37), (34, 9), (31, 38), (29, 37), (1, 35), (24, 16), (15, 22), (34, 12), (31, 32), (34, 43), (40, 31), (1, 11), (10, 31), (40, 8), (10, 35), (33, 18), (19, 26), (21, 46), (40, 7), (35, 37), (14, 32), (13, 28), (6, 13), (8, 9), (33, 29), (5, 31), (29, 11), (22, 16), (25, 1), (30, 1), (31, 6), (23, 20), (35, 30), (22, 32), (10, 6), (39, 38), (15, 31), (4, 15), (13, 42), (36, 14), (35, 29), (3, 15), (25, 22), (4, 32), (14, 41), (4, 0), (23, 0), (13, 0), (13, 29), (13, 40), (20, 10), (5, 24), (32, 0), (16, 42), (23, 41), (6, 8), (39, 9), (22, 18), (7, 34), (4, 2), (8, 26), (17, 39), (14, 46), (22, 38), (35, 8), (23, 28), (3, 42), (23, 1), (7, 0), (32, 29), (26, 36), (7, 10), (29, 28), (18, 19), (20, 30), (27, 23), (35, 22), (2, 39), (23, 40), (2, 27), (15, 26), (12, 13), (15, 46), (9, 18), (32, 36), (2, 13), (14, 17), (34, 31), (36, 7), (13, 39), (21, 2), (1, 3), (30, 44), (29, 42), (3, 11), (9, 44), (33, 46), (11, 22), (30, 33), (23, 15), (15, 11), (2, 2), (9, 40), (11, 14), (28, 45), (40, 0), (22, 43), (39, 7), (24, 13), (13, 16), (11, 32), (19, 43), (33, 6), (1, 16), (35, 28), (10, 13), (20, 28), (33, 32), (17, 16), (33, 35), (6, 44), (12, 8), (34, 41), (38, 13), (24, 39), (8, 33), (22, 45), (36, 41), (11, 25), (7, 31), (39, 22), (35, 45), (31, 28), (2, 4), (9, 13), (23, 32), (6, 34), (30, 10), (13, 10), (27, 4), (19, 33), (24, 43), (1, 15), (17, 43), (25, 6), (18, 41), (7, 18), (21, 32), (16, 7), (26, 8), (39, 0), (12, 43), (32, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 1), (26, 13), (40, 0), (27, 37), (12, 10), (25, 28), (6, 36), (23, 5), (16, 20), (39, 11), (41, 31), (0, 1), (39, 17), (27, 13), (11, 8), (0, 9), (40, 11), (34, 36), (39, 16), (9, 7), (18, 36), (18, 14), (38, 9), (16, 16), (41, 36), (6, 19), (8, 25), (16, 25), (24, 17), (11, 12), (20, 22), (35, 10), (32, 13), (11, 27), (37, 13), (37, 3), (16, 28), (9, 35), (34, 9), (18, 20), (25, 24), (29, 20), (1, 11), (16, 10), (10, 15), (9, 2), (21, 29), (32, 6), (36, 27), (8, 3), (39, 5), (9, 26), (24, 4), (21, 0), (11, 4), (9, 36), (17, 22), (3, 2), (0, 14), (34, 5), (21, 17), (5, 33), (28, 27), (3, 5), (12, 5), (14, 6), (5, 22), (15, 15), (0, 34), (32, 19), (31, 11), (18, 19), (26, 6), (9, 34), (2, 6), (33, 20), (5, 16), (6, 24), (36, 17), (38, 27), (21, 14), (40, 33), (20, 37), (5, 3), (26, 29), (11, 2), (40, 9), (18, 12), (13, 38), (37, 19), (9, 24), (41, 32), (16, 5), (31, 35), (26, 39), (23, 14), (6, 28), (35, 15), (3, 27), (14, 32), (3, 30), (18, 28), (23, 38), (34, 3), (11, 19), (34, 31), (27, 23), (27, 34), (12, 22), (30, 11), (37, 34), (14, 11), (6, 17), (35, 12), (41, 7), (15, 34), (27, 17), (22, 14), (29, 12), (31, 5), (28, 15), (18, 5), (11, 20), (4, 17), (20, 25), (19, 37), (37, 21), (37, 5), (1, 8), (26, 28), (7, 37), (24, 18), (7, 20), (18, 10), (25, 13), (20, 17), (40, 2), (13, 34), (40, 36), (1, 12), (5, 28), (13, 12), (35, 37), (17, 8), (33, 38), (38, 30), (24, 19), (20, 4), (23, 24), (30, 12), (7, 15), (28, 22), (38, 13), (0, 7), (7, 7), (9, 19), (25, 19), (41, 33), (23, 30), (35, 8), (27, 2), (31, 34), (18, 33), (23, 29), (4, 28), (28, 12), (10, 1), (38, 39), (14, 1), (3, 33), (13, 27), (34, 38), (24, 8), (21, 31), (11, 5), (25, 27), (12, 18), (9, 25), (36, 16), (7, 21), (8, 39), (15, 17), (24, 14), (36, 3), (32, 31), (10, 32), (16, 39), (27, 29), (8, 22), (2, 17), (5, 20), (15, 33), (29, 32), (10, 9), (41, 34), (21, 4), (23, 26), (40, 17), (21, 20), (27, 9), (3, 15), (10, 13), (38, 31), (15, 0), (14, 7), (11, 26), (24, 21), (5, 24), (20, 5), (18, 16), (39, 9), (34, 2), (18, 0), (14, 12), (27, 38), (3, 26), (41, 15), (30, 19), (7, 3), (4, 2), (3, 7), (16, 4), (4, 4), (8, 10), (9, 22), (16, 9), (6, 25), (17, 7), (7, 10), (39, 28), (24, 29), (19, 15), (36, 1), (17, 32), (38, 21), (23, 1), (40, 13), (2, 8), (31, 8), (40, 27), (36, 22), (18, 32), (41, 24), (13, 3), (13, 13), (31, 22), (28, 39), (4, 15), (20, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 32), (39, 13), (36, 25), (15, 35), (16, 36), (36, 4), (15, 14), (38, 10), (32, 14), (42, 19), (41, 35), (14, 13), (1, 29), (43, 32), (6, 9), (3, 34), (5, 9), (26, 18), (0, 31), (6, 2), (14, 16), (20, 28), (7, 0), (19, 12), (38, 2), (4, 31), (35, 11), (35, 33), (11, 1), (27, 24), (23, 33), (28, 0), (20, 2), (10, 34), (22, 16), (30, 29), (39, 18), (21, 34), (13, 25), (13, 35), (4, 29), (17, 6), (8, 4), (7, 35), (12, 14), (18, 21), (9, 8), (6, 33), (3, 30), (20, 7), (8, 38), (10, 20), (25, 34), (15, 4), (21, 23), (44, 0), (16, 14), (43, 10), (8, 10), (5, 14), (4, 38), (25, 9), (27, 4), (35, 37), (1, 32), (31, 23), (28, 9), (33, 23), (39, 27), (36, 8), (11, 29), (42, 3), (24, 22), (38, 37), (25, 39), (4, 21), (37, 0), (21, 19), (36, 5), (21, 9), (0, 22), (41, 7), (20, 1), (16, 12), (12, 26), (20, 4), (5, 32), (28, 11), (43, 21), (6, 16), (5, 29), (21, 5), (38, 36), (37, 19), (1, 34), (11, 13), (38, 23), (5, 28), (14, 26), (40, 28), (42, 29), (38, 3), (16, 1), (6, 1), (18, 23), (10, 16), (37, 14), (38, 13), (20, 13), (15, 19), (38, 11), (34, 6), (43, 8), (29, 22), (34, 30), (16, 24), (8, 9), (28, 36), (40, 14), (36, 10), (13, 34), (3, 23), (7, 3), (19, 31), (21, 33), (3, 36), (1, 1), (8, 37), (14, 25), (12, 29), (27, 19), (17, 36), (27, 7), (40, 0), (21, 29), (44, 6), (41, 15), (32, 25), (34, 25), (33, 10), (8, 21), (40, 6), (3, 26), (8, 1), (29, 21), (32, 26), (30, 36), (32, 34), (29, 1), (39, 28), (20, 20), (10, 35), (10, 6), (8, 14), (5, 31), (37, 2), (4, 37), (41, 21), (19, 35), (32, 1), (21, 2), (2, 8), (27, 20), (1, 0), (43, 24), (38, 35), (8, 20), (11, 11), (26, 20), (33, 26), (19, 18), (25, 0), (2, 31), (5, 34), (3, 38), (19, 10), (27, 30), (28, 17), (14, 20), (20, 30), (25, 4), (14, 17), (16, 34), (28, 27), (3, 32), (5, 27), (2, 14), (38, 0), (2, 1), (34, 28), (28, 32), (2, 6), (35, 18), (29, 15), (39, 10), (40, 29), (14, 3), (36, 38), (13, 30), (5, 12), (40, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 34), (7, 14), (29, 45), (34, 36), (2, 44), (20, 28), (15, 42), (12, 46), (25, 17), (15, 6), (19, 44), (29, 21), (36, 42), (31, 34), (13, 8), (37, 44), (7, 19), (37, 28), (32, 1), (0, 15), (30, 11), (16, 36), (27, 42), (4, 25), (14, 4), (3, 16), (33, 29), (3, 33), (28, 32), (30, 31), (35, 9), (3, 6), (5, 40), (22, 45), (25, 12), (9, 47), (1, 36), (31, 8), (19, 12), (26, 35), (22, 6), (34, 38), (26, 28), (23, 5), (21, 41), (16, 4), (9, 10), (31, 17), (29, 46), (8, 21), (18, 22), (8, 25), (2, 16), (30, 40), (9, 3), (24, 40), (17, 39), (32, 34), (24, 29), (0, 28), (16, 45), (8, 19), (18, 15), (40, 29), (14, 48), (28, 38), (27, 12), (41, 23), (26, 10), (2, 6), (21, 27), (22, 36), (34, 37), (18, 8), (28, 28), (7, 47), (16, 23), (2, 43), (40, 37), (17, 14), (32, 43), (14, 36), (29, 32), (24, 18), (7, 40), (14, 15), (26, 39), (40, 0), (4, 46), (1, 29), (23, 16), (39, 14), (33, 8), (26, 36), (5, 4), (32, 27), (16, 39), (10, 48), (10, 28), (22, 2), (4, 39), (12, 23), (34, 6), (4, 17), (19, 38), (25, 44), (32, 48), (15, 12), (16, 12), (19, 36), (16, 8), (15, 4), (29, 8), (15, 26), (12, 37), (11, 3), (3, 43), (8, 27), (36, 27), (40, 19), (27, 30), (22, 3), (30, 34), (35, 31), (33, 48), (26, 42), (16, 35), (13, 19), (20, 15), (2, 39), (3, 9), (18, 5), (36, 34), (15, 19), (41, 7), (22, 7), (16, 28), (40, 33), (41, 0), (19, 2), (40, 6), (3, 13), (6, 7), (25, 11), (30, 48), (16, 7), (35, 39), (31, 46), (34, 20), (11, 5), (1, 35), (29, 37), (40, 20), (36, 23), (16, 30), (30, 12), (2, 41), (35, 42), (5, 32), (2, 34), (7, 9), (33, 47), (6, 39), (39, 6), (10, 0), (25, 7), (27, 14), (24, 9), (33, 41), (29, 38), (23, 18), (26, 5), (15, 8), (18, 32), (22, 35), (39, 3), (2, 45), (18, 46), (10, 17), (8, 18), (16, 43), (33, 17), (10, 7), (23, 27), (29, 16), (3, 26), (36, 33), (22, 17), (9, 38), (41, 2), (9, 17), (13, 43), (34, 0), (11, 2), (38, 22), (3, 47), (10, 13), (9, 6), (22, 16), (8, 9), (20, 46), (7, 21), (28, 24), (0, 20), (35, 4), (38, 35), (21, 24), (17, 27), (19, 11), (18, 30), (29, 23), (11, 15), (3, 3), (29, 31), (17, 5), (26, 0), (7, 43), (41, 22), (17, 7), (4, 0), (10, 4), (37, 45), (28, 12), (41, 29), (27, 32), (15, 34), (7, 42), (3, 42), (13, 40), (7, 0), (18, 25), (5, 8), (6, 24), (2, 38), (34, 15), (23, 32), (34, 35), (22, 5), (6, 41), (9, 24), (33, 30), (23, 47), (13, 32), (16, 13), (36, 22), (30, 38), (21, 4), (38, 42), (12, 16), (35, 30), (10, 41), (28, 4), (37, 10), (5, 46), (36, 7), (16, 42), (33, 11), (15, 35), (24, 28), (30, 45), (24, 12), (37, 39), (20, 19), (35, 27), (38, 24), (10, 46), (9, 40), (17, 28), (12, 0), (37, 24), (6, 25), (14, 6), (41, 45), (7, 45), (33, 18), (29, 10), (15, 21), (21, 14), (1, 2), (13, 15), (34, 18), (25, 10), (18, 23), (38, 40), (35, 0), (7, 32), (29, 11), (38, 12), (16, 26), (16, 31), (38, 27), (26, 33), (21, 29), (38, 39), (1, 28), (24, 6), (28, 48), (39, 5), (24, 39), (31, 10), (8, 4), (27, 4), (6, 2), (8, 30), (29, 27), (25, 25), (39, 21), (28, 47), (14, 10), (31, 26), (41, 35), (4, 23), (16, 3), (9, 41), (30, 29), (33, 15), (32, 46), (36, 8), (29, 36), (10, 2), (23, 25), (23, 14), (34, 33), (5, 30), (25, 40), (20, 1), (34, 40), (18, 35), (0, 9), (10, 27), (20, 40), (12, 26), (5, 38), (12, 19), (31, 35), (41, 15), (23, 41), (29, 5), (40, 31), (15, 30), (0, 41), (18, 39), (24, 15), (31, 15), (0, 5), (4, 3), (41, 43), (36, 32), (39, 4), (0, 34), (9, 28), (36, 45), (26, 12), (14, 28), (1, 39), (33, 33), (32, 15), (22, 29), (17, 16), (3, 20), (13, 16), (7, 18), (41, 46), (36, 12), (35, 24), (13, 38), (29, 48), (29, 34), (24, 42), (40, 5), (36, 20), (37, 37), (35, 6), (25, 0), (25, 2), (3, 15), (15, 13), (7, 13), (8, 22), (0, 30), (1, 6), (31, 31), (27, 5), (11, 22), (23, 22), (5, 41), (13, 0), (13, 29), (22, 33), (27, 48)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 20), (6, 32), (11, 6), (1, 13), (19, 26), (27, 17), (27, 14), (7, 21), (4, 38), (18, 29), (46, 34), (18, 30), (43, 12), (1, 21), (42, 7), (12, 24), (32, 30), (1, 3), (6, 37), (33, 1), (35, 28), (36, 8), (39, 29), (25, 2), (20, 19), (19, 22), (0, 26), (11, 4), (17, 19), (38, 16), (15, 39), (10, 16), (13, 27), (32, 12), (29, 15), (33, 0), (2, 17), (0, 23), (40, 36), (41, 20), (47, 30), (20, 7), (38, 21), (8, 25), (15, 12), (22, 17), (36, 7), (3, 28), (44, 22), (22, 26), (14, 9), (13, 18), (37, 3), (24, 33), (36, 35), (12, 1), (6, 13), (29, 1), (20, 25), (0, 30), (26, 1), (42, 38), (31, 14), (10, 36), (34, 16), (13, 36), (36, 9), (15, 29), (21, 23), (9, 27), (46, 18), (16, 8), (25, 38), (30, 14), (32, 36), (31, 29), (45, 17), (15, 6), (11, 31), (39, 33), (16, 20), (10, 19), (5, 33), (41, 33), (32, 0), (43, 39), (8, 32), (20, 34), (4, 19), (46, 30), (28, 30), (24, 12), (3, 38), (13, 19), (31, 33), (29, 12), (37, 5), (29, 4), (35, 38), (40, 14), (48, 32), (32, 19), (48, 29), (6, 20), (7, 12), (26, 11), (37, 17), (28, 15), (35, 23), (44, 39), (10, 34), (44, 29), (12, 22), (26, 21), (14, 1), (32, 21), (17, 33), (1, 2), (18, 4), (12, 9), (2, 3), (21, 16), (14, 37), (1, 31), (25, 3), (38, 32), (27, 37), (25, 16), (17, 23), (0, 1), (39, 15), (40, 3), (43, 24), (13, 13), (14, 31), (9, 36), (2, 13), (0, 35), (23, 23), (34, 19), (40, 16), (20, 10), (39, 9), (35, 29), (16, 34), (3, 23), (9, 6), (29, 17), (36, 13), (24, 26), (29, 10), (32, 29), (5, 26), (35, 0), (8, 36), (12, 27), (25, 25), (36, 27), (41, 10), (8, 12), (30, 7), (36, 11), (12, 13), (31, 17), (19, 16), (20, 13), (44, 14), (19, 25), (10, 10), (31, 21), (37, 29), (26, 3), (8, 37), (32, 23), (45, 19), (11, 29), (43, 37), (16, 23), (38, 6), (34, 33), (38, 33), (41, 28), (29, 5), (30, 6), (45, 5), (48, 11), (1, 6), (35, 25), (45, 9), (42, 15), (24, 18), (13, 33), (25, 5), (9, 26), (42, 11), (29, 29), (13, 20), (44, 8), (5, 31), (34, 13), (27, 1), (40, 20), (2, 1), (7, 20), (18, 10), (48, 10), (45, 26), (9, 30), (43, 2), (46, 10), (43, 7), (36, 17), (20, 9), (46, 16), (45, 27), (42, 32), (28, 31), (26, 35), (5, 0), (34, 37), (13, 28), (33, 14), (25, 21), (12, 31), (17, 14), (21, 10), (26, 20), (0, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 37), (28, 29), (16, 11), (7, 27), (2, 3), (23, 40), (30, 38), (9, 18), (22, 34), (2, 12), (25, 16), (21, 37), (4, 28), (14, 1), (7, 6), (40, 40), (24, 8), (4, 9), (18, 14), (37, 11), (21, 4), (2, 32), (22, 0), (5, 3), (6, 37), (32, 19), (30, 8), (23, 38), (38, 39), (19, 36), (1, 28), (38, 19), (36, 15), (38, 29), (5, 0), (42, 6), (26, 26), (38, 24), (15, 4), (24, 42), (33, 14), (15, 5), (37, 30), (1, 0), (9, 31), (29, 12), (0, 14), (41, 3), (36, 38), (35, 28), (17, 11), (6, 7), (19, 38), (39, 30), (30, 32), (26, 3), (43, 24), (20, 24), (23, 30), (27, 34), (39, 22), (2, 13), (2, 22), (7, 24), (0, 32), (38, 7), (9, 23), (39, 23), (21, 21), (18, 9), (35, 29), (40, 22), (2, 11), (9, 38), (40, 20), (36, 35), (34, 11), (20, 25), (2, 8), (2, 31), (26, 13), (41, 16), (11, 23), (35, 32), (12, 41), (38, 14), (24, 12), (22, 39), (10, 36), (12, 4), (9, 2), (14, 30), (3, 2), (38, 22), (38, 38), (22, 6), (37, 16), (2, 10), (16, 7), (13, 40), (13, 34), (9, 13), (27, 16), (21, 19), (25, 31), (32, 26), (27, 8), (22, 12), (8, 1), (33, 10), (33, 0), (10, 40), (0, 7), (39, 41), (13, 11), (14, 26), (15, 3), (31, 0), (5, 40), (19, 4), (33, 25), (28, 30), (23, 18), (11, 15), (4, 39), (24, 19), (27, 10), (19, 24), (30, 41), (15, 26), (28, 1), (14, 35), (27, 20), (32, 11), (30, 13), (40, 34), (34, 37), (4, 8), (6, 10), (37, 13), (33, 30), (11, 26), (10, 9), (37, 20), (17, 26), (36, 24), (18, 22), (22, 4), (9, 33), (6, 32), (41, 5), (27, 38), (22, 20), (4, 23), (10, 27), (35, 8), (25, 33), (31, 8), (39, 14), (29, 28), (41, 33), (35, 14), (18, 37), (11, 30), (36, 14), (20, 29), (17, 15), (29, 30), (19, 30), (29, 14), (23, 6), (42, 41), (29, 9), (17, 23), (16, 1), (30, 19), (34, 32), (2, 4), (24, 22), (18, 27), (14, 10), (43, 41), (34, 18), (22, 1), (9, 21), (24, 9), (14, 0), (28, 38), (34, 19), (41, 21), (36, 25), (1, 21), (3, 36), (22, 15), (39, 27), (13, 17), (25, 18), (23, 42), (13, 8), (1, 10), (37, 34), (41, 18), (25, 17), (25, 28), (31, 14), (30, 20), (37, 37), (31, 35), (30, 24), (36, 41), (12, 15), (38, 4), (41, 41), (25, 0), (15, 29), (42, 5), (34, 42), (12, 39), (13, 27), (23, 31), (16, 26), (15, 34), (0, 2), (9, 6), (41, 40), (28, 37), (22, 14), (13, 14), (27, 42), (0, 35), (9, 22), (32, 12), (14, 27), (26, 0), (19, 42), (25, 24), (23, 14), (20, 20), (35, 16), (12, 34), (12, 10), (8, 8), (24, 18), (19, 16), (4, 26), (19, 35), (7, 14), (21, 27), (38, 11), (37, 41), (25, 9), (40, 27), (9, 11), (12, 28), (19, 41), (21, 20), (26, 23), (25, 21), (8, 12), (6, 39), (41, 28), (38, 23), (37, 31), (36, 11), (2, 35), (36, 10), (4, 2), (36, 3), (14, 37), (34, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 47x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 31), (35, 28), (40, 0), (36, 8), (14, 22), (27, 40), (40, 23), (2, 22), (43, 41), (39, 1), (44, 24), (9, 5), (8, 23), (0, 31), (15, 40), (36, 39), (18, 9), (3, 39), (16, 31), (22, 30), (23, 36), (44, 23), (28, 23), (17, 23), (14, 33), (3, 40), (34, 19), (42, 7), (43, 2), (11, 34), (7, 7), (44, 26), (46, 23), (11, 12), (39, 3), (15, 41), (11, 25), (24, 17), (42, 3), (18, 12), (39, 5), (46, 33), (41, 21), (3, 6), (9, 19), (41, 26), (28, 2), (29, 25), (37, 9), (19, 34), (30, 11), (17, 10), (16, 17), (27, 29), (34, 21), (44, 29), (20, 34), (9, 37), (44, 33), (11, 37), (36, 10), (9, 1), (17, 12), (45, 28), (19, 29), (8, 11), (31, 26), (27, 24), (0, 24), (36, 19), (18, 7), (17, 1), (45, 37), (32, 6), (13, 41), (12, 9), (24, 16), (13, 2), (36, 33), (22, 5), (46, 16), (0, 41), (19, 24), (39, 30), (39, 16), (38, 37), (6, 39), (11, 24), (2, 3), (20, 29), (30, 39), (6, 4), (17, 24), (45, 29), (19, 28), (45, 7), (26, 34), (3, 2), (34, 40), (37, 20), (21, 19), (0, 16), (3, 20), (30, 5), (29, 15), (41, 23), (14, 29), (14, 36), (14, 19), (35, 9), (44, 22), (1, 27), (22, 7), (20, 28), (44, 9), (25, 0), (24, 6), (40, 11), (35, 16), (1, 39), (42, 12), (46, 19), (41, 19), (2, 16), (27, 13), (41, 24), (19, 9), (44, 34), (33, 17), (40, 3), (16, 4), (44, 6), (21, 35), (31, 11), (4, 21), (20, 14), (42, 20), (42, 41), (26, 28), (26, 17), (26, 13), (31, 0), (26, 16), (12, 3), (16, 32), (29, 30), (8, 38), (4, 32), (18, 18), (9, 11), (0, 13), (17, 20), (29, 12), (17, 25), (40, 25), (17, 8), (1, 41), (40, 1), (4, 35), (37, 13), (37, 40), (15, 2), (22, 8), (22, 28), (36, 14), (13, 38), (28, 20), (31, 23), (39, 12), (11, 20), (45, 10), (32, 5), (25, 11), (45, 20), (28, 37), (36, 2), (40, 10), (35, 20), (33, 1), (28, 11), (30, 18), (36, 25), (35, 25), (37, 31), (3, 15), (42, 38), (11, 33), (20, 41), (43, 11), (26, 30), (19, 35), (22, 11), (30, 35), (37, 23), (20, 27), (0, 1), (27, 17), (0, 26), (32, 25), (6, 17), (22, 18), (6, 13), (16, 1), (28, 25), (33, 19), (22, 22), (20, 21), (17, 14), (27, 12), (5, 35), (4, 17), (45, 1), (34, 23), (11, 10), (20, 11), (45, 2), (15, 10), (10, 27), (43, 39), (29, 28), (19, 41), (29, 3), (38, 14), (29, 41), (17, 21), (42, 11), (7, 16), (12, 32), (4, 34), (15, 12), (22, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 40), (12, 26), (3, 1), (2, 19), (34, 20), (21, 36), (11, 4), (23, 7), (38, 16), (20, 22), (17, 23), (8, 3), (28, 11), (34, 7), (17, 25), (40, 5), (21, 5), (26, 6), (15, 39), (2, 14), (19, 1), (41, 9), (28, 2), (12, 40), (30, 36), (1, 40), (38, 32), (33, 31), (8, 38), (33, 24), (27, 6), (4, 2), (33, 35), (2, 18), (12, 27), (24, 23), (39, 35), (24, 11), (22, 28), (16, 38), (7, 17), (40, 4), (29, 11), (31, 30), (25, 10), (27, 2), (21, 28), (9, 12), (5, 0), (34, 14), (21, 9), (16, 16), (24, 27), (14, 28), (34, 26), (19, 25), (0, 38), (1, 22), (29, 34), (13, 15), (39, 2), (35, 5), (27, 30), (34, 3), (37, 18), (21, 12), (9, 18), (4, 29), (3, 13), (35, 13), (13, 0), (13, 19), (40, 38), (1, 34), (16, 21), (39, 34), (8, 39), (15, 14), (18, 29), (36, 12), (9, 29), (41, 11), (3, 17), (22, 34), (41, 27), (30, 11), (16, 17), (27, 29), (3, 16), (32, 36), (30, 3), (27, 37), (36, 2), (18, 13), (41, 7), (1, 36), (5, 30), (28, 27), (10, 20), (14, 23), (38, 27), (5, 19), (26, 20), (14, 13), (38, 6), (23, 37), (35, 10), (10, 4), (25, 4), (19, 12), (24, 22), (6, 2), (6, 4), (23, 8), (34, 37), (34, 16), (30, 13), (31, 36), (34, 6), (1, 35), (9, 28), (23, 36), (22, 35), (19, 3), (4, 36), (26, 19), (11, 20), (20, 15), (25, 6), (18, 37), (36, 3), (5, 24), (16, 37), (33, 40), (28, 37), (9, 1), (16, 39), (24, 29), (32, 6), (3, 38), (41, 32), (31, 9), (39, 19), (3, 21), (3, 14), (32, 28), (29, 35), (2, 23), (29, 3), (39, 23), (14, 34), (37, 15), (21, 7), (24, 37), (7, 2), (41, 5), (39, 39), (33, 6), (17, 12), (35, 27), (38, 0), (10, 9), (18, 38), (18, 8), (11, 3), (31, 33), (15, 35), (9, 8), (14, 31), (12, 12), (3, 12), (35, 18), (4, 20), (36, 14), (5, 27), (2, 27), (36, 18), (41, 22), (10, 0), (7, 29), (11, 0), (10, 14), (26, 39), (40, 3), (33, 27), (39, 12), (11, 33), (39, 37), (14, 8), (21, 15), (8, 19), (30, 12), (19, 37), (0, 26), (15, 19), (23, 20), (39, 36), (0, 29), (14, 29), (22, 33), (38, 7), (7, 5), (30, 24), (22, 37), (36, 37), (33, 2), (6, 17), (31, 27), (10, 30), (17, 7), (40, 21), (0, 27), (29, 31), (27, 35), (11, 37), (29, 1), (39, 29), (31, 19), (32, 0), (15, 8), (17, 11), (9, 25), (26, 22), (34, 29), (10, 3), (9, 33), (14, 10), (22, 1), (39, 30), (28, 8), (27, 34), (40, 34), (40, 13), (28, 18), (15, 25), (4, 38), (25, 14), (17, 32), (2, 40), (19, 11), (19, 33), (15, 2), (29, 30), (11, 12), (8, 8), (32, 18), (12, 0), (27, 32), (36, 1), (22, 5), (27, 12), (4, 15), (20, 18), (12, 20), (32, 40), (29, 14), (8, 1), (30, 21), (9, 10), (7, 30), (2, 9), (9, 27), (10, 40), (11, 18), (33, 30), (37, 33), (20, 19), (10, 28), (0, 12), (35, 30), (31, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 13), (42, 0), (0, 18), (15, 40), (1, 38), (38, 2), (24, 40), (16, 33), (4, 0), (30, 30), (40, 1), (12, 19), (30, 27), (39, 20), (35, 31), (17, 22), (32, 14), (41, 17), (35, 29), (30, 10), (22, 10), (16, 5), (26, 35), (45, 0), (13, 23), (20, 34), (1, 34), (17, 19), (35, 32), (25, 41), (15, 0), (28, 30), (29, 28), (15, 21), (1, 4), (17, 2), (28, 28), (36, 19), (9, 3), (34, 29), (23, 7), (22, 21), (6, 15), (13, 25), (7, 15), (1, 5), (14, 39), (16, 30), (16, 35), (8, 16), (34, 9), (2, 20), (42, 25), (11, 13), (36, 1), (0, 39), (32, 30), (2, 6), (12, 41), (13, 4), (3, 5), (37, 10), (17, 1), (5, 38), (22, 25), (20, 38), (20, 37), (5, 16), (3, 39), (16, 16), (36, 25), (9, 15), (45, 22), (21, 8), (6, 22), (1, 9), (15, 20), (20, 22), (0, 28), (38, 3), (26, 32), (45, 23), (1, 31), (21, 7), (40, 5), (23, 40), (21, 33), (9, 30), (8, 24), (35, 26), (22, 23), (43, 29), (0, 23), (23, 24), (43, 39), (18, 21), (23, 31), (36, 32), (30, 31), (14, 19), (16, 12), (33, 11), (29, 17), (14, 9), (5, 17), (42, 21), (11, 12), (11, 16), (25, 10), (16, 21), (16, 0), (22, 38), (22, 11), (6, 16), (20, 40), (39, 0), (24, 26), (17, 8), (17, 38), (42, 34), (7, 10), (25, 33), (14, 14), (34, 15), (18, 18), (7, 37), (2, 40), (21, 17), (32, 2), (5, 9), (32, 1), (28, 9), (38, 24), (42, 23), (38, 12), (44, 27), (13, 38), (34, 18), (12, 8), (40, 20), (26, 8), (15, 32), (23, 20), (30, 13), (31, 5), (20, 13), (9, 37), (13, 8), (33, 4), (7, 19), (36, 37), (17, 32), (45, 40), (5, 11), (17, 41), (40, 19), (2, 13), (19, 22), (39, 36), (39, 33), (45, 18), (18, 29), (19, 4), (35, 12), (16, 7), (37, 41), (24, 10), (34, 10), (2, 12), (25, 28), (8, 15), (27, 8), (41, 13), (28, 13), (3, 41), (23, 30), (41, 38), (41, 7), (16, 32), (15, 11), (10, 24), (43, 2), (20, 7), (18, 12), (7, 39), (24, 35), (20, 1), (14, 21), (28, 33), (23, 21), (36, 39), (13, 15), (45, 13), (17, 24), (32, 16), (9, 17), (18, 28), (31, 1), (16, 1), (4, 7), (5, 30), (5, 34), (0, 27), (13, 26), (31, 17), (20, 0), (39, 35), (20, 25), (43, 10), (11, 31), (36, 20), (0, 33), (35, 18), (23, 26), (9, 5), (21, 35), (0, 30), (38, 25), (20, 30), (40, 2), (12, 32), (22, 36), (16, 19), (28, 18), (24, 28), (8, 29), (14, 30), (6, 25), (28, 11), (33, 34), (3, 10), (1, 19), (17, 15), (35, 30), (8, 20), (10, 38), (11, 30), (25, 6), (44, 38), (32, 39), (20, 24), (24, 1), (3, 27), (5, 0), (44, 34), (14, 22), (38, 18), (25, 19), (20, 28), (15, 28), (28, 5), (12, 6), (19, 24), (28, 38), (28, 0), (33, 23), (0, 13), (19, 21), (11, 35), (16, 11), (10, 15), (36, 12), (41, 9), (36, 17), (30, 32), (3, 14), (33, 38), (37, 19), (12, 10), (15, 6), (33, 0), (31, 21), (43, 1), (26, 39), (15, 1), (29, 37), (19, 18), (7, 4), (28, 14), (10, 7), (42, 39), (2, 3), (22, 31), (13, 24), (14, 5), (24, 31), (6, 10), (18, 37), (43, 22), (26, 21), (3, 20), (34, 24), (2, 10), (8, 28), (25, 16), (12, 37), (29, 31), (0, 20), (0, 19), (33, 21), (23, 36), (42, 4), (6, 34), (44, 8), (37, 28), (19, 8), (1, 33), (14, 27), (40, 25), (0, 16), (5, 32), (35, 5), (39, 13), (11, 20), (35, 41), (13, 32), (36, 31), (0, 8), (37, 13), (24, 9), (20, 19), (10, 5), (45, 1), (37, 6), (32, 31), (40, 35), (35, 27), (39, 8), (34, 26), (7, 18), (16, 8), (26, 26), (16, 13), (0, 3), (1, 41), (21, 15), (4, 39), (35, 7), (26, 7), (38, 36), (2, 5), (22, 24), (8, 35), (21, 3), (21, 24), (32, 38), (39, 7), (6, 7), (32, 25), (9, 16), (36, 21), (3, 17), (38, 34), (36, 41), (23, 38), (19, 40), (45, 10), (22, 33), (27, 9), (10, 19), (30, 6), (17, 35), (42, 9), (18, 17), (45, 11), (38, 1), (11, 26), (2, 14), (7, 26), (32, 11), (37, 7), (30, 1), (35, 21), (15, 9), (0, 40), (29, 22), (33, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 41), (30, 28), (8, 0), (32, 11), (38, 36), (0, 30), (23, 21), (19, 26), (9, 42), (35, 22), (21, 6), (47, 9), (14, 30), (26, 0), (27, 41), (25, 20), (38, 17), (22, 28), (22, 43), (35, 24), (2, 25), (13, 29), (42, 7), (44, 5), (17, 43), (38, 9), (42, 10), (37, 37), (46, 3), (1, 13), (4, 17), (24, 34), (7, 18), (42, 2), (30, 38), (43, 23), (9, 41), (14, 44), (41, 33), (43, 13), (9, 34), (20, 11), (29, 35), (21, 27), (22, 14), (43, 20), (23, 26), (4, 43), (47, 24), (34, 14), (34, 16), (18, 25), (14, 20), (45, 35), (24, 10), (0, 9), (13, 1), (45, 44), (10, 38), (7, 12), (6, 22), (12, 1), (22, 29), (15, 40), (25, 23), (26, 36), (37, 18), (23, 12), (7, 17), (25, 8), (28, 25), (29, 15), (13, 27), (26, 33), (43, 6), (23, 5), (46, 34), (20, 26), (28, 22), (3, 44), (43, 40), (27, 31), (32, 17), (22, 20), (41, 18), (4, 13), (47, 30), (9, 16), (1, 40), (44, 6), (0, 38), (19, 27), (24, 3), (39, 40), (7, 37), (14, 38), (11, 3), (42, 17), (47, 32), (17, 24), (26, 35), (33, 20), (46, 2), (18, 5), (42, 14), (41, 0), (33, 33), (34, 37), (27, 14), (12, 13), (38, 20), (26, 3), (3, 42), (16, 28), (37, 35), (30, 13), (37, 26), (4, 15), (2, 0), (7, 35), (32, 18), (2, 23), (23, 23), (1, 21), (39, 22), (47, 33), (34, 38), (18, 29), (42, 32), (10, 29), (23, 27), (32, 44), (37, 41), (5, 22), (10, 1), (25, 27), (36, 41), (39, 30), (26, 21), (16, 36), (23, 20), (18, 37), (6, 30), (10, 25), (35, 35), (31, 8), (35, 27), (25, 44), (46, 10), (27, 7), (22, 3), (13, 15), (33, 2), (14, 4), (0, 41), (22, 27), (34, 30), (38, 40), (36, 1), (13, 20), (32, 8), (35, 23), (25, 42), (22, 19), (6, 9), (6, 1), (3, 31), (43, 26), (20, 13), (19, 15), (42, 9), (43, 0), (42, 6), (12, 21), (46, 33), (21, 11), (6, 43), (11, 29), (44, 43), (47, 13), (7, 9), (6, 28), (13, 5), (17, 33), (1, 5), (3, 0), (46, 14), (15, 10), (37, 17), (34, 6), (16, 35), (15, 15), (23, 10), (17, 44), (2, 13), (39, 10), (45, 22), (47, 16), (47, 39), (21, 12), (9, 32), (22, 16), (21, 4), (19, 24), (23, 42), (16, 4), (4, 8), (10, 4), (17, 35), (4, 11), (9, 4), (2, 44), (44, 40), (27, 15), (20, 28), (42, 1), (3, 9), (13, 38), (13, 42), (29, 2), (35, 31), (43, 29), (23, 36), (6, 27), (36, 32), (36, 8), (21, 18), (28, 31), (37, 19), (38, 33), (29, 5), (17, 20), (28, 30), (16, 38), (10, 40), (5, 7), (16, 25), (14, 26), (5, 43), (29, 7), (34, 9), (6, 36), (5, 5), (41, 37), (12, 22), (46, 28), (26, 26), (25, 38), (12, 34), (9, 2), (32, 31), (17, 10), (32, 35), (8, 7), (10, 41), (38, 29), (27, 42), (21, 23), (5, 32), (10, 28), (3, 6), (4, 7), (33, 3), (35, 19), (0, 17), (15, 12), (13, 25), (12, 19), (22, 11), (45, 9), (21, 13), (16, 3), (17, 15), (9, 39), (27, 40), (47, 11), (28, 35), (34, 42), (47, 22), (29, 12), (21, 33), (30, 19), (38, 13), (33, 40), (36, 20), (45, 20), (36, 5), (7, 32), (46, 7), (46, 44), (17, 12), (45, 27), (18, 8), (46, 24), (32, 25), (4, 26), (9, 17), (33, 11), (41, 9), (19, 42), (40, 34), (41, 24), (26, 1), (44, 9), (17, 1), (20, 8), (39, 15), (33, 1), (11, 34), (40, 43), (22, 6), (21, 5), (25, 37), (23, 9), (32, 20), (12, 12), (5, 36), (28, 23), (10, 20), (46, 32), (5, 37), (22, 33), (3, 34), (41, 40), (10, 13), (32, 5), (8, 24), (24, 26), (23, 1), (38, 23), (13, 30), (43, 31), (22, 44), (34, 8), (13, 33), (44, 1), (12, 36), (0, 18), (22, 36), (32, 19), (40, 39), (28, 15), (36, 43), (11, 14), (18, 31), (32, 36), (13, 16), (28, 32), (40, 15), (10, 36), (12, 38), (33, 30), (41, 38), (12, 23), (26, 38), (34, 40), (14, 27), (14, 0), (27, 5), (2, 38), (22, 31), (3, 37), (28, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 39), (23, 16), (8, 34), (20, 29), (4, 18), (39, 6), (8, 30), (34, 37), (42, 41), (42, 18), (46, 41), (21, 12), (14, 9), (38, 41), (29, 19), (3, 41), (41, 27), (29, 1), (16, 13), (8, 5), (5, 28), (22, 27), (14, 22), (32, 6), (21, 6), (42, 5), (37, 31), (29, 37), (17, 43), (11, 14), (37, 11), (4, 38), (13, 39), (9, 5), (35, 34), (26, 37), (24, 35), (24, 0), (44, 14), (30, 5), (22, 10), (29, 39), (22, 28), (0, 43), (33, 1), (14, 41), (40, 0), (27, 1), (19, 19), (45, 15), (38, 32), (21, 30), (34, 26), (45, 13), (44, 43), (6, 39), (7, 34), (16, 39), (3, 21), (19, 14), (31, 35), (0, 15), (20, 2), (44, 35), (24, 25), (34, 30), (19, 32), (4, 33), (33, 32), (16, 11), (6, 43), (34, 32), (15, 2), (15, 19), (15, 6), (41, 21), (36, 7), (9, 9), (41, 26), (29, 9), (25, 24), (25, 19), (2, 43), (27, 11), (19, 35), (32, 4), (36, 9), (1, 21), (3, 2), (37, 6), (32, 16), (8, 42), (13, 28), (12, 2), (35, 9), (27, 8), (20, 21), (20, 31), (31, 7), (28, 11), (25, 2), (44, 21), (43, 39), (14, 4), (7, 36), (41, 31), (17, 19), (27, 26), (6, 10), (23, 21), (28, 20), (2, 20), (24, 31), (16, 17), (11, 38), (28, 23), (41, 42), (32, 21), (36, 11), (41, 22), (2, 36), (1, 20), (22, 39), (38, 17), (12, 16), (12, 12), (42, 30), (41, 16), (6, 37), (12, 13), (37, 14), (11, 33), (26, 38), (42, 34), (22, 26), (37, 39), (21, 34), (25, 11), (34, 13), (21, 8), (5, 36), (40, 36), (34, 31), (16, 42), (27, 38), (4, 20), (38, 38), (18, 30), (20, 4), (45, 11), (7, 2), (23, 12), (24, 32), (30, 13), (41, 15), (28, 19), (1, 17), (8, 18), (12, 10), (4, 30), (3, 36), (44, 24), (21, 38), (44, 4), (16, 29), (9, 24), (12, 19), (9, 21), (30, 36), (23, 6), (25, 6), (12, 39), (41, 14), (27, 29), (4, 2), (20, 30), (27, 37), (46, 12), (39, 14), (41, 39), (26, 26), (4, 21), (5, 7), (22, 34), (37, 40), (35, 21), (9, 28), (11, 2), (30, 38), (40, 18), (17, 22), (45, 23), (3, 9), (8, 37), (16, 0), (45, 22), (26, 27), (34, 3), (23, 24), (5, 10), (25, 16), (29, 6), (7, 8), (32, 26), (41, 17), (18, 12), (12, 30), (11, 29), (4, 19), (7, 9), (15, 16), (11, 6), (25, 23), (37, 21), (30, 10), (39, 5), (23, 15), (23, 34), (12, 4), (21, 41), (13, 13), (22, 38), (3, 7), (45, 20), (0, 18), (21, 3), (39, 25), (26, 33), (12, 20), (31, 16), (29, 33), (41, 2), (7, 22), (41, 3), (15, 12), (12, 23), (43, 22), (38, 43), (43, 5), (46, 21), (42, 12), (2, 0), (23, 28), (8, 12), (35, 2), (39, 22), (4, 22), (11, 22), (25, 3), (43, 12), (28, 16), (24, 41), (22, 24), (15, 0), (46, 36), (46, 2), (12, 21), (21, 2), (27, 23), (40, 5), (8, 14), (42, 21), (27, 9), (24, 43), (30, 7), (28, 24), (45, 2), (14, 15), (43, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 19), (22, 16), (6, 20), (3, 3), (24, 26), (14, 16), (5, 27), (39, 5), (8, 3), (12, 33), (5, 6), (21, 7), (4, 36), (5, 1), (20, 37), (28, 42), (23, 35), (31, 33), (20, 10), (28, 32), (14, 27), (5, 43), (19, 34), (14, 3), (40, 40), (36, 24), (10, 34), (13, 16), (9, 4), (41, 35), (12, 42), (12, 38), (5, 5), (32, 17), (8, 38), (3, 22), (37, 23), (14, 4), (7, 1), (6, 40), (28, 21), (19, 12), (8, 39), (9, 20), (18, 26), (19, 16), (18, 35), (6, 16), (26, 33), (17, 41), (3, 36), (23, 38), (3, 23), (6, 28), (27, 26), (29, 22), (18, 37), (25, 32), (31, 3), (17, 28), (17, 25), (27, 31), (34, 32), (41, 17), (5, 39), (34, 38), (24, 23), (8, 4), (2, 10), (13, 5), (36, 31), (0, 1), (30, 41), (10, 3), (13, 38), (26, 25), (31, 26), (8, 2), (38, 26), (25, 15), (13, 36), (40, 5), (11, 29), (23, 21), (38, 27), (7, 41), (26, 44), (33, 26), (14, 37), (1, 19), (15, 35), (10, 27), (10, 18), (30, 19), (28, 39), (36, 7), (22, 32), (26, 43), (26, 8), (9, 26), (39, 36), (40, 30), (14, 6), (40, 26), (26, 42), (39, 19), (41, 0), (18, 15), (29, 17), (21, 2), (3, 43), (1, 24), (4, 7), (33, 0), (12, 15), (19, 18), (32, 39), (31, 4), (13, 7), (30, 2), (15, 2), (10, 14), (16, 2), (17, 5), (31, 11), (27, 21), (16, 21), (41, 27), (24, 25), (21, 26), (5, 42), (41, 26), (12, 32), (33, 1), (24, 6), (1, 39), (36, 33), (11, 14), (41, 34), (33, 28), (27, 35), (14, 23), (2, 31), (27, 12), (2, 44), (1, 7), (0, 33), (13, 42), (20, 15), (13, 0), (3, 12), (16, 17), (33, 12), (40, 18), (32, 12), (37, 36), (36, 2), (1, 10), (34, 30), (4, 29), (29, 9), (27, 40), (20, 39), (16, 37), (21, 10), (3, 17), (8, 42), (25, 21), (17, 11), (0, 12), (40, 43), (29, 13), (40, 22), (39, 40), (22, 18), (32, 44), (35, 42), (5, 19), (40, 4), (1, 8), (23, 42), (38, 20), (0, 4), (36, 34), (31, 38), (35, 26), (24, 43), (23, 20), (19, 0), (13, 40), (41, 5), (25, 44), (0, 38), (14, 42), (39, 34), (16, 3), (25, 10), (20, 26), (3, 2), (25, 38), (41, 19), (32, 15), (9, 22), (11, 9), (12, 0), (21, 14), (35, 38), (7, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 12), (15, 8), (3, 3), (20, 42), (23, 12), (35, 34), (8, 13), (11, 13), (3, 14), (8, 45), (5, 46), (6, 27), (12, 22), (30, 29), (2, 3), (39, 12), (33, 28), (19, 16), (21, 12), (23, 22), (31, 44), (38, 31), (2, 43), (27, 40), (11, 7), (28, 46), (20, 11), (13, 24), (0, 36), (38, 20), (25, 14), (39, 16), (15, 40), (4, 5), (13, 2), (2, 5), (9, 23), (14, 37), (36, 22), (25, 8), (27, 26), (10, 26), (24, 28), (33, 13), (10, 28), (34, 27), (16, 28), (20, 4), (10, 39), (16, 40), (3, 23), (32, 13), (17, 11), (37, 20), (19, 20), (1, 40), (36, 33), (19, 19), (32, 9), (30, 24), (29, 19), (6, 35), (35, 5), (37, 36), (0, 24), (11, 36), (1, 2), (38, 36), (22, 46), (25, 37), (11, 42), (1, 33), (40, 3), (19, 38), (33, 46), (12, 6), (37, 21), (6, 13), (15, 15), (17, 34), (31, 11), (3, 31), (40, 41), (26, 30), (25, 46), (26, 44), (7, 38), (35, 40), (1, 31), (36, 34), (4, 36), (1, 25), (21, 37), (19, 46), (16, 14), (9, 45), (40, 33), (4, 25), (11, 22), (10, 34), (3, 24), (18, 34), (27, 35), (16, 15), (6, 41), (22, 0), (5, 8), (9, 39), (9, 2), (40, 43), (8, 12), (12, 40), (29, 35), (4, 39), (12, 27), (4, 17), (32, 26), (32, 17), (1, 0), (28, 6), (12, 7), (11, 35), (21, 17), (22, 12), (29, 14), (12, 43), (24, 19), (13, 7), (39, 11), (10, 7), (7, 28), (5, 45), (9, 44), (13, 39), (40, 1), (14, 9), (5, 39), (19, 37), (24, 44), (31, 36), (13, 30), (10, 44), (36, 18), (17, 27), (36, 42), (26, 24), (33, 45), (2, 11), (6, 39), (35, 22), (25, 10), (13, 20), (20, 14), (31, 7), (17, 10), (3, 11), (0, 32), (24, 37), (18, 43), (23, 34), (29, 5), (33, 44), (31, 3), (16, 26), (27, 29), (25, 4), (5, 37), (3, 26), (29, 2), (33, 6), (1, 10), (23, 16), (38, 15), (17, 9), (35, 41), (18, 9), (17, 35), (18, 24), (19, 17), (8, 16), (27, 1), (36, 23), (6, 31), (10, 24), (38, 29), (32, 2), (7, 35), (39, 39), (23, 0), (37, 41), (5, 32), (12, 23), (1, 8), (21, 43), (3, 34), (40, 34), (3, 35), (18, 42), (2, 7), (5, 43), (17, 42), (28, 21), (25, 43), (4, 7), (0, 3), (12, 46), (20, 1), (27, 24), (32, 28), (12, 19), (27, 19), (40, 22), (21, 6), (34, 33), (16, 12), (32, 29), (34, 14), (17, 24), (0, 31), (0, 15), (35, 37), (8, 40), (14, 43), (22, 10), (22, 2), (20, 37), (37, 11), (20, 39), (32, 22), (37, 14), (24, 21), (6, 28), (26, 3), (14, 18), (31, 30), (14, 19), (26, 19), (12, 9), (5, 11), (39, 4), (17, 37), (37, 32), (25, 21), (38, 14), (13, 6), (17, 22), (10, 23), (33, 23), (24, 40), (30, 13), (20, 15), (30, 2), (13, 16), (17, 6), (17, 23), (31, 25), (22, 17), (22, 13), (20, 41), (22, 11), (8, 19), (6, 45), (36, 43), (19, 3), (21, 16), (27, 14), (23, 5), (3, 38), (33, 14), (7, 19), (34, 42), (11, 12), (36, 2), (34, 17), (38, 8), (4, 26), (7, 22), (23, 1), (26, 18), (25, 3), (13, 22), (34, 41), (39, 46), (8, 33), (37, 15), (10, 0), (26, 33), (0, 45), (14, 40), (30, 36), (17, 4), (38, 26), (14, 26), (12, 42), (13, 4), (6, 16), (18, 2), (16, 17), (24, 20), (18, 8), (5, 25), (40, 35), (10, 32), (6, 30), (3, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 32), (39, 24), (20, 7), (21, 6), (39, 34), (43, 5), (32, 35), (2, 3), (4, 22), (34, 4), (9, 32), (43, 1), (9, 8), (40, 27), (46, 30), (42, 41), (15, 21), (17, 12), (24, 5), (9, 20), (41, 38), (37, 21), (17, 39), (12, 28), (31, 11), (1, 31), (25, 37), (22, 42), (37, 26), (1, 25), (31, 21), (40, 9), (38, 17), (41, 46), (26, 2), (3, 14), (33, 41), (44, 36), (22, 13), (0, 27), (42, 38), (6, 42), (43, 29), (24, 28), (43, 41), (10, 32), (13, 20), (39, 2), (30, 42), (4, 46), (24, 41), (38, 35), (44, 12), (33, 26), (45, 36), (43, 36), (20, 16), (44, 45), (11, 45), (11, 10), (6, 8), (17, 5), (33, 24), (8, 41), (32, 16), (2, 0), (32, 11), (26, 31), (8, 3), (33, 21), (8, 0), (30, 36), (16, 18), (37, 37), (20, 23), (38, 15), (37, 12), (7, 39), (3, 7), (29, 46), (14, 45), (25, 12), (12, 39), (3, 2), (25, 44), (16, 10), (39, 6), (22, 9), (44, 33), (35, 12), (16, 19), (41, 14), (23, 31), (26, 28), (26, 23), (14, 17), (21, 27), (29, 14), (8, 32), (21, 4), (6, 40), (9, 46), (39, 44), (27, 8), (40, 41), (37, 11), (5, 17), (39, 1), (29, 4), (39, 0), (14, 39), (2, 39), (30, 17), (33, 39), (13, 19), (10, 31), (11, 26), (16, 31), (26, 12), (17, 11), (27, 0), (12, 21), (12, 35), (9, 15), (2, 43), (15, 15), (2, 34), (40, 45), (2, 30), (18, 44), (16, 43), (41, 26), (45, 8), (36, 25), (37, 17), (27, 19), (7, 15), (26, 27), (40, 17), (20, 9), (30, 39), (21, 11), (42, 17), (44, 22), (14, 7), (38, 23), (13, 13), (2, 31), (38, 6), (30, 13), (22, 30), (9, 4), (42, 27), (4, 19), (45, 28), (4, 32), (45, 46), (13, 30), (22, 32), (29, 28), (44, 35), (23, 13), (18, 33), (35, 32), (5, 16), (8, 16), (40, 31), (42, 8), (39, 40), (20, 39), (42, 13), (28, 15), (33, 17), (12, 1), (24, 39), (27, 24), (11, 2), (27, 41), (45, 29), (42, 4), (25, 7), (9, 2), (4, 28), (34, 18), (41, 21), (31, 37), (6, 13), (6, 18), (33, 46), (16, 24), (46, 21), (9, 29), (7, 0), (3, 25), (39, 14), (30, 32), (45, 11), (15, 30), (26, 30), (36, 18), (39, 30), (16, 0), (6, 29), (12, 27), (4, 18), (4, 43), (7, 30), (38, 20), (11, 33), (20, 6), (10, 44), (17, 27), (17, 36), (18, 6), (35, 37), (4, 36), (45, 37), (31, 17), (16, 17), (10, 10), (36, 32), (7, 41), (26, 45), (17, 1), (29, 13), (46, 18), (17, 28), (15, 2), (2, 45), (33, 43), (20, 11), (19, 1), (10, 7), (25, 32), (40, 28), (37, 6), (29, 22), (19, 29), (26, 32), (22, 39), (26, 35), (34, 36), (13, 17), (6, 4), (2, 11), (46, 32), (13, 37), (6, 25), (2, 26), (41, 12), (15, 7), (17, 23), (16, 16), (20, 42), (30, 40), (33, 22), (8, 28), (5, 10), (34, 23), (29, 31), (17, 46), (30, 45), (33, 14), (20, 28), (1, 4), (23, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (46, 21), (44, 12), (8, 22), (14, 6), (28, 35), (33, 24), (25, 30), (35, 31), (30, 33), (2, 17), (3, 26), (16, 42), (29, 23), (8, 3), (32, 23), (8, 26), (0, 11), (41, 2), (6, 21), (15, 7), (22, 24), (22, 7), (22, 15), (45, 42), (39, 17), (28, 18), (23, 19), (12, 41), (21, 13), (16, 35), (8, 14), (26, 22), (46, 16), (15, 33), (10, 28), (45, 26), (41, 9), (11, 37), (14, 10), (26, 4), (41, 28), (4, 34), (42, 39), (15, 23), (40, 27), (21, 8), (15, 25), (21, 33), (5, 29), (2, 39), (22, 8), (34, 39), (29, 33), (46, 2), (3, 9), (36, 30), (11, 27), (27, 35), (27, 38), (21, 20), (42, 25), (12, 37), (8, 24), (25, 6), (1, 21), (15, 14), (42, 1), (34, 26), (35, 27), (43, 8), (20, 23), (27, 8), (22, 20), (11, 35), (18, 13), (39, 33), (13, 36), (36, 14), (28, 15), (22, 10), (45, 30), (35, 42), (31, 22), (17, 12), (33, 40), (3, 32), (14, 19), (19, 42), (20, 8), (25, 29), (17, 9), (19, 12), (24, 4), (14, 16), (47, 18), (33, 20), (36, 21), (40, 31), (17, 41), (6, 34), (20, 16), (35, 30), (25, 18), (40, 6), (38, 33), (28, 38), (21, 28), (15, 36), (47, 22), (8, 38), (27, 36), (8, 35), (41, 29), (13, 15), (21, 4), (3, 34), (18, 8), (12, 26), (36, 11), (40, 21), (16, 17), (34, 24), (12, 6), (7, 7), (32, 0), (37, 24), (15, 37), (47, 33), (39, 21), (10, 13), (29, 16), (2, 34), (24, 40), (11, 18), (6, 41), (1, 19), (23, 18), (44, 30), (43, 9), (17, 30), (16, 12), (14, 13), (32, 17), (36, 24), (42, 12), (13, 40), (17, 24), (37, 25), (29, 22), (43, 11), (6, 8), (26, 5), (0, 8), (7, 19), (27, 25), (23, 20), (5, 18), (12, 5), (21, 37), (17, 25), (43, 1), (10, 41), (26, 19), (13, 7), (3, 16), (2, 0), (20, 1), (33, 10), (42, 37), (22, 21), (11, 33), (27, 20), (4, 18), (43, 42), (34, 32), (45, 13), (20, 17), (31, 34), (44, 23), (17, 27), (13, 37), (7, 8), (34, 5), (36, 20), (30, 41), (15, 30), (32, 21), (30, 3), (16, 24), (21, 39), (28, 2), (0, 30), (29, 1), (20, 35), (45, 34), (8, 4), (0, 6), (45, 29), (29, 34), (28, 9), (40, 23), (8, 18), (27, 28), (35, 20), (14, 36), (40, 5), (27, 0), (36, 32), (27, 37), (35, 26), (16, 34), (9, 12), (4, 38), (37, 12), (47, 24), (31, 10), (3, 13), (13, 34), (20, 21), (35, 16), (35, 41), (0, 42), (43, 29), (37, 8), (22, 31), (18, 33), (16, 11), (23, 24), (2, 22), (0, 14), (25, 5), (19, 22), (10, 12), (21, 3), (43, 36), (42, 27), (20, 6), (36, 2), (10, 29), (26, 21), (28, 27), (9, 4), (11, 28), (37, 33), (35, 12), (4, 20), (45, 36), (1, 30), (44, 33), (23, 31), (5, 19), (45, 22), (25, 13), (39, 2), (2, 20), (29, 39), (7, 38), (33, 27), (12, 38), (45, 6), (31, 0), (31, 26), (2, 3), (22, 9), (47, 12), (5, 17), (42, 30), (6, 22), (17, 22), (18, 7), (14, 2), (38, 4), (23, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (47, 18), (42, 16), (10, 23), (7, 18), (44, 41), (35, 20), (27, 26), (11, 24), (3, 35), (35, 39), (26, 13), (32, 32), (25, 37), (19, 24), (14, 18), (12, 30), (39, 37), (41, 16), (26, 44), (21, 3), (41, 14), (7, 33), (48, 42), (28, 45), (10, 18), (23, 23), (17, 27), (2, 20), (22, 12), (34, 30), (29, 45), (39, 30), (18, 2), (42, 17), (33, 39), (10, 31), (2, 24), (16, 24), (8, 5), (24, 23), (40, 33), (36, 10), (43, 13), (42, 46), (29, 8), (15, 24), (28, 43), (34, 42), (33, 25), (40, 43), (7, 20), (29, 5), (44, 48), (24, 38), (23, 40), (6, 13), (7, 5), (6, 7), (22, 17), (3, 17), (44, 5), (18, 23), (7, 46), (32, 33), (23, 13), (48, 31), (27, 44), (22, 38), (0, 7), (12, 20), (0, 11), (0, 27), (23, 14), (25, 39), (44, 25), (9, 46), (19, 1), (8, 15), (32, 4), (20, 6), (4, 43), (34, 18), (39, 26), (4, 33), (17, 6), (48, 17), (31, 2), (5, 33), (9, 19), (33, 43), (19, 34), (18, 11), (32, 29), (41, 21), (1, 31), (23, 3), (18, 35), (18, 44), (13, 28), (22, 29), (10, 41), (8, 26), (25, 26), (29, 42), (25, 19), (9, 0), (18, 27), (43, 40), (26, 6), (17, 43), (13, 41), (21, 48), (5, 35), (18, 21), (46, 36), (29, 10), (39, 31), (46, 32), (27, 39), (34, 5), (12, 23), (11, 19), (10, 32), (29, 35), (13, 25), (48, 15), (25, 3), (15, 21), (19, 42), (28, 8), (3, 38), (40, 39), (37, 48), (28, 21), (3, 45), (41, 40), (6, 35), (33, 34), (21, 15), (27, 38), (24, 11), (33, 4), (29, 21), (25, 12), (33, 40), (29, 13), (0, 10), (5, 26), (23, 47), (34, 31), (33, 42), (41, 3), (30, 12), (10, 16), (16, 6), (23, 31), (10, 26), (42, 20), (7, 35), (18, 48), (14, 34), (5, 32), (19, 35), (9, 45), (36, 12), (38, 11), (48, 37), (15, 5), (46, 8), (1, 0), (45, 3), (36, 35), (41, 28), (0, 14), (13, 18), (18, 19), (20, 31), (20, 22), (47, 13), (13, 2), (12, 14), (46, 23), (34, 0), (13, 6), (8, 8), (6, 18), (21, 37), (43, 42), (2, 25), (19, 14), (22, 22), (10, 10), (22, 5), (7, 28), (3, 46), (23, 26), (33, 29), (5, 8), (34, 36), (30, 17), (46, 39), (8, 1), (0, 38), (31, 7), (20, 0), (19, 38), (36, 45), (33, 35), (38, 14), (46, 45), (5, 3), (31, 13), (1, 23), (33, 46), (3, 7), (40, 36), (40, 23), (7, 22), (32, 47), (15, 19), (3, 24), (10, 38), (18, 30), (17, 41), (12, 34), (2, 10), (30, 28), (1, 15), (43, 11), (32, 39), (37, 0), (1, 17), (26, 48), (14, 11), (21, 46), (28, 15), (14, 2), (23, 46), (18, 46), (44, 30), (2, 16), (38, 33), (12, 21), (40, 42), (25, 24), (43, 32), (39, 28), (42, 13), (4, 19), (3, 14), (21, 32), (4, 36), (9, 41), (45, 27), (27, 15), (10, 0), (18, 34), (6, 33), (15, 32), (43, 5), (14, 30), (31, 15), (18, 41), (36, 1), (34, 16), (41, 26), (32, 7), (24, 45), (31, 1), (37, 35), (26, 12), (23, 10), (29, 28), (36, 13), (12, 28), (32, 2), (35, 41), (16, 13), (18, 4), (48, 32), (7, 13), (20, 47), (42, 14), (34, 12), (35, 4), (45, 15), (37, 1), (44, 19), (31, 23), (36, 44), (33, 15), (25, 5), (37, 4), (32, 30), (3, 33), (21, 1), (35, 28), (23, 48), (31, 41), (7, 37), (46, 0), (3, 32), (11, 6), (26, 16), (16, 40), (18, 25), (32, 27), (47, 31), (30, 9), (24, 18), (24, 8), (48, 46), (4, 20), (42, 36), (1, 34), (18, 15), (9, 22), (13, 9), (31, 11), (27, 42), (17, 3), (32, 16), (29, 7), (15, 6), (34, 23), (34, 11), (17, 11), (48, 44), (16, 5), (48, 12), (30, 34), (29, 1), (6, 20), (15, 9), (31, 12), (40, 48), (29, 46), (6, 4), (40, 2), (6, 21), (4, 18), (37, 43), (21, 29), (43, 33), (37, 12), (24, 21), (42, 31), (30, 3), (39, 46), (29, 14), (24, 40), (43, 24), (2, 5), (25, 15), (42, 3), (15, 46), (29, 17), (18, 26), (25, 9), (39, 18), (34, 32), (29, 36), (3, 26), (43, 20), (4, 32), (11, 43), (10, 45), (48, 3), (35, 23), (31, 3), (45, 45), (17, 29), (0, 9), (10, 28), (32, 31), (1, 9), (10, 48), (40, 20), (16, 19), (3, 5), (14, 31), (38, 0), (39, 33), (37, 14), (19, 6), (37, 32), (48, 14), (46, 46), (17, 25), (17, 31), (2, 21), (6, 25), (45, 32), (48, 7), (8, 21), (28, 25), (3, 40), (11, 37), (32, 23), (16, 39), (34, 3), (45, 31), (40, 35), (46, 48), (15, 34), (26, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 38), (38, 31), (37, 26), (35, 3), (1, 35), (4, 44), (29, 18), (18, 21), (3, 32), (18, 30), (39, 40), (26, 22), (27, 21), (38, 14), (3, 10), (26, 41), (24, 31), (0, 15), (8, 44), (42, 36), (26, 7), (35, 44), (38, 30), (31, 13), (14, 27), (31, 18), (11, 17), (32, 16), (1, 14), (41, 29), (40, 20), (29, 26), (30, 29), (17, 14), (17, 16), (3, 24), (42, 17), (29, 45), (3, 1), (36, 30), (27, 31), (16, 42), (3, 19), (20, 22), (12, 23), (9, 6), (14, 44), (40, 45), (16, 30), (28, 20), (20, 10), (5, 1), (0, 42), (28, 37), (27, 8), (27, 1), (32, 44), (26, 43), (5, 29), (27, 44), (8, 22), (3, 28), (20, 40), (38, 37), (19, 13), (29, 44), (4, 11), (19, 14), (38, 41), (12, 35), (7, 24), (3, 12), (32, 38), (36, 19), (39, 31), (39, 42), (16, 12), (17, 22), (1, 31), (38, 35), (37, 2), (28, 16), (26, 25), (14, 7), (11, 23), (30, 28), (41, 45), (21, 21), (37, 0), (1, 34), (37, 3), (26, 39), (45, 18), (25, 0), (16, 35), (13, 17), (40, 36), (17, 12), (27, 45), (18, 12), (24, 1), (33, 32), (18, 18), (38, 18), (1, 29), (37, 9), (20, 7), (21, 11), (19, 21), (42, 44), (44, 39), (38, 27), (23, 14), (13, 13), (28, 10), (13, 45), (11, 3), (13, 36), (41, 12), (2, 4), (13, 26), (24, 17), (32, 28), (18, 3), (24, 44), (43, 3), (16, 23), (7, 35), (38, 40), (18, 28), (32, 18), (44, 25), (35, 12), (37, 19), (33, 20), (15, 24), (9, 38), (40, 16), (7, 2), (0, 35), (12, 0), (24, 28), (12, 34), (26, 37), (39, 1), (25, 39), (14, 35), (30, 3), (43, 16), (15, 7), (16, 10), (34, 27), (6, 43), (3, 9), (1, 26), (2, 44), (33, 18), (15, 15), (41, 37), (42, 38), (34, 15), (22, 10), (36, 20), (26, 38), (2, 17), (44, 35), (2, 18), (43, 15), (16, 9), (9, 12), (34, 17), (12, 33), (19, 45), (42, 20), (15, 40), (34, 23), (23, 17), (24, 32), (22, 26), (22, 25), (33, 22), (31, 22), (28, 17), (20, 21), (11, 22), (44, 33), (33, 45), (21, 15), (45, 30), (5, 30), (35, 40), (4, 19), (10, 42), (13, 2), (21, 16), (11, 45), (35, 25), (4, 10), (25, 11), (40, 44), (0, 5), (16, 15), (40, 3), (43, 24), (38, 25), (32, 27), (25, 19), (27, 34), (36, 44), (18, 36), (7, 20), (33, 0), (23, 33), (25, 38), (2, 19), (18, 10), (41, 17), (44, 28), (5, 35), (25, 34), (22, 40), (20, 15), (23, 1), (31, 34), (33, 29), (25, 17), (21, 41), (31, 6), (35, 21), (18, 9), (37, 43), (5, 0), (30, 18), (9, 27), (9, 43), (30, 8), (22, 32), (36, 13), (22, 35), (27, 9), (27, 10), (8, 28), (31, 30), (40, 11), (33, 15), (19, 36), (27, 20), (11, 12), (24, 33), (9, 40), (28, 19), (21, 44), (26, 30), (32, 8), (22, 24), (2, 37), (43, 31), (30, 2), (20, 5), (3, 25), (43, 5), (26, 18), (17, 4), (33, 9), (7, 5), (8, 33), (7, 7), (24, 24), (6, 4), (29, 12), (41, 25), (0, 45), (27, 17), (19, 41), (15, 4), (24, 40), (44, 3), (24, 3), (2, 0), (43, 44), (28, 8), (0, 4), (18, 19), (27, 29), (28, 2), (16, 3), (31, 45), (13, 9), (40, 32), (41, 16), (32, 9), (9, 29), (31, 28), (0, 32), (32, 0), (5, 33), (2, 40), (43, 32), (41, 13), (21, 25), (2, 16), (41, 42), (42, 12), (36, 39), (37, 14), (10, 17), (1, 1), (4, 26), (5, 39), (9, 30), (38, 22), (5, 22), (20, 23), (22, 33), (29, 40), (8, 35), (6, 38), (26, 0), (23, 36), (28, 45), (13, 34), (39, 2), (24, 25), (1, 27), (21, 9), (35, 41), (9, 13), (35, 6), (35, 10), (14, 14), (18, 7), (31, 37), (33, 37), (11, 39), (6, 15), (30, 20), (33, 30), (19, 33), (1, 0), (15, 2), (31, 23), (24, 45), (35, 1), (21, 43), (4, 12), (27, 39), (19, 17), (41, 23), (39, 8), (13, 11), (11, 35), (41, 7), (10, 3), (10, 15), (20, 33), (17, 41), (3, 26), (11, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 16), (41, 7), (1, 45), (40, 25), (5, 42), (28, 6), (19, 15), (41, 21), (47, 38), (29, 22), (37, 17), (27, 25), (37, 41), (39, 37), (38, 12), (5, 16), (26, 43), (38, 31), (26, 27), (6, 45), (4, 17), (2, 14), (4, 2), (47, 36), (18, 21), (15, 46), (3, 7), (1, 29), (10, 11), (16, 40), (14, 21), (3, 23), (30, 7), (14, 36), (23, 36), (17, 20), (11, 8), (44, 22), (39, 19), (35, 12), (11, 6), (28, 2), (20, 23), (29, 3), (20, 13), (6, 36), (40, 45), (21, 43), (10, 23), (37, 23), (8, 18), (9, 36), (33, 17), (36, 9), (17, 43), (22, 23), (16, 37), (20, 35), (37, 13), (42, 38), (18, 7), (38, 23), (33, 14), (1, 16), (23, 10), (17, 8), (38, 8), (8, 38), (29, 37), (34, 6), (7, 21), (3, 44), (18, 19), (10, 31), (37, 18), (40, 33), (36, 25), (9, 17), (45, 36), (13, 0), (13, 24), (47, 35), (22, 22), (39, 30), (3, 5), (28, 30), (18, 16), (11, 24), (16, 10), (32, 8), (12, 6), (32, 28), (17, 25), (34, 9), (42, 37), (12, 8), (17, 3), (17, 45), (18, 32), (21, 13), (24, 28), (1, 36), (46, 21), (8, 44), (19, 11), (35, 38), (3, 15), (43, 26), (10, 15), (41, 27), (46, 19), (33, 38), (2, 31), (9, 8), (3, 11), (9, 13), (7, 8), (44, 37), (40, 17), (4, 31), (29, 0), (20, 34), (1, 32), (41, 46), (24, 34), (1, 0), (29, 27), (28, 20), (8, 28), (34, 3), (40, 0), (16, 41), (25, 30), (43, 46), (32, 15), (5, 13), (38, 24), (18, 39), (14, 24), (43, 21), (37, 24), (20, 2), (12, 34), (19, 26), (32, 29), (46, 4), (12, 26), (28, 40), (2, 43), (38, 5), (31, 32), (19, 40), (12, 28), (36, 29), (3, 35), (38, 7), (1, 17), (40, 11), (38, 22), (47, 26), (25, 29), (1, 25), (44, 45), (38, 0), (39, 25), (7, 13), (21, 44), (30, 13), (23, 16), (42, 24), (6, 4), (33, 20), (10, 46), (1, 30), (31, 39), (13, 15), (7, 20), (26, 20), (24, 43), (25, 13), (29, 39), (16, 22), (46, 2), (29, 38), (22, 17), (0, 28), (42, 30), (46, 20), (16, 30), (23, 22), (10, 24), (1, 39), (37, 2), (4, 7), (38, 18), (38, 6), (44, 31), (35, 39), (0, 4), (34, 34), (41, 39), (23, 14), (20, 32), (19, 13), (16, 43), (13, 26), (5, 8), (35, 6), (9, 29), (37, 26), (31, 26), (4, 5), (5, 36), (23, 3), (28, 43), (23, 13), (20, 20), (4, 6), (11, 34), (9, 46), (11, 21), (35, 15), (8, 23), (18, 9), (20, 26), (36, 11), (24, 10), (21, 6), (26, 34), (38, 17), (41, 30), (46, 30), (39, 18), (2, 8), (37, 32), (18, 34), (12, 15), (26, 26), (2, 9), (21, 10), (11, 9), (20, 25), (30, 32), (16, 28), (45, 12), (35, 28), (34, 19), (4, 1), (5, 24), (24, 13), (40, 10), (35, 40), (45, 19), (31, 15), (19, 16), (11, 16), (42, 7), (41, 33), (28, 45), (43, 8), (13, 30), (44, 44), (18, 0), (6, 14), (36, 17), (28, 17), (20, 12), (17, 27), (35, 10), (0, 40), (36, 45), (8, 11), (9, 7), (37, 5), (42, 28), (18, 4), (32, 18), (38, 21), (32, 0), (21, 16), (23, 1), (29, 17), (14, 29), (8, 7), (25, 5), (45, 18), (17, 23), (13, 12), (42, 44), (17, 14), (22, 26), (23, 33), (0, 18), (44, 11), (7, 36), (34, 27), (9, 32), (9, 21), (27, 7), (45, 20), (16, 45), (12, 20), (34, 15), (38, 25), (30, 40), (40, 16), (3, 26), (25, 8), (20, 11), (0, 6), (42, 15), (26, 17), (8, 24), (24, 24), (18, 44), (22, 9), (33, 32), (44, 28), (0, 16), (3, 4), (43, 5), (14, 17), (8, 35), (46, 9), (31, 28), (45, 2), (32, 43), (27, 44), (28, 9), (7, 30), (31, 11), (15, 12), (22, 5), (38, 30), (19, 37), (27, 16), (43, 3), (34, 10), (27, 4), (46, 7), (8, 32), (47, 40), (43, 37), (41, 6), (42, 33), (47, 2), (23, 45), (0, 23), (19, 41), (4, 22), (10, 37), (31, 25), (46, 37), (16, 8), (17, 31), (3, 45), (22, 13), (40, 6), (39, 41), (31, 18), (29, 41), (11, 40), (14, 38), (9, 15), (36, 6), (40, 43), (41, 29), (23, 26), (30, 11), (0, 13), (24, 37), (24, 7), (5, 43), (20, 38), (6, 34), (19, 45), (8, 27), (16, 7), (28, 25), (3, 0), (42, 45), (25, 2), (40, 1), (46, 35), (36, 21), (32, 27), (26, 39), (20, 19), (22, 21), (30, 28), (7, 2), (24, 35), (36, 24), (5, 4), (14, 41), (8, 22), (26, 23), (35, 20), (27, 20), (38, 42), (22, 11), (37, 14), (47, 13), (25, 9), (0, 37), (30, 16), (0, 2), (12, 38), (25, 11), (37, 3), (30, 8), (38, 32), (41, 43), (11, 10), (3, 32), (37, 36), (21, 29), (40, 42), (9, 23), (15, 18), (7, 27), (3, 30), (46, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (31, 2), (28, 36), (25, 35), (33, 23), (16, 19), (22, 4), (37, 37), (1, 23), (27, 43), (13, 32), (8, 29), (28, 38), (17, 15), (18, 11), (40, 39), (35, 13), (13, 39), (30, 34), (3, 1), (6, 26), (27, 42), (16, 37), (33, 41), (34, 24), (3, 23), (10, 7), (2, 35), (22, 9), (27, 32), (12, 18), (13, 4), (8, 40), (16, 30), (26, 25), (23, 10), (35, 40), (11, 13), (20, 7), (15, 7), (39, 11), (13, 13), (18, 25), (14, 27), (38, 13), (25, 44), (41, 27), (13, 24), (14, 9), (34, 21), (9, 20), (27, 39), (11, 0), (42, 4), (23, 0), (23, 22), (32, 31), (1, 37), (41, 10), (39, 25), (38, 29), (26, 42), (22, 31), (4, 9), (36, 7), (28, 32), (7, 11), (31, 46), (40, 27), (32, 30), (33, 16), (15, 31), (36, 38), (36, 44), (2, 24), (40, 45), (8, 42), (1, 30), (0, 1), (34, 22), (33, 2), (17, 3), (37, 32), (28, 39), (10, 39), (14, 16), (33, 25), (42, 15), (9, 10), (32, 32), (8, 41), (37, 38), (14, 36), (41, 35), (37, 1), (22, 26), (3, 18), (36, 12), (38, 1), (17, 36), (25, 15), (29, 23), (22, 22), (40, 1), (35, 21), (25, 18), (34, 0), (42, 26), (33, 1), (10, 6), (1, 9), (12, 1), (23, 38), (38, 25), (3, 8), (11, 1), (28, 30), (35, 33), (6, 41), (4, 21), (4, 2), (15, 23), (27, 23), (23, 30), (30, 31), (23, 32), (1, 12), (18, 10), (41, 8), (22, 39), (35, 31), (34, 46), (36, 33), (11, 45), (32, 26), (18, 27), (6, 25), (8, 34), (8, 22), (27, 35), (30, 20), (12, 9), (19, 9), (40, 43), (38, 22), (10, 0), (41, 14), (26, 30), (37, 35), (19, 46), (19, 30), (22, 20), (12, 11), (42, 24), (0, 9), (39, 7), (21, 1), (1, 8), (9, 38), (42, 12), (36, 23), (35, 23), (41, 1), (14, 4), (1, 41), (32, 33), (16, 4), (17, 47), (8, 35), (5, 16), (27, 36), (15, 20), (7, 9), (6, 33), (12, 32), (3, 36), (29, 5), (26, 8), (25, 26), (16, 42), (37, 21), (3, 26), (2, 23), (2, 0), (9, 29), (38, 47), (22, 10), (40, 14), (30, 42), (18, 30), (27, 0), (42, 34), (34, 23), (20, 2), (4, 22), (30, 28), (21, 18), (6, 13), (30, 41), (22, 32), (26, 24), (36, 2), (17, 4), (32, 19), (2, 17), (3, 47), (30, 30), (27, 44), (20, 17), (30, 47), (31, 38), (20, 47), (42, 11), (41, 22), (4, 0), (15, 36), (20, 38), (17, 9), (20, 6), (42, 44), (22, 18), (38, 35), (37, 30), (37, 47), (37, 4), (36, 42), (22, 11), (25, 22), (12, 7), (18, 7), (39, 36), (28, 5), (27, 18), (23, 16), (28, 28), (25, 17), (28, 23), (6, 31), (39, 30), (2, 37), (32, 7), (42, 14), (33, 11), (16, 47), (12, 3), (5, 2), (38, 9), (33, 3), (29, 39), (13, 1), (15, 2), (21, 3), (0, 11), (24, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 0), (9, 26), (20, 14), (39, 36), (20, 30), (7, 24), (30, 19), (15, 39), (40, 3), (4, 22), (38, 6), (30, 38), (18, 3), (19, 38), (18, 36), (31, 32), (42, 29), (5, 24), (42, 38), (38, 3), (9, 24), (10, 11), (40, 20), (12, 22), (37, 38), (6, 21), (42, 14), (7, 18), (22, 12), (23, 8), (19, 2), (16, 21), (42, 12), (15, 2), (22, 21), (22, 9), (30, 30), (33, 9), (37, 22), (24, 15), (2, 39), (37, 32), (41, 22), (15, 17), (17, 35), (9, 31), (10, 36), (33, 12), (21, 33), (16, 15), (2, 23), (32, 39), (21, 30), (29, 37), (13, 24), (42, 28), (9, 35), (6, 23), (20, 23), (11, 3), (35, 0), (30, 0), (20, 19), (38, 29), (39, 3), (30, 10), (13, 4), (32, 21), (20, 4), (31, 36), (1, 31), (5, 8), (12, 23), (18, 34), (14, 23), (11, 29), (9, 19), (0, 12), (4, 19), (34, 27), (18, 25), (5, 11), (33, 28), (28, 25), (1, 6), (28, 27), (0, 1), (27, 1), (23, 33), (37, 19), (3, 8), (19, 17), (38, 17), (39, 17), (13, 8), (11, 13), (30, 23), (0, 35), (5, 4), (0, 22), (32, 15), (39, 28), (17, 3), (14, 33), (3, 19), (16, 33), (28, 10), (37, 21), (36, 1), (35, 34), (9, 27), (24, 36), (21, 8), (28, 15), (9, 14), (28, 0), (32, 10), (0, 39), (33, 38), (23, 37), (8, 21), (28, 3), (13, 0), (41, 18), (5, 2), (12, 39), (41, 29), (14, 13), (41, 3), (12, 27), (28, 19), (31, 37), (2, 7), (7, 14), (42, 3), (20, 33), (10, 30), (31, 31), (32, 28), (22, 34), (27, 33), (18, 6), (13, 26), (25, 39), (33, 39), (6, 27), (21, 39), (16, 28), (3, 25), (19, 19), (37, 39), (14, 17), (42, 7), (6, 1), (25, 17), (6, 14), (3, 11), (12, 24), (33, 11), (41, 28), (31, 8), (21, 20), (31, 16), (21, 15), (6, 20), (36, 10), (2, 2), (38, 7), (20, 9), (31, 29), (20, 10), (18, 11), (31, 22), (28, 4), (26, 24), (26, 36), (34, 33), (25, 12), (12, 15), (23, 29), (11, 0), (4, 8), (15, 21), (23, 12), (0, 26), (29, 7), (24, 27), (9, 8), (42, 26), (13, 3), (18, 26), (30, 17), (21, 19), (30, 6), (17, 23), (23, 6), (35, 6), (5, 20), (1, 33), (2, 27), (21, 7), (42, 9), (5, 32), (0, 18), (19, 20), (19, 4), (4, 25), (39, 7), (24, 14), (6, 8), (38, 30), (10, 14), (36, 11), (1, 18), (18, 38), (37, 17), (7, 17), (10, 22), (33, 31), (14, 2), (16, 19), (23, 7), (25, 22), (18, 37), (24, 20), (36, 0), (20, 24), (13, 27), (15, 7), (7, 20), (2, 1), (18, 24), (4, 21), (25, 34), (42, 22), (15, 14), (26, 34), (12, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 26), (38, 34), (8, 0), (12, 37), (27, 29), (38, 21), (31, 43), (19, 28), (12, 27), (16, 32), (42, 23), (35, 25), (32, 34), (41, 2), (19, 12), (34, 33), (20, 24), (6, 42), (29, 41), (14, 18), (19, 8), (41, 37), (34, 9), (39, 26), (38, 8), (0, 19), (27, 26), (15, 4), (32, 38), (13, 32), (27, 44), (5, 36), (16, 31), (26, 44), (34, 36), (29, 30), (3, 18), (4, 32), (41, 40), (25, 35), (10, 28), (24, 44), (41, 19), (19, 19), (42, 40), (33, 36), (22, 38), (6, 36), (16, 27), (40, 42), (3, 29), (40, 16), (14, 28), (23, 6), (15, 35), (22, 1), (23, 23), (38, 17), (8, 17), (42, 22), (13, 36), (40, 35), (9, 23), (8, 6), (6, 1), (1, 46), (27, 11), (13, 21), (30, 31), (25, 1), (32, 0), (2, 3), (34, 32), (24, 37), (33, 6), (41, 9), (5, 35), (18, 42), (29, 23), (25, 18), (20, 35), (11, 19), (29, 13), (8, 27), (1, 28), (26, 32), (9, 29), (32, 32), (34, 2), (19, 22), (2, 9), (22, 45), (21, 20), (41, 17), (0, 23), (4, 17), (7, 16), (28, 32), (40, 37), (19, 36), (29, 2), (13, 31), (41, 1), (6, 14), (38, 40), (16, 30), (41, 38), (31, 1), (40, 24), (32, 11), (0, 43), (40, 19), (23, 1), (18, 10), (39, 38), (30, 7), (30, 11), (4, 45), (35, 2), (1, 38), (2, 39), (10, 25), (11, 39), (2, 11), (30, 13), (12, 21), (39, 31), (27, 24), (10, 34), (0, 32), (28, 4), (42, 1), (38, 25), (38, 20), (9, 41), (22, 19), (29, 17), (11, 45), (16, 38), (19, 41), (17, 7), (38, 27), (40, 26), (5, 13), (20, 27), (39, 43), (28, 16), (13, 2), (25, 5), (2, 29), (29, 43), (39, 25), (6, 28), (32, 33), (24, 30), (14, 26), (12, 38), (6, 35), (4, 40), (38, 4), (2, 2), (34, 8), (1, 34), (2, 43), (15, 44), (30, 2), (3, 27), (27, 0), (1, 43), (30, 17), (41, 10), (35, 29), (31, 27), (0, 6), (16, 0), (2, 33), (32, 46), (11, 44), (10, 7), (30, 46), (7, 30), (24, 39), (3, 7), (22, 37), (34, 35), (29, 8), (31, 19), (37, 31), (20, 12), (19, 2), (26, 13), (32, 24), (23, 35), (14, 5), (13, 7), (8, 26), (37, 38), (36, 1), (33, 12), (23, 13), (29, 33), (28, 34), (0, 1), (10, 26), (8, 39), (25, 12), (26, 35), (8, 21), (1, 8), (18, 34), (29, 39), (22, 36), (19, 26), (12, 23), (22, 24), (0, 31), (33, 22), (25, 14), (12, 26), (9, 13), (13, 19), (42, 44), (22, 43), (24, 33), (5, 27), (25, 40), (34, 15), (12, 39), (42, 38), (13, 30), (21, 43), (3, 9), (25, 44), (20, 43), (11, 46), (18, 1), (40, 11), (3, 40), (14, 19), (18, 29), (42, 45), (7, 26), (12, 10), (38, 13), (6, 12), (17, 21), (26, 34), (11, 13), (22, 15), (31, 32), (12, 29), (2, 13), (38, 30), (31, 8), (28, 22), (34, 22), (12, 31), (26, 39), (10, 4), (37, 14), (16, 13), (33, 28), (23, 24), (11, 20), (22, 9), (26, 2), (4, 42), (37, 19), (24, 19), (7, 42), (11, 1), (29, 34), (20, 32), (9, 19), (2, 36), (9, 40), (21, 5), (38, 18), (25, 6), (28, 11), (26, 7), (30, 18), (40, 27), (33, 25), (19, 6), (38, 1), (8, 38), (6, 4), (35, 45), (4, 1), (11, 23), (27, 5), (41, 31), (8, 15), (33, 45), (8, 10), (19, 42), (16, 10), (33, 0), (31, 12), (18, 15), (36, 43), (23, 0), (6, 24), (31, 2), (5, 3), (22, 2), (11, 11), (15, 0), (29, 26), (37, 24), (30, 10), (10, 46), (12, 5), (40, 7), (27, 39), (3, 13), (14, 12), (6, 32), (37, 12), (21, 15), (32, 30), (1, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 15), (12, 42), (31, 45), (20, 28), (38, 39), (5, 3), (2, 38), (26, 10), (9, 45), (13, 41), (5, 5), (18, 7), (11, 31), (20, 33), (28, 26), (18, 0), (8, 20), (19, 30), (15, 44), (25, 31), (34, 38), (25, 24), (33, 29), (30, 30), (4, 23), (30, 33), (28, 14), (0, 33), (18, 10), (14, 42), (14, 32), (11, 5), (38, 36), (20, 0), (30, 28), (25, 39), (15, 37), (1, 9), (15, 7), (18, 3), (37, 16), (16, 18), (19, 39), (37, 39), (32, 30), (32, 1), (10, 45), (20, 43), (30, 43), (0, 41), (30, 3), (31, 26), (10, 21), (36, 35), (3, 9), (3, 34), (27, 20), (20, 13), (29, 14), (21, 15), (32, 7), (4, 8), (15, 22), (39, 10), (5, 36), (9, 30), (29, 26), (11, 7), (11, 37), (35, 41), (30, 35), (38, 11), (22, 11), (11, 28), (13, 30), (37, 9), (17, 13), (24, 12), (31, 28), (25, 20), (13, 21), (7, 25), (33, 26), (1, 36), (2, 14), (1, 38), (36, 34), (29, 18), (20, 10), (6, 43), (23, 20), (11, 33), (18, 9), (30, 44), (36, 13), (36, 4), (8, 42), (29, 24), (13, 8), (25, 33), (2, 25), (28, 5), (14, 19), (35, 0), (35, 25), (9, 38), (7, 18), (8, 25), (33, 19), (4, 1), (7, 28), (29, 11), (37, 4), (33, 31), (3, 2), (38, 3), (6, 16), (19, 10), (38, 25), (35, 7), (1, 34), (27, 7), (15, 30), (32, 14), (31, 27), (14, 25), (22, 34), (18, 20), (8, 22), (39, 30), (38, 22), (6, 22), (22, 45), (25, 16), (39, 23), (28, 28), (39, 25), (3, 16), (11, 2), (31, 0), (16, 19), (18, 35), (15, 18), (16, 25), (23, 7), (10, 33), (17, 36), (17, 17), (7, 35), (39, 40), (13, 42), (12, 39), (30, 23), (8, 18), (3, 30), (8, 14), (1, 33), (32, 13), (25, 14), (33, 23), (9, 24), (17, 24), (29, 21), (6, 44), (14, 30), (30, 32), (37, 12), (27, 15), (38, 5), (30, 29), (15, 29), (8, 26), (13, 39), (21, 5), (0, 4), (3, 24), (18, 38), (7, 17), (4, 28), (5, 26), (27, 11), (31, 29), (24, 8), (39, 37), (34, 32), (35, 10), (17, 27), (30, 4), (10, 16), (4, 42), (25, 36), (21, 34), (9, 35), (17, 5), (6, 13), (34, 43), (36, 12), (2, 32), (17, 42), (1, 31), (35, 1), (24, 10), (11, 39), (25, 13), (6, 0), (29, 16), (2, 24), (25, 43), (3, 31), (4, 2), (39, 8), (10, 30), (24, 39), (13, 11), (0, 6), (37, 33), (20, 44), (30, 45), (20, 42), (38, 29), (26, 17), (9, 40), (0, 45), (29, 39), (24, 5), (9, 33), (3, 27), (29, 17), (11, 15), (4, 7), (10, 25), (2, 40), (20, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 16), (12, 4), (33, 5), (5, 25), (10, 25), (5, 18), (18, 0), (7, 32), (37, 5), (37, 25), (13, 22), (24, 34), (39, 48), (40, 32), (14, 25), (4, 43), (14, 27), (15, 25), (11, 36), (11, 23), (16, 42), (31, 27), (31, 3), (40, 8), (13, 17), (26, 18), (29, 21), (32, 20), (24, 7), (39, 20), (16, 19), (5, 14), (26, 36), (1, 26), (22, 19), (10, 29), (29, 6), (12, 19), (13, 10), (22, 8), (32, 23), (30, 1), (39, 28), (12, 5), (18, 45), (29, 4), (2, 17), (24, 42), (6, 11), (36, 16), (14, 35), (1, 37), (8, 2), (38, 34), (12, 43), (9, 16), (25, 0), (37, 0), (22, 29), (13, 5), (24, 45), (40, 29), (12, 23), (35, 0), (32, 18), (1, 12), (7, 46), (37, 10), (20, 9), (30, 38), (28, 48), (11, 16), (33, 10), (35, 36), (35, 42), (26, 11), (4, 42), (41, 23), (25, 18), (26, 48), (0, 15), (41, 13), (25, 3), (7, 44), (19, 45), (6, 41), (11, 14), (22, 28), (7, 7), (40, 40), (32, 11), (3, 29), (12, 21), (32, 12), (15, 3), (23, 40), (3, 32), (41, 2), (30, 2), (1, 27), (33, 40), (2, 38), (6, 13), (38, 36), (13, 9), (7, 9), (2, 13), (6, 14), (33, 3), (11, 20), (30, 18), (15, 29), (27, 1), (16, 20), (5, 1), (33, 19), (3, 17), (4, 12), (25, 14), (9, 17), (14, 31), (20, 0), (20, 16), (3, 5), (14, 15), (38, 4), (33, 29), (3, 31), (27, 12), (22, 47), (13, 43), (40, 20), (20, 45), (17, 22), (41, 22), (2, 46), (23, 47), (33, 33), (19, 37), (9, 2), (41, 25), (40, 41), (23, 33), (40, 46), (24, 26), (35, 31), (41, 6), (0, 4), (31, 17), (0, 30), (11, 9), (24, 24), (5, 41), (39, 36), (16, 43), (25, 20), (37, 44), (0, 5), (6, 26), (9, 29), (22, 24), (27, 18), (8, 38), (14, 29), (22, 7), (41, 11), (22, 14), (15, 2), (7, 8), (39, 40), (30, 44), (34, 17), (1, 39), (17, 4), (14, 1), (19, 41), (33, 35), (31, 33), (1, 24), (35, 4), (27, 2), (11, 37), (36, 33), (29, 5), (41, 29), (29, 3), (15, 48), (2, 10), (0, 2), (25, 47), (4, 11), (10, 32), (9, 44), (28, 23), (3, 23), (22, 42), (8, 40), (32, 31), (24, 29), (33, 27), (13, 39), (36, 12), (0, 14), (41, 21), (14, 17), (32, 40), (18, 29), (22, 32), (8, 14), (32, 47), (6, 38), (20, 22), (36, 23), (22, 37), (39, 37), (3, 34), (11, 2), (2, 7), (22, 34), (4, 3), (32, 15), (15, 40), (5, 31), (35, 48), (19, 2), (23, 18), (39, 15), (24, 33), (13, 48), (3, 22), (19, 14), (29, 26), (38, 46), (12, 18), (39, 44), (2, 43), (37, 20), (16, 4), (28, 16), (11, 13), (27, 47), (35, 47), (19, 25), (27, 23), (6, 10), (1, 2), (34, 36), (19, 32), (8, 33), (6, 39), (23, 41), (37, 12), (18, 17), (18, 32), (18, 38), (5, 21), (39, 10), (20, 46), (8, 7), (27, 30), (29, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 40), (45, 39), (5, 22), (0, 40), (40, 27), (24, 25), (1, 14), (33, 27), (29, 9), (26, 23), (3, 30), (15, 12), (1, 29), (47, 3), (38, 5), (14, 26), (16, 19), (24, 42), (11, 11), (0, 34), (45, 41), (35, 16), (29, 5), (39, 27), (6, 24), (3, 39), (45, 25), (22, 7), (17, 26), (32, 0), (1, 42), (41, 36), (15, 21), (10, 13), (46, 14), (8, 36), (12, 6), (43, 30), (28, 30), (14, 12), (19, 28), (18, 10), (41, 27), (9, 1), (18, 20), (38, 6), (41, 42), (3, 17), (5, 3), (1, 4), (44, 12), (30, 3), (25, 35), (1, 13), (43, 19), (17, 41), (28, 20), (7, 7), (18, 0), (17, 34), (12, 23), (17, 19), (21, 41), (2, 10), (39, 29), (21, 26), (46, 3), (35, 13), (39, 37), (38, 1), (29, 4), (46, 42), (26, 36), (3, 35), (11, 3), (39, 13), (0, 29), (42, 5), (12, 38), (28, 15), (46, 5), (40, 40), (22, 12), (26, 6), (29, 7), (5, 40), (34, 0), (8, 33), (14, 6), (25, 6), (45, 20), (15, 18), (28, 8), (31, 15), (48, 19), (27, 40), (45, 10), (30, 30), (25, 10), (42, 37), (1, 17), (38, 0), (25, 22), (0, 33), (11, 20), (46, 7), (39, 1), (13, 11), (36, 7), (7, 30), (5, 36), (42, 23), (30, 33), (18, 4), (12, 37), (34, 31), (12, 13), (16, 37), (18, 18), (43, 6), (1, 2), (8, 38), (26, 21), (0, 11), (46, 24), (4, 16), (43, 3), (29, 36), (14, 28), (12, 20), (1, 3), (7, 26), (21, 23), (44, 37), (43, 23), (12, 5), (16, 36), (43, 41), (8, 12), (27, 23), (16, 24), (45, 4), (32, 33), (34, 41), (41, 23), (37, 42), (36, 32), (29, 27), (8, 16), (10, 25), (44, 5), (13, 22), (7, 22), (23, 21), (45, 3), (47, 30), (41, 2), (22, 16), (28, 12), (10, 36), (43, 13), (22, 41), (28, 34), (9, 4), (24, 31), (4, 0), (13, 3), (28, 6), (14, 35), (30, 28), (17, 21), (11, 41), (45, 1), (10, 15), (31, 10), (12, 3), (25, 39), (6, 11), (20, 39), (48, 18), (31, 31), (0, 32), (34, 42), (28, 11), (7, 8), (13, 40), (32, 23), (23, 42), (34, 39), (18, 9), (5, 1), (14, 5), (41, 8), (1, 16), (8, 22), (29, 33), (42, 22), (7, 38), (21, 13), (20, 3), (48, 31), (16, 21), (45, 12), (41, 33), (47, 24), (36, 1), (30, 27), (31, 26), (37, 24), (8, 32), (4, 13), (15, 37), (29, 42), (46, 12), (24, 23), (43, 25), (14, 18), (18, 3), (42, 1), (18, 24), (18, 13), (34, 5), (20, 9), (26, 35), (34, 7), (23, 39), (7, 14), (13, 23), (17, 11), (13, 15), (31, 14), (48, 5), (31, 24), (4, 22), (2, 9), (5, 30), (44, 33), (37, 32), (47, 28), (34, 28), (18, 14), (42, 30), (47, 7), (6, 26), (4, 24), (45, 19), (12, 25), (34, 18), (15, 19), (34, 20), (9, 33), (44, 8), (15, 27), (13, 32), (28, 41), (27, 4), (34, 36), (6, 23), (27, 22), (21, 14), (36, 24), (9, 16), (39, 7), (10, 27), (27, 19), (42, 40), (21, 10), (31, 9), (38, 40), (12, 7), (25, 33), (44, 18), (18, 40), (12, 24), (1, 39), (8, 29), (25, 27), (27, 32), (10, 6), (20, 1), (12, 31), (25, 12), (2, 23), (30, 25), (7, 35), (30, 24), (13, 42), (35, 11), (22, 18), (3, 27), (28, 28), (41, 34), (21, 28), (43, 9), (24, 8), (7, 41), (16, 1), (26, 0), (28, 38), (2, 13), (34, 24), (3, 34), (38, 31), (16, 33), (18, 5), (6, 9), (4, 17), (5, 26), (29, 8), (31, 41), (8, 6), (30, 21), (45, 35), (5, 42), (40, 29), (31, 11), (42, 33), (41, 31), (7, 12), (10, 11), (29, 41), (35, 40), (17, 29), (32, 4), (46, 4), (18, 34), (16, 34), (0, 17), (23, 23), (21, 9), (25, 25), (21, 15), (39, 9), (18, 16), (29, 39), (2, 11), (29, 19), (3, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 32), (24, 40), (36, 35), (34, 4), (28, 10), (18, 47), (35, 30), (4, 26), (16, 23), (11, 26), (29, 15), (20, 44), (37, 38), (4, 16), (24, 10), (38, 11), (13, 40), (7, 7), (2, 37), (13, 14), (40, 0), (35, 34), (13, 42), (27, 3), (24, 8), (38, 28), (8, 36), (1, 1), (39, 23), (10, 16), (35, 37), (0, 3), (15, 0), (9, 16), (20, 21), (23, 30), (11, 44), (38, 37), (5, 31), (5, 10), (1, 37), (14, 27), (24, 41), (10, 23), (7, 15), (34, 47), (28, 8), (12, 6), (30, 2), (22, 39), (18, 31), (33, 6), (31, 23), (6, 38), (36, 26), (28, 37), (28, 30), (24, 30), (26, 36), (26, 6), (28, 22), (30, 10), (5, 9), (19, 3), (31, 6), (21, 17), (19, 4), (10, 10), (25, 46), (37, 3), (13, 22), (34, 28), (0, 37), (36, 17), (9, 27), (3, 9), (31, 26), (17, 47), (0, 36), (36, 30), (20, 1), (39, 24), (26, 20), (31, 17), (27, 35), (19, 23), (12, 11), (15, 47), (25, 13), (18, 45), (20, 0), (34, 13), (27, 5), (37, 39), (12, 12), (26, 19), (9, 2), (13, 10), (4, 35), (11, 34), (22, 45), (19, 30), (5, 13), (39, 39), (34, 29), (2, 42), (9, 18), (29, 36), (11, 3), (20, 6), (31, 25), (14, 37), (18, 26), (4, 1), (5, 40), (32, 26), (4, 39), (30, 38), (21, 35), (33, 24), (22, 17), (25, 23), (32, 25), (27, 7), (30, 13), (29, 26), (9, 46), (33, 23), (22, 27), (15, 42), (32, 10), (1, 28), (37, 7), (10, 2), (11, 39), (12, 0), (14, 16), (9, 10), (10, 13), (24, 4), (1, 47), (20, 8), (28, 2), (0, 14), (12, 18), (1, 3), (40, 41), (37, 13), (11, 20), (18, 38), (32, 27), (36, 40), (2, 9), (5, 47), (36, 15), (35, 2), (4, 21), (37, 26), (19, 37), (12, 32), (10, 21), (14, 18), (31, 14), (16, 43), (34, 18), (12, 29), (4, 22), (31, 15), (38, 15), (22, 46), (39, 26), (14, 6), (29, 46), (34, 8), (22, 34), (38, 44), (13, 6), (5, 28), (8, 46), (29, 45), (5, 36), (19, 40), (28, 25), (10, 30), (34, 15), (9, 30), (30, 11), (19, 11), (24, 6), (40, 29), (35, 38), (16, 24), (26, 25), (23, 31), (38, 5), (5, 43), (16, 47), (4, 42), (11, 29), (5, 41), (7, 21), (35, 27), (6, 25), (6, 11), (33, 29), (25, 47), (35, 12), (31, 3), (24, 47), (12, 27), (34, 37), (37, 25), (4, 8), (7, 42), (26, 27), (35, 7), (10, 46), (31, 4), (2, 6), (39, 25), (29, 14), (36, 28), (38, 43), (36, 3), (8, 35), (5, 42), (1, 36), (15, 22), (4, 11), (27, 45), (17, 33), (32, 40), (22, 3), (40, 11), (18, 17), (25, 31), (7, 33), (23, 18), (39, 4), (37, 18), (3, 14), (35, 41), (28, 12), (9, 39), (12, 30), (26, 26), (20, 43), (38, 38), (14, 32), (30, 18), (12, 5), (11, 7), (26, 8), (33, 9), (12, 4), (36, 36), (31, 19), (20, 42), (17, 20), (19, 29), (8, 47), (15, 21), (2, 43), (18, 20), (12, 42), (22, 2), (37, 45), (26, 37), (17, 19), (5, 32), (13, 34), (12, 46), (21, 20), (10, 12), (28, 13), (22, 36), (7, 45), (19, 25), (23, 19), (26, 39), (1, 30), (1, 17), (33, 27), (13, 44), (27, 29), (35, 0), (25, 35), (8, 28), (23, 40), (40, 9), (18, 11), (34, 35), (11, 33), (16, 33), (24, 32), (1, 5), (1, 38), (15, 30), (12, 15), (10, 35), (27, 2), (23, 12), (5, 1), (4, 47), (17, 40), (31, 38), (30, 8), (20, 16), (7, 3), (2, 44), (21, 25), (11, 17), (2, 38), (18, 19), (40, 43), (24, 26), (27, 42), (40, 32), (15, 44), (20, 19), (23, 20), (33, 34), (13, 30), (18, 10), (8, 39), (20, 30), (39, 1), (27, 34), (24, 9), (19, 12), (32, 36), (24, 0), (26, 31), (16, 28), (17, 27), (18, 2), (24, 31), (15, 46), (5, 15), (34, 5), (4, 2), (16, 2), (39, 27), (10, 5), (11, 43), (11, 4), (33, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 18), (34, 41), (8, 5), (12, 0), (21, 16), (20, 10), (27, 0), (34, 6), (7, 30), (9, 5), (39, 4), (42, 25), (31, 23), (20, 1), (24, 33), (39, 29), (1, 34), (24, 32), (39, 25), (0, 34), (44, 23), (38, 2), (36, 16), (39, 3), (7, 16), (28, 11), (26, 39), (5, 0), (1, 4), (25, 39), (32, 33), (22, 9), (42, 33), (35, 30), (28, 18), (36, 42), (21, 15), (18, 24), (2, 31), (40, 11), (18, 16), (20, 23), (23, 5), (13, 34), (20, 30), (28, 7), (14, 5), (0, 2), (3, 15), (1, 37), (11, 13), (9, 32), (44, 32), (28, 6), (14, 28), (40, 27), (13, 15), (3, 27), (31, 37), (2, 35), (19, 15), (7, 39), (17, 3), (23, 22), (40, 15), (7, 0), (3, 30), (42, 1), (2, 17), (29, 25), (0, 10), (31, 19), (12, 41), (41, 8), (4, 31), (30, 37), (28, 28), (11, 5), (41, 21), (13, 16), (8, 15), (0, 23), (39, 37), (27, 33), (34, 24), (18, 12), (16, 9), (34, 1), (41, 29), (0, 20), (43, 34), (42, 26), (10, 8), (12, 13), (12, 37), (43, 12), (34, 16), (9, 14), (28, 19), (35, 19), (37, 3), (42, 14), (44, 30), (18, 0), (23, 42), (31, 14), (13, 0), (16, 37), (18, 3), (30, 26), (4, 14), (3, 19), (36, 38), (26, 26), (7, 5), (22, 38), (14, 29), (16, 18), (32, 10), (4, 40), (44, 21), (20, 14), (34, 32), (39, 42), (9, 42), (41, 28), (31, 18), (15, 41), (19, 16), (19, 7), (13, 21), (1, 20), (25, 35), (18, 40), (14, 15), (26, 14), (34, 29), (38, 14), (18, 22), (5, 35), (19, 37), (5, 39), (6, 13), (40, 3), (13, 17), (17, 34), (19, 11), (18, 11), (33, 15), (1, 1), (26, 21), (9, 12), (15, 38), (34, 22), (36, 3), (16, 2), (42, 24), (26, 25), (31, 34), (39, 33), (3, 40), (7, 12), (2, 10), (4, 0), (21, 13), (21, 20), (25, 24), (30, 8), (25, 29), (36, 25), (30, 6), (29, 7), (8, 26), (37, 24), (11, 4), (13, 11), (1, 24), (28, 0), (19, 27), (38, 25), (31, 41), (19, 2), (15, 9), (25, 17), (15, 37), (35, 38), (33, 38), (43, 8), (41, 1), (2, 9), (33, 6), (15, 0), (22, 31), (43, 32), (26, 0), (5, 6), (44, 6), (32, 3), (39, 30), (40, 2), (10, 21), (22, 21), (35, 37), (33, 31), (33, 20), (27, 26), (14, 1), (15, 4), (18, 4), (38, 26), (30, 25), (28, 13), (14, 10), (37, 42), (25, 3), (20, 7), (15, 11), (24, 26), (13, 18), (11, 6), (15, 15), (12, 16), (25, 1), (6, 8), (31, 22), (24, 39), (11, 2), (8, 17), (23, 0), (1, 26), (23, 15), (28, 41), (29, 39), (18, 30), (34, 21), (5, 38), (37, 13), (38, 12), (36, 30), (39, 26), (25, 13), (2, 40), (22, 24), (12, 7), (38, 33), (33, 24), (41, 16), (2, 22), (29, 17), (5, 37), (17, 22), (12, 42), (42, 8), (40, 34), (9, 4), (30, 36), (6, 22), (20, 36), (21, 34), (27, 2), (8, 21), (28, 3), (25, 15), (36, 27), (8, 35), (41, 37), (8, 29), (28, 5), (36, 31), (9, 22), (33, 42), (14, 33), (19, 41), (21, 39), (4, 28), (27, 23), (11, 38), (7, 42), (30, 10), (15, 34), (1, 19), (43, 24), (7, 32), (13, 26), (27, 38), (16, 12), (41, 25), (14, 27), (19, 24), (20, 29), (21, 37), (11, 24), (1, 17), (25, 33), (9, 33), (30, 28), (25, 14), (13, 23), (21, 4), (14, 2), (9, 37), (36, 1), (38, 15), (35, 11), (30, 14), (16, 39), (26, 24), (26, 17), (24, 18), (1, 33), (3, 2), (0, 32), (16, 13), (3, 4), (8, 38), (28, 42), (22, 6), (44, 13), (8, 3), (28, 12), (1, 21), (24, 41), (37, 22), (23, 35), (11, 14), (19, 19), (15, 6), (11, 19), (44, 33), (32, 40), (44, 37), (3, 18), (28, 30), (23, 32), (29, 21), (30, 24), (43, 1), (15, 32), (10, 32), (14, 36), (35, 15), (11, 29), (33, 36), (10, 14), (32, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 43x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 7), (29, 10), (26, 12), (7, 17), (18, 34), (38, 25), (36, 26), (10, 11), (0, 4), (1, 35), (1, 10), (16, 14), (29, 14), (10, 25), (35, 1), (3, 41), (36, 8), (29, 3), (21, 21), (15, 11), (28, 13), (32, 17), (12, 33), (16, 3), (32, 42), (0, 45), (39, 2), (35, 30), (30, 43), (31, 19), (7, 6), (11, 41), (18, 36), (35, 36), (11, 0), (32, 25), (9, 5), (25, 9), (26, 35), (6, 0), (41, 3), (14, 15), (14, 10), (3, 31), (38, 0), (29, 5), (1, 37), (22, 20), (17, 9), (34, 10), (35, 0), (27, 15), (42, 26), (36, 17), (7, 20), (14, 30), (31, 10), (6, 24), (28, 27), (21, 30), (11, 4), (3, 10), (11, 26), (40, 36), (36, 32), (35, 16), (26, 7), (28, 20), (34, 28), (41, 32), (11, 19), (15, 21), (19, 27), (34, 2), (5, 19), (15, 33), (42, 0), (26, 19), (6, 1), (5, 43), (21, 14), (1, 8), (21, 24), (16, 22), (31, 39), (36, 12), (12, 39), (9, 36), (10, 17), (16, 33), (1, 12), (19, 4), (32, 40), (26, 40), (21, 35), (6, 37), (22, 22), (38, 4), (42, 32), (39, 19), (26, 0), (30, 37), (19, 6), (16, 13), (30, 12), (0, 6), (33, 16), (22, 36), (39, 29), (5, 3), (42, 17), (13, 31), (35, 29), (0, 12), (32, 14), (0, 17), (20, 20), (25, 19), (17, 14), (8, 7), (6, 34), (25, 33), (25, 37), (38, 18), (38, 19), (1, 16), (19, 14), (37, 24), (27, 6), (27, 40), (9, 12), (36, 0), (41, 25), (31, 23), (37, 3), (27, 41), (27, 30), (40, 15), (14, 44), (18, 15), (6, 6), (6, 2), (33, 18), (7, 41), (24, 2), (7, 30), (11, 17), (37, 23), (10, 36), (33, 26), (37, 5), (31, 22), (13, 40), (13, 9), (26, 20), (26, 4), (40, 0), (30, 3), (35, 13), (29, 45), (20, 23), (23, 7), (31, 18), (6, 16), (10, 8), (16, 1), (23, 44), (8, 19), (35, 45), (36, 30), (12, 40), (17, 27), (5, 2), (21, 44), (9, 16), (13, 24), (38, 26), (41, 40), (9, 2), (16, 9), (9, 14), (35, 33), (23, 38), (18, 11), (1, 42), (10, 45), (36, 15), (26, 29), (15, 2), (3, 28), (19, 45), (1, 39), (40, 26), (27, 10), (19, 16), (21, 20), (21, 27), (13, 33), (8, 9), (41, 41), (11, 34), (22, 5), (29, 30), (33, 41), (29, 20), (0, 23), (11, 24), (8, 23), (14, 41), (26, 44), (21, 18), (16, 7), (24, 19), (33, 2), (8, 26), (25, 4), (9, 44), (4, 19), (33, 13), (33, 40), (18, 18), (5, 20), (8, 42), (19, 2), (41, 16), (2, 0), (42, 38), (30, 39), (34, 44), (2, 40), (4, 33), (1, 22), (5, 8), (0, 18), (29, 11), (1, 17), (29, 39), (17, 8), (10, 38), (15, 26), (20, 44), (8, 0), (32, 13), (35, 8), (20, 28), (7, 12), (11, 9), (3, 33), (20, 6), (23, 26), (36, 22), (5, 35), (13, 7), (24, 33), (9, 21), (16, 19), (39, 24), (33, 23), (27, 22), (6, 41), (35, 44), (10, 6), (41, 1), (32, 32), (33, 45), (42, 39), (26, 22), (18, 37), (41, 8), (25, 38), (26, 17), (32, 6), (41, 28), (31, 1), (42, 3), (30, 20), (3, 19), (21, 29), (21, 23), (17, 26), (34, 26), (36, 2), (42, 15), (35, 22), (39, 3), (33, 10), (1, 15), (12, 7), (14, 1), (25, 11), (29, 38), (22, 25), (32, 19), (24, 23), (30, 15), (7, 19), (42, 27), (37, 41), (31, 7), (15, 45), (14, 39), (23, 3), (33, 22), (32, 37), (24, 28), (18, 39), (42, 24), (27, 28), (26, 42), (7, 45), (11, 10), (36, 11), (42, 20), (18, 44), (34, 37), (2, 33), (25, 40), (28, 10), (2, 41), (19, 13), (16, 44), (34, 33), (22, 26), (30, 11), (22, 7), (20, 10), (16, 26), (22, 8), (37, 11), (36, 29), (32, 28), (19, 29), (2, 1), (39, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 44), (13, 16), (0, 31), (19, 26), (25, 40), (35, 4), (27, 20), (22, 27), (15, 12), (6, 9), (7, 12), (20, 6), (14, 18), (15, 0), (24, 38), (36, 39), (32, 35), (23, 5), (6, 37), (23, 41), (43, 5), (13, 30), (20, 37), (27, 35), (38, 23), (43, 9), (16, 42), (21, 10), (1, 13), (23, 17), (3, 10), (29, 19), (37, 36), (6, 15), (28, 28), (19, 8), (22, 42), (29, 3), (9, 2), (5, 29), (16, 44), (42, 11), (2, 31), (43, 28), (31, 18), (33, 26), (38, 36), (12, 16), (29, 41), (24, 18), (20, 13), (41, 0), (32, 21), (12, 5), (14, 9), (30, 24), (4, 32), (10, 24), (12, 10), (14, 39), (16, 41), (37, 14), (9, 12), (17, 13), (23, 35), (41, 23), (27, 25), (0, 14), (36, 0), (7, 5), (18, 32), (39, 9), (43, 30), (37, 23), (24, 37), (3, 32), (5, 0), (30, 3), (27, 23), (43, 20), (23, 3), (40, 20), (31, 39), (37, 17), (36, 5), (0, 8), (22, 2), (33, 28), (15, 39), (6, 18), (29, 24), (41, 24), (11, 22), (42, 36), (3, 42), (31, 3), (9, 29), (24, 4), (41, 8), (7, 2), (22, 43), (42, 3), (3, 15), (40, 1), (5, 44), (11, 10), (8, 2), (33, 19), (26, 14), (39, 34), (29, 4), (13, 36), (24, 43), (6, 4), (16, 16), (5, 17), (21, 36), (18, 5), (38, 10), (9, 21), (32, 1), (8, 3), (32, 38), (13, 25), (28, 22), (14, 35), (32, 44), (13, 44), (34, 2), (43, 23), (4, 29), (27, 12), (23, 7), (1, 11), (8, 10), (7, 10), (21, 7), (14, 17), (38, 37), (17, 4), (22, 7), (25, 34), (42, 6), (4, 23), (27, 36), (24, 28), (17, 16), (2, 42), (33, 40), (18, 39), (8, 15), (8, 4), (32, 6), (18, 36), (15, 8), (35, 25), (26, 36), (18, 11), (36, 16), (12, 12), (37, 34), (36, 10), (0, 21), (20, 24), (21, 3), (0, 42), (41, 38), (14, 32), (43, 12), (16, 31), (20, 20), (43, 42), (25, 28), (10, 8), (37, 25), (12, 33), (24, 39), (30, 28), (37, 19), (18, 20), (20, 26), (40, 41), (27, 8), (30, 10), (2, 27), (36, 28), (44, 11), (27, 28), (16, 24), (36, 17), (31, 33), (35, 12), (0, 39), (32, 23), (16, 27), (30, 1), (24, 40), (6, 16), (1, 33), (7, 25), (28, 6), (21, 22), (0, 29), (19, 24), (32, 11), (32, 9), (7, 30), (43, 37), (26, 40), (37, 44), (22, 35), (20, 36), (3, 0), (13, 1), (28, 33), (16, 32), (29, 1), (31, 31), (4, 22), (19, 20), (0, 37), (42, 10), (26, 21), (14, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 28), (13, 21), (3, 35), (7, 33), (28, 31), (9, 32), (14, 36), (16, 29), (39, 28), (17, 22), (19, 2), (16, 12), (39, 26), (40, 7), (10, 26), (15, 8), (9, 39), (32, 15), (39, 21), (46, 21), (32, 39), (38, 6), (39, 37), (0, 10), (47, 13), (14, 31), (45, 36), (28, 17), (31, 5), (11, 39), (43, 12), (34, 39), (9, 4), (16, 19), (24, 33), (12, 23), (32, 7), (47, 19), (39, 39), (22, 7), (1, 11), (34, 10), (31, 3), (18, 30), (7, 24), (47, 30), (5, 26), (17, 38), (22, 21), (47, 24), (22, 12), (18, 39), (7, 5), (29, 19), (23, 12), (9, 38), (0, 24), (29, 21), (32, 30), (45, 30), (44, 7), (25, 13), (0, 15), (24, 27), (23, 13), (36, 2), (45, 22), (13, 36), (0, 31), (0, 13), (45, 39), (31, 22), (24, 0), (46, 37), (46, 29), (44, 10), (40, 3), (17, 10), (32, 0), (32, 25), (22, 19), (38, 10), (41, 26), (1, 25), (19, 9), (7, 38), (12, 30), (45, 29), (32, 11), (45, 38), (43, 36), (8, 0), (28, 15), (25, 3), (21, 18), (10, 38), (25, 27), (37, 9), (31, 26), (34, 27), (41, 32), (37, 36), (38, 15), (26, 8), (30, 35), (26, 37), (38, 37), (18, 32), (33, 24), (43, 23), (3, 10), (29, 24), (40, 6), (35, 9), (13, 28), (34, 21), (37, 18), (33, 21), (30, 16), (28, 14), (19, 20), (46, 5), (24, 8), (16, 16), (4, 34), (9, 37), (12, 27), (23, 36), (3, 37), (2, 15), (47, 16), (10, 39), (39, 38), (5, 35), (27, 5), (4, 32), (21, 15), (14, 21), (32, 24), (12, 0), (29, 10), (10, 3), (27, 11), (40, 1), (13, 35), (31, 8), (12, 5), (14, 17), (22, 27), (34, 31), (2, 10), (13, 20), (32, 4), (35, 26), (1, 2), (21, 29), (3, 17), (11, 29), (17, 29), (39, 30), (13, 32), (12, 31), (4, 12), (30, 25), (26, 33), (32, 28), (9, 23), (10, 10), (46, 24), (37, 38), (31, 34), (6, 31), (13, 12), (27, 9), (35, 21), (8, 25), (20, 14), (29, 33), (26, 18), (45, 25), (26, 22), (43, 13), (19, 13), (46, 34), (0, 22), (29, 6), (0, 19), (38, 26), (14, 3), (21, 28), (31, 7), (24, 32), (38, 17), (6, 39), (5, 20), (11, 15), (2, 0), (5, 16), (8, 15), (14, 19), (42, 10), (32, 13), (29, 32), (35, 1), (11, 1), (6, 1), (14, 28), (42, 17), (21, 1), (24, 15), (0, 8), (37, 23), (19, 29), (25, 39), (46, 4), (3, 14), (28, 9), (19, 0), (25, 12), (7, 21), (16, 3), (24, 4), (36, 31), (2, 4), (13, 9), (10, 22), (47, 34), (5, 28), (13, 29), (17, 14), (35, 10), (40, 5), (31, 19), (41, 23), (21, 33), (32, 34), (33, 2), (30, 37), (24, 22), (35, 13), (47, 14), (7, 3), (43, 27), (16, 10), (36, 32), (45, 11), (9, 16), (1, 24), (29, 4), (28, 27), (12, 7), (39, 9), (34, 30), (15, 33), (19, 31), (4, 33), (38, 39), (42, 37), (41, 17), (38, 5), (20, 22), (14, 35), (30, 30), (38, 33), (0, 2), (35, 33), (9, 26), (25, 35), (39, 20), (30, 2), (27, 4), (15, 13), (39, 7), (40, 17), (1, 9), (37, 32), (44, 35), (41, 8), (20, 28), (0, 39), (3, 26), (15, 9), (26, 10), (8, 39), (18, 36), (8, 5), (34, 17), (22, 24), (12, 17), (23, 8), (24, 30), (11, 35), (42, 31), (0, 3), (10, 30), (42, 36), (12, 12), (47, 1), (13, 38), (0, 23), (3, 12), (40, 29), (45, 9), (1, 3), (44, 27), (34, 1), (29, 31), (22, 16), (43, 9), (20, 31), (27, 13), (36, 5), (16, 39), (45, 5), (40, 34), (42, 29), (28, 16), (19, 30), (1, 30), (26, 27), (20, 1), (19, 35), (20, 34), (38, 2), (19, 39), (12, 21), (28, 11), (17, 21), (40, 15), (6, 13), (16, 34), (0, 30), (18, 24), (35, 19), (3, 31), (32, 21), (34, 19), (44, 31), (4, 14), (9, 18), (36, 37), (14, 15), (23, 23), (23, 3), (18, 16), (11, 20), (18, 1), (8, 29), (34, 7), (13, 6), (38, 25), (14, 18), (29, 9), (14, 24), (39, 13), (44, 34), (43, 11), (47, 0), (21, 19), (29, 1), (44, 38), (44, 18), (36, 0), (38, 34), (10, 6), (47, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (0, 38), (27, 19), (26, 1), (30, 12), (38, 10), (17, 28), (43, 35), (11, 36), (18, 25), (43, 13), (35, 29), (30, 2), (41, 35), (24, 33), (41, 21), (16, 11), (33, 6), (34, 20), (26, 10), (8, 6), (36, 16), (40, 6), (36, 22), (17, 9), (9, 5), (18, 6), (10, 12), (19, 22), (19, 21), (17, 23), (28, 10), (40, 33), (30, 7), (14, 35), (24, 18), (27, 27), (35, 8), (35, 4), (3, 30), (18, 16), (36, 26), (29, 21), (18, 33), (30, 20), (27, 1), (39, 36), (26, 39), (1, 16), (3, 34), (12, 26), (8, 18), (6, 3), (25, 28), (19, 5), (34, 5), (2, 25), (2, 22), (4, 8), (24, 2), (39, 12), (18, 8), (19, 1), (14, 31), (3, 27), (3, 17), (13, 4), (25, 33), (38, 3), (16, 25), (21, 11), (33, 33), (0, 25), (2, 15), (14, 16), (20, 4), (32, 10), (40, 7), (36, 28), (12, 27), (27, 4), (39, 10), (34, 31), (40, 25), (35, 1), (34, 24), (7, 20), (16, 34), (29, 5), (27, 30), (30, 29), (35, 17), (40, 26), (17, 18), (4, 32), (16, 23), (23, 20), (9, 11), (35, 36), (14, 2), (26, 2), (22, 4), (5, 16), (33, 27), (17, 33), (39, 2), (5, 32), (6, 29), (0, 7), (26, 23), (27, 23), (36, 8), (35, 37), (16, 36), (15, 1), (0, 21), (29, 19), (38, 33), (2, 16), (27, 36), (13, 1), (12, 11), (35, 7), (29, 28), (40, 19), (37, 11), (29, 22), (32, 5), (34, 27), (17, 13), (4, 27), (39, 25), (17, 37), (16, 31), (36, 33), (19, 38), (38, 27), (15, 22), (29, 18), (4, 29), (25, 38), (24, 11), (31, 27), (3, 11), (14, 7), (41, 38), (2, 10), (10, 33), (18, 21), (10, 17), (29, 1), (23, 33), (19, 15), (36, 21), (36, 12), (38, 8), (15, 7), (16, 4), (9, 12), (27, 8), (39, 35), (31, 16), (40, 37), (35, 3), (32, 6), (8, 37), (8, 13), (35, 28), (11, 19), (25, 0), (27, 12), (38, 16), (39, 26), (20, 12), (24, 3), (35, 33), (37, 32), (10, 22), (27, 39), (23, 9), (24, 21), (18, 4), (35, 19), (23, 35), (21, 8), (22, 33), (3, 1), (27, 13), (5, 6), (1, 29), (40, 22), (32, 0), (27, 3), (9, 21), (8, 5), (12, 39), (8, 4), (6, 13), (10, 6), (12, 33), (16, 7), (36, 35), (18, 12), (3, 22), (17, 27), (20, 33), (33, 24), (33, 31), (32, 26), (25, 32), (11, 15), (20, 8), (18, 36), (24, 5), (24, 8), (18, 1), (39, 33), (26, 36), (28, 16), (3, 8), (4, 31), (0, 24), (24, 37), (4, 23), (4, 33), (39, 22), (1, 25), (31, 19), (8, 9), (10, 1), (29, 6), (40, 2), (3, 39), (36, 14), (41, 23), (20, 16), (38, 12), (27, 38), (6, 35), (16, 12), (34, 37), (7, 3), (0, 15), (6, 37), (43, 7), (14, 19), (20, 34), (32, 21), (30, 18), (8, 24), (21, 5), (14, 37), (37, 14), (17, 10), (15, 33), (39, 30), (43, 29), (14, 20), (23, 26), (5, 8), (15, 24), (8, 23), (20, 6), (15, 2), (23, 38), (26, 4), (38, 7), (7, 1), (34, 1), (12, 20), (26, 33), (40, 38), (37, 24), (11, 13), (2, 38), (23, 10), (43, 27), (35, 18), (24, 39), (28, 0), (3, 29), (10, 0), (37, 35), (11, 11), (13, 33), (29, 36), (42, 30), (6, 2), (16, 38), (9, 6), (24, 30), (33, 22), (12, 23), (11, 1), (11, 28), (11, 24), (7, 15), (24, 23), (9, 15), (26, 21), (2, 32), (0, 6), (5, 29), (1, 8), (39, 32), (9, 22), (14, 18), (27, 10), (23, 7), (42, 9), (21, 1), (39, 6), (13, 26), (20, 18), (4, 18), (9, 18), (29, 35), (38, 20), (0, 5), (26, 18), (28, 18), (9, 8), (22, 2), (41, 32), (43, 37), (33, 8), (2, 34), (41, 33), (26, 29), (8, 33), (12, 29), (31, 5), (39, 37), (0, 29), (11, 22), (19, 9), (2, 0), (40, 30), (15, 10), (31, 28), (36, 38), (31, 3), (26, 24), (22, 19), (38, 30), (6, 4), (8, 22), (17, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 32), (40, 9), (43, 2), (13, 24), (3, 24), (20, 31), (41, 31), (25, 0), (36, 5), (42, 35), (22, 32), (43, 17), (43, 35), (24, 20), (9, 38), (38, 30), (3, 39), (31, 31), (5, 4), (12, 28), (39, 16), (19, 23), (44, 19), (32, 3), (43, 20), (43, 6), (9, 1), (17, 22), (26, 17), (27, 24), (4, 4), (45, 26), (28, 21), (38, 39), (5, 26), (9, 17), (18, 4), (26, 24), (17, 10), (23, 11), (10, 31), (6, 9), (39, 17), (21, 21), (11, 19), (18, 24), (34, 36), (7, 25), (33, 31), (24, 22), (28, 29), (5, 20), (1, 24), (45, 34), (15, 2), (39, 26), (4, 0), (28, 27), (25, 18), (33, 11), (34, 27), (5, 28), (44, 10), (3, 16), (38, 4), (45, 0), (16, 14), (34, 19), (6, 23), (33, 14), (30, 1), (9, 21), (9, 16), (6, 14), (22, 38), (14, 27), (18, 35), (24, 14), (11, 6), (8, 28), (33, 32), (28, 10), (27, 11), (34, 10), (21, 5), (4, 29), (36, 17), (4, 7), (38, 0), (15, 4), (23, 32), (35, 29), (42, 22), (2, 5), (7, 16), (30, 16), (39, 0), (17, 23), (5, 35), (6, 16), (39, 12), (16, 33), (34, 20), (36, 13), (26, 22), (26, 12), (24, 29), (23, 2), (29, 16), (10, 9), (12, 38), (13, 39), (18, 31), (35, 25), (29, 33), (18, 5), (20, 16), (17, 18), (36, 33), (45, 12), (11, 31), (33, 10), (36, 23), (35, 22), (37, 37), (9, 19), (27, 5), (0, 25), (29, 28), (21, 23), (15, 20), (16, 22), (6, 26), (45, 29), (21, 4), (5, 38), (14, 23), (44, 30), (16, 39), (19, 15), (19, 39), (13, 17), (15, 3), (8, 13), (26, 15), (21, 20), (38, 6), (39, 39), (20, 22), (20, 27), (0, 11), (43, 25), (2, 38), (27, 16), (29, 26), (12, 15), (26, 10), (22, 12), (43, 16), (8, 32), (21, 32), (28, 15), (3, 33), (18, 29), (15, 14), (10, 7), (32, 38), (34, 37), (23, 7), (31, 7), (13, 23), (7, 13), (40, 10), (36, 27), (44, 29), (44, 39), (15, 37), (0, 31), (42, 25), (17, 27), (9, 33), (6, 37), (7, 33), (45, 2), (30, 20), (22, 15), (2, 9), (1, 6), (26, 27), (4, 9), (23, 18), (35, 34), (38, 34), (32, 2), (37, 32), (2, 15), (37, 10), (22, 30), (14, 0), (29, 0), (44, 5), (37, 21), (15, 36), (0, 16), (39, 14), (36, 7), (40, 5), (31, 9), (34, 28), (24, 34), (29, 4), (3, 6), (44, 22), (25, 39), (5, 36), (7, 0), (27, 6), (19, 8), (36, 9), (12, 25), (41, 26), (17, 28), (30, 31), (8, 26), (42, 21), (43, 23), (27, 7), (40, 34), (17, 15), (42, 34), (18, 21), (6, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 37), (40, 15), (27, 23), (19, 8), (32, 6), (2, 37), (20, 17), (18, 38), (0, 46), (9, 35), (24, 11), (37, 37), (11, 33), (15, 14), (10, 28), (39, 31), (5, 46), (12, 26), (1, 35), (2, 21), (21, 45), (16, 4), (1, 23), (31, 32), (39, 7), (18, 17), (30, 28), (34, 29), (35, 43), (40, 17), (17, 29), (17, 40), (14, 42), (35, 28), (22, 18), (18, 20), (13, 12), (6, 23), (33, 0), (15, 22), (33, 47), (34, 46), (16, 10), (10, 17), (40, 41), (18, 35), (29, 25), (26, 25), (29, 9), (32, 3), (1, 24), (26, 42), (4, 14), (11, 36), (27, 13), (1, 34), (6, 3), (36, 4), (9, 31), (21, 7), (10, 3), (6, 33), (14, 26), (6, 39), (20, 14), (24, 31), (23, 33), (21, 0), (19, 11), (28, 16), (19, 30), (27, 36), (25, 36), (23, 7), (14, 31), (36, 47), (22, 12), (23, 41), (10, 22), (34, 15), (5, 6), (5, 3), (28, 35), (19, 0), (5, 9), (14, 6), (19, 18), (32, 42), (16, 46), (33, 14), (5, 34), (20, 42), (20, 45), (31, 27), (37, 35), (4, 24), (29, 11), (12, 0), (31, 15), (7, 8), (11, 27), (5, 44), (20, 8), (32, 9), (13, 5), (11, 25), (38, 10), (5, 27), (29, 15), (23, 30), (32, 16), (39, 0), (13, 4), (1, 33), (28, 34), (13, 35), (36, 21), (7, 37), (27, 1), (5, 32), (5, 18), (0, 1), (35, 15), (36, 1), (11, 31), (15, 34), (17, 19), (18, 29), (14, 8), (9, 8), (21, 41), (27, 17), (21, 39), (17, 10), (10, 47), (9, 17), (3, 40), (24, 10), (8, 0), (8, 26), (6, 37), (26, 1), (3, 11), (17, 7), (21, 46), (33, 37), (21, 43), (6, 24), (38, 3), (21, 31), (28, 42), (7, 3), (37, 1), (8, 13), (18, 36), (28, 33), (4, 39), (17, 8), (8, 46), (13, 26), (25, 16), (23, 9), (6, 19), (36, 26), (21, 47), (0, 40), (28, 23), (5, 38), (23, 38), (35, 7), (16, 19), (7, 30), (16, 35), (39, 41), (8, 33), (38, 23), (10, 10), (13, 10), (20, 25), (29, 0), (6, 17), (7, 2), (13, 43), (30, 5), (11, 9), (11, 0), (20, 19), (19, 2), (37, 28), (12, 46), (7, 31), (35, 35), (29, 14), (23, 43), (5, 19), (1, 15), (7, 6), (32, 33), (2, 29), (20, 6), (39, 5), (38, 4), (25, 35), (40, 5), (27, 4), (4, 46), (3, 1), (33, 9), (35, 23), (1, 39), (23, 18), (40, 46), (31, 6), (39, 37), (4, 27), (40, 31), (28, 43), (39, 15), (33, 28), (10, 45), (36, 39), (2, 44), (1, 20), (5, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 15), (1, 11), (25, 25), (10, 16), (13, 16), (18, 34), (23, 29), (15, 19), (10, 29), (24, 25), (10, 15), (41, 0), (13, 18), (23, 35), (26, 29), (20, 12), (34, 35), (34, 3), (17, 6), (40, 33), (30, 33), (13, 38), (13, 5), (8, 39), (16, 31), (10, 36), (32, 36), (11, 26), (5, 8), (9, 5), (26, 15), (32, 2), (41, 8), (27, 34), (0, 29), (33, 28), (10, 6), (17, 18), (37, 36), (32, 22), (7, 39), (1, 14), (8, 6), (39, 3), (13, 0), (19, 7), (41, 4), (20, 31), (28, 4), (36, 8), (12, 13), (4, 36), (27, 7), (34, 1), (13, 28), (27, 11), (2, 28), (17, 31), (35, 12), (42, 9), (42, 21), (28, 16), (42, 36), (15, 18), (38, 32), (21, 21), (15, 41), (31, 25), (31, 41), (16, 15), (14, 10), (2, 21), (42, 14), (40, 26), (25, 3), (13, 10), (2, 15), (13, 39), (29, 14), (23, 22), (32, 34), (31, 26), (2, 41), (33, 37), (16, 3), (5, 11), (11, 10), (12, 17), (4, 23), (39, 18), (4, 26), (35, 34), (19, 21), (35, 20), (37, 39), (42, 19), (15, 3), (25, 24), (23, 14), (16, 14), (35, 35), (39, 34), (36, 35), (12, 18), (42, 8), (1, 13), (5, 40), (24, 20), (9, 7), (24, 41), (32, 15), (6, 28), (39, 33), (41, 18), (9, 24), (12, 24), (1, 34), (1, 39), (29, 21), (15, 38), (12, 0), (18, 38), (38, 19), (21, 31), (26, 13), (30, 12), (0, 35), (23, 11), (16, 40), (23, 26), (19, 40), (15, 33), (11, 14), (21, 30), (15, 26), (38, 39), (14, 15), (4, 9), (6, 0), (11, 27), (16, 5), (5, 17), (27, 36), (41, 5), (35, 9), (22, 35), (7, 23), (7, 26), (20, 8), (8, 33), (0, 27), (26, 36), (34, 16), (10, 34), (2, 6), (40, 24), (19, 35), (20, 30), (36, 21), (3, 41), (25, 7), (35, 8), (38, 3), (13, 2), (15, 12), (29, 34), (1, 7), (18, 3), (38, 41), (9, 28), (6, 12), (5, 23), (30, 15), (24, 31), (35, 2), (41, 24), (7, 12), (16, 22), (21, 15), (34, 28), (16, 33), (25, 2), (22, 7), (26, 21), (4, 24), (37, 6), (24, 30), (42, 3), (23, 24), (16, 7), (34, 9), (16, 28), (10, 40), (25, 10), (25, 32), (10, 18), (24, 26), (34, 26), (12, 37), (10, 12), (37, 27), (39, 12), (23, 23), (37, 9), (34, 27), (6, 17), (9, 23), (0, 26), (36, 18), (17, 19), (39, 13), (16, 20), (2, 11), (34, 22), (40, 1), (33, 16), (34, 4), (35, 24), (28, 35), (38, 38), (18, 7), (1, 2), (3, 33), (41, 40), (10, 2), (18, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 24), (2, 30), (21, 13), (8, 29), (33, 37), (14, 9), (15, 19), (7, 19), (20, 30), (33, 35), (20, 9), (8, 26), (19, 30), (17, 15), (0, 23), (38, 20), (40, 22), (24, 24), (37, 15), (28, 11), (1, 3), (21, 18), (23, 0), (0, 17), (22, 15), (22, 41), (28, 28), (1, 35), (5, 25), (12, 28), (23, 17), (33, 17), (26, 13), (17, 0), (19, 9), (12, 36), (23, 36), (28, 40), (4, 36), (11, 35), (23, 24), (27, 25), (4, 35), (20, 39), (13, 7), (32, 16), (11, 20), (29, 38), (7, 24), (39, 26), (7, 34), (31, 39), (35, 40), (2, 20), (40, 32), (37, 12), (35, 2), (4, 41), (5, 20), (18, 9), (33, 12), (23, 22), (10, 6), (26, 29), (21, 10), (33, 6), (10, 7), (6, 22), (15, 4), (16, 26), (21, 41), (14, 33), (34, 35), (10, 25), (35, 5), (10, 38), (37, 28), (9, 27), (25, 1), (18, 42), (5, 37), (13, 1), (17, 38), (27, 28), (16, 24), (40, 11), (35, 37), (38, 12), (41, 31), (36, 13), (3, 18), (39, 0), (38, 17), (15, 20), (20, 36), (0, 31), (27, 17), (29, 42), (19, 27), (6, 5), (40, 17), (19, 40), (29, 6), (8, 41), (21, 25), (38, 5), (14, 6), (19, 12), (29, 24), (38, 41), (18, 37), (40, 34), (24, 9), (26, 42), (31, 38), (9, 26), (0, 29), (19, 1), (6, 17), (35, 7), (0, 32), (17, 22), (1, 41), (24, 27), (5, 18), (6, 2), (38, 25), (5, 41), (26, 7), (31, 22), (40, 25), (25, 6), (14, 20), (40, 39), (27, 39), (22, 10), (18, 22), (26, 26), (35, 6), (12, 2), (36, 15), (22, 3), (23, 26), (30, 13), (2, 13), (20, 41), (21, 27), (19, 42), (6, 1), (26, 15), (40, 31), (26, 9), (1, 29), (8, 15), (20, 11), (23, 28), (14, 17), (19, 6), (7, 1), (24, 28), (9, 42), (9, 34), (37, 38), (18, 15), (28, 41), (27, 16), (25, 22), (32, 19), (40, 35), (0, 19), (38, 38), (27, 14), (24, 30), (37, 10), (24, 2), (25, 21), (35, 9), (8, 23), (35, 18), (20, 2), (11, 9), (33, 1), (17, 16), (30, 2), (29, 39), (38, 31), (22, 42), (25, 38), (38, 19), (12, 3), (39, 32), (19, 5), (16, 41), (22, 20), (39, 39), (37, 9), (26, 30), (33, 5), (1, 16), (30, 15), (12, 9), (8, 25), (32, 21), (21, 22), (4, 38), (8, 3), (29, 41), (40, 38), (3, 36), (7, 29), (3, 37), (4, 1), (23, 33), (37, 26), (18, 32), (7, 15), (37, 35), (40, 13), (4, 18), (4, 30), (23, 23), (30, 33), (12, 23), (16, 19), (13, 34), (31, 0), (10, 34), (9, 16), (6, 25), (21, 29), (27, 21), (16, 4), (38, 23), (34, 14), (19, 23), (35, 42), (19, 41), (34, 15), (23, 11), (7, 12), (19, 39), (13, 12), (30, 18), (41, 40), (8, 39), (30, 9), (7, 41), (2, 18), (3, 40), (3, 38), (10, 39), (28, 15), (32, 5), (11, 25), (29, 37), (21, 28), (13, 38), (41, 30), (24, 4), (31, 32), (0, 21), (29, 22), (41, 38), (33, 32), (14, 28), (19, 28), (35, 17), (14, 25), (1, 1), (20, 12), (8, 21), (13, 2), (39, 40), (32, 34), (11, 10), (13, 24), (41, 28), (20, 14), (25, 33), (23, 40), (4, 25), (13, 30), (29, 7), (1, 11), (7, 20), (2, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 33), (20, 33), (12, 9), (40, 40), (39, 16), (10, 15), (6, 32), (30, 1), (1, 27), (5, 7), (15, 41), (21, 25), (15, 17), (8, 40), (36, 30), (0, 19), (1, 39), (23, 21), (9, 1), (25, 8), (23, 24), (27, 0), (10, 7), (38, 33), (36, 23), (11, 36), (1, 42), (29, 8), (9, 28), (19, 25), (7, 0), (13, 26), (29, 14), (2, 15), (37, 28), (16, 35), (8, 42), (25, 37), (23, 38), (36, 38), (24, 41), (37, 40), (8, 15), (28, 25), (26, 34), (27, 11), (31, 39), (3, 29), (33, 25), (8, 21), (7, 18), (1, 26), (25, 3), (9, 5), (4, 35), (40, 1), (38, 31), (6, 10), (8, 12), (13, 0), (10, 20), (4, 11), (29, 40), (19, 1), (6, 0), (5, 28), (0, 5), (3, 40), (12, 41), (36, 32), (7, 21), (24, 32), (30, 24), (35, 22), (1, 17), (37, 11), (24, 25), (7, 15), (2, 42), (28, 20), (7, 9), (4, 37), (27, 23), (38, 26), (40, 29), (19, 10), (6, 4), (16, 37), (9, 16), (3, 39), (4, 25), (26, 22), (26, 37), (21, 28), (0, 39), (26, 28), (25, 34), (36, 25), (24, 22), (18, 27), (27, 31), (17, 7), (9, 19), (23, 16), (33, 31), (24, 38), (7, 36), (12, 0), (26, 0), (39, 27), (27, 4), (37, 41), (32, 25), (32, 35), (10, 32), (11, 32), (3, 13), (18, 4), (16, 30), (37, 31), (12, 25), (7, 11), (22, 37), (30, 23), (23, 25), (32, 38), (20, 40), (4, 15), (25, 42), (11, 22), (9, 34), (40, 38), (19, 27), (36, 20), (28, 30), (4, 28), (14, 14), (12, 30), (8, 20), (19, 11), (12, 22), (23, 5), (24, 9), (34, 18), (19, 24), (11, 23), (24, 4), (35, 36), (39, 21), (20, 10), (35, 41), (0, 37), (14, 9), (25, 21), (39, 22), (37, 29), (4, 14), (12, 29), (36, 21), (40, 15), (1, 1), (19, 36), (38, 38), (28, 5), (4, 34), (33, 22), (21, 36), (9, 41), (22, 11), (9, 25), (40, 2), (17, 41), (39, 1), (26, 8), (29, 38), (2, 10), (5, 19), (18, 8), (2, 38), (39, 25), (2, 20), (21, 41), (11, 14), (2, 31), (26, 26), (6, 6), (26, 29), (40, 11), (10, 40), (28, 1), (36, 15), (36, 0), (17, 2), (28, 40), (29, 9), (30, 25), (2, 5), (28, 36), (31, 23), (40, 22), (25, 17), (27, 1), (33, 4), (40, 17), (33, 36), (11, 24), (35, 40), (31, 14), (34, 27), (29, 17), (11, 17), (35, 33), (29, 33), (5, 10), (23, 7), (38, 42), (10, 30), (38, 4), (28, 15), (31, 41), (18, 13), (5, 39), (31, 21), (17, 15), (15, 5), (18, 37), (24, 39), (8, 22), (9, 14), (11, 21), (4, 9), (23, 12), (6, 3), (19, 13), (10, 24), (3, 5), (12, 32), (35, 13), (37, 35), (16, 4), (21, 40), (21, 14), (28, 34), (9, 36), (17, 28), (6, 31), (39, 6), (36, 35), (21, 19), (10, 3), (40, 34), (33, 10), (34, 38), (0, 28), (13, 27), (31, 8), (8, 13), (39, 19), (28, 39), (39, 42), (33, 28), (15, 14), (5, 27), (13, 12), (40, 39), (3, 38), (18, 23), (13, 13), (38, 41), (25, 26), (4, 38), (10, 21), (5, 6), (31, 36), (20, 19), (4, 3), (1, 2), (7, 38), (24, 8), (40, 6), (15, 15), (34, 5), (3, 3), (11, 0), (19, 35), (37, 36), (11, 27), (27, 24), (16, 16), (29, 24), (5, 24), (17, 18), (28, 8), (26, 12), (36, 27), (2, 18), (39, 4), (33, 18), (34, 24), (4, 16), (13, 35), (0, 26), (13, 25), (2, 27), (37, 13), (14, 4), (24, 6), (3, 11), (11, 41), (4, 1), (12, 14), (30, 12), (10, 4), (28, 41), (30, 22), (30, 8), (2, 11), (23, 39), (27, 18), (31, 10), (20, 8), (2, 6), (13, 8), (22, 2), (19, 6), (35, 31), (18, 35), (4, 2), (31, 29), (28, 24), (39, 35), (40, 37), (1, 16), (25, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (22, 24), (16, 9), (1, 24), (30, 15), (18, 0), (6, 11), (31, 29), (30, 20), (45, 30), (27, 30), (41, 2), (15, 5), (18, 35), (16, 30), (19, 18), (44, 7), (47, 6), (43, 7), (21, 22), (46, 15), (7, 39), (16, 5), (43, 29), (3, 18), (43, 37), (39, 36), (22, 26), (30, 24), (27, 23), (14, 7), (38, 0), (38, 25), (31, 11), (48, 41), (26, 35), (28, 10), (47, 23), (25, 17), (34, 36), (30, 38), (24, 33), (30, 22), (14, 35), (13, 17), (7, 32), (3, 13), (17, 24), (10, 26), (39, 24), (28, 19), (31, 0), (38, 32), (24, 31), (25, 34), (11, 20), (2, 21), (19, 33), (19, 6), (0, 10), (16, 14), (29, 33), (2, 5), (16, 13), (35, 17), (2, 24), (28, 36), (31, 42), (43, 34), (11, 1), (21, 2), (35, 8), (34, 24), (6, 0), (12, 41), (3, 40), (45, 36), (35, 26), (15, 28), (13, 26), (40, 35), (8, 23), (44, 20), (23, 11), (21, 39), (19, 1), (42, 16), (15, 23), (38, 3), (16, 4), (17, 41), (30, 17), (40, 9), (42, 13), (17, 19), (6, 8), (47, 30), (34, 9), (27, 31), (14, 16), (5, 9), (29, 5), (32, 40), (20, 11), (2, 15), (24, 38), (13, 6), (43, 28), (13, 34), (3, 35), (1, 0), (14, 30), (32, 20), (21, 7), (3, 34), (47, 17), (35, 20), (9, 6), (9, 35), (47, 20), (48, 5), (40, 28), (16, 25), (12, 19), (17, 17), (41, 27), (37, 30), (36, 18), (42, 29), (13, 30), (34, 21), (39, 12), (17, 40), (35, 40), (1, 28), (19, 23), (47, 37), (12, 22), (6, 36), (29, 16), (10, 39), (22, 23), (33, 24), (14, 2), (15, 17), (47, 10), (26, 14), (20, 25), (18, 3), (1, 34), (18, 38), (24, 4), (29, 2), (21, 21), (27, 5), (20, 3), (42, 8), (23, 43), (37, 1), (47, 8), (38, 2), (0, 19), (44, 3), (32, 21), (22, 36), (45, 41), (48, 38), (4, 34), (7, 29), (36, 5), (40, 33), (48, 31), (15, 14), (41, 21), (26, 7), (17, 13), (38, 33), (33, 42), (48, 12), (0, 29), (25, 25), (30, 18), (12, 18), (8, 30), (10, 28), (32, 12), (15, 37), (3, 33), (14, 4), (24, 29), (39, 2), (44, 18), (9, 0), (37, 32), (48, 30), (3, 11), (1, 15), (31, 25), (8, 42), (43, 21), (26, 13), (24, 20), (6, 39), (38, 15), (45, 31), (20, 29), (22, 30), (3, 39), (46, 41), (48, 16), (12, 13), (12, 10), (15, 6), (26, 20), (2, 43), (17, 20), (44, 38), (12, 39), (11, 25), (36, 21), (38, 35), (35, 13), (26, 26), (12, 29), (42, 25), (39, 27), (21, 26), (39, 14), (29, 14), (28, 22), (36, 20), (32, 27), (1, 12), (12, 42), (14, 18), (43, 31), (17, 26), (5, 0), (8, 24), (5, 28), (40, 29), (4, 19), (37, 27), (8, 27), (43, 10), (27, 34), (18, 18), (41, 29), (21, 43), (42, 39), (20, 35), (44, 41), (17, 16), (36, 0), (45, 13), (40, 43), (42, 40), (10, 6), (32, 35), (29, 42), (6, 12), (19, 28), (10, 0), (43, 2), (30, 16), (14, 43), (14, 34), (2, 31), (32, 11), (0, 30), (41, 12), (27, 17), (22, 9), (3, 3), (32, 29), (23, 8), (46, 8), (26, 32), (35, 39), (24, 22), (37, 31), (12, 38), (41, 25), (19, 40), (38, 12), (35, 1), (36, 19), (7, 37), (48, 35), (23, 37), (5, 25), (42, 18), (11, 22), (30, 25), (31, 19), (46, 28), (19, 11), (46, 33), (10, 20), (4, 33), (3, 22), (1, 19), (29, 11), (5, 39), (9, 11), (33, 28), (41, 11), (26, 21), (2, 37), (13, 28), (18, 1), (0, 6), (48, 14), (6, 17), (45, 8), (19, 24), (30, 37), (8, 13), (20, 4), (4, 28), (14, 24), (6, 4), (3, 31), (13, 10), (40, 14), (36, 22), (5, 43), (25, 9), (10, 25), (38, 4), (19, 19), (44, 8), (29, 18), (15, 32), (43, 15), (31, 26), (23, 1), (23, 30), (27, 35), (19, 32), (7, 6), (37, 15), (6, 25), (39, 6), (0, 28), (3, 38), (16, 42), (5, 3), (20, 38), (36, 24), (42, 24), (23, 25), (25, 20), (41, 34), (7, 22), (32, 18), (46, 43), (2, 9), (36, 25), (17, 11), (9, 13), (6, 42), (17, 8), (41, 14), (30, 2), (0, 15), (11, 9), (47, 21), (38, 29), (14, 12), (4, 1), (20, 34), (23, 21), (6, 10), (3, 26), (46, 9), (24, 7), (39, 21), (7, 21), (18, 36), (31, 28), (1, 31), (37, 17), (39, 29), (22, 32), (33, 18), (36, 11), (6, 15), (29, 9), (45, 26), (37, 0), (4, 43), (33, 9), (19, 15), (42, 22), (10, 42), (38, 6), (14, 33), (34, 8), (44, 40), (43, 36), (17, 29), (22, 2), (3, 5), (44, 16), (35, 30), (0, 35), (41, 15), (47, 26), (20, 31), (43, 26), (23, 16), (1, 37), (35, 0), (34, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 12), (17, 28), (37, 37), (29, 0), (35, 27), (26, 5), (24, 34), (27, 21), (10, 35), (13, 21), (9, 22), (24, 8), (31, 35), (33, 35), (28, 38), (18, 30), (24, 21), (10, 30), (6, 35), (0, 15), (20, 19), (19, 31), (23, 22), (8, 17), (32, 32), (27, 25), (18, 0), (16, 11), (30, 32), (19, 11), (4, 11), (20, 42), (11, 42), (27, 42), (29, 16), (24, 14), (39, 6), (20, 21), (25, 9), (5, 11), (7, 8), (32, 12), (30, 15), (13, 39), (20, 38), (39, 19), (11, 29), (13, 10), (43, 19), (29, 1), (21, 36), (6, 13), (16, 16), (36, 37), (43, 25), (35, 31), (7, 24), (42, 35), (41, 6), (23, 0), (30, 30), (2, 26), (31, 11), (14, 37), (4, 33), (41, 16), (9, 28), (3, 9), (0, 28), (2, 0), (19, 26), (19, 37), (25, 16), (8, 22), (31, 40), (14, 6), (34, 9), (5, 8), (29, 34), (16, 23), (11, 34), (28, 8), (3, 0), (30, 17), (43, 9), (18, 37), (6, 18), (13, 37), (4, 31), (40, 6), (14, 26), (29, 37), (1, 30), (9, 20), (24, 11), (0, 18), (8, 24), (36, 27), (3, 3), (10, 33), (13, 4), (40, 40), (6, 29), (20, 29), (13, 9), (38, 2), (9, 40), (29, 26), (28, 20), (8, 42), (39, 27), (39, 8), (3, 37), (19, 19), (15, 9), (28, 41), (20, 23), (23, 39), (9, 37), (40, 7), (35, 22), (40, 12), (17, 33), (21, 7), (15, 36), (35, 6), (2, 37), (26, 29), (9, 39), (1, 31), (10, 28), (43, 0), (24, 28), (9, 15), (4, 3), (5, 10), (11, 14), (16, 24), (30, 13), (42, 38), (12, 39), (15, 25), (7, 2), (36, 38), (19, 25), (19, 13), (38, 20), (9, 14), (31, 5), (14, 39), (25, 34), (40, 9), (16, 30), (16, 0), (33, 16), (19, 27), (21, 42), (7, 7), (2, 3), (37, 27), (22, 11), (9, 3), (24, 2), (19, 7), (0, 19), (22, 9), (10, 39), (10, 27), (8, 28), (7, 0), (32, 18), (31, 20), (11, 40), (13, 30), (15, 11), (35, 9), (27, 5), (13, 36), (5, 15), (9, 8), (39, 22), (22, 1), (3, 8), (2, 8), (39, 5), (3, 26), (40, 39), (0, 9), (4, 14), (30, 29), (14, 12), (9, 2), (10, 26), (17, 11), (30, 22), (7, 14), (13, 23), (13, 41), (22, 3), (21, 2), (27, 35), (0, 3), (36, 21), (3, 5), (10, 38), (14, 1), (38, 10), (12, 2), (15, 2), (27, 17), (39, 15), (41, 25), (10, 21), (12, 37), (13, 24), (1, 20), (9, 36), (22, 33), (11, 21), (0, 20), (42, 42), (1, 42), (26, 34), (25, 35), (21, 31), (2, 23), (14, 11), (17, 20), (25, 37), (17, 4), (36, 17), (40, 19), (31, 14), (16, 18), (19, 6), (6, 38), (25, 30), (11, 31), (28, 13), (13, 17), (23, 2), (16, 28), (6, 31), (38, 32), (19, 10), (27, 12), (4, 22), (8, 11), (8, 23), (0, 4), (30, 3), (7, 21), (42, 23), (7, 13), (11, 26), (26, 32), (17, 21), (8, 15), (31, 12), (17, 14), (32, 1), (38, 4), (19, 18), (16, 22), (19, 4), (14, 17), (12, 29), (23, 11), (8, 36), (3, 14), (0, 37), (41, 30), (32, 21), (43, 29), (16, 39), (30, 18), (21, 13), (32, 22), (20, 9), (15, 29), (29, 18), (38, 39), (14, 32), (42, 21), (29, 9), (16, 20), (37, 1), (34, 42), (42, 39), (20, 5), (21, 5), (23, 3), (14, 35), (27, 23), (31, 42), (5, 36), (23, 18), (5, 0), (10, 37), (19, 42), (18, 10), (35, 34), (23, 36), (6, 2), (23, 7), (5, 32), (28, 24), (0, 1), (10, 0), (17, 2), (14, 33), (2, 22), (29, 17), (6, 42), (22, 40), (23, 28), (9, 35), (27, 22), (5, 41), (2, 1), (14, 23), (15, 5), (38, 28), (42, 27), (29, 5), (28, 40), (6, 23), (7, 31), (38, 8), (21, 19), (29, 23), (23, 34), (23, 4), (15, 3), (27, 33), (30, 31), (7, 9), (26, 28), (41, 24), (27, 16), (29, 21), (4, 17), (33, 18), (37, 21), (37, 29), (35, 41), (16, 12), (35, 30), (16, 25), (37, 35), (0, 35), (33, 17), (31, 15), (12, 8), (7, 16), (1, 5), (18, 21), (10, 11), (10, 23), (23, 40), (4, 4), (40, 31), (14, 27), (27, 4), (2, 16), (11, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 8), (11, 0), (11, 37), (30, 4), (6, 11), (2, 42), (21, 2), (27, 46), (15, 15), (16, 40), (18, 17), (22, 6), (9, 15), (7, 16), (12, 33), (34, 17), (33, 17), (29, 29), (16, 46), (23, 19), (4, 28), (3, 26), (1, 46), (10, 44), (29, 36), (18, 13), (36, 23), (36, 18), (29, 11), (30, 7), (7, 11), (14, 32), (39, 31), (37, 42), (16, 18), (1, 21), (7, 47), (33, 39), (36, 4), (2, 44), (21, 38), (39, 22), (36, 27), (38, 28), (33, 14), (26, 29), (8, 22), (6, 28), (0, 27), (2, 19), (10, 30), (2, 9), (26, 47), (10, 21), (36, 12), (17, 23), (14, 18), (5, 18), (8, 43), (1, 27), (4, 44), (11, 23), (30, 47), (31, 42), (11, 47), (37, 43), (9, 2), (4, 35), (5, 3), (20, 30), (25, 26), (30, 25), (40, 3), (23, 25), (11, 44), (22, 27), (24, 2), (28, 32), (2, 20), (6, 43), (16, 47), (36, 6), (1, 7), (6, 10), (27, 45), (8, 5), (23, 30), (13, 28), (28, 42), (9, 12), (13, 37), (31, 36), (3, 28), (21, 22), (11, 10), (8, 28), (28, 3), (4, 34), (28, 44), (1, 1), (15, 17), (16, 10), (11, 41), (23, 22), (22, 29), (0, 19), (13, 44), (17, 33), (27, 34), (32, 37), (30, 37), (17, 16), (9, 6), (9, 24), (16, 6), (1, 37), (33, 18), (27, 31), (8, 24), (0, 1), (12, 2), (6, 29), (5, 39), (1, 5), (15, 7), (18, 22), (11, 26), (22, 39), (19, 40), (40, 36), (17, 28), (26, 40), (8, 17), (1, 40), (1, 3), (24, 9), (28, 4), (18, 2), (38, 16), (32, 33), (39, 23), (40, 16), (10, 3), (27, 32), (29, 23), (4, 46), (22, 35), (7, 34), (24, 34), (1, 44), (16, 32), (31, 38), (2, 31), (34, 21), (26, 14), (3, 47), (18, 18), (37, 10), (19, 21), (2, 11), (19, 19), (6, 25), (35, 20), (18, 33), (0, 12), (9, 8), (29, 27), (15, 33), (26, 22), (13, 39), (7, 14), (13, 15), (34, 34), (20, 6), (33, 12), (23, 35), (21, 11), (14, 44), (9, 32), (17, 22), (16, 16), (11, 2), (21, 35), (38, 22), (31, 28), (21, 33), (16, 19), (12, 3), (6, 2), (38, 43), (28, 40), (38, 45), (12, 5), (25, 44), (1, 28), (25, 25), (8, 0), (32, 24), (16, 33), (5, 36), (8, 19), (0, 3), (36, 38), (35, 31), (40, 38), (34, 35), (28, 7), (27, 40), (5, 27), (28, 31), (29, 15), (19, 0), (27, 25), (24, 5), (3, 31), (20, 23), (40, 8), (5, 47), (36, 32), (16, 13), (29, 20), (38, 1), (36, 15), (31, 11), (14, 35), (31, 15), (10, 29), (19, 46), (6, 20), (5, 21), (18, 19), (24, 37), (23, 23), (13, 0), (28, 30), (18, 47), (10, 5), (22, 7), (20, 43), (33, 22), (28, 27), (24, 1), (6, 41), (28, 25), (20, 5), (21, 5), (37, 13), (23, 4), (27, 39), (32, 6), (38, 12), (29, 46), (10, 2), (7, 42), (35, 4), (12, 38), (35, 46), (24, 30), (9, 26), (4, 21), (37, 21), (9, 37), (7, 30), (21, 26), (11, 7), (7, 5), (14, 17), (11, 33), (13, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 22), (19, 20), (1, 14), (28, 35), (15, 24), (12, 18), (36, 41), (7, 33), (13, 15), (0, 16), (33, 16), (42, 37), (43, 1), (34, 19), (16, 24), (33, 17), (15, 25), (19, 6), (10, 5), (33, 20), (31, 31), (2, 36), (8, 17), (41, 13), (38, 40), (4, 6), (36, 33), (2, 41), (10, 35), (39, 37), (43, 11), (3, 34), (2, 6), (21, 36), (35, 12), (45, 23), (19, 3), (17, 27), (13, 0), (40, 20), (37, 31), (12, 22), (7, 31), (25, 14), (21, 35), (22, 8), (18, 21), (29, 21), (2, 35), (44, 26), (21, 4), (37, 15), (31, 32), (44, 5), (6, 1), (11, 1), (44, 7), (23, 33), (20, 26), (12, 7), (19, 10), (1, 30), (39, 19), (39, 5), (11, 3), (33, 23), (22, 33), (18, 19), (31, 28), (38, 31), (29, 29), (31, 12), (35, 35), (20, 32), (12, 14), (7, 4), (26, 40), (10, 10), (30, 21), (18, 34), (28, 42), (9, 2), (9, 9), (5, 4), (40, 18), (14, 1), (18, 17), (30, 8), (39, 4), (12, 2), (2, 22), (25, 6), (18, 39), (38, 32), (25, 37), (15, 5), (18, 30), (8, 5), (0, 36), (26, 1), (19, 36), (28, 37), (14, 17), (31, 17), (44, 13), (4, 7), (31, 14), (43, 17), (6, 8), (26, 7), (30, 0), (18, 38), (26, 41), (21, 18), (20, 19), (12, 0), (8, 0), (43, 42), (45, 41), (29, 0), (31, 22), (40, 4), (4, 39), (4, 25), (11, 37), (2, 14), (21, 15), (4, 10), (30, 7), (3, 21), (6, 38), (1, 0), (6, 19), (21, 1), (14, 23), (1, 38), (24, 36), (43, 0), (9, 4), (41, 35), (15, 0), (32, 33), (41, 36), (28, 2), (24, 1), (15, 4), (28, 34), (13, 21), (6, 23), (27, 12), (23, 37), (42, 36), (28, 31), (26, 22), (35, 29), (16, 14), (19, 12), (44, 6), (37, 8), (21, 17), (38, 21), (0, 35), (43, 4), (33, 1), (15, 35), (27, 0), (25, 27), (33, 15), (29, 20), (11, 9), (21, 10), (21, 26), (15, 9), (32, 12), (5, 16), (2, 17), (5, 5), (26, 14), (27, 38), (6, 27), (27, 36), (24, 13), (16, 5), (16, 12), (19, 39), (2, 19), (38, 20), (23, 25), (45, 34), (6, 7), (32, 27), (13, 29), (2, 9), (44, 40), (24, 33), (4, 9), (44, 38), (6, 22), (39, 2), (31, 35), (11, 16), (25, 23), (15, 8), (45, 29), (22, 9), (31, 24), (2, 42), (16, 30), (37, 14), (13, 32), (19, 5), (12, 40), (44, 31), (22, 40), (42, 13), (40, 28), (0, 18), (27, 31), (32, 9), (1, 1), (25, 21), (0, 15), (31, 25), (20, 33), (4, 37), (15, 12), (36, 30), (12, 1), (15, 17), (40, 8), (32, 21), (44, 37), (11, 14), (36, 27), (26, 15), (22, 4), (33, 7), (22, 21), (20, 40), (41, 21), (33, 40), (45, 33), (21, 9), (36, 35), (11, 21), (0, 19), (45, 22), (41, 1), (28, 3), (15, 23), (15, 6), (16, 4), (19, 18), (44, 21), (33, 11), (28, 40), (45, 2), (41, 3), (37, 25), (39, 10), (23, 6), (17, 0), (28, 20), (5, 37), (4, 3), (24, 28), (15, 37), (13, 22), (13, 33), (18, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 40), (30, 18), (5, 27), (26, 26), (19, 28), (8, 25), (27, 24), (26, 6), (33, 16), (39, 19), (6, 6), (35, 35), (11, 13), (26, 2), (13, 37), (0, 20), (40, 15), (15, 15), (4, 8), (12, 35), (0, 33), (14, 5), (10, 28), (20, 13), (16, 34), (7, 4), (39, 35), (29, 5), (19, 22), (2, 23), (1, 13), (9, 17), (40, 32), (22, 33), (21, 32), (4, 5), (10, 24), (17, 33), (27, 2), (27, 40), (0, 29), (40, 20), (6, 32), (3, 29), (0, 34), (10, 9), (18, 13), (2, 18), (16, 0), (18, 21), (32, 20), (17, 26), (15, 29), (14, 9), (37, 35), (25, 17), (14, 7), (39, 2), (8, 35), (15, 30), (16, 14), (31, 13), (16, 25), (24, 38), (41, 14), (22, 30), (25, 6), (11, 17), (34, 25), (8, 40), (23, 10), (29, 31), (22, 7), (10, 13), (31, 38), (22, 39), (36, 30), (12, 6), (5, 22), (9, 25), (23, 34), (19, 10), (18, 20), (13, 17), (11, 2), (11, 27), (30, 11), (30, 17), (16, 29), (21, 10), (34, 1), (34, 14), (20, 23), (35, 6), (9, 39), (35, 39), (13, 8), (30, 8), (32, 11), (29, 32), (31, 40), (7, 5), (6, 28), (30, 6), (22, 28), (26, 20), (27, 0), (19, 32), (2, 38), (16, 37), (29, 6), (4, 20), (37, 34), (5, 11), (8, 8), (25, 37), (22, 38), (15, 10), (21, 13), (5, 28), (41, 37), (34, 37), (24, 39), (21, 36), (28, 17), (2, 3), (17, 32), (24, 3), (3, 35), (41, 0), (6, 29), (4, 39), (4, 22), (8, 12), (27, 17), (0, 26), (9, 9), (15, 9), (21, 28), (5, 30), (10, 27), (11, 22), (37, 17), (10, 22), (12, 14), (5, 13), (10, 36), (33, 33), (2, 40), (23, 24), (37, 5), (1, 2), (32, 18), (23, 30), (12, 5), (27, 3), (5, 39), (22, 22), (41, 33), (12, 24), (17, 31), (34, 13), (32, 37), (22, 40), (5, 25), (2, 1), (31, 22), (12, 40), (28, 22), (17, 21), (37, 4), (15, 12), (7, 7), (22, 10), (3, 22), (8, 28), (5, 18), (36, 34), (8, 22), (25, 8), (4, 14), (36, 40), (12, 3), (14, 26), (6, 5), (14, 24), (6, 0), (19, 36), (31, 35), (14, 20), (36, 19), (16, 20), (25, 35), (15, 4), (5, 38), (24, 33), (19, 3), (13, 21), (16, 16), (26, 22), (9, 12), (2, 26), (3, 5), (13, 2), (24, 7), (8, 31), (18, 12), (21, 37), (20, 35), (13, 34), (12, 26), (15, 34), (7, 17), (33, 39), (34, 9), (5, 15), (16, 26), (17, 3), (26, 1), (15, 20), (0, 13), (28, 21), (23, 18), (36, 14), (34, 0), (39, 20), (0, 38), (8, 24), (37, 2), (15, 33), (18, 34), (2, 16), (1, 32), (8, 38), (33, 31), (16, 35), (25, 31), (28, 28), (28, 34), (17, 7), (15, 25), (10, 25), (11, 30), (20, 1), (29, 30), (40, 25), (0, 10), (1, 8), (16, 31), (32, 10), (38, 21), (22, 14), (8, 34), (33, 4), (22, 16), (21, 1), (0, 31), (39, 33), (17, 6), (36, 39), (18, 19), (11, 31), (4, 17), (35, 27), (28, 0), (12, 1), (31, 21), (17, 22), (6, 17), (24, 10), (12, 10), (41, 3), (19, 37), (16, 38), (36, 26), (20, 40), (20, 0), (20, 37), (37, 14), (32, 4), (18, 15), (13, 22), (15, 11), (4, 16), (36, 36), (26, 3), (26, 32), (1, 20), (36, 12), (22, 29), (29, 34), (6, 8), (35, 11), (1, 0), (39, 23), (30, 1), (37, 3), (30, 38), (34, 22), (36, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 22), (15, 29), (11, 15), (9, 27), (0, 1), (34, 19), (9, 4), (23, 23), (29, 38), (3, 1), (12, 12), (1, 34), (30, 20), (29, 20), (41, 27), (15, 20), (23, 21), (22, 4), (18, 40), (19, 40), (28, 41), (13, 34), (30, 16), (13, 5), (18, 26), (4, 14), (33, 37), (23, 34), (22, 7), (19, 28), (2, 14), (25, 2), (33, 7), (37, 4), (6, 20), (11, 24), (38, 5), (41, 12), (4, 29), (30, 2), (3, 16), (26, 33), (28, 20), (21, 14), (38, 37), (29, 14), (9, 6), (18, 35), (22, 33), (38, 9), (38, 31), (15, 8), (37, 34), (8, 4), (27, 2), (26, 19), (5, 19), (15, 0), (12, 21), (26, 37), (1, 13), (35, 37), (9, 32), (34, 15), (29, 17), (21, 34), (6, 31), (38, 35), (40, 31), (24, 5), (40, 40), (21, 22), (19, 26), (5, 41), (6, 2), (5, 3), (38, 17), (9, 18), (29, 39), (7, 32), (5, 18), (28, 35), (13, 41), (0, 16), (33, 18), (37, 40), (11, 6), (32, 20), (26, 25), (4, 1), (34, 9), (16, 5), (18, 29), (19, 17), (18, 30), (28, 39), (34, 33), (28, 6), (17, 40), (19, 27), (8, 17), (8, 8), (1, 32), (11, 40), (25, 3), (26, 15), (30, 40), (14, 11), (14, 32), (0, 12), (39, 10), (25, 4), (20, 0), (30, 36), (1, 7), (33, 24), (34, 18), (35, 24), (35, 38), (9, 39), (32, 13), (13, 27), (41, 8), (34, 3), (21, 2), (33, 33), (20, 11), (41, 24), (9, 14), (35, 39), (4, 17), (15, 1), (30, 1), (40, 14), (35, 14), (16, 25), (32, 5), (15, 25), (5, 20), (16, 8), (26, 32), (19, 2), (6, 24), (26, 12), (20, 31), (5, 2), (24, 13), (5, 13), (39, 9), (4, 26), (25, 37), (33, 40), (21, 1), (40, 20), (13, 12), (39, 36), (5, 10), (20, 21), (0, 24), (16, 40), (31, 3), (39, 15), (31, 27), (32, 41), (36, 21), (38, 2), (16, 21), (21, 11), (14, 13), (25, 15), (3, 31), (17, 15), (27, 10), (15, 39), (41, 36), (19, 30), (6, 7), (29, 24), (34, 14), (36, 24), (12, 9), (16, 18), (32, 17), (24, 7), (13, 21), (30, 0), (2, 21), (40, 5), (25, 13), (17, 36), (36, 19), (39, 29), (37, 17), (38, 33), (0, 30), (37, 14), (2, 13), (1, 9), (37, 35), (22, 36), (38, 4), (17, 8), (6, 5), (31, 4), (29, 36), (39, 35), (20, 12), (9, 2), (0, 26), (4, 9), (10, 26), (8, 23), (2, 22), (8, 28), (21, 23), (33, 12), (1, 8), (34, 17), (39, 37), (35, 2), (40, 19), (0, 37), (36, 32), (21, 38), (21, 40), (28, 8), (35, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 13), (2, 15), (39, 21), (3, 31), (8, 37), (9, 9), (14, 26), (35, 10), (40, 39), (32, 5), (4, 39), (14, 38), (16, 29), (34, 17), (41, 9), (9, 38), (22, 9), (39, 28), (36, 10), (38, 11), (5, 5), (5, 36), (11, 12), (6, 14), (22, 3), (0, 11), (38, 32), (27, 11), (32, 33), (29, 17), (44, 4), (25, 13), (39, 3), (3, 29), (43, 7), (16, 23), (17, 14), (33, 29), (30, 36), (31, 32), (40, 16), (20, 0), (13, 27), (6, 23), (5, 10), (25, 36), (29, 12), (29, 15), (8, 3), (2, 6), (27, 2), (39, 26), (37, 3), (26, 30), (41, 12), (23, 24), (18, 15), (22, 6), (15, 12), (43, 4), (9, 21), (35, 35), (13, 4), (29, 39), (29, 30), (20, 21), (33, 0), (34, 25), (3, 10), (9, 37), (36, 21), (37, 30), (37, 15), (10, 38), (34, 10), (2, 23), (30, 0), (10, 27), (22, 22), (21, 1), (23, 6), (2, 1), (17, 36), (13, 13), (18, 24), (1, 27), (30, 30), (11, 24), (17, 24), (8, 18), (33, 5), (4, 38), (33, 20), (12, 17), (29, 24), (23, 39), (29, 3), (0, 5), (43, 30), (27, 1), (18, 1), (37, 5), (17, 5), (33, 13), (21, 28), (22, 26), (7, 37), (14, 25), (10, 18), (7, 36), (43, 6), (26, 31), (28, 8), (26, 24), (14, 34), (9, 1), (0, 22), (20, 15), (27, 10), (17, 17), (34, 16), (34, 39), (19, 7), (16, 15), (14, 22), (33, 6), (7, 8), (17, 2), (40, 29), (38, 14), (35, 23), (27, 13), (41, 4), (30, 21), (20, 12), (43, 27), (34, 32), (12, 0), (2, 13), (31, 24), (8, 19), (16, 10), (40, 15), (41, 35), (33, 30), (44, 34), (14, 30), (15, 30), (3, 18), (19, 24), (29, 34), (9, 10), (42, 23), (35, 37), (40, 18), (15, 25), (23, 7), (27, 39), (39, 37), (19, 5), (36, 14), (24, 27), (11, 7), (39, 14), (41, 25), (18, 36), (20, 39), (22, 36), (41, 15), (9, 22), (9, 31), (20, 25), (34, 20), (14, 32), (4, 11), (43, 22), (26, 5), (15, 11), (12, 36), (36, 15), (1, 24), (0, 37), (15, 23), (33, 39), (15, 33), (5, 19), (22, 28), (29, 0), (4, 25), (15, 18), (44, 7), (33, 23), (36, 38), (15, 9), (7, 5), (28, 35), (2, 3), (35, 21), (22, 7), (27, 12), (1, 1), (28, 3), (33, 37), (11, 4), (31, 26), (18, 0), (26, 20), (33, 36), (26, 14), (15, 31), (13, 2), (23, 30), (0, 10), (3, 21), (22, 8), (3, 37), (16, 14), (6, 7), (36, 24), (16, 1), (3, 32), (19, 33), (17, 25), (26, 17), (9, 36), (0, 29), (36, 29), (22, 18), (27, 6), (36, 0), (31, 15), (29, 2), (42, 31), (4, 30), (7, 35), (17, 37), (3, 1), (23, 21), (36, 35), (33, 21), (32, 25), (22, 19), (1, 37), (33, 25), (36, 4), (1, 17), (44, 29), (30, 9), (11, 11), (41, 37), (32, 34), (10, 3), (29, 27), (33, 16), (22, 23), (33, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 15), (21, 8), (28, 36), (38, 17), (44, 41), (43, 39), (10, 7), (28, 2), (19, 8), (39, 20), (25, 29), (31, 12), (6, 25), (22, 36), (46, 21), (23, 9), (23, 30), (16, 4), (19, 27), (33, 36), (45, 19), (8, 12), (46, 8), (32, 13), (9, 6), (27, 12), (46, 33), (9, 21), (35, 9), (8, 18), (35, 31), (24, 34), (45, 0), (30, 15), (30, 1), (10, 20), (43, 9), (39, 4), (1, 34), (46, 0), (29, 1), (40, 30), (26, 15), (17, 23), (14, 39), (15, 27), (44, 20), (36, 15), (35, 20), (27, 11), (15, 12), (39, 38), (37, 3), (44, 3), (18, 38), (33, 2), (4, 2), (3, 7), (43, 40), (15, 4), (1, 28), (45, 33), (4, 31), (34, 5), (32, 38), (17, 1), (16, 20), (0, 16), (8, 7), (22, 33), (8, 37), (12, 5), (11, 17), (31, 26), (23, 16), (1, 19), (37, 35), (16, 39), (36, 23), (18, 26), (30, 40), (25, 30), (20, 26), (30, 10), (40, 8), (2, 14), (7, 40), (11, 41), (12, 16), (4, 35), (29, 7), (35, 24), (24, 31), (18, 5), (27, 17), (38, 26), (46, 10), (17, 32), (35, 39), (0, 32), (10, 1), (44, 14), (27, 27), (21, 6), (27, 32), (9, 32), (23, 41), (20, 36), (30, 35), (31, 21), (26, 12), (14, 35), (37, 9), (13, 1), (25, 10), (4, 22), (35, 5), (26, 25), (4, 41), (29, 9), (38, 22), (27, 6), (2, 16), (36, 9), (1, 21), (10, 41), (23, 7), (0, 13), (43, 5), (43, 37), (7, 9), (35, 41), (37, 10), (13, 30), (6, 3), (39, 27), (6, 35), (42, 21), (7, 17), (28, 3), (26, 0), (7, 13), (23, 20), (10, 9), (28, 31), (20, 13), (36, 20), (15, 2), (44, 24), (37, 27), (39, 1), (25, 41), (38, 39), (5, 21), (39, 12), (15, 38), (31, 41), (30, 24), (22, 21), (25, 22), (8, 23), (46, 35), (27, 1), (17, 4), (18, 16), (44, 37), (10, 5), (41, 3), (36, 10), (24, 38), (5, 6), (5, 39), (30, 29), (32, 10), (26, 17), (45, 35), (6, 29), (22, 17), (28, 22), (40, 9), (41, 26), (11, 5), (13, 28), (25, 8), (45, 40), (25, 16), (17, 40), (3, 4), (19, 38), (22, 24), (11, 0), (25, 1), (26, 6), (27, 35), (28, 29), (22, 31), (12, 38), (45, 9), (2, 13), (17, 17), (23, 17), (7, 20), (14, 37), (1, 13), (6, 11), (26, 5), (12, 10), (10, 16), (25, 28), (20, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 15), (21, 31), (35, 36), (18, 18), (11, 30), (29, 5), (6, 1), (36, 29), (14, 41), (18, 28), (34, 27), (3, 43), (11, 37), (32, 15), (37, 27), (40, 1), (13, 18), (6, 6), (16, 7), (8, 25), (8, 14), (40, 3), (22, 25), (1, 35), (28, 3), (4, 14), (26, 43), (39, 30), (8, 41), (14, 19), (26, 35), (1, 14), (16, 40), (18, 22), (39, 18), (26, 13), (20, 36), (23, 9), (35, 15), (8, 2), (34, 41), (7, 1), (11, 25), (29, 29), (4, 0), (36, 13), (3, 29), (4, 41), (9, 25), (22, 3), (36, 41), (36, 20), (29, 32), (17, 30), (22, 29), (40, 41), (3, 13), (27, 6), (7, 20), (29, 0), (12, 28), (38, 32), (37, 41), (15, 7), (7, 33), (23, 31), (5, 12), (6, 28), (25, 24), (14, 15), (5, 0), (15, 34), (35, 10), (0, 24), (13, 12), (14, 30), (18, 32), (18, 1), (38, 10), (0, 11), (29, 12), (27, 14), (16, 9), (10, 6), (40, 33), (24, 38), (6, 12), (30, 20), (20, 15), (30, 30), (9, 21), (9, 36), (32, 26), (9, 33), (3, 20), (1, 18), (31, 17), (3, 5), (22, 35), (14, 0), (31, 38), (12, 16), (34, 20), (1, 24), (15, 9), (12, 24), (39, 14), (10, 41), (24, 25), (12, 35), (33, 0), (32, 28), (19, 34), (22, 26), (26, 38), (39, 16), (29, 27), (10, 26), (1, 42), (27, 13), (24, 42), (14, 21), (40, 23), (13, 27), (30, 3), (0, 42), (19, 11), (11, 1), (33, 11), (25, 9), (26, 1), (31, 22), (3, 21), (5, 24), (6, 39), (13, 8), (12, 8), (10, 10), (36, 23), (37, 21), (14, 43), (26, 21), (31, 14), (12, 25), (19, 31), (38, 27), (23, 18), (32, 10), (29, 21), (34, 16), (21, 9), (6, 16), (22, 11), (37, 4), (32, 40), (19, 6), (1, 27), (19, 13), (2, 16), (1, 37), (25, 26), (14, 2), (17, 29), (7, 18), (8, 33), (18, 4), (36, 27), (40, 7), (10, 22), (39, 6), (24, 14), (33, 15), (26, 15), (2, 11), (25, 22), (23, 26), (5, 18), (0, 7), (19, 14), (11, 38), (37, 20), (31, 39), (19, 38), (21, 34), (14, 36), (16, 17), (4, 2), (2, 36), (4, 42), (8, 3), (38, 38), (2, 21), (8, 20), (6, 26), (7, 22), (9, 27), (21, 8), (13, 10), (14, 29), (5, 30), (28, 38), (15, 29), (5, 37), (6, 7), (25, 34), (23, 0), (33, 23), (15, 31), (33, 19), (35, 1), (31, 34), (31, 9), (3, 32), (13, 6), (14, 13), (25, 36), (0, 16), (38, 23), (19, 2), (37, 8), (23, 24), (10, 2), (24, 4), (31, 5), (0, 22), (30, 41), (15, 33), (38, 21), (35, 24), (20, 25), (23, 5), (37, 7), (39, 41), (2, 10), (20, 32), (10, 39), (21, 0), (22, 36), (24, 2), (8, 21), (33, 29), (22, 17), (39, 42), (32, 42), (38, 14), (15, 40), (23, 21), (34, 11), (7, 26), (39, 33), (24, 26), (11, 9), (18, 41), (13, 17), (14, 37), (10, 30), (3, 25), (15, 37), (8, 9), (17, 4), (14, 14), (40, 25), (4, 9), (12, 36), (24, 9), (4, 31), (21, 40), (6, 37), (8, 28), (23, 40), (20, 34), (5, 21), (14, 11), (5, 10), (4, 15), (21, 37), (12, 21), (18, 34), (24, 22), (29, 19), (36, 8), (17, 34), (13, 33), (18, 26), (7, 28), (39, 7), (15, 16), (23, 22), (28, 14), (9, 13), (21, 17), (20, 41), (33, 18), (18, 15), (4, 22), (40, 0), (26, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 43), (15, 30), (35, 23), (34, 36), (23, 6), (41, 31), (21, 27), (16, 6), (43, 29), (18, 43), (28, 29), (12, 6), (6, 5), (5, 17), (39, 4), (20, 24), (43, 42), (5, 42), (32, 43), (42, 7), (18, 5), (40, 35), (22, 29), (39, 9), (28, 31), (33, 12), (29, 19), (11, 33), (27, 16), (31, 41), (33, 20), (43, 15), (23, 26), (13, 31), (17, 1), (26, 11), (23, 21), (5, 32), (42, 1), (8, 30), (15, 12), (27, 18), (26, 39), (39, 34), (20, 12), (27, 0), (17, 8), (36, 0), (35, 29), (38, 37), (6, 39), (42, 42), (4, 22), (22, 14), (43, 31), (3, 18), (13, 34), (16, 26), (41, 9), (35, 10), (35, 3), (43, 34), (37, 10), (25, 22), (19, 23), (32, 2), (43, 33), (3, 37), (32, 6), (37, 20), (0, 10), (25, 9), (33, 7), (32, 9), (30, 31), (26, 18), (33, 6), (3, 10), (39, 21), (6, 22), (7, 30), (9, 27), (32, 37), (39, 22), (29, 43), (4, 1), (9, 39), (7, 29), (42, 34), (3, 13), (10, 18), (7, 7), (10, 42), (34, 12), (8, 3), (35, 31), (13, 22), (21, 40), (9, 19), (15, 23), (7, 11), (19, 31), (23, 25), (21, 8), (8, 2), (31, 24), (28, 41), (35, 15), (39, 25), (0, 17), (6, 7), (41, 11), (2, 28), (14, 23), (31, 1), (16, 30), (38, 14), (30, 34), (7, 18), (40, 11), (39, 26), (6, 31), (20, 25), (0, 34), (19, 43), (2, 30), (23, 18), (6, 9), (11, 40), (38, 31), (12, 5), (32, 41), (16, 32), (16, 42), (13, 2), (20, 31), (5, 4), (16, 33), (2, 35), (7, 19), (4, 5), (39, 30), (4, 6), (20, 34), (16, 12), (28, 34), (29, 14), (19, 36), (11, 14), (5, 6), (9, 37), (40, 28), (26, 14), (4, 37), (4, 0), (43, 2), (8, 35), (20, 10), (25, 32), (36, 33), (13, 26), (41, 10), (12, 32), (43, 8), (20, 23), (3, 41), (6, 6), (18, 25), (23, 24), (30, 33), (26, 28), (31, 8), (43, 16), (30, 4), (0, 22), (28, 10), (5, 1), (27, 4), (15, 15), (17, 12), (0, 41), (3, 8), (9, 12), (28, 13), (39, 0), (24, 24), (29, 9), (12, 11), (18, 18), (25, 29), (7, 1), (43, 25), (24, 15), (40, 3), (10, 34), (5, 28), (32, 21), (13, 11), (4, 17), (10, 40), (29, 42), (34, 21), (23, 10), (5, 20), (27, 9), (12, 41), (12, 22), (26, 43), (32, 22), (35, 16), (42, 27), (41, 40), (10, 24), (33, 42), (15, 20), (32, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 20), (17, 6), (19, 18), (2, 38), (34, 1), (32, 45), (17, 31), (31, 1), (23, 28), (3, 33), (24, 23), (24, 4), (10, 35), (29, 0), (24, 34), (34, 31), (15, 33), (32, 11), (16, 30), (38, 28), (9, 8), (37, 38), (3, 12), (19, 41), (20, 20), (27, 23), (35, 20), (20, 33), (34, 39), (36, 41), (32, 1), (22, 40), (23, 16), (2, 21), (31, 19), (13, 13), (29, 11), (25, 25), (27, 17), (32, 31), (34, 33), (17, 22), (10, 11), (35, 32), (24, 30), (34, 8), (1, 37), (30, 24), (3, 14), (24, 24), (24, 13), (33, 9), (21, 36), (0, 38), (23, 38), (16, 2), (20, 10), (0, 6), (33, 40), (7, 16), (16, 17), (26, 26), (27, 11), (4, 41), (25, 15), (24, 36), (8, 15), (2, 2), (0, 17), (22, 30), (12, 32), (30, 35), (9, 45), (21, 43), (36, 29), (17, 39), (21, 39), (37, 23), (38, 34), (27, 28), (5, 7), (21, 4), (13, 44), (18, 37), (33, 41), (24, 31), (24, 18), (4, 15), (30, 19), (11, 21), (16, 40), (20, 16), (17, 41), (16, 19), (36, 45), (31, 24), (15, 16), (24, 17), (20, 45), (22, 21), (28, 12), (26, 13), (30, 41), (7, 25), (31, 37), (31, 7), (38, 21), (9, 26), (3, 22), (17, 42), (0, 2), (31, 26), (9, 40), (20, 37), (21, 26), (5, 24), (6, 28), (19, 34), (19, 42), (39, 28), (25, 1), (24, 33), (7, 42), (7, 33), (21, 19), (2, 10), (15, 29), (5, 13), (28, 38), (10, 27), (28, 31), (13, 14), (9, 34), (22, 45), (34, 18), (0, 26), (30, 12), (38, 20), (4, 24), (23, 10), (26, 20), (21, 20), (8, 38), (25, 43), (37, 12), (2, 22), (6, 17), (30, 8), (22, 27), (8, 8), (11, 16), (25, 20), (39, 19), (11, 15), (3, 37), (25, 42), (2, 19), (9, 5), (33, 16), (0, 12), (2, 40), (8, 1), (15, 39), (8, 31), (5, 30), (4, 5), (3, 41), (11, 27), (27, 39), (8, 12), (5, 8), (15, 6), (24, 26), (25, 32), (12, 7), (4, 28), (32, 22), (24, 25), (27, 24), (0, 28), (17, 38), (37, 35), (2, 41), (9, 28), (36, 37), (7, 31), (18, 38), (20, 7), (5, 3), (34, 13), (13, 31), (29, 20), (17, 30), (11, 43), (25, 40), (35, 21), (15, 11), (26, 21), (19, 26), (15, 36), (7, 40), (31, 6), (37, 29), (14, 29), (4, 31), (29, 22), (34, 23), (31, 21), (33, 39), (29, 21), (21, 3), (6, 36), (31, 11), (39, 37), (2, 31), (8, 40), (39, 30), (2, 7), (8, 36), (0, 44), (5, 18), (18, 25), (35, 43), (10, 33), (10, 13), (3, 31), (31, 14), (3, 21), (39, 40), (16, 29), (4, 43), (11, 11), (7, 0), (22, 5), (28, 25), (38, 4), (31, 31), (37, 15), (14, 22), (23, 3), (1, 5), (15, 23), (9, 27), (4, 38), (19, 16), (4, 0), (14, 10), (16, 4), (34, 42), (37, 21), (11, 22), (5, 34), (1, 35), (20, 39), (30, 9), (26, 41), (35, 5), (38, 45), (5, 25), (23, 42), (2, 20), (16, 20), (20, 4), (36, 24), (27, 2), (8, 21), (35, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 26), (33, 29), (22, 17), (21, 43), (15, 39), (15, 36), (21, 1), (29, 39), (20, 19), (35, 36), (17, 11), (27, 8), (1, 5), (38, 14), (20, 17), (2, 0), (17, 43), (23, 40), (12, 34), (0, 5), (40, 43), (36, 17), (3, 23), (34, 13), (18, 20), (23, 28), (6, 23), (9, 13), (37, 30), (17, 8), (40, 17), (13, 36), (32, 31), (38, 6), (32, 28), (34, 29), (24, 10), (32, 21), (24, 40), (23, 19), (10, 34), (21, 8), (20, 8), (27, 34), (10, 27), (31, 27), (35, 40), (13, 41), (10, 5), (7, 26), (1, 24), (32, 47), (19, 10), (26, 6), (33, 26), (24, 19), (40, 25), (25, 33), (24, 16), (16, 9), (10, 46), (39, 35), (28, 47), (2, 17), (20, 43), (9, 22), (28, 0), (22, 18), (18, 39), (19, 12), (40, 12), (35, 29), (23, 31), (17, 20), (37, 36), (11, 7), (29, 20), (33, 1), (32, 43), (34, 45), (8, 30), (16, 13), (30, 45), (32, 3), (7, 7), (22, 7), (10, 15), (31, 24), (32, 1), (5, 37), (40, 35), (24, 7), (38, 12), (11, 16), (1, 8), (26, 36), (16, 33), (3, 29), (38, 42), (7, 19), (1, 13), (3, 11), (13, 17), (10, 3), (37, 38), (32, 2), (12, 3), (27, 33), (29, 21), (7, 37), (20, 14), (25, 24), (38, 22), (17, 14), (35, 37), (11, 45), (27, 40), (28, 46), (5, 24), (9, 7), (37, 12), (0, 18), (25, 34), (22, 23), (39, 11), (11, 12), (8, 8), (11, 24), (23, 34), (17, 32), (23, 8), (16, 18), (4, 5), (32, 16), (25, 8), (21, 19), (2, 46), (28, 33), (35, 41), (14, 19), (5, 6), (6, 35), (29, 25), (17, 6), (39, 2), (19, 22), (3, 44), (38, 45), (18, 12), (28, 25), (4, 7), (8, 6), (5, 12), (14, 31), (16, 29), (25, 30), (22, 24), (4, 40), (5, 1), (14, 30), (40, 0), (39, 30), (30, 28), (38, 15), (11, 42), (20, 38), (37, 47), (28, 13), (2, 42), (29, 36), (29, 6), (35, 4), (32, 29), (2, 8), (40, 27), (7, 41), (25, 47), (10, 12), (14, 17), (14, 5), (5, 3), (1, 39), (24, 27), (2, 1), (30, 18), (23, 13), (29, 1), (18, 43), (5, 27), (22, 29), (14, 46), (19, 39), (23, 47), (15, 20), (18, 19), (1, 40), (15, 46), (31, 44), (3, 43), (9, 4), (17, 10), (7, 18), (8, 39), (0, 33), (40, 33), (27, 38), (39, 5), (39, 27), (37, 19), (28, 41), (40, 14), (10, 7), (33, 37), (38, 28), (37, 21), (27, 6), (29, 32), (6, 14), (2, 4), (13, 29), (32, 17), (39, 14), (34, 41), (32, 38), (26, 22), (12, 4), (34, 19), (15, 5), (34, 21), (10, 10), (9, 41), (1, 3), (24, 46), (26, 25), (9, 19), (20, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 33), (24, 23), (27, 21), (27, 20), (22, 13), (48, 37), (36, 2), (9, 4), (4, 1), (11, 26), (39, 33), (21, 28), (35, 23), (14, 28), (18, 18), (47, 5), (17, 4), (42, 14), (13, 12), (13, 34), (30, 27), (38, 35), (35, 8), (35, 27), (24, 9), (9, 1), (11, 0), (29, 28), (2, 7), (14, 17), (10, 25), (39, 3), (43, 24), (15, 4), (26, 27), (4, 16), (31, 0), (14, 1), (20, 11), (20, 6), (22, 24), (1, 0), (19, 33), (18, 28), (10, 30), (15, 12), (40, 29), (17, 37), (34, 23), (3, 40), (24, 13), (1, 38), (29, 36), (35, 22), (29, 11), (4, 21), (12, 10), (9, 23), (13, 2), (5, 19), (45, 34), (48, 12), (36, 3), (46, 29), (24, 37), (48, 38), (6, 18), (45, 14), (17, 22), (5, 23), (35, 36), (41, 13), (13, 31), (40, 25), (43, 8), (39, 22), (44, 18), (44, 8), (38, 13), (44, 38), (13, 36), (10, 29), (37, 21), (30, 34), (6, 26), (1, 28), (1, 31), (34, 11), (8, 3), (2, 20), (35, 25), (17, 1), (0, 29), (30, 2), (20, 23), (16, 13), (21, 34), (42, 3), (24, 16), (29, 2), (14, 29), (33, 40), (2, 0), (0, 33), (35, 4), (28, 32), (2, 23), (24, 35), (27, 10), (48, 27), (36, 36), (44, 16), (5, 21), (40, 33), (0, 20), (43, 5), (6, 5), (24, 24), (7, 38), (47, 20), (4, 24), (16, 7), (33, 3), (34, 7), (37, 28), (20, 8), (35, 6), (28, 34), (2, 2), (39, 11), (37, 5), (33, 11), (38, 23), (4, 34), (32, 39), (23, 32), (36, 12), (14, 38), (40, 3), (15, 31), (12, 4), (17, 17), (2, 16), (2, 15), (36, 11), (40, 8), (17, 27), (6, 32), (45, 17), (39, 9), (46, 39), (4, 39), (7, 16), (21, 19), (15, 26), (6, 39), (3, 4), (20, 37), (33, 22), (46, 21), (38, 10), (40, 28), (14, 15), (32, 27), (12, 1), (6, 7), (18, 5), (26, 1), (36, 27), (42, 10), (43, 36), (5, 13), (39, 36), (1, 29), (21, 18), (42, 26), (35, 18), (2, 28), (14, 14), (11, 8), (1, 7), (48, 9), (32, 20), (3, 1), (44, 20), (20, 26), (16, 31), (41, 14), (15, 6), (4, 40), (21, 37), (37, 4), (44, 23), (15, 9), (28, 40), (20, 29), (45, 2), (6, 9), (7, 10), (32, 6), (30, 19), (38, 14), (2, 26), (5, 3), (43, 15), (26, 18), (38, 7), (47, 28), (20, 16), (11, 32), (22, 12), (47, 26), (41, 22), (29, 13), (38, 18), (41, 9), (26, 28), (14, 3), (26, 31), (23, 13), (22, 23), (1, 16), (30, 25), (39, 21), (9, 29), (38, 39), (43, 0), (23, 27), (38, 33), (24, 26), (5, 20), (10, 6), (30, 18), (19, 34), (40, 15), (34, 19), (2, 18), (15, 8), (3, 17), (45, 37), (40, 14), (3, 15), (27, 25), (40, 9), (32, 30), (31, 37), (0, 19), (32, 28), (18, 38), (28, 28), (9, 22), (38, 12), (23, 26), (9, 37), (18, 24), (43, 21), (27, 23), (10, 38), (28, 21), (3, 34), (28, 23), (14, 30), (31, 39), (6, 1), (14, 32), (16, 26), (37, 34), (45, 9), (25, 24), (1, 3), (4, 15), (38, 4), (21, 36), (12, 38), (48, 1), (25, 4), (44, 40), (2, 14), (9, 12), (42, 4), (17, 21), (8, 9), (1, 12), (45, 4), (8, 6), (46, 25), (47, 9), (39, 26), (44, 29), (30, 21), (43, 7), (4, 25), (8, 8), (1, 1), (8, 23), (40, 7), (19, 23), (22, 16), (36, 0), (28, 30), (37, 30), (45, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 1), (4, 39), (35, 27), (14, 5), (34, 29), (27, 38), (11, 42), (31, 38), (5, 11), (13, 32), (36, 39), (37, 0), (5, 5), (33, 35), (26, 16), (31, 5), (34, 42), (21, 11), (4, 10), (35, 15), (9, 18), (29, 4), (4, 3), (13, 7), (40, 4), (0, 17), (28, 21), (6, 15), (18, 14), (18, 12), (26, 6), (15, 40), (32, 29), (4, 28), (30, 14), (18, 11), (38, 39), (12, 18), (34, 37), (25, 12), (22, 41), (20, 16), (19, 10), (5, 0), (26, 42), (13, 14), (29, 18), (1, 25), (35, 1), (32, 44), (38, 10), (27, 28), (31, 16), (2, 44), (2, 11), (37, 34), (17, 26), (6, 36), (8, 15), (31, 44), (18, 26), (22, 16), (30, 12), (30, 27), (35, 38), (35, 18), (25, 14), (36, 3), (1, 40), (6, 38), (16, 17), (36, 0), (14, 38), (32, 17), (18, 8), (29, 39), (14, 17), (6, 18), (11, 30), (33, 18), (19, 21), (22, 2), (32, 5), (10, 2), (13, 36), (29, 35), (6, 17), (27, 20), (17, 7), (6, 10), (7, 23), (2, 19), (17, 36), (32, 11), (40, 31), (17, 5), (29, 5), (39, 21), (9, 43), (39, 27), (4, 2), (11, 7), (1, 29), (9, 36), (3, 18), (34, 16), (3, 40), (17, 19), (22, 13), (19, 39), (17, 30), (4, 27), (2, 1), (2, 25), (16, 22), (13, 40), (23, 32), (25, 25), (36, 20), (31, 43), (36, 41), (17, 20), (28, 7), (3, 38), (24, 3), (11, 26), (11, 18), (15, 34), (23, 2), (35, 21), (0, 43), (31, 19), (31, 23), (34, 7), (18, 24), (26, 11), (1, 13), (24, 11), (13, 11), (3, 2), (39, 33), (4, 13), (35, 17), (10, 27), (30, 35), (28, 31), (33, 42), (1, 12), (38, 27), (28, 2), (31, 9), (33, 27), (2, 23), (10, 40), (20, 39), (34, 43), (35, 36), (10, 8), (25, 5), (22, 7), (16, 27), (31, 12), (3, 26), (0, 21), (17, 41), (26, 4), (34, 36), (3, 23), (19, 27), (8, 23), (13, 16), (2, 20), (21, 20), (1, 19), (11, 2), (37, 30), (13, 31), (6, 43), (10, 16), (29, 3), (16, 9), (33, 25), (19, 32), (13, 3), (25, 22), (16, 10), (15, 2), (10, 42), (24, 21), (18, 0), (15, 44), (2, 13), (15, 35), (12, 34), (22, 8), (29, 32), (18, 18), (8, 19), (32, 31), (30, 3), (9, 9), (0, 9), (29, 15), (1, 36), (22, 42), (9, 38), (8, 11), (3, 36), (10, 9), (13, 0), (27, 12), (13, 4), (3, 30), (38, 18), (30, 1), (10, 33), (9, 15), (36, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 41), (36, 2), (30, 36), (26, 45), (28, 16), (23, 13), (39, 41), (15, 32), (24, 45), (0, 16), (25, 6), (13, 28), (24, 46), (34, 42), (32, 48), (15, 22), (35, 8), (12, 5), (11, 10), (18, 27), (24, 25), (25, 3), (19, 47), (7, 34), (25, 45), (33, 13), (34, 30), (15, 7), (4, 24), (14, 13), (17, 19), (23, 37), (0, 11), (29, 27), (38, 46), (18, 10), (43, 44), (31, 30), (17, 28), (1, 16), (10, 25), (12, 40), (26, 46), (29, 39), (40, 46), (21, 30), (33, 0), (1, 27), (8, 20), (45, 19), (27, 23), (45, 40), (2, 16), (19, 26), (26, 18), (24, 17), (38, 29), (17, 44), (37, 11), (14, 7), (7, 46), (0, 31), (44, 9), (12, 1), (27, 43), (6, 47), (9, 47), (7, 32), (0, 1), (14, 20), (9, 41), (12, 22), (3, 16), (25, 13), (4, 33), (28, 19), (21, 34), (27, 12), (13, 0), (7, 40), (39, 17), (27, 24), (44, 19), (36, 27), (30, 26), (17, 0), (39, 19), (14, 5), (45, 33), (43, 24), (18, 34), (44, 8), (28, 13), (36, 16), (43, 39), (15, 23), (4, 34), (0, 25), (43, 36), (34, 47), (27, 38), (44, 25), (32, 0), (25, 21), (6, 31), (39, 31), (6, 25), (2, 28), (19, 41), (2, 26), (21, 3), (27, 16), (21, 7), (16, 40), (23, 41), (6, 24), (24, 13), (39, 25), (15, 3), (39, 38), (1, 13), (13, 29), (29, 37), (43, 3), (34, 25), (44, 6), (25, 22), (20, 14), (36, 34), (21, 37), (26, 43), (25, 25), (10, 44), (0, 5), (27, 30), (43, 43), (27, 15), (31, 13), (23, 25), (45, 12), (22, 22), (38, 43), (31, 32), (5, 11), (28, 39), (42, 31), (40, 17), (33, 44), (16, 36), (20, 16), (35, 35), (23, 44), (6, 46), (22, 32), (32, 46), (35, 20), (36, 24), (28, 31), (6, 18), (0, 34), (5, 48), (34, 33), (23, 9), (13, 4), (1, 30), (32, 37), (11, 18), (19, 48), (33, 3), (32, 11), (32, 20), (35, 28), (24, 31), (7, 39), (30, 48), (17, 27), (5, 31), (21, 21), (23, 39), (6, 48), (21, 5), (30, 14), (20, 19), (14, 32), (32, 30), (33, 21), (43, 26), (25, 39), (40, 7), (3, 0), (30, 41), (3, 15), (35, 39), (18, 31), (5, 5), (38, 44), (34, 9), (27, 42), (30, 33), (30, 22), (8, 4), (12, 11), (0, 3), (1, 39), (23, 31), (24, 33), (43, 1), (19, 25), (5, 6), (31, 33), (45, 1), (30, 13), (32, 32), (21, 16), (4, 16), (24, 9), (34, 21), (38, 12), (40, 38), (10, 23), (37, 7), (32, 31), (42, 25), (7, 18), (17, 33), (36, 15), (10, 24), (31, 27), (25, 18), (8, 6), (37, 40), (9, 13), (3, 10), (31, 41), (13, 23), (43, 15), (42, 1), (14, 34), (32, 38), (45, 20), (26, 22), (16, 43), (13, 10), (11, 0), (5, 34), (18, 20), (2, 41), (37, 4), (31, 1), (1, 17), (45, 2), (22, 12), (5, 2), (9, 32), (1, 31), (42, 45), (9, 40), (11, 32), (4, 8), (34, 8), (22, 3), (37, 16), (10, 15), (44, 11), (18, 38), (0, 4), (39, 16), (37, 13), (32, 43), (14, 22), (26, 34), (40, 9), (21, 12), (42, 32), (7, 26), (42, 42), (22, 38), (45, 30), (10, 4), (21, 23), (30, 30), (43, 18), (25, 29), (39, 21), (16, 28), (14, 6), (35, 48), (41, 42), (14, 8), (10, 13), (11, 24), (27, 8), (0, 39), (36, 41), (34, 15), (25, 35), (19, 6), (20, 13), (17, 26), (21, 45), (20, 30), (2, 9), (18, 0), (41, 41), (14, 12), (33, 27), (14, 29), (1, 12), (8, 19), (40, 2), (24, 36), (35, 43), (40, 3), (8, 12), (41, 19), (38, 15), (6, 27), (40, 13), (35, 5), (2, 8), (40, 48), (3, 22), (16, 31), (42, 29), (16, 18), (16, 7), (15, 38), (11, 7), (41, 40), (32, 45), (5, 17), (24, 23), (27, 26), (3, 4), (7, 24), (6, 39), (23, 19), (29, 24), (41, 23), (21, 1), (39, 36), (30, 42), (41, 20), (21, 39), (15, 31), (40, 21), (8, 7), (3, 13), (37, 32), (45, 29), (30, 37), (14, 3), (31, 26), (16, 8), (45, 22), (27, 31), (0, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 37), (34, 4), (15, 26), (36, 12), (3, 36), (25, 6), (40, 40), (17, 37), (16, 22), (41, 25), (36, 2), (5, 4), (17, 2), (41, 2), (42, 24), (21, 34), (20, 30), (12, 22), (29, 40), (7, 15), (7, 26), (3, 13), (25, 21), (15, 38), (16, 0), (6, 25), (33, 14), (42, 26), (4, 23), (12, 30), (9, 25), (19, 17), (25, 16), (20, 20), (18, 24), (32, 27), (20, 3), (15, 2), (26, 24), (32, 3), (39, 5), (24, 2), (1, 22), (8, 27), (3, 9), (38, 4), (17, 29), (29, 17), (33, 8), (31, 38), (25, 30), (29, 3), (20, 24), (1, 13), (35, 29), (6, 29), (3, 20), (39, 18), (30, 27), (39, 3), (38, 39), (11, 16), (35, 12), (25, 12), (29, 1), (33, 35), (9, 27), (29, 27), (8, 2), (42, 30), (11, 32), (36, 11), (23, 26), (19, 2), (24, 38), (1, 35), (15, 15), (0, 31), (28, 15), (32, 11), (36, 19), (3, 22), (20, 22), (21, 5), (22, 17), (1, 33), (38, 34), (41, 35), (37, 2), (34, 10), (37, 37), (15, 40), (14, 30), (1, 5), (25, 25), (11, 7), (0, 29), (14, 35), (40, 38), (25, 32), (15, 13), (11, 33), (36, 38), (31, 9), (19, 30), (22, 29), (3, 37), (16, 10), (42, 15), (34, 20), (38, 1), (15, 4), (36, 22), (42, 1), (34, 26), (37, 8), (25, 13), (23, 13), (27, 33), (39, 13), (27, 30), (21, 9), (15, 20), (28, 12), (13, 37), (38, 21), (11, 6), (36, 33), (5, 22), (32, 25), (10, 23), (11, 28), (42, 2), (27, 10), (19, 13), (26, 25), (36, 3), (28, 35), (40, 5), (3, 7), (41, 28), (1, 12), (11, 35), (4, 10), (42, 17), (32, 23), (38, 28), (8, 30), (2, 5), (17, 17), (15, 27), (14, 34), (6, 40), (37, 12), (29, 34), (36, 6), (31, 8), (31, 18), (34, 3), (16, 13), (33, 31), (33, 3), (29, 9), (25, 4), (23, 32), (27, 9), (38, 30), (18, 8), (8, 39), (6, 15), (32, 32), (26, 9), (18, 28), (35, 35), (34, 6), (29, 19), (7, 39), (1, 10), (40, 8), (12, 3), (26, 30), (31, 23), (41, 40), (19, 0), (16, 19), (22, 27), (31, 1), (2, 26), (19, 34), (26, 0), (31, 36), (34, 9), (24, 10), (9, 15), (8, 7), (35, 21), (12, 21), (37, 25), (5, 19), (35, 28), (31, 13), (41, 24), (10, 34), (42, 31), (12, 1), (24, 3), (17, 32), (8, 18), (4, 3), (23, 5), (31, 3), (28, 30), (42, 8), (37, 38), (26, 16), (6, 26), (34, 8), (16, 26), (33, 2), (17, 15), (26, 39), (35, 33), (26, 19), (42, 0), (1, 17), (27, 36), (34, 35), (40, 27), (17, 23), (32, 10), (25, 29), (40, 7), (6, 18), (7, 18), (24, 32), (31, 4), (14, 5), (16, 34), (20, 5), (42, 33), (13, 6), (20, 19), (1, 20), (2, 11), (7, 29), (39, 0), (22, 26), (20, 0), (10, 19), (7, 16), (18, 10), (36, 10), (35, 13), (29, 16), (11, 2), (15, 11), (13, 17), (25, 40), (10, 38), (16, 32), (10, 17), (5, 16), (37, 31), (21, 35), (21, 24), (26, 21), (11, 11), (11, 40), (31, 19), (31, 20), (33, 20), (15, 16), (0, 11), (38, 7), (5, 38), (32, 0), (13, 16), (18, 1), (32, 15), (25, 11), (22, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 43), (15, 40), (25, 31), (26, 8), (39, 34), (1, 36), (21, 9), (27, 45), (10, 41), (22, 2), (29, 29), (28, 18), (25, 16), (29, 44), (6, 28), (26, 1), (11, 34), (28, 29), (8, 16), (38, 18), (42, 26), (23, 42), (10, 17), (2, 12), (22, 45), (41, 17), (42, 15), (40, 1), (17, 35), (0, 26), (39, 8), (37, 5), (13, 0), (23, 7), (31, 36), (31, 11), (19, 12), (25, 20), (21, 36), (27, 42), (2, 4), (1, 44), (23, 27), (39, 20), (40, 25), (27, 38), (4, 41), (0, 20), (3, 1), (13, 9), (42, 5), (37, 13), (26, 40), (26, 17), (41, 24), (22, 42), (30, 2), (24, 20), (12, 12), (15, 5), (33, 23), (7, 11), (8, 29), (40, 16), (4, 7), (14, 24), (40, 33), (5, 44), (20, 31), (12, 27), (28, 2), (5, 43), (24, 16), (21, 11), (4, 26), (24, 18), (3, 21), (0, 43), (9, 19), (37, 25), (36, 32), (9, 4), (31, 4), (41, 38), (10, 32), (31, 42), (29, 21), (12, 36), (24, 5), (27, 27), (14, 35), (35, 12), (22, 13), (6, 24), (23, 40), (16, 7), (38, 42), (9, 29), (9, 8), (36, 4), (16, 28), (12, 31), (26, 21), (15, 34), (37, 10), (17, 22), (27, 26), (35, 36), (14, 21), (30, 34), (10, 40), (24, 26), (2, 2), (17, 34), (8, 32), (13, 6), (23, 20), (40, 20), (23, 22), (19, 6), (37, 36), (27, 46), (34, 9), (42, 42), (14, 38), (5, 7), (34, 27), (2, 6), (3, 38), (6, 42), (30, 18), (37, 22), (26, 10), (18, 27), (42, 35), (41, 4), (32, 5), (39, 32), (34, 21), (20, 13), (42, 6), (3, 19), (22, 40), (22, 35), (28, 19), (33, 43), (9, 46), (6, 44), (11, 18), (35, 9), (16, 37), (42, 11), (10, 13), (24, 38), (0, 1), (0, 7), (16, 16), (20, 22), (21, 10), (32, 25), (11, 41), (0, 10), (9, 2), (10, 25), (0, 33), (12, 8), (36, 43), (13, 25), (37, 20), (35, 18), (33, 38), (4, 34), (17, 8), (18, 1), (42, 18), (16, 25), (21, 37), (11, 23), (29, 17), (20, 1), (12, 45), (30, 3), (2, 19), (5, 14), (6, 34), (38, 23), (33, 11), (18, 28), (7, 42), (0, 34), (23, 6), (3, 11), (20, 39), (37, 46), (16, 15), (38, 19), (3, 18), (9, 36), (5, 18), (33, 12), (5, 13), (25, 24), (39, 2), (41, 22), (31, 46), (4, 33), (31, 29), (12, 25), (40, 12), (31, 17), (3, 27), (8, 1), (21, 0), (25, 30), (26, 2), (33, 7), (3, 45), (41, 31), (27, 1), (4, 9), (39, 10), (15, 15), (33, 36), (35, 8), (1, 15), (40, 7), (35, 40), (2, 16), (31, 35), (20, 10), (34, 28), (39, 7), (34, 8), (16, 27), (14, 17), (18, 19), (13, 44), (14, 26), (4, 12), (11, 31), (7, 10), (38, 38), (35, 35), (11, 42), (2, 3), (19, 15), (21, 24), (32, 1), (20, 17), (20, 12), (34, 0), (19, 30), (42, 2), (31, 12), (21, 15), (0, 35), (3, 8), (0, 8), (27, 2), (38, 17), (16, 20), (11, 7), (27, 4), (6, 15), (4, 16), (17, 16), (21, 8), (23, 37), (4, 40), (22, 16), (29, 14), (9, 34), (5, 10), (37, 40), (15, 23), (41, 9), (8, 6), (34, 5), (24, 21), (16, 45), (15, 13), (15, 43), (32, 42), (31, 34), (6, 4), (5, 0), (4, 45), (15, 2), (34, 17), (22, 9), (9, 1), (36, 3), (35, 13), (29, 3), (19, 43), (14, 25), (21, 19), (35, 2), (21, 33), (4, 32), (26, 46), (17, 27), (20, 44), (7, 9), (25, 39), (19, 18), (13, 38), (40, 44), (18, 8), (33, 26), (34, 39), (39, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 18), (38, 31), (24, 30), (4, 25), (22, 30), (39, 35), (33, 7), (13, 8), (10, 12), (12, 2), (2, 9), (7, 34), (13, 31), (35, 17), (33, 29), (39, 12), (14, 40), (1, 30), (15, 17), (35, 18), (19, 10), (22, 10), (7, 3), (5, 19), (8, 19), (37, 33), (11, 21), (15, 0), (4, 15), (7, 18), (37, 29), (25, 6), (0, 33), (4, 3), (38, 22), (28, 10), (33, 5), (5, 20), (28, 20), (11, 0), (9, 16), (29, 5), (16, 23), (18, 22), (37, 38), (6, 8), (22, 14), (9, 37), (34, 18), (21, 23), (38, 6), (28, 2), (37, 30), (12, 17), (15, 2), (28, 25), (26, 8), (0, 1), (20, 7), (4, 21), (29, 39), (35, 30), (32, 18), (19, 30), (20, 15), (22, 37), (37, 35), (20, 24), (39, 36), (19, 21), (21, 35), (19, 24), (38, 29), (25, 17), (7, 36), (6, 7), (24, 4), (16, 34), (20, 28), (19, 13), (25, 11), (21, 4), (2, 40), (33, 17), (15, 16), (24, 23), (29, 24), (1, 3), (15, 18), (8, 7), (13, 15), (25, 38), (33, 12), (10, 19), (9, 9), (30, 0), (30, 9), (8, 15), (1, 12), (21, 7), (12, 10), (38, 28), (4, 2), (25, 14), (37, 34), (9, 2), (30, 34), (14, 27), (20, 3), (13, 4), (16, 8), (16, 1), (27, 28), (20, 25), (33, 6), (24, 31), (29, 6), (21, 28), (20, 36), (11, 8), (23, 38), (38, 11), (17, 33), (29, 29), (12, 1), (13, 0), (25, 2), (9, 7), (13, 23), (36, 7), (19, 4), (33, 35), (36, 27), (5, 22), (22, 12), (20, 38), (2, 38), (13, 39), (27, 20), (17, 24), (23, 24), (36, 15), (23, 27), (36, 2), (20, 27), (20, 26), (32, 24), (29, 37), (12, 7), (28, 1), (11, 38), (29, 26), (21, 34), (35, 14), (16, 22), (6, 24), (3, 21), (34, 28), (31, 9), (37, 37), (25, 18), (17, 31), (38, 36), (25, 32), (16, 24), (30, 32), (22, 39), (14, 16), (0, 26), (34, 20), (36, 4), (29, 36), (20, 11), (17, 3), (31, 25), (16, 3), (6, 14), (22, 4), (10, 9), (23, 13), (5, 40), (35, 25), (15, 10), (27, 27), (13, 36), (22, 27), (26, 34), (2, 5), (17, 11), (15, 24), (37, 39), (36, 36), (24, 36), (19, 9), (25, 30), (33, 38), (26, 26), (6, 4), (31, 14), (19, 2), (35, 35), (3, 6), (28, 34), (4, 17), (24, 32), (17, 7), (6, 11), (17, 34), (8, 11), (8, 14), (37, 10), (18, 18), (20, 12), (2, 10), (37, 32), (12, 4), (6, 25), (17, 22), (32, 36), (5, 8), (11, 6), (4, 20), (28, 14), (33, 37), (23, 34), (5, 36), (36, 1), (38, 37), (16, 27), (0, 22), (28, 13), (9, 13), (26, 23), (13, 9), (37, 28), (33, 39), (26, 15), (30, 29), (16, 16), (14, 0), (17, 36), (22, 2), (15, 28), (10, 32), (19, 34), (12, 32), (22, 25), (35, 11), (16, 28), (30, 5), (6, 0), (11, 34), (23, 1), (36, 10), (17, 23), (30, 24), (24, 15), (19, 36), (32, 16), (14, 25), (34, 19), (31, 38), (4, 7), (27, 23), (33, 20), (31, 13), (14, 23), (30, 3), (7, 4), (28, 23), (17, 5), (30, 26), (13, 19), (26, 17), (9, 11), (32, 5), (4, 1), (12, 15), (19, 15), (23, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (47, 9), (22, 21), (41, 19), (21, 12), (44, 15), (13, 24), (12, 37), (28, 22), (41, 28), (10, 30), (37, 0), (26, 18), (8, 41), (40, 0), (43, 9), (11, 18), (24, 38), (26, 10), (32, 13), (47, 19), (2, 22), (7, 0), (46, 4), (38, 1), (40, 14), (42, 36), (39, 3), (47, 15), (25, 7), (34, 31), (6, 7), (45, 7), (15, 15), (26, 35), (10, 20), (42, 37), (38, 38), (16, 20), (35, 30), (19, 15), (37, 9), (24, 37), (13, 11), (38, 17), (40, 18), (47, 41), (26, 22), (48, 6), (33, 18), (38, 20), (32, 34), (27, 28), (7, 36), (11, 37), (42, 16), (42, 1), (38, 0), (13, 42), (4, 26), (35, 42), (39, 26), (39, 36), (2, 9), (40, 40), (15, 5), (20, 22), (39, 1), (45, 11), (34, 8), (28, 27), (5, 26), (15, 11), (42, 41), (22, 8), (19, 32), (34, 15), (36, 8), (9, 23), (41, 24), (8, 5), (43, 29), (44, 0), (38, 36), (11, 7), (5, 39), (1, 37), (32, 24), (19, 36), (12, 8), (14, 12), (29, 34), (21, 18), (4, 19), (48, 20), (11, 2), (2, 10), (38, 30), (42, 10), (20, 34), (42, 30), (40, 11), (11, 16), (44, 31), (43, 20), (18, 25), (22, 18), (38, 21), (22, 2), (18, 35), (36, 30), (41, 33), (24, 28), (13, 1), (43, 28), (17, 18), (27, 24), (38, 40), (22, 3), (46, 0), (48, 13), (21, 16), (39, 11), (32, 17), (18, 15), (7, 19), (23, 14), (40, 20), (3, 42), (23, 6), (22, 14), (32, 10), (23, 28), (14, 29), (21, 34), (40, 29), (34, 6), (26, 31), (10, 14), (9, 0), (18, 40), (16, 40), (23, 24), (12, 42), (42, 24), (45, 33), (11, 13), (21, 40), (30, 28), (48, 39), (17, 6), (15, 21), (40, 35), (38, 28), (6, 4), (47, 38), (45, 38), (27, 37), (45, 13), (38, 10), (9, 34), (17, 5), (34, 39), (16, 35), (23, 20), (41, 41), (41, 29), (35, 3), (13, 8), (40, 30), (13, 38), (36, 21), (8, 38), (17, 40), (35, 24), (31, 23), (23, 27), (10, 4), (4, 14), (48, 9), (15, 19), (4, 32), (8, 21), (19, 12), (46, 37), (27, 26), (41, 37), (16, 33), (33, 35), (47, 26), (30, 41), (44, 19), (2, 28), (23, 22), (3, 31), (9, 30), (26, 12), (45, 23), (11, 1), (33, 2), (37, 42), (14, 4), (24, 7), (17, 25), (2, 34), (35, 18), (37, 10), (43, 19), (17, 3), (3, 26), (39, 27), (24, 36), (19, 42), (46, 18), (34, 29), (16, 7), (20, 35), (47, 20), (36, 42), (3, 28), (32, 16), (13, 16), (36, 33), (5, 28), (32, 3), (9, 35), (31, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 34), (27, 11), (33, 12), (11, 43), (37, 26), (4, 36), (1, 34), (18, 9), (35, 36), (40, 10), (33, 2), (24, 8), (15, 28), (19, 8), (38, 20), (37, 35), (7, 23), (12, 0), (1, 33), (39, 9), (34, 5), (18, 18), (16, 42), (4, 18), (16, 32), (39, 31), (6, 24), (37, 14), (24, 39), (31, 3), (28, 25), (19, 31), (39, 8), (18, 28), (29, 38), (5, 0), (25, 34), (0, 11), (4, 39), (8, 43), (21, 7), (23, 22), (12, 10), (33, 1), (21, 41), (15, 14), (37, 24), (35, 29), (21, 0), (28, 3), (6, 23), (1, 32), (7, 17), (2, 8), (14, 13), (20, 32), (25, 4), (10, 34), (36, 26), (34, 35), (36, 31), (32, 5), (26, 23), (19, 39), (9, 30), (13, 9), (38, 11), (31, 13), (24, 13), (14, 26), (22, 0), (7, 4), (20, 18), (2, 29), (34, 18), (24, 4), (20, 0), (19, 29), (32, 20), (22, 2), (17, 20), (0, 26), (31, 16), (6, 1), (30, 41), (4, 37), (34, 36), (0, 17), (39, 42), (3, 11), (31, 4), (30, 24), (7, 14), (40, 6), (23, 28), (29, 6), (37, 36), (22, 4), (26, 22), (13, 27), (30, 30), (35, 28), (27, 13), (0, 25), (12, 33), (13, 18), (5, 40), (20, 19), (33, 3), (22, 43), (2, 26), (29, 39), (20, 21), (27, 19), (9, 25), (7, 5), (31, 35), (20, 37), (37, 17), (33, 40), (0, 12), (25, 22), (26, 43), (26, 5), (34, 19), (11, 35), (25, 33), (39, 24), (19, 38), (12, 37), (31, 0), (0, 29), (26, 0), (39, 23), (12, 43), (19, 19), (34, 30), (32, 13), (23, 40), (12, 32), (14, 2), (25, 23), (24, 21), (6, 39), (38, 8), (40, 30), (23, 29), (39, 35), (36, 6), (3, 3), (33, 36), (36, 16), (11, 24), (36, 24), (31, 31), (28, 6), (34, 29), (7, 31), (4, 33), (23, 13), (38, 38), (31, 32), (6, 12), (21, 6), (4, 34), (31, 43), (10, 4), (0, 22), (28, 38), (5, 26), (40, 37), (31, 9), (10, 26), (29, 19), (7, 22), (27, 40), (8, 12), (14, 35), (5, 19), (28, 18), (39, 2), (11, 28), (17, 41), (13, 0), (22, 19), (37, 3), (14, 14), (40, 41), (36, 5), (10, 11), (17, 34), (13, 41), (23, 6), (14, 37), (0, 8), (17, 18), (32, 0), (19, 21), (6, 22), (17, 36), (24, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 13), (45, 33), (29, 7), (47, 39), (28, 45), (5, 14), (9, 12), (47, 14), (6, 44), (14, 0), (36, 28), (34, 17), (24, 16), (27, 23), (17, 28), (25, 30), (19, 44), (44, 43), (39, 24), (19, 31), (14, 34), (48, 30), (47, 25), (31, 0), (24, 39), (9, 41), (8, 40), (5, 33), (35, 28), (24, 35), (21, 5), (5, 32), (2, 13), (21, 41), (32, 2), (45, 5), (9, 0), (1, 3), (0, 20), (7, 36), (42, 41), (16, 14), (46, 2), (16, 44), (36, 29), (16, 13), (6, 36), (29, 39), (5, 19), (19, 25), (21, 27), (43, 30), (48, 7), (30, 29), (28, 8), (12, 2), (5, 23), (11, 41), (45, 38), (33, 30), (47, 38), (40, 10), (31, 23), (5, 7), (4, 32), (16, 27), (41, 33), (35, 24), (17, 41), (29, 31), (3, 33), (29, 0), (22, 3), (41, 36), (4, 28), (6, 3), (33, 1), (0, 41), (22, 40), (32, 33), (23, 25), (39, 0), (18, 6), (22, 18), (19, 10), (44, 17), (23, 40), (8, 37), (43, 41), (7, 17), (20, 23), (17, 0), (22, 12), (32, 42), (40, 34), (39, 34), (31, 43), (3, 19), (4, 23), (7, 44), (31, 44), (44, 6), (18, 40), (31, 14), (1, 36), (34, 7), (40, 39), (36, 5), (42, 20), (33, 17), (38, 23), (15, 30), (36, 39), (16, 5), (3, 9), (10, 22), (32, 28), (17, 43), (11, 34), (36, 38), (11, 9), (12, 29), (9, 17), (3, 15), (31, 13), (5, 6), (37, 28), (5, 12), (36, 33), (17, 38), (30, 4), (45, 34), (32, 35), (3, 38), (26, 24), (0, 32), (47, 29), (37, 23), (34, 38), (45, 20), (41, 24), (12, 26), (0, 14), (45, 28), (8, 42), (17, 30), (19, 29), (14, 23), (16, 28), (16, 29), (36, 17), (15, 22), (4, 42), (22, 28), (16, 33), (44, 26), (10, 36), (21, 16), (47, 20), (26, 21), (31, 19), (40, 6), (45, 23), (45, 42), (0, 16), (1, 0), (30, 22), (39, 36), (46, 26), (25, 41), (20, 9), (19, 3), (44, 5), (17, 5), (31, 42), (43, 43), (36, 12), (24, 40), (47, 24), (2, 32), (18, 27), (39, 45), (25, 29), (22, 25), (15, 12), (42, 44), (13, 28), (38, 28), (43, 1), (2, 19), (48, 35), (25, 16), (47, 33), (12, 25), (25, 9), (22, 16), (35, 13), (13, 2), (42, 24), (42, 38), (8, 32), (17, 45), (38, 11), (3, 6), (29, 26), (2, 38), (14, 18), (10, 9), (13, 33), (40, 37), (48, 44), (7, 19), (34, 14), (42, 16), (7, 9), (8, 11), (28, 6), (12, 39), (5, 34), (30, 35), (7, 32), (20, 18), (45, 26), (31, 37), (21, 6), (19, 40), (30, 31), (2, 18), (42, 4), (19, 35), (15, 34), (40, 22), (16, 3), (41, 45), (19, 23), (12, 22), (46, 33), (36, 26), (5, 3), (31, 28), (13, 27), (33, 15), (33, 34), (14, 17), (33, 8), (13, 40), (20, 16), (16, 31), (28, 27), (43, 11), (43, 15), (33, 2), (13, 9), (20, 43), (46, 14), (22, 24), (39, 5), (48, 31), (19, 0), (16, 8), (25, 13), (2, 41), (47, 2), (7, 12), (8, 13), (21, 10), (18, 38), (45, 14), (29, 45), (3, 17), (4, 17), (20, 1), (38, 31), (42, 10), (47, 44), (45, 2), (31, 6), (0, 17), (45, 31), (23, 35), (33, 29), (33, 0), (43, 33), (4, 5), (32, 12), (11, 42), (10, 19), (38, 18), (24, 34), (31, 34), (33, 14), (33, 13), (8, 14), (30, 17), (3, 25), (35, 44), (9, 7), (24, 21), (0, 2), (2, 4), (11, 30), (12, 19), (38, 40), (26, 13), (46, 1), (12, 33), (1, 43), (4, 0), (26, 3), (48, 2), (5, 44), (43, 24), (17, 2), (20, 38), (45, 25), (41, 9), (48, 19), (47, 11), (35, 0), (1, 22), (38, 27), (48, 3), (40, 36), (1, 5), (22, 13), (38, 14), (25, 15), (11, 36), (11, 32), (41, 41), (5, 9), (8, 20), (2, 25), (6, 35), (36, 3), (7, 31), (30, 26), (9, 27), (16, 37), (30, 11), (38, 42), (12, 14), (2, 9), (39, 28), (7, 10), (4, 13), (9, 28), (10, 30), (18, 1), (28, 1), (17, 31), (40, 43), (42, 45), (39, 12), (19, 33), (28, 9), (26, 8), (30, 32), (1, 20), (37, 41), (47, 37), (21, 39), (33, 9), (13, 3), (41, 1), (9, 43), (19, 45), (21, 15), (3, 30), (7, 0), (12, 28), (15, 31), (20, 7), (24, 2), (40, 27), (31, 21), (24, 1), (40, 32), (24, 18), (27, 6), (37, 27), (7, 30), (25, 44), (8, 34), (17, 26), (24, 26), (11, 5), (2, 6), (6, 34), (23, 2), (17, 12), (21, 31), (1, 32), (46, 22), (10, 10), (40, 14), (43, 10), (43, 5), (32, 27), (34, 10), (26, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 10), (36, 9), (21, 33), (27, 36), (26, 2), (39, 6), (13, 39), (32, 2), (5, 7), (17, 17), (16, 24), (35, 40), (14, 30), (39, 32), (18, 3), (33, 18), (18, 40), (23, 11), (19, 18), (19, 0), (13, 18), (1, 3), (2, 34), (17, 16), (25, 39), (16, 22), (18, 23), (37, 8), (7, 22), (7, 0), (37, 13), (25, 27), (36, 30), (23, 37), (8, 10), (28, 21), (12, 3), (23, 25), (37, 39), (28, 16), (40, 33), (2, 32), (29, 17), (22, 15), (35, 31), (8, 38), (19, 3), (14, 21), (17, 2), (41, 18), (33, 21), (28, 28), (7, 31), (27, 19), (32, 15), (16, 17), (13, 3), (28, 31), (39, 20), (36, 3), (40, 36), (23, 7), (11, 0), (20, 27), (17, 41), (27, 8), (24, 18), (26, 18), (28, 12), (16, 25), (3, 29), (34, 31), (34, 17), (12, 31), (36, 23), (26, 5), (32, 36), (38, 3), (41, 26), (7, 15), (28, 37), (37, 28), (30, 19), (38, 14), (2, 9), (11, 20), (16, 13), (3, 34), (9, 27), (22, 12), (15, 4), (15, 21), (12, 34), (36, 1), (34, 14), (31, 7), (31, 5), (39, 35), (38, 28), (31, 16), (28, 35), (36, 27), (29, 0), (32, 28), (22, 0), (35, 11), (14, 10), (33, 24), (3, 5), (16, 39), (4, 31), (35, 6), (12, 18), (10, 28), (19, 16), (24, 40), (29, 18), (9, 0), (25, 40), (27, 28), (34, 11), (18, 34), (35, 23), (28, 33), (24, 38), (3, 38), (32, 14), (13, 26), (19, 5), (16, 6), (2, 26), (28, 27), (9, 19), (39, 26), (20, 35), (30, 23), (16, 27), (28, 26), (32, 27), (5, 36), (38, 35), (31, 29), (33, 30), (42, 4), (10, 35), (12, 13), (29, 25), (12, 30), (15, 13), (12, 16), (20, 34), (23, 5), (26, 32), (13, 7), (2, 2), (7, 1), (21, 15), (10, 19), (17, 39), (7, 25), (32, 10), (30, 15), (27, 30), (27, 23), (38, 18), (9, 3), (24, 16), (3, 28), (33, 5), (42, 40), (40, 19), (34, 29), (14, 33), (33, 7), (33, 25), (22, 39), (24, 0), (15, 26), (30, 12), (11, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 36), (1, 7), (7, 29), (29, 14), (30, 9), (34, 19), (27, 0), (40, 6), (42, 23), (29, 22), (13, 36), (15, 6), (39, 12), (29, 3), (1, 16), (39, 38), (37, 25), (2, 23), (26, 19), (14, 12), (1, 10), (33, 32), (31, 0), (20, 21), (2, 33), (27, 34), (43, 16), (41, 23), (20, 33), (30, 34), (38, 3), (21, 30), (22, 24), (25, 6), (38, 29), (43, 8), (29, 2), (24, 20), (30, 0), (9, 29), (36, 32), (23, 2), (24, 38), (18, 24), (35, 25), (35, 32), (10, 16), (5, 13), (27, 21), (28, 24), (4, 36), (25, 33), (22, 2), (4, 21), (32, 40), (10, 29), (14, 20), (12, 39), (29, 11), (14, 1), (31, 3), (29, 17), (2, 17), (24, 33), (20, 39), (34, 34), (38, 41), (19, 12), (9, 2), (17, 6), (43, 20), (9, 1), (36, 24), (12, 10), (6, 0), (42, 19), (8, 20), (19, 6), (8, 37), (33, 0), (36, 18), (24, 28), (41, 6), (18, 23), (20, 38), (16, 23), (5, 11), (38, 19), (31, 33), (25, 37), (42, 39), (42, 5), (10, 17), (2, 28), (28, 16), (26, 23), (4, 26), (2, 27), (4, 32), (21, 21), (0, 31), (16, 10), (25, 41), (5, 28), (40, 41), (38, 39), (12, 6), (41, 25), (2, 41), (32, 29), (41, 8), (6, 17), (33, 22), (23, 20), (10, 18), (36, 14), (31, 4), (29, 33), (41, 0), (0, 14), (22, 7), (13, 7), (14, 27), (36, 28), (10, 40), (25, 17), (1, 1), (9, 37), (7, 3), (35, 14), (35, 5), (1, 35), (34, 18), (29, 26), (29, 37), (18, 26), (32, 16), (6, 16), (32, 11), (29, 25), (28, 34), (1, 17), (20, 3), (20, 20), (27, 9), (39, 22), (13, 34), (28, 8), (3, 14), (39, 16), (21, 0), (26, 38), (28, 35), (25, 19), (34, 31), (38, 21), (38, 4), (10, 33), (1, 33), (11, 1), (23, 28), (0, 7), (35, 4), (15, 20), (23, 9), (20, 35), (11, 38), (37, 34), (2, 15), (34, 16), (18, 1), (28, 36), (0, 33), (23, 27), (37, 29), (43, 38), (35, 19), (16, 3), (31, 37), (5, 30), (26, 39), (33, 7), (34, 40), (17, 22), (10, 27), (25, 27), (19, 20), (1, 22), (17, 18), (6, 28), (19, 17), (6, 10), (32, 13), (43, 14), (20, 6), (14, 35), (38, 15), (12, 1), (3, 37), (25, 16), (5, 37), (35, 1), (15, 25), (32, 8), (32, 12), (26, 35), (0, 16), (39, 14), (24, 0), (33, 2), (29, 10), (11, 32), (40, 2), (12, 18), (29, 23), (2, 34), (24, 22), (6, 15), (20, 19), (14, 18), (29, 6), (24, 10), (32, 30), (38, 24), (31, 6), (4, 11), (7, 27), (8, 22), (30, 33), (8, 39), (20, 15), (40, 30), (0, 3), (15, 31), (31, 28), (3, 15), (35, 8), (23, 15), (21, 18), (4, 18), (1, 32), (38, 35), (18, 8), (24, 12), (23, 31), (3, 31), (25, 4), (3, 36), (0, 9), (28, 33), (35, 22), (27, 29), (9, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 13), (42, 20), (6, 46), (9, 36), (38, 44), (0, 20), (24, 4), (32, 0), (24, 14), (42, 33), (29, 30), (3, 1), (38, 8), (21, 28), (9, 26), (38, 33), (38, 17), (26, 43), (22, 27), (33, 45), (20, 1), (35, 41), (32, 4), (30, 8), (25, 18), (8, 31), (30, 43), (36, 26), (18, 0), (13, 2), (39, 47), (11, 44), (42, 38), (37, 5), (16, 4), (18, 20), (33, 42), (32, 26), (31, 3), (3, 43), (31, 15), (11, 26), (40, 30), (5, 34), (10, 30), (28, 35), (34, 27), (35, 37), (23, 30), (16, 8), (30, 38), (11, 10), (40, 28), (35, 8), (19, 16), (27, 18), (36, 9), (40, 37), (4, 17), (5, 42), (42, 29), (12, 20), (26, 3), (9, 14), (31, 24), (32, 25), (24, 27), (12, 15), (29, 45), (37, 25), (13, 20), (39, 28), (9, 4), (44, 12), (39, 3), (31, 13), (1, 4), (22, 39), (42, 26), (5, 44), (40, 22), (36, 33), (5, 10), (43, 5), (29, 46), (29, 40), (9, 17), (7, 4), (19, 43), (27, 40), (29, 6), (8, 35), (6, 25), (4, 12), (24, 46), (15, 41), (13, 22), (16, 37), (0, 35), (1, 35), (2, 2), (20, 21), (41, 37), (26, 27), (15, 9), (26, 16), (19, 4), (3, 41), (10, 24), (5, 16), (14, 10), (10, 45), (17, 27), (39, 5), (2, 14), (34, 6), (32, 29), (19, 7), (28, 22), (24, 18), (37, 39), (28, 1), (28, 17), (15, 34), (33, 15), (31, 14), (14, 45), (30, 0), (43, 45), (37, 46), (18, 40), (35, 12), (23, 37), (26, 33), (27, 27), (12, 9), (18, 46), (35, 0), (32, 40), (41, 12), (19, 23), (11, 16), (39, 4), (23, 38), (22, 47), (11, 37), (0, 15), (26, 32), (41, 47), (16, 34), (6, 6), (38, 32), (11, 32), (20, 11), (40, 0), (27, 29), (9, 11), (11, 30), (38, 26), (21, 42), (12, 37), (40, 6), (5, 22), (35, 36), (3, 10), (5, 8), (3, 33), (18, 17), (42, 8), (34, 42), (18, 27), (4, 3), (20, 45), (7, 9), (37, 7), (39, 37), (4, 22), (41, 46), (31, 2), (2, 1), (14, 27), (21, 15), (43, 21), (32, 17), (39, 17), (39, 44), (29, 35), (23, 1), (10, 31), (17, 34), (2, 40), (25, 20), (10, 2), (20, 31), (29, 19), (6, 23), (13, 41), (29, 10), (17, 32), (14, 11), (43, 2), (21, 18), (28, 41), (32, 5), (37, 0), (8, 11), (13, 24), (26, 46), (23, 43), (31, 20), (42, 46), (20, 28), (12, 23), (9, 30), (11, 35), (8, 42), (9, 24), (24, 21), (7, 15), (4, 23), (40, 24), (29, 34), (16, 39), (15, 13), (21, 4), (33, 22), (12, 30), (0, 38), (38, 35), (11, 25), (15, 29), (7, 28), (17, 36), (36, 39), (7, 42), (40, 34), (11, 20), (24, 44), (5, 37), (22, 11), (28, 2), (17, 31), (40, 13), (18, 11), (4, 38), (0, 18), (26, 21), (32, 34), (41, 20), (13, 30), (18, 38), (10, 39), (11, 12), (27, 9), (26, 1), (12, 47), (29, 33), (20, 47), (8, 9), (9, 0), (33, 33), (26, 47), (38, 25), (35, 19), (19, 33), (6, 18), (25, 46), (43, 8), (12, 13), (4, 44), (2, 21), (2, 20), (33, 13), (18, 41), (29, 16), (21, 1), (20, 18), (1, 39), (32, 30), (18, 13), (12, 2), (24, 20), (13, 36), (43, 29), (14, 22), (4, 37), (7, 46), (21, 33), (4, 43), (31, 27), (24, 16), (30, 34), (37, 21), (24, 32), (14, 1), (27, 31), (26, 28), (9, 15), (26, 35), (28, 4), (33, 8), (14, 30), (37, 15), (19, 6), (19, 19), (9, 29), (30, 3), (7, 37), (27, 25), (2, 32), (38, 11), (19, 36), (36, 45), (8, 1), (42, 30), (16, 40), (32, 19), (39, 43), (18, 1), (33, 10), (36, 20), (41, 5), (25, 41), (42, 15), (30, 31), (41, 16), (38, 3), (16, 15), (39, 46), (9, 45), (30, 13), (31, 44), (36, 38), (24, 47), (25, 35), (2, 11), (28, 0), (6, 32), (32, 28), (35, 3), (2, 0), (3, 34), (5, 1), (18, 16), (1, 6), (36, 15), (41, 28), (12, 29), (25, 1), (14, 2), (35, 39), (42, 41), (1, 12), (12, 25), (10, 17), (23, 14), (23, 33), (0, 9), (44, 18), (32, 44), (13, 45), (29, 15), (6, 42), (11, 8), (43, 39), (29, 28), (25, 34), (31, 34), (20, 39), (1, 46), (25, 4), (9, 37), (35, 47), (22, 35), (3, 12), (17, 3), (32, 6), (22, 0), (13, 25), (8, 12), (1, 41), (5, 4), (27, 39), (38, 9), (16, 12), (32, 33), (36, 13), (36, 21), (0, 31), (40, 26), (7, 36), (36, 4), (22, 13), (8, 15), (41, 11), (3, 13), (19, 44), (5, 25), (35, 23), (14, 42), (30, 39), (36, 7), (10, 22), (34, 5), (43, 34), (1, 25), (16, 44), (29, 9), (36, 40), (4, 28), (8, 2), (28, 21), (38, 40), (17, 30), (23, 11), (37, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 1), (5, 24), (30, 30), (38, 0), (33, 41), (46, 27), (38, 33), (25, 34), (30, 40), (33, 14), (3, 14), (44, 32), (26, 34), (37, 39), (25, 29), (37, 37), (17, 11), (5, 1), (35, 37), (0, 22), (38, 28), (33, 31), (33, 12), (48, 12), (18, 35), (47, 8), (6, 30), (42, 6), (33, 17), (40, 14), (43, 5), (7, 40), (30, 42), (7, 17), (4, 1), (36, 1), (3, 25), (7, 16), (19, 6), (19, 21), (14, 13), (23, 32), (35, 31), (11, 9), (4, 8), (17, 19), (34, 36), (14, 10), (32, 17), (11, 12), (6, 36), (3, 21), (41, 23), (12, 34), (8, 3), (4, 18), (41, 39), (13, 20), (44, 4), (29, 37), (20, 33), (31, 9), (31, 21), (42, 31), (27, 16), (32, 24), (47, 33), (30, 32), (3, 24), (8, 12), (3, 6), (22, 14), (11, 28), (41, 15), (6, 8), (22, 0), (8, 40), (26, 29), (25, 15), (5, 18), (19, 20), (44, 18), (15, 4), (10, 6), (6, 41), (7, 28), (37, 4), (29, 42), (41, 30), (4, 9), (40, 39), (24, 42), (36, 12), (10, 33), (32, 31), (39, 19), (4, 31), (1, 9), (21, 7), (40, 9), (7, 25), (19, 0), (27, 19), (41, 0), (28, 8), (43, 36), (17, 27), (27, 20), (3, 3), (36, 37), (9, 0), (37, 26), (4, 28), (45, 11), (14, 41), (41, 21), (37, 14), (24, 34), (8, 34), (35, 33), (37, 5), (21, 9), (8, 15), (25, 12), (18, 31), (44, 21), (31, 14), (30, 34), (43, 7), (45, 22), (0, 12), (26, 20), (14, 3), (23, 10), (1, 1), (42, 9), (7, 18), (37, 2), (19, 27), (7, 31), (47, 42), (30, 13), (20, 4), (2, 35), (19, 30), (34, 16), (39, 10), (13, 6), (20, 10), (17, 20), (7, 2), (11, 13), (17, 37), (23, 8), (18, 26), (42, 21), (37, 42), (33, 35), (27, 21), (9, 10), (24, 2), (9, 35), (23, 23), (35, 5), (21, 2), (44, 22), (11, 31), (19, 18), (43, 19), (24, 31), (33, 10), (47, 5), (7, 15), (22, 16), (32, 29), (36, 21), (29, 3), (20, 30), (11, 4), (8, 19), (39, 21), (8, 0), (26, 38), (5, 11), (10, 13), (45, 31), (3, 37), (9, 26), (19, 40), (38, 29), (27, 10), (7, 1), (43, 9), (37, 0), (9, 1), (28, 0), (6, 18), (30, 23), (27, 28), (46, 32), (36, 40), (32, 38), (45, 19), (18, 3), (10, 18), (24, 4), (28, 37), (23, 28), (27, 35), (38, 34), (34, 7), (13, 34), (12, 32), (20, 42), (6, 3), (16, 4), (47, 18), (10, 19), (48, 2), (33, 22), (12, 38), (37, 9), (48, 17), (20, 25), (34, 12), (27, 11), (3, 35), (47, 40), (11, 22), (21, 11), (22, 32), (22, 42), (10, 0), (34, 32), (18, 19), (23, 3), (7, 29), (30, 17), (23, 36), (10, 8), (8, 7), (13, 28), (22, 21), (48, 29), (24, 14), (41, 26), (13, 41), (45, 14), (9, 9), (37, 6), (47, 37), (13, 23), (15, 39), (27, 25), (45, 38), (19, 12), (19, 37), (24, 7), (22, 36), (38, 22), (40, 26), (10, 11), (40, 35), (1, 14), (7, 21), (19, 5), (34, 13), (26, 11), (4, 41), (40, 37), (38, 2), (34, 21), (2, 28), (43, 4), (45, 28), (45, 16), (0, 38), (39, 37), (33, 37), (2, 21), (7, 26), (39, 30), (16, 29), (42, 33), (2, 32), (44, 12), (15, 33), (35, 42), (37, 27), (8, 1), (39, 5), (0, 15), (39, 12), (2, 34), (7, 9), (9, 28), (14, 36), (17, 42), (3, 28), (14, 32), (44, 2), (26, 2), (37, 40), (23, 29), (9, 8), (30, 4), (28, 17), (0, 29), (48, 36), (9, 16), (37, 8), (43, 23), (23, 14), (4, 4), (26, 23), (45, 10), (21, 18), (23, 20), (43, 31), (34, 15), (14, 25), (0, 24), (35, 2), (48, 40), (48, 10), (29, 8), (30, 15), (46, 26), (11, 18), (21, 23), (23, 4), (46, 39), (4, 12), (18, 6), (22, 3), (47, 16), (17, 36), (41, 13), (38, 5), (23, 25), (17, 25), (20, 18), (44, 42), (41, 31), (1, 8), (23, 15), (40, 28), (16, 20), (24, 0), (39, 29), (28, 30), (48, 27), (46, 6), (17, 34), (43, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 13), (1, 9), (7, 13), (41, 34), (9, 22), (41, 4), (9, 11), (45, 2), (31, 16), (42, 41), (27, 8), (32, 34), (1, 40), (2, 45), (39, 28), (43, 20), (26, 5), (0, 14), (5, 28), (8, 42), (16, 25), (34, 42), (43, 30), (22, 8), (13, 43), (18, 42), (6, 14), (38, 37), (35, 43), (35, 2), (18, 4), (34, 8), (19, 5), (34, 9), (42, 18), (23, 15), (26, 26), (16, 32), (41, 6), (39, 19), (43, 10), (15, 36), (25, 21), (10, 13), (16, 41), (36, 41), (7, 15), (28, 19), (4, 5), (30, 9), (39, 27), (31, 9), (6, 40), (28, 15), (45, 36), (31, 40), (13, 42), (14, 11), (37, 32), (38, 9), (9, 41), (9, 40), (14, 26), (44, 37), (32, 4), (25, 41), (17, 4), (40, 32), (9, 39), (42, 10), (30, 31), (23, 24), (41, 7), (17, 7), (7, 3), (14, 39), (7, 24), (44, 41), (27, 23), (13, 26), (13, 13), (19, 16), (15, 42), (23, 40), (36, 11), (43, 9), (43, 31), (9, 14), (9, 31), (29, 2), (44, 7), (24, 9), (21, 14), (11, 23), (12, 26), (23, 34), (42, 26), (31, 12), (43, 14), (46, 5), (44, 10), (26, 25), (33, 9), (7, 14), (3, 36), (40, 0), (12, 14), (41, 19), (38, 33), (7, 9), (19, 36), (29, 44), (44, 21), (46, 16), (42, 45), (15, 14), (10, 10), (40, 12), (12, 19), (17, 32), (14, 2), (8, 33), (38, 42), (24, 8), (12, 39), (45, 28), (28, 6), (24, 12), (38, 21), (23, 23), (9, 2), (1, 31), (43, 24), (5, 23), (39, 14), (35, 3), (40, 31), (14, 24), (1, 13), (38, 3), (44, 34), (15, 8), (36, 44), (8, 18), (41, 28), (22, 42), (30, 15), (17, 18), (0, 1), (41, 16), (15, 17), (0, 7), (26, 8), (42, 29), (2, 17), (39, 0), (43, 1), (7, 37), (34, 7), (33, 13), (9, 8), (12, 1), (23, 9), (12, 15), (9, 26), (43, 39), (20, 13), (16, 13), (2, 12), (1, 16), (8, 17), (23, 44), (4, 41), (4, 26), (35, 38), (0, 4), (10, 33), (7, 33), (31, 25), (24, 38), (3, 35), (17, 6), (28, 37), (6, 8), (10, 27), (38, 12), (19, 37), (22, 2), (34, 3), (14, 4), (35, 20), (39, 15), (11, 22), (0, 10), (15, 11), (26, 23), (10, 18), (12, 24), (25, 13), (9, 20), (22, 3), (37, 38), (21, 2), (8, 4), (26, 43), (41, 20), (34, 25), (3, 26), (4, 9), (5, 13), (45, 32), (28, 16), (13, 23), (40, 44), (7, 35), (22, 43), (0, 20), (21, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 29), (10, 29), (17, 33), (34, 24), (30, 39), (39, 10), (39, 19), (8, 1), (27, 13), (4, 43), (40, 2), (38, 4), (20, 3), (25, 32), (31, 1), (21, 25), (37, 43), (1, 14), (0, 11), (20, 40), (21, 20), (29, 34), (37, 30), (1, 32), (19, 42), (19, 19), (20, 19), (8, 16), (40, 20), (12, 34), (4, 37), (27, 17), (3, 7), (5, 11), (21, 4), (19, 32), (20, 27), (8, 33), (37, 3), (25, 17), (28, 18), (39, 34), (35, 22), (36, 36), (10, 8), (1, 16), (31, 35), (16, 1), (27, 39), (29, 20), (32, 35), (22, 6), (40, 41), (28, 24), (37, 24), (40, 10), (11, 40), (13, 2), (31, 12), (35, 25), (9, 10), (28, 14), (29, 36), (26, 4), (38, 12), (9, 14), (4, 13), (38, 29), (3, 27), (25, 38), (3, 22), (20, 35), (30, 14), (15, 8), (14, 1), (3, 39), (1, 19), (22, 7), (32, 11), (29, 23), (6, 11), (30, 42), (14, 26), (13, 5), (13, 29), (6, 38), (12, 3), (5, 35), (17, 14), (7, 25), (19, 39), (22, 35), (7, 22), (10, 28), (18, 3), (15, 26), (15, 35), (33, 39), (25, 3), (38, 6), (12, 1), (38, 21), (16, 36), (24, 33), (23, 19), (25, 28), (10, 18), (36, 7), (31, 25), (14, 3), (18, 17), (25, 11), (36, 1), (24, 43), (8, 37), (35, 37), (25, 0), (14, 6), (19, 9), (23, 42), (9, 29), (26, 14), (24, 2), (1, 3), (2, 3), (33, 22), (33, 24), (36, 29), (12, 13), (32, 40), (9, 13), (25, 24), (8, 22), (19, 15), (39, 1), (25, 23), (11, 28), (38, 25), (36, 9), (19, 3), (10, 5), (31, 29), (9, 41), (33, 42), (39, 5), (38, 11), (27, 16), (25, 33), (3, 25), (28, 19), (14, 27), (24, 15), (1, 9), (13, 19), (8, 26), (22, 9), (35, 40), (9, 26), (18, 25), (6, 5), (19, 12), (38, 27), (15, 7), (18, 26), (10, 42), (23, 5), (13, 12), (28, 5), (27, 30), (14, 33), (25, 43), (22, 8), (1, 23), (26, 21), (12, 37), (19, 40), (29, 0), (17, 5), (38, 17), (30, 35), (2, 17), (31, 22), (20, 43), (27, 8), (23, 18), (32, 7), (23, 29), (32, 0), (27, 33), (31, 19), (22, 18), (32, 29), (9, 19), (27, 2), (34, 33), (35, 28), (36, 40), (21, 5), (32, 23), (13, 23), (3, 37), (32, 16), (1, 2), (32, 24), (23, 17), (20, 5), (34, 29), (7, 3), (17, 32), (34, 34), (26, 9), (3, 28), (15, 3), (20, 16), (6, 31), (3, 23), (4, 9), (6, 22), (13, 34), (1, 39), (28, 34), (13, 9), (35, 32), (6, 8), (21, 38), (33, 27), (16, 0), (31, 39), (26, 10), (24, 35), (23, 20), (39, 27), (25, 14), (7, 9), (25, 40), (8, 2), (34, 4), (20, 13), (13, 14), (27, 22), (26, 40), (11, 36), (3, 42), (34, 27), (35, 17), (17, 11), (24, 22), (10, 27), (10, 12), (18, 11), (4, 1), (14, 5), (1, 24), (8, 25), (18, 20), (27, 35), (2, 31), (13, 0), (9, 40), (11, 21), (7, 0), (40, 13), (31, 38), (40, 17), (36, 34), (21, 3), (21, 42), (25, 34), (6, 2), (3, 13), (10, 37), (39, 24), (21, 18), (21, 10), (32, 27), (40, 39), (33, 21), (17, 41), (16, 27), (37, 23), (21, 24), (33, 30), (18, 42), (14, 10), (39, 30), (0, 41), (20, 36), (15, 29), (13, 33), (32, 37), (10, 19), (5, 10), (36, 21), (9, 20), (22, 29), (14, 38), (40, 7), (3, 26), (22, 32), (40, 23), (19, 36), (31, 34), (26, 7), (37, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (45, 1), (28, 7), (46, 15), (42, 38), (9, 33), (31, 11), (35, 31), (6, 25), (41, 1), (20, 30), (16, 38), (24, 33), (23, 33), (23, 29), (38, 15), (41, 14), (40, 19), (25, 29), (46, 28), (17, 34), (31, 16), (10, 36), (0, 13), (26, 34), (18, 16), (16, 25), (3, 4), (16, 29), (18, 10), (17, 4), (29, 6), (27, 0), (40, 24), (26, 20), (37, 2), (44, 27), (40, 26), (38, 22), (21, 6), (26, 16), (19, 19), (16, 17), (2, 18), (14, 3), (15, 25), (29, 17), (46, 19), (37, 39), (33, 33), (18, 29), (44, 34), (12, 39), (22, 23), (37, 4), (38, 17), (7, 1), (33, 17), (42, 30), (34, 30), (42, 27), (1, 0), (16, 35), (17, 25), (13, 35), (0, 22), (42, 4), (6, 8), (34, 23), (13, 37), (20, 33), (29, 18), (46, 26), (11, 26), (10, 3), (31, 22), (19, 37), (20, 21), (33, 20), (46, 3), (44, 7), (19, 32), (25, 6), (24, 35), (28, 31), (13, 10), (10, 34), (25, 2), (12, 27), (8, 22), (4, 9), (41, 29), (17, 24), (43, 4), (43, 6), (41, 32), (46, 16), (13, 23), (5, 35), (2, 34), (2, 23), (2, 25), (42, 21), (28, 35), (26, 1), (6, 9), (34, 18), (47, 38), (4, 2), (26, 18), (37, 31), (1, 25), (7, 17), (5, 16), (1, 23), (10, 15), (27, 20), (21, 36), (0, 33), (20, 27), (18, 19), (30, 37), (22, 3), (31, 5), (10, 31), (13, 11), (38, 19), (9, 39), (1, 31), (40, 30), (15, 20), (18, 1), (11, 34), (21, 8), (30, 20), (14, 22), (14, 4), (41, 15), (22, 30), (35, 33), (17, 21), (18, 0), (20, 14), (42, 34), (33, 6), (0, 37), (30, 7), (26, 7), (25, 35), (28, 11), (46, 33), (3, 32), (47, 34), (19, 1), (2, 22), (21, 20), (42, 32), (39, 34), (38, 28), (45, 23), (0, 27), (43, 16), (1, 19), (11, 20), (45, 7), (14, 11), (2, 14), (14, 9), (32, 39), (27, 26), (28, 25), (4, 31), (15, 17), (44, 17), (30, 0), (32, 30), (29, 0), (26, 39), (32, 9), (6, 3), (1, 12), (8, 19), (32, 11), (13, 19), (17, 17), (10, 33), (22, 13), (10, 37), (43, 14), (7, 31), (19, 9), (4, 6), (20, 10), (17, 20), (44, 1), (13, 18), (3, 18), (37, 17), (6, 27), (43, 28), (18, 33), (2, 32), (34, 37), (39, 3), (17, 26), (31, 13), (2, 16), (47, 7), (39, 32), (39, 25), (16, 16), (24, 18), (31, 10), (30, 34), (8, 10), (33, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 41), (34, 13), (15, 23), (15, 41), (3, 21), (5, 31), (1, 17), (11, 31), (8, 0), (16, 30), (34, 26), (41, 13), (6, 41), (15, 8), (28, 28), (29, 29), (37, 32), (26, 5), (10, 9), (20, 13), (13, 17), (8, 23), (14, 5), (14, 35), (28, 43), (27, 23), (13, 27), (14, 7), (36, 27), (25, 18), (36, 34), (30, 43), (2, 5), (12, 39), (8, 15), (20, 29), (37, 16), (32, 41), (0, 3), (11, 24), (35, 11), (18, 18), (29, 30), (27, 5), (35, 34), (30, 25), (31, 13), (22, 28), (26, 29), (23, 39), (20, 17), (13, 35), (22, 29), (38, 15), (6, 7), (7, 4), (32, 19), (24, 40), (5, 19), (9, 40), (17, 10), (33, 21), (15, 34), (28, 31), (29, 12), (32, 34), (8, 42), (17, 25), (4, 3), (8, 5), (30, 16), (39, 33), (9, 31), (37, 37), (27, 34), (33, 6), (26, 1), (22, 39), (21, 39), (0, 12), (5, 38), (26, 15), (37, 10), (30, 6), (13, 15), (17, 22), (13, 39), (40, 40), (7, 41), (31, 40), (25, 22), (10, 19), (2, 22), (5, 43), (36, 2), (35, 12), (29, 42), (34, 21), (41, 41), (15, 24), (29, 10), (7, 7), (2, 23), (16, 43), (34, 18), (10, 11), (26, 13), (5, 20), (14, 9), (39, 0), (27, 39), (9, 30), (7, 31), (13, 1), (40, 36), (36, 28), (41, 0), (18, 2), (26, 18), (28, 27), (27, 7), (32, 38), (15, 28), (5, 4), (14, 14), (17, 30), (10, 35), (12, 34), (31, 22), (29, 38), (36, 36), (39, 34), (1, 26), (41, 33), (31, 36), (26, 19), (34, 37), (26, 38), (36, 20), (41, 36), (34, 36), (30, 3), (17, 0), (8, 4), (40, 7), (14, 19), (34, 39), (18, 35), (19, 25), (38, 38), (23, 15), (2, 25), (2, 36), (4, 35), (11, 5), (34, 3), (41, 21), (33, 29), (29, 1), (34, 14), (1, 7), (6, 8), (4, 29), (33, 5), (3, 28), (38, 35), (18, 43), (19, 16), (13, 18), (16, 39), (29, 15), (26, 7), (37, 5), (29, 41), (40, 33), (25, 11), (38, 42), (14, 31), (32, 8), (15, 2), (6, 23), (37, 36), (11, 28), (25, 33), (37, 9), (4, 25), (25, 0), (31, 43), (34, 12), (14, 43), (6, 18), (5, 34), (0, 26), (4, 17), (30, 19), (30, 8), (7, 26), (11, 3), (15, 12), (25, 7), (30, 34), (41, 18), (40, 4), (8, 36), (6, 0), (36, 11), (40, 21), (7, 12), (22, 2), (0, 43), (29, 13), (12, 19), (10, 18), (18, 0), (4, 6), (12, 40), (29, 4), (20, 21), (40, 31), (7, 16), (14, 23), (15, 25), (29, 7), (26, 12), (9, 2), (19, 12), (16, 6), (31, 15), (13, 4), (21, 20), (1, 41), (39, 42), (35, 7), (41, 25), (33, 18), (3, 34), (25, 4), (21, 15), (0, 28), (35, 4), (25, 3), (38, 30), (40, 3), (9, 3), (21, 32), (25, 29), (37, 1), (16, 7), (32, 27), (40, 9), (12, 32), (1, 9), (9, 5), (10, 17), (2, 27), (25, 39), (14, 27), (22, 30), (30, 27), (0, 2), (16, 14), (39, 18), (35, 14), (4, 43), (35, 9), (27, 9), (9, 27), (36, 43), (10, 6), (14, 28), (30, 11), (21, 34), (34, 29), (13, 42), (15, 32), (11, 18), (24, 0), (2, 3), (22, 25), (28, 22), (13, 30), (27, 26), (1, 5), (22, 3), (17, 34), (22, 16), (29, 0), (33, 33), (41, 34), (21, 38), (23, 42), (34, 27), (2, 17), (23, 24), (0, 34), (36, 14), (9, 17), (10, 15), (31, 20), (23, 32), (13, 21), (35, 43), (3, 29), (36, 33), (19, 37), (36, 15), (35, 5), (5, 37), (41, 8), (19, 26), (24, 14), (7, 38), (4, 15), (30, 33), (7, 37), (14, 11), (7, 5), (17, 4), (28, 11), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 13), (7, 25), (20, 30), (9, 27), (15, 31), (40, 1), (21, 16), (3, 39), (12, 2), (4, 16), (20, 31), (0, 29), (29, 23), (0, 22), (36, 35), (9, 13), (40, 33), (33, 28), (4, 1), (16, 13), (27, 18), (27, 1), (12, 38), (19, 25), (15, 10), (23, 39), (0, 28), (37, 18), (28, 5), (40, 25), (34, 34), (10, 32), (36, 0), (37, 3), (10, 17), (35, 17), (5, 33), (21, 6), (1, 6), (11, 38), (1, 1), (1, 24), (25, 40), (1, 9), (18, 31), (4, 23), (5, 37), (16, 34), (33, 5), (26, 30), (28, 26), (34, 4), (3, 32), (25, 36), (31, 39), (6, 37), (30, 20), (35, 4), (23, 20), (13, 33), (23, 5), (24, 2), (24, 9), (40, 4), (28, 34), (10, 6), (8, 5), (5, 30), (14, 36), (34, 19), (11, 5), (5, 11), (29, 40), (13, 25), (5, 12), (12, 39), (11, 21), (30, 34), (17, 13), (22, 35), (34, 35), (19, 39), (35, 30), (30, 11), (25, 7), (5, 6), (7, 14), (5, 32), (13, 27), (22, 16), (18, 17), (30, 17), (40, 5), (37, 17), (28, 36), (35, 23), (0, 10), (12, 11), (6, 9), (21, 22), (4, 24), (7, 26), (27, 28), (7, 2), (14, 33), (35, 18), (3, 22), (34, 1), (14, 40), (14, 12), (4, 13), (30, 32), (26, 8), (3, 4), (26, 11), (29, 2), (27, 3), (1, 20), (8, 0), (40, 9), (36, 39), (34, 10), (36, 6), (21, 31), (26, 5), (35, 14), (15, 12), (14, 3), (28, 19), (17, 16), (7, 22), (24, 40), (26, 12), (0, 4), (4, 39), (14, 31), (19, 12), (22, 27), (3, 34), (25, 31), (29, 0), (17, 22), (30, 29), (2, 3), (4, 19), (12, 36), (19, 5), (7, 8), (35, 20), (7, 31), (15, 28), (38, 18), (6, 6), (2, 37), (6, 24), (14, 7), (23, 2), (39, 13), (37, 15), (0, 16), (40, 29), (25, 12), (9, 16), (21, 8), (38, 29), (10, 19), (36, 12), (16, 40), (2, 5), (39, 27), (14, 17), (15, 26), (34, 29), (17, 5), (17, 33), (1, 18), (36, 15), (40, 37), (3, 31), (35, 40), (0, 17), (14, 16), (14, 37), (26, 21), (31, 2), (3, 23), (2, 7), (35, 12), (23, 12), (37, 1), (36, 33), (1, 23), (7, 36), (38, 30), (3, 8), (3, 13), (24, 19), (34, 26), (23, 29), (39, 30), (6, 39), (39, 11), (7, 13), (25, 11), (19, 32), (12, 4), (19, 36), (39, 34), (8, 27), (39, 37), (25, 38), (5, 17), (4, 22), (37, 5), (36, 37), (8, 32), (1, 12), (27, 32), (7, 9), (11, 1), (13, 40), (24, 27), (13, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 17), (4, 8), (10, 35), (38, 33), (28, 16), (21, 18), (29, 38), (0, 12), (4, 23), (10, 22), (9, 7), (41, 18), (2, 5), (18, 1), (28, 6), (8, 25), (8, 33), (11, 17), (39, 18), (4, 41), (41, 40), (34, 13), (8, 28), (11, 41), (13, 2), (21, 41), (5, 34), (27, 38), (28, 23), (3, 9), (33, 0), (1, 34), (4, 20), (17, 3), (6, 12), (37, 28), (37, 10), (24, 0), (31, 21), (36, 10), (10, 32), (30, 24), (38, 31), (16, 30), (41, 38), (6, 22), (13, 33), (25, 6), (7, 26), (3, 42), (34, 34), (9, 30), (30, 8), (2, 40), (11, 22), (6, 42), (32, 7), (2, 0), (23, 12), (35, 9), (18, 11), (8, 8), (14, 4), (12, 28), (33, 36), (17, 12), (36, 12), (18, 9), (25, 35), (33, 17), (12, 35), (35, 23), (0, 33), (0, 6), (28, 21), (36, 28), (27, 2), (14, 16), (42, 15), (15, 3), (8, 16), (25, 4), (35, 39), (6, 2), (28, 18), (28, 36), (18, 17), (3, 36), (14, 2), (42, 21), (8, 10), (26, 27), (22, 28), (32, 35), (27, 11), (14, 30), (37, 23), (25, 2), (41, 9), (1, 5), (38, 13), (3, 6), (30, 18), (33, 27), (40, 12), (14, 7), (16, 28), (29, 35), (27, 36), (29, 6), (18, 3), (6, 9), (19, 27), (33, 35), (30, 7), (36, 22), (26, 7), (0, 31), (4, 2), (8, 35), (21, 30), (23, 22), (38, 10), (33, 30), (19, 4), (3, 35), (28, 35), (20, 36), (19, 0), (16, 25), (31, 13), (0, 1), (2, 1), (7, 16), (30, 34), (33, 39), (31, 24), (22, 8), (17, 28), (19, 42), (22, 36), (17, 11), (9, 28), (4, 33), (8, 40), (35, 34), (29, 34), (6, 8), (34, 10), (19, 19), (18, 23), (31, 26), (13, 4), (5, 40), (38, 34), (11, 11), (24, 24), (17, 0), (16, 20), (5, 15), (27, 15), (9, 22), (17, 35), (21, 8), (31, 5), (18, 35), (28, 33), (12, 4), (16, 10), (19, 6), (32, 27), (42, 2), (6, 25), (21, 22), (40, 24), (25, 10), (30, 11), (14, 3), (34, 24), (20, 30), (1, 13), (0, 37), (37, 16), (34, 9), (30, 35), (30, 14), (3, 32), (26, 25), (41, 7), (6, 24), (36, 26), (14, 34), (42, 5), (4, 30), (5, 11), (12, 23), (13, 3), (25, 9), (15, 7), (27, 28), (42, 19), (23, 9), (23, 29), (19, 36), (31, 16), (16, 9), (24, 21), (20, 8), (32, 6), (29, 29), (9, 20), (41, 15), (41, 36), (42, 23), (25, 23), (7, 13), (35, 36), (12, 33), (1, 31), (18, 27), (32, 25), (17, 34), (35, 5), (40, 18), (16, 42), (19, 41), (22, 7), (7, 40), (32, 39), (40, 36), (26, 28), (13, 42), (12, 18), (1, 3), (2, 34), (42, 4), (8, 38), (16, 5), (3, 18), (18, 5), (39, 22), (25, 3), (14, 26), (17, 8), (25, 25), (32, 21), (5, 39), (13, 22), (23, 13), (22, 30), (40, 5), (22, 42), (28, 34), (35, 41), (3, 26), (38, 36), (9, 4), (30, 13), (17, 23), (38, 27), (30, 39), (40, 33), (23, 3), (15, 31), (24, 19), (24, 15), (20, 18), (8, 34), (30, 21), (9, 2), (5, 20), (29, 24), (8, 32), (1, 40), (20, 28), (18, 24), (32, 36), (31, 41), (6, 30), (32, 2), (19, 29), (6, 16), (20, 11), (16, 27), (37, 39), (9, 24), (17, 39), (21, 21), (18, 14), (25, 1), (15, 8), (3, 33), (6, 14), (40, 22), (11, 19), (6, 37), (25, 27), (0, 17), (26, 31), (8, 22), (38, 26), (25, 33), (16, 16), (29, 41), (40, 7), (42, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 30), (4, 35), (44, 45), (19, 43), (17, 39), (41, 0), (26, 11), (30, 24), (23, 48), (2, 46), (4, 20), (35, 25), (1, 31), (2, 3), (2, 16), (29, 0), (47, 26), (10, 11), (22, 11), (1, 5), (0, 23), (13, 13), (32, 25), (44, 19), (35, 19), (44, 43), (18, 46), (14, 27), (1, 6), (7, 22), (22, 27), (8, 30), (19, 37), (43, 5), (30, 31), (15, 35), (9, 36), (33, 28), (25, 43), (31, 28), (43, 46), (32, 0), (0, 12), (14, 37), (45, 10), (14, 28), (14, 17), (15, 29), (3, 20), (28, 38), (6, 29), (39, 43), (16, 12), (14, 45), (9, 5), (28, 7), (3, 39), (42, 22), (20, 32), (33, 29), (44, 17), (5, 4), (18, 24), (47, 25), (5, 47), (16, 15), (39, 28), (22, 29), (23, 18), (27, 48), (43, 33), (30, 36), (27, 25), (2, 34), (15, 28), (40, 20), (14, 8), (39, 32), (8, 36), (31, 11), (26, 18), (36, 2), (28, 2), (20, 35), (3, 26), (23, 42), (8, 14), (22, 7), (39, 44), (6, 40), (31, 27), (44, 6), (39, 21), (24, 35), (28, 30), (16, 47), (36, 38), (13, 1), (13, 32), (43, 48), (21, 40), (38, 37), (42, 12), (43, 36), (23, 21), (44, 44), (5, 29), (36, 19), (27, 41), (43, 23), (37, 18), (43, 37), (46, 24), (20, 33), (31, 4), (27, 37), (45, 3), (27, 9), (41, 16), (0, 1), (30, 6), (41, 19), (47, 38), (24, 30), (13, 29), (6, 38), (10, 32), (44, 25), (27, 47), (25, 38), (26, 9), (15, 21), (28, 9), (9, 28), (20, 5), (0, 25), (7, 17), (6, 28), (11, 14), (5, 39), (47, 36), (7, 19), (29, 19), (26, 36), (22, 19), (45, 6), (31, 26), (21, 11), (34, 25), (28, 24), (3, 21), (45, 39), (14, 25), (18, 3), (34, 5), (4, 3), (34, 30), (27, 22), (29, 47), (10, 0), (34, 40), (24, 19), (23, 1), (23, 28), (4, 16), (31, 1), (21, 12), (7, 12), (47, 37), (23, 0), (46, 5), (27, 43), (16, 37), (19, 38), (30, 11), (32, 44), (25, 23), (0, 2), (45, 33), (6, 10), (18, 10), (7, 43), (18, 30), (44, 39), (18, 13), (26, 10), (37, 48), (15, 15), (32, 3), (32, 18), (24, 29), (28, 4), (24, 27), (14, 36), (8, 35), (29, 4), (9, 44), (15, 1), (41, 25), (34, 33), (29, 12), (8, 17), (29, 9), (38, 5), (6, 37), (28, 13), (18, 42), (2, 41), (10, 15), (11, 38), (44, 2), (27, 42), (41, 37), (25, 45), (18, 19), (34, 47), (32, 1), (47, 42), (43, 1), (38, 16), (14, 4), (28, 33), (26, 32), (15, 18), (4, 40), (24, 6), (47, 29), (7, 36), (39, 34), (45, 35), (18, 16), (46, 26), (4, 46), (16, 27), (18, 28), (19, 8), (0, 34), (41, 12), (16, 9), (35, 31), (10, 9), (43, 47), (16, 44), (4, 44), (11, 8), (13, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 34), (18, 21), (29, 4), (21, 7), (30, 12), (6, 26), (16, 16), (38, 2), (5, 26), (24, 4), (29, 11), (36, 4), (12, 24), (8, 9), (20, 12), (2, 19), (23, 34), (19, 23), (21, 8), (38, 33), (6, 19), (27, 6), (1, 15), (13, 17), (35, 40), (37, 40), (25, 19), (7, 6), (0, 41), (25, 20), (11, 29), (34, 34), (19, 38), (39, 17), (15, 39), (16, 2), (34, 2), (1, 1), (34, 37), (25, 23), (3, 28), (11, 28), (10, 15), (6, 27), (23, 5), (17, 1), (32, 12), (15, 18), (1, 17), (14, 27), (7, 24), (31, 26), (3, 23), (28, 36), (30, 38), (16, 24), (23, 8), (7, 14), (18, 22), (18, 26), (26, 24), (26, 22), (7, 34), (20, 28), (17, 12), (30, 30), (10, 14), (31, 1), (38, 25), (28, 37), (37, 4), (5, 23), (19, 20), (17, 13), (35, 11), (29, 23), (39, 15), (37, 28), (19, 17), (3, 17), (8, 21), (3, 34), (14, 39), (1, 35), (10, 23), (3, 1), (29, 18), (10, 8), (28, 33), (14, 4), (36, 7), (28, 5), (23, 2), (17, 21), (26, 15), (21, 13), (19, 8), (19, 28), (13, 37), (32, 2), (19, 0), (7, 30), (39, 31), (1, 8), (26, 34), (18, 38), (30, 32), (34, 32), (37, 37), (20, 18), (25, 40), (34, 8), (20, 30), (34, 1), (22, 21), (14, 25), (14, 1), (2, 16), (25, 5), (33, 4), (38, 1), (13, 32), (37, 12), (6, 22), (24, 30), (30, 34), (19, 5), (31, 33), (21, 16), (20, 3), (9, 10), (34, 39), (12, 32), (25, 35), (3, 26), (26, 35), (17, 16), (33, 21), (4, 13), (30, 29), (37, 18), (28, 34), (10, 34), (21, 5), (11, 24), (18, 14), (1, 19), (17, 7), (5, 11), (35, 39), (34, 12), (36, 35), (35, 15), (37, 15), (20, 41), (38, 38), (18, 33), (24, 12), (25, 7), (31, 25), (25, 37), (16, 25), (38, 11), (14, 37), (9, 33), (11, 36), (3, 14), (7, 40), (30, 16), (16, 12), (39, 24), (22, 37), (33, 17), (6, 39), (9, 4), (19, 31), (17, 32), (18, 17), (16, 19), (25, 29), (39, 7), (18, 25), (35, 2), (2, 34), (32, 32), (33, 11), (6, 30), (7, 17), (35, 28), (27, 36), (33, 37), (19, 29), (5, 1), (12, 3), (11, 20), (29, 33), (16, 23), (19, 41), (38, 40), (35, 5), (23, 30), (11, 3), (3, 15), (4, 18), (5, 21), (29, 34), (8, 26), (5, 20), (0, 24), (13, 35), (5, 41), (8, 31), (21, 34), (8, 3), (7, 2), (18, 29), (2, 22), (12, 1), (28, 32), (28, 24), (29, 25), (33, 28), (22, 8), (18, 30), (20, 11), (13, 29), (23, 36), (10, 24), (8, 32), (19, 33), (27, 10), (18, 9), (36, 17), (15, 31), (2, 11), (27, 34), (28, 26), (33, 39), (2, 41), (1, 14), (28, 17), (9, 3), (33, 0), (28, 39), (30, 23), (22, 1), (26, 14), (0, 5), (28, 1), (35, 10), (9, 16), (4, 0), (39, 5), (22, 2), (5, 7), (9, 17), (30, 15), (5, 0), (4, 26), (4, 29), (36, 25), (18, 3), (4, 22), (13, 0), (27, 39), (6, 12), (33, 26), (27, 9), (39, 40), (36, 33), (35, 24), (39, 14), (16, 5), (31, 9), (13, 11), (28, 30), (33, 12), (21, 21), (31, 20), (7, 11), (18, 32), (4, 31), (27, 41), (18, 0), (0, 3), (1, 28), (1, 9), (21, 6), (21, 36), (4, 35), (18, 20), (12, 33), (29, 26), (27, 23), (15, 33), (37, 9), (25, 32), (24, 34), (15, 35), (38, 19), (16, 41), (19, 30), (34, 38), (16, 8), (24, 31), (28, 7), (14, 36), (15, 25), (22, 29), (23, 24), (32, 13), (7, 37), (26, 39), (22, 34), (19, 15), (12, 26), (23, 4), (31, 39), (25, 8), (32, 0), (28, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 37), (6, 5), (26, 14), (44, 0), (27, 41), (14, 38), (25, 27), (38, 27), (6, 24), (20, 9), (23, 16), (33, 18), (22, 14), (1, 2), (42, 8), (12, 28), (15, 18), (25, 4), (10, 5), (30, 39), (37, 27), (37, 16), (43, 32), (28, 20), (4, 18), (42, 6), (28, 30), (18, 14), (37, 13), (33, 33), (16, 27), (29, 27), (31, 9), (25, 30), (32, 1), (32, 17), (12, 29), (23, 7), (13, 15), (23, 40), (38, 15), (12, 22), (24, 39), (26, 39), (19, 7), (39, 28), (25, 8), (23, 34), (10, 1), (4, 28), (25, 40), (18, 20), (8, 5), (35, 22), (28, 18), (10, 21), (3, 4), (41, 1), (4, 19), (30, 35), (35, 28), (16, 10), (29, 32), (14, 4), (28, 39), (30, 24), (41, 41), (18, 11), (37, 23), (34, 41), (43, 7), (22, 36), (4, 38), (37, 5), (11, 17), (38, 2), (35, 16), (6, 18), (3, 31), (43, 34), (13, 16), (14, 39), (41, 8), (34, 8), (14, 18), (17, 18), (43, 26), (42, 4), (28, 34), (31, 32), (15, 23), (25, 31), (38, 37), (27, 16), (15, 35), (23, 24), (21, 25), (33, 34), (18, 10), (26, 0), (38, 25), (42, 41), (36, 36), (44, 30), (44, 15), (43, 25), (8, 16), (13, 2), (31, 15), (11, 22), (25, 26), (7, 2), (26, 10), (16, 17), (33, 7), (1, 38), (30, 22), (36, 19), (39, 41), (6, 7), (25, 32), (34, 31), (23, 32), (7, 21), (43, 39), (8, 10), (14, 23), (32, 38), (31, 27), (24, 18), (36, 1), (43, 35), (5, 21), (20, 20), (12, 16), (17, 8), (14, 8), (19, 38), (1, 23), (18, 19), (37, 1), (29, 37), (12, 25), (24, 35), (39, 2), (26, 1), (0, 19), (21, 18), (12, 33), (20, 41), (32, 20), (23, 17), (26, 34), (8, 1), (35, 20), (4, 2), (1, 22), (43, 2), (41, 31), (6, 39), (11, 28), (33, 2), (4, 41), (34, 10), (29, 34), (7, 33), (36, 17), (36, 15), (40, 30), (2, 10), (36, 31), (18, 27), (21, 2), (26, 31), (30, 6), (39, 8), (10, 20), (6, 11), (19, 16), (26, 2), (34, 29), (31, 18), (42, 10), (14, 19), (2, 6), (19, 35), (21, 17), (8, 30), (18, 9), (8, 25), (11, 10), (23, 25), (13, 12), (2, 9), (32, 16), (25, 39), (42, 30), (2, 12), (6, 14), (0, 13), (15, 31), (32, 40), (35, 34), (35, 31), (20, 14), (30, 41), (44, 7), (10, 22), (34, 0), (4, 17), (24, 3), (32, 7), (44, 37), (2, 27), (8, 0), (17, 22), (20, 19), (33, 17), (20, 37), (12, 18), (38, 22), (6, 22), (26, 38), (17, 17), (37, 41), (6, 35), (31, 38), (24, 31), (22, 9), (35, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 4), (14, 4), (9, 41), (7, 33), (14, 37), (34, 32), (8, 8), (2, 24), (4, 40), (13, 5), (36, 15), (1, 28), (12, 16), (21, 31), (3, 21), (39, 0), (34, 6), (11, 20), (33, 7), (34, 28), (28, 20), (9, 1), (19, 33), (5, 39), (3, 17), (19, 22), (32, 30), (8, 21), (38, 24), (33, 18), (36, 24), (14, 20), (30, 12), (11, 16), (31, 15), (16, 33), (19, 36), (25, 27), (20, 2), (24, 35), (18, 25), (4, 1), (29, 5), (7, 14), (14, 12), (22, 33), (32, 29), (37, 32), (30, 21), (42, 6), (10, 22), (33, 12), (2, 25), (28, 6), (5, 31), (23, 17), (7, 0), (38, 2), (41, 27), (0, 33), (40, 8), (21, 26), (38, 11), (22, 10), (29, 15), (23, 42), (7, 16), (28, 11), (23, 21), (31, 27), (24, 3), (6, 31), (35, 29), (19, 5), (13, 30), (27, 20), (1, 3), (21, 14), (17, 37), (34, 19), (31, 35), (22, 8), (36, 27), (38, 29), (21, 16), (26, 33), (19, 3), (11, 7), (4, 38), (37, 3), (42, 5), (30, 23), (42, 40), (21, 28), (24, 33), (23, 5), (1, 8), (30, 9), (28, 10), (26, 23), (11, 13), (39, 5), (37, 33), (7, 23), (29, 38), (38, 27), (30, 37), (7, 19), (40, 14), (40, 24), (33, 29), (42, 0), (0, 3), (31, 31), (35, 10), (31, 7), (23, 7), (2, 35), (37, 31), (11, 42), (35, 32), (38, 7), (14, 8), (18, 30), (19, 40), (29, 16), (20, 21), (19, 21), (35, 38), (4, 16), (42, 37), (17, 18), (15, 13), (39, 41), (12, 31), (15, 23), (12, 13), (29, 28), (0, 9), (22, 21), (38, 6), (2, 7), (8, 3), (24, 32), (27, 41), (36, 8), (29, 14), (42, 11), (1, 21), (11, 24), (35, 19), (6, 39), (31, 26), (14, 42), (17, 17), (26, 34), (32, 7), (36, 40), (31, 8), (24, 2), (17, 41), (4, 33), (22, 32), (20, 37), (29, 8), (36, 7), (10, 38), (26, 8), (1, 27), (10, 26), (20, 13), (39, 27), (12, 41), (42, 8), (5, 38), (32, 38), (39, 24), (36, 42), (38, 4), (25, 32), (23, 29), (10, 17), (0, 23), (21, 34), (5, 10), (18, 35), (24, 9), (34, 23), (17, 22), (10, 39), (35, 8), (15, 35), (39, 25), (42, 3), (29, 31), (41, 35), (5, 22), (9, 21), (4, 41), (23, 9), (20, 41), (3, 0), (9, 0), (20, 10), (38, 10), (27, 4), (27, 26), (27, 5), (5, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 28), (30, 33), (12, 36), (42, 11), (21, 32), (34, 33), (25, 30), (11, 14), (10, 12), (10, 3), (8, 28), (29, 4), (32, 30), (16, 10), (32, 25), (16, 35), (44, 19), (36, 35), (32, 1), (9, 38), (26, 6), (43, 10), (35, 21), (43, 24), (22, 39), (28, 32), (22, 30), (20, 3), (6, 14), (42, 7), (30, 2), (4, 36), (44, 33), (22, 11), (34, 23), (28, 30), (0, 7), (3, 8), (39, 39), (11, 37), (28, 34), (3, 23), (19, 22), (12, 8), (10, 37), (6, 18), (10, 10), (6, 3), (25, 35), (24, 32), (22, 28), (29, 14), (7, 33), (36, 28), (11, 24), (44, 38), (25, 12), (1, 19), (43, 25), (20, 30), (18, 0), (17, 19), (42, 25), (1, 11), (32, 12), (27, 16), (32, 19), (15, 25), (4, 33), (11, 2), (19, 17), (36, 15), (26, 13), (26, 7), (18, 27), (9, 7), (17, 10), (3, 0), (26, 22), (41, 6), (32, 38), (34, 20), (2, 34), (16, 16), (14, 8), (32, 21), (27, 12), (37, 12), (29, 31), (37, 22), (15, 12), (33, 29), (30, 12), (5, 28), (33, 17), (36, 30), (36, 18), (2, 23), (25, 14), (8, 17), (18, 8), (19, 9), (32, 27), (0, 36), (14, 38), (44, 15), (7, 5), (11, 19), (36, 13), (20, 9), (9, 24), (29, 30), (14, 17), (11, 17), (12, 22), (44, 8), (3, 15), (30, 29), (34, 11), (17, 7), (41, 32), (16, 19), (6, 24), (38, 7), (26, 12), (44, 21), (13, 7), (1, 34), (10, 17), (35, 0), (40, 38), (8, 4), (23, 12), (29, 7), (26, 27), (0, 38), (13, 26), (29, 25), (13, 38), (16, 17), (13, 4), (31, 30), (43, 37), (12, 9), (9, 36), (0, 15), (13, 14), (41, 39), (16, 26), (4, 37), (23, 2), (9, 35), (16, 28), (28, 14), (4, 27), (8, 38), (39, 36), (32, 17), (1, 2), (18, 19), (28, 16), (27, 5), (23, 25), (6, 32), (36, 0), (4, 14), (33, 15), (41, 13), (6, 9), (25, 32), (18, 20), (27, 31), (19, 32), (5, 30), (42, 20), (3, 37), (36, 37), (22, 14), (5, 17), (33, 1), (43, 6), (34, 5), (22, 23), (6, 21), (10, 11), (36, 24), (6, 6), (32, 0), (17, 39), (41, 4), (8, 25), (16, 27), (9, 16), (0, 3), (7, 23), (32, 39), (22, 35), (38, 28), (7, 32), (18, 3), (0, 23), (17, 14), (22, 29), (14, 10), (32, 35), (0, 5), (2, 17), (10, 16), (39, 26), (19, 1), (34, 25), (9, 14), (31, 11), (1, 7), (14, 22), (29, 35), (28, 28), (42, 24), (2, 31), (44, 34), (30, 16), (31, 9), (0, 26), (23, 38), (0, 2), (34, 37), (20, 20), (14, 2), (11, 3), (40, 0), (30, 26), (33, 37), (7, 10), (38, 15), (28, 20), (31, 19), (31, 36), (2, 18), (7, 30), (25, 29), (20, 0), (38, 34), (33, 38), (18, 36), (28, 39), (38, 2), (35, 17), (5, 18), (3, 28), (40, 5), (19, 2), (38, 0), (30, 15), (39, 2), (21, 14), (33, 24), (24, 13), (43, 8), (12, 23), (27, 21), (29, 33), (8, 30), (12, 20), (10, 26), (6, 15), (24, 16), (29, 19), (39, 9), (35, 16), (9, 8), (15, 10), (12, 21), (17, 12), (26, 28), (32, 9), (41, 23), (7, 19), (30, 21), (43, 38), (32, 33), (30, 28), (15, 5), (28, 13), (25, 15), (33, 6), (5, 36), (16, 13), (26, 24), (42, 31), (1, 3), (19, 36), (42, 21), (16, 3), (7, 8), (11, 11), (30, 19), (26, 30), (29, 36), (18, 17), (10, 9), (37, 10), (34, 19), (7, 25), (40, 32), (6, 28), (24, 11), (17, 15), (4, 30), (19, 16), (9, 5), (26, 2), (27, 8), (15, 8), (13, 17), (23, 23), (15, 9), (36, 20), (7, 21), (37, 31), (36, 39), (21, 3), (31, 25), (18, 1), (42, 2), (14, 32), (38, 37), (28, 9), (11, 0), (23, 14), (15, 3), (18, 38), (44, 27), (21, 38), (35, 22), (42, 6), (40, 1), (28, 1), (22, 2), (44, 11), (32, 26), (30, 39), (23, 26), (10, 0), (16, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 0), (3, 28), (24, 26), (41, 1), (43, 2), (40, 35), (3, 22), (44, 24), (11, 24), (46, 13), (8, 2), (29, 34), (29, 9), (30, 19), (22, 6), (20, 4), (38, 9), (46, 12), (43, 16), (7, 29), (36, 5), (8, 28), (13, 22), (7, 10), (46, 4), (21, 0), (10, 21), (23, 35), (1, 31), (10, 8), (46, 22), (2, 7), (24, 34), (36, 20), (44, 28), (11, 32), (16, 2), (29, 26), (22, 31), (30, 35), (43, 0), (13, 13), (15, 11), (23, 37), (19, 16), (38, 20), (0, 5), (18, 14), (26, 4), (25, 18), (34, 10), (32, 6), (37, 16), (33, 31), (33, 19), (27, 24), (9, 26), (5, 24), (29, 16), (20, 14), (10, 17), (2, 26), (39, 24), (4, 24), (44, 6), (10, 27), (26, 40), (33, 5), (30, 22), (13, 25), (36, 18), (17, 14), (32, 3), (46, 25), (36, 33), (19, 19), (41, 25), (12, 15), (23, 24), (23, 34), (40, 32), (25, 5), (37, 39), (5, 0), (40, 24), (14, 3), (13, 28), (27, 11), (5, 3), (31, 31), (0, 24), (19, 27), (45, 1), (18, 24), (0, 9), (2, 18), (12, 35), (20, 9), (7, 33), (20, 25), (16, 15), (30, 33), (11, 18), (3, 38), (42, 16), (33, 22), (41, 31), (4, 3), (30, 7), (24, 28), (47, 0), (46, 28), (5, 37), (4, 19), (27, 9), (21, 31), (12, 24), (20, 38), (38, 37), (18, 3), (14, 39), (5, 20), (4, 13), (21, 22), (36, 14), (4, 25), (31, 9), (13, 24), (33, 26), (0, 31), (6, 4), (19, 36), (42, 21), (42, 28), (35, 22), (17, 6), (17, 39), (48, 18), (23, 25), (19, 35), (44, 12), (22, 27), (14, 36), (28, 1), (36, 39), (11, 0), (25, 40), (19, 13), (30, 29), (14, 23), (33, 32), (4, 2), (6, 37), (25, 16), (42, 39), (41, 22), (15, 26), (17, 24), (28, 26), (31, 29), (28, 37), (5, 1), (20, 21), (0, 39), (32, 15), (28, 36), (32, 0), (22, 39), (22, 36), (25, 20), (40, 21), (7, 22), (36, 11), (47, 22), (42, 19), (6, 0), (12, 38), (21, 39), (40, 30), (26, 34), (8, 3), (6, 14), (23, 13), (22, 40), (23, 33), (5, 17), (12, 4), (8, 40), (42, 8), (39, 39), (28, 8), (32, 22), (16, 12), (40, 5), (39, 14), (0, 18), (45, 0), (28, 33), (11, 33), (42, 5), (5, 6), (14, 1), (34, 4), (20, 31), (26, 22), (13, 16), (37, 10), (25, 28), (20, 39), (34, 11), (2, 37), (38, 0), (1, 0), (19, 8), (36, 12), (37, 14), (6, 17), (15, 22), (9, 2), (32, 2), (43, 18), (36, 24), (1, 9), (22, 20), (18, 18), (42, 22), (23, 22), (24, 6), (44, 10), (45, 6), (1, 7), (43, 8), (13, 29), (32, 27), (43, 29), (30, 24), (14, 38), (47, 34), (26, 24), (38, 33), (20, 13), (27, 0), (41, 38), (18, 26), (36, 1), (8, 9), (32, 29), (2, 39), (8, 10), (14, 8), (8, 15), (33, 11), (25, 27), (34, 28), (43, 6), (28, 2), (22, 17), (45, 2), (23, 12), (42, 4), (22, 24), (20, 11), (3, 13), (4, 27), (43, 37), (3, 29), (28, 5), (47, 28), (15, 14), (32, 28), (40, 26), (32, 21), (34, 19), (13, 2), (6, 35), (29, 1), (45, 7), (10, 33), (46, 10), (38, 3), (1, 34), (41, 37), (44, 7), (45, 33), (11, 21), (38, 16), (25, 6), (48, 0), (15, 20), (3, 21), (32, 32), (13, 32), (7, 37), (1, 36), (7, 30), (9, 10), (12, 37), (31, 6), (20, 1), (11, 10), (32, 13), (13, 38), (23, 29), (39, 23), (24, 5), (33, 34), (16, 14), (0, 34), (45, 40), (9, 13), (27, 28), (17, 35), (42, 1), (20, 26), (47, 19), (41, 15), (19, 25), (1, 11), (0, 20), (7, 1), (2, 30), (48, 11), (6, 21), (10, 12), (10, 1), (29, 40), (34, 13), (40, 25), (0, 30), (21, 4), (36, 27), (40, 31), (39, 9), (25, 13), (0, 29), (21, 11), (38, 18), (30, 9), (11, 12), (0, 37), (20, 20), (26, 0), (32, 11), (15, 18), (15, 33), (4, 31), (47, 11), (3, 24), (14, 18), (5, 35), (40, 18), (10, 15), (26, 5), (26, 32), (19, 37), (46, 33), (32, 4), (47, 32), (48, 30), (26, 7), (23, 16), (30, 40), (15, 8), (42, 37), (2, 38), (37, 19), (37, 23), (15, 19), (17, 37), (26, 6), (17, 29), (15, 4), (47, 16), (19, 10), (18, 13), (47, 30), (32, 20), (11, 35), (6, 13), (7, 9), (46, 36), (36, 10), (43, 21), (38, 40), (4, 7), (31, 20), (27, 5), (34, 37), (31, 4), (46, 34), (42, 38), (10, 40), (22, 29), (5, 25), (26, 1), (4, 38), (26, 36), (45, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 22), (10, 3), (39, 23), (26, 23), (29, 24), (0, 3), (25, 32), (11, 32), (23, 1), (15, 0), (9, 18), (27, 33), (15, 26), (12, 20), (2, 4), (38, 30), (13, 34), (8, 17), (19, 7), (34, 15), (13, 31), (17, 12), (12, 3), (10, 33), (29, 39), (2, 2), (29, 36), (0, 28), (31, 22), (14, 8), (18, 32), (4, 18), (1, 18), (13, 15), (6, 21), (7, 23), (13, 13), (1, 8), (23, 37), (20, 14), (15, 31), (21, 14), (0, 24), (3, 25), (4, 13), (27, 30), (14, 5), (34, 4), (10, 39), (22, 27), (6, 33), (19, 21), (21, 7), (6, 18), (35, 38), (22, 37), (18, 10), (38, 0), (7, 33), (28, 26), (29, 12), (22, 1), (2, 39), (4, 8), (11, 0), (38, 28), (28, 33), (29, 10), (34, 8), (24, 3), (17, 36), (13, 29), (10, 37), (12, 27), (14, 36), (15, 23), (37, 2), (12, 11), (34, 18), (8, 11), (17, 15), (2, 21), (0, 38), (7, 22), (38, 3), (28, 30), (14, 34), (0, 21), (37, 0), (7, 14), (36, 16), (23, 16), (36, 39), (5, 20), (1, 19), (33, 4), (9, 10), (2, 35), (34, 7), (8, 26), (6, 20), (39, 1), (30, 16), (36, 13), (32, 7), (7, 30), (28, 1), (0, 8), (36, 2), (36, 17), (14, 26), (26, 34), (11, 24), (18, 39), (12, 19), (16, 30), (24, 15), (28, 25), (14, 35), (11, 38), (35, 39), (36, 31), (25, 17), (14, 20), (8, 25), (25, 24), (23, 3), (24, 12), (18, 19), (17, 31), (9, 23), (24, 20), (39, 3), (30, 35), (28, 13), (38, 21), (30, 8), (27, 12), (22, 5), (38, 31), (14, 27), (0, 32), (0, 36), (19, 10), (18, 15), (34, 11), (35, 25), (13, 30), (37, 8), (32, 30), (14, 3), (38, 1), (38, 24), (12, 4), (15, 13), (38, 4), (33, 37), (22, 18), (32, 18), (0, 29), (30, 29), (10, 11), (2, 36), (29, 21), (5, 12), (7, 37), (19, 25), (38, 39), (14, 16), (31, 28), (21, 8), (27, 34), (11, 13), (13, 7), (29, 37), (15, 5), (31, 29), (22, 34), (5, 16), (16, 20), (0, 23), (22, 39), (33, 12), (20, 3), (28, 11), (38, 5), (24, 13), (35, 20), (1, 28), (36, 23), (33, 0), (4, 25), (13, 5), (4, 31), (23, 28), (13, 33), (28, 29), (28, 22), (33, 2), (8, 10), (1, 36), (30, 32), (0, 18), (14, 7), (21, 3), (25, 15), (19, 26), (26, 1), (13, 12), (13, 28), (21, 27), (13, 22), (12, 7), (28, 36), (6, 1), (32, 8), (21, 2), (17, 8), (33, 5), (0, 16), (18, 4), (24, 22), (12, 30), (27, 29), (37, 39), (21, 39), (35, 11), (12, 18), (34, 14), (1, 24), (8, 2), (4, 1), (18, 25), (35, 30), (12, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 5), (43, 14), (42, 25), (37, 20), (43, 27), (46, 4), (36, 2), (20, 8), (31, 33), (10, 13), (12, 19), (29, 2), (17, 34), (41, 9), (43, 26), (22, 1), (16, 36), (2, 42), (17, 42), (25, 6), (41, 19), (10, 7), (13, 9), (41, 29), (4, 43), (18, 9), (44, 8), (22, 8), (44, 21), (38, 17), (8, 20), (36, 23), (30, 19), (11, 21), (44, 24), (14, 28), (28, 35), (40, 10), (0, 4), (36, 3), (8, 14), (39, 35), (36, 27), (46, 41), (1, 35), (48, 20), (7, 27), (20, 43), (45, 29), (29, 32), (7, 38), (37, 32), (18, 38), (13, 27), (18, 30), (43, 13), (35, 35), (14, 26), (5, 12), (43, 9), (42, 36), (26, 25), (30, 23), (17, 40), (7, 10), (0, 2), (21, 16), (23, 14), (4, 7), (20, 21), (0, 15), (45, 37), (10, 6), (39, 42), (46, 23), (3, 40), (20, 6), (35, 17), (9, 16), (36, 1), (29, 27), (13, 22), (8, 0), (16, 41), (34, 17), (39, 36), (26, 24), (45, 39), (47, 16), (4, 15), (43, 38), (28, 4), (46, 15), (11, 22), (25, 7), (29, 29), (37, 40), (8, 15), (37, 22), (8, 8), (2, 18), (47, 13), (0, 21), (47, 22), (1, 40), (16, 37), (7, 34), (48, 38), (37, 39), (8, 21), (13, 0), (48, 8), (5, 10), (44, 38), (4, 27), (21, 27), (8, 42), (5, 8), (12, 8), (28, 39), (9, 29), (42, 26), (19, 38), (13, 3), (47, 10), (26, 16), (21, 21), (23, 16), (42, 24), (11, 6), (25, 14), (38, 16), (22, 16), (35, 28), (1, 36), (23, 8), (4, 38), (41, 8), (1, 11), (3, 31), (2, 6), (13, 13), (32, 24), (47, 30), (2, 2), (38, 3), (24, 19), (2, 24), (23, 13), (6, 27), (27, 36), (20, 7), (39, 34), (16, 13), (46, 10), (16, 25), (47, 35), (38, 34), (28, 2), (14, 6), (0, 31), (44, 4), (5, 11), (26, 21), (11, 17), (36, 14), (5, 0), (9, 22), (37, 19), (2, 13), (33, 36), (41, 13), (18, 33), (35, 0), (7, 35), (2, 40), (29, 22), (10, 41), (44, 40), (21, 23), (6, 12), (41, 31), (23, 30), (29, 40), (15, 10), (6, 42), (22, 32), (27, 23), (8, 5), (36, 24), (42, 31), (21, 8), (13, 32), (31, 40), (16, 0), (27, 34), (7, 18), (29, 8), (16, 33), (42, 3), (43, 34), (45, 36), (35, 2), (33, 4), (4, 24), (0, 35), (19, 39), (35, 41), (29, 18), (42, 5), (6, 11), (14, 31), (2, 16), (48, 37), (5, 15), (8, 24), (12, 21), (23, 11), (16, 11), (47, 12), (42, 43), (39, 3), (29, 12), (46, 6), (17, 0), (48, 0), (35, 42), (1, 33), (6, 17), (10, 40), (6, 23), (25, 30), (25, 0), (34, 38), (34, 29), (11, 27), (9, 1), (27, 25), (2, 12), (11, 15), (33, 24), (4, 14), (13, 11), (39, 1), (0, 29), (29, 36), (19, 19), (22, 29), (11, 19), (10, 4), (48, 33), (0, 7), (19, 8), (7, 37), (25, 41), (36, 21), (12, 10), (15, 22), (33, 31), (37, 2), (28, 7), (48, 26), (31, 2), (40, 17), (28, 5), (20, 1), (46, 14), (33, 17), (17, 33), (2, 0), (0, 23), (14, 2), (3, 10), (28, 20), (24, 37), (3, 34), (38, 12), (45, 2), (4, 41), (0, 39), (6, 5), (13, 20), (11, 23), (7, 28), (10, 1), (11, 11), (24, 7), (46, 40), (35, 15), (33, 10), (21, 29), (18, 34), (6, 13), (17, 38), (30, 15), (44, 7), (30, 12), (25, 20), (20, 24), (22, 4), (33, 30), (10, 37), (22, 24), (17, 23), (39, 10), (31, 25), (29, 5), (34, 12), (43, 22), (21, 5), (1, 18), (28, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 26), (41, 16), (36, 17), (29, 33), (23, 26), (19, 1), (41, 33), (18, 37), (42, 30), (38, 6), (41, 9), (41, 7), (12, 2), (39, 13), (22, 6), (3, 3), (19, 4), (18, 2), (35, 33), (18, 26), (15, 12), (8, 41), (38, 31), (29, 16), (9, 41), (26, 16), (11, 5), (21, 22), (26, 19), (41, 34), (28, 39), (37, 19), (18, 15), (14, 3), (30, 30), (29, 13), (36, 32), (43, 3), (28, 21), (37, 34), (12, 16), (17, 10), (33, 34), (3, 9), (0, 6), (10, 18), (23, 18), (2, 15), (11, 17), (22, 18), (26, 5), (4, 22), (10, 23), (27, 34), (11, 33), (42, 31), (28, 10), (6, 17), (23, 10), (19, 38), (33, 21), (35, 18), (11, 1), (44, 7), (42, 16), (5, 41), (26, 7), (45, 14), (35, 13), (28, 25), (9, 38), (19, 33), (13, 2), (32, 32), (20, 37), (22, 29), (34, 25), (42, 5), (26, 6), (15, 32), (30, 1), (31, 27), (36, 7), (43, 15), (4, 37), (18, 36), (40, 36), (28, 26), (34, 23), (7, 35), (26, 37), (7, 10), (29, 3), (37, 14), (29, 6), (24, 19), (40, 32), (31, 38), (28, 8), (26, 24), (8, 39), (29, 25), (37, 25), (0, 8), (43, 0), (25, 15), (35, 37), (9, 29), (0, 5), (34, 11), (17, 3), (43, 18), (5, 22), (37, 9), (31, 40), (27, 21), (3, 18), (25, 26), (20, 31), (37, 15), (7, 19), (40, 23), (34, 1), (18, 11), (33, 29), (40, 18), (8, 5), (27, 30), (29, 21), (6, 39), (21, 29), (26, 40), (38, 8), (1, 30), (34, 37), (15, 0), (25, 40), (4, 1), (44, 19), (12, 15), (41, 18), (32, 0), (33, 24), (44, 39), (17, 2), (20, 5), (31, 39), (9, 35), (13, 16), (12, 38), (23, 33), (30, 18), (5, 10), (3, 36), (1, 24), (2, 35), (45, 33), (33, 9), (1, 34), (35, 41), (40, 0), (8, 18), (21, 17), (18, 1), (22, 36), (18, 38), (12, 12), (24, 38), (27, 5), (40, 12), (5, 11), (33, 38), (24, 28), (41, 4), (22, 27), (19, 27), (33, 23), (21, 2), (33, 36), (35, 29), (8, 24), (25, 41), (7, 4), (12, 8), (12, 36), (32, 7), (4, 3), (23, 38), (15, 38), (35, 7), (41, 31), (2, 7), (23, 41), (25, 6), (38, 3), (23, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (39, 0), (0, 40), (14, 40), (30, 5), (8, 14), (4, 6), (19, 16), (44, 41), (0, 14), (11, 35), (5, 2), (33, 0), (42, 18), (20, 20), (40, 33), (7, 16), (35, 4), (34, 0), (36, 0), (24, 24), (14, 25), (20, 4), (40, 34), (7, 25), (23, 18), (36, 27), (26, 22), (23, 44), (32, 1), (22, 5), (18, 12), (32, 35), (2, 28), (27, 39), (1, 13), (15, 28), (28, 43), (37, 7), (33, 11), (38, 38), (15, 37), (21, 24), (1, 20), (41, 17), (39, 6), (33, 22), (11, 13), (20, 30), (18, 11), (44, 23), (5, 10), (18, 41), (45, 2), (41, 35), (26, 2), (37, 39), (30, 10), (22, 9), (40, 42), (11, 0), (34, 35), (0, 23), (36, 42), (16, 25), (24, 29), (24, 20), (9, 22), (23, 36), (21, 28), (31, 26), (34, 24), (5, 24), (26, 32), (8, 18), (4, 43), (35, 8), (42, 22), (20, 8), (19, 11), (38, 26), (17, 43), (39, 20), (23, 11), (0, 34), (7, 38), (24, 2), (28, 24), (0, 8), (5, 1), (23, 39), (29, 26), (34, 40), (29, 19), (32, 33), (2, 7), (7, 33), (28, 26), (6, 31), (8, 35), (7, 8), (33, 33), (44, 25), (30, 22), (12, 15), (2, 23), (37, 36), (21, 18), (2, 10), (41, 3), (4, 44), (38, 41), (42, 16), (17, 16), (45, 11), (33, 28), (39, 31), (37, 21), (27, 25), (42, 25), (43, 9), (39, 29), (37, 22), (36, 22), (21, 27), (25, 41), (40, 44), (30, 16), (4, 38), (35, 6), (5, 20), (30, 24), (5, 19), (16, 42), (16, 30), (17, 33), (37, 38), (3, 24), (17, 28), (3, 37), (42, 29), (19, 40), (26, 39), (16, 29), (32, 4), (41, 15), (28, 1), (29, 1), (10, 10), (1, 2), (9, 39), (39, 8), (8, 24), (5, 40), (27, 0), (43, 1), (34, 6), (0, 10), (25, 25), (35, 11), (20, 28), (31, 24), (25, 36), (21, 9), (4, 19), (38, 12), (34, 8), (34, 41), (38, 23), (6, 32), (14, 23), (37, 28), (6, 29), (18, 5), (22, 10), (3, 8), (22, 3), (17, 8), (8, 3), (10, 36), (3, 27), (45, 29), (34, 9), (4, 13), (32, 13), (14, 1), (21, 17), (33, 8), (40, 8), (3, 39), (24, 10), (21, 41), (35, 15), (28, 19), (0, 43), (20, 1), (9, 11), (38, 20), (4, 1), (30, 31), (23, 1), (24, 25), (11, 39), (23, 28), (24, 12), (35, 13), (20, 43), (45, 6), (30, 34), (10, 34), (21, 32), (24, 26), (42, 28), (43, 39), (43, 10), (20, 31), (28, 33), (24, 19), (1, 16), (36, 18), (31, 15), (4, 20), (1, 29), (31, 0), (18, 36), (44, 22), (15, 38), (41, 42), (7, 30), (45, 9), (32, 3), (13, 35), (6, 37), (36, 17), (44, 18), (8, 40), (11, 23), (11, 6), (27, 1), (13, 19), (37, 20), (9, 33), (12, 30), (12, 17), (36, 10), (43, 0), (4, 41), (42, 27), (39, 25), (20, 26), (14, 20), (41, 37), (26, 20), (14, 31), (36, 5), (31, 18), (19, 6), (27, 10), (39, 34), (13, 36), (35, 21), (31, 19), (27, 38), (0, 9), (39, 44), (45, 38), (40, 40), (36, 20), (33, 39), (13, 29), (0, 13), (43, 34), (1, 0), (37, 11), (40, 24), (2, 12), (42, 8), (21, 7), (26, 31), (7, 44), (16, 5), (28, 35), (44, 26), (8, 7), (26, 28), (21, 26), (1, 14), (8, 26), (35, 42), (12, 6), (15, 10), (18, 15), (29, 20), (13, 41), (21, 21), (8, 33), (41, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 4), (36, 40), (4, 22), (20, 16), (28, 11), (2, 34), (23, 1), (26, 19), (35, 11), (9, 12), (34, 19), (9, 5), (37, 36), (44, 5), (38, 30), (1, 26), (42, 39), (41, 29), (41, 12), (3, 44), (0, 12), (9, 21), (6, 12), (38, 48), (0, 23), (20, 15), (14, 34), (41, 21), (30, 11), (19, 19), (24, 15), (32, 13), (35, 30), (30, 7), (30, 28), (0, 41), (16, 2), (30, 0), (1, 6), (10, 11), (33, 36), (39, 26), (23, 26), (42, 16), (32, 30), (39, 43), (10, 5), (23, 14), (13, 34), (16, 44), (0, 35), (1, 3), (1, 31), (35, 35), (15, 40), (19, 0), (23, 25), (2, 45), (41, 2), (43, 33), (2, 41), (32, 0), (43, 28), (22, 30), (23, 42), (19, 42), (26, 20), (2, 29), (6, 4), (9, 27), (38, 13), (26, 6), (40, 26), (16, 22), (9, 31), (36, 11), (44, 28), (22, 15), (32, 16), (2, 24), (34, 22), (10, 16), (3, 43), (28, 36), (14, 28), (7, 30), (6, 7), (18, 39), (26, 47), (18, 36), (44, 31), (23, 3), (13, 10), (33, 47), (1, 39), (34, 47), (8, 6), (28, 5), (6, 33), (17, 13), (39, 6), (13, 0), (6, 48), (35, 37), (16, 23), (7, 45), (18, 12), (25, 25), (17, 28), (37, 24), (5, 13), (18, 37), (38, 0), (40, 2), (2, 13), (7, 32), (19, 46), (2, 47), (22, 44), (17, 47), (30, 10), (40, 12), (5, 12), (3, 32), (6, 14), (3, 6), (31, 2), (30, 20), (18, 40), (31, 13), (9, 35), (40, 36), (36, 9), (15, 43), (40, 39), (31, 18), (11, 21), (26, 40), (44, 7), (41, 9), (20, 39), (4, 15), (0, 13), (14, 24), (26, 42), (5, 10), (26, 17), (17, 24), (8, 36), (9, 23), (27, 22), (22, 38), (13, 31), (21, 35), (1, 7), (34, 9), (8, 22), (17, 42), (43, 23), (33, 28), (20, 27), (26, 14), (11, 15), (44, 16), (13, 18), (11, 26), (12, 17), (5, 40), (36, 12), (5, 39), (0, 11), (37, 41), (12, 36), (38, 29), (38, 21), (43, 8), (27, 5), (15, 11), (14, 4), (43, 43), (22, 2), (21, 40), (43, 46), (44, 39), (11, 40), (21, 20), (38, 44), (19, 17), (44, 47), (31, 47), (21, 48), (39, 29), (32, 1), (5, 30), (8, 14), (17, 34), (0, 38), (20, 11), (22, 31), (27, 35), (28, 17), (14, 3), (24, 6), (9, 48), (6, 13), (15, 27), (36, 15), (32, 41), (26, 30), (0, 14), (41, 6), (35, 17), (15, 20), (14, 16), (12, 16), (25, 30), (12, 38), (4, 32), (40, 4), (38, 26), (44, 33), (32, 14), (3, 29), (42, 27), (27, 10), (42, 4), (23, 47), (6, 20), (4, 12), (28, 29), (16, 24), (4, 9), (39, 16), (41, 0), (42, 29), (30, 23), (4, 24), (33, 21), (18, 43), (1, 36), (23, 6), (21, 33), (38, 38), (1, 43), (34, 29), (29, 8), (11, 37), (40, 19), (30, 37), (1, 30), (22, 23), (31, 6), (38, 11), (7, 27), (16, 21), (22, 13), (33, 9), (37, 22), (34, 13), (4, 10), (17, 1), (14, 37), (39, 44), (22, 5), (8, 38), (10, 13), (35, 34), (38, 28), (36, 23), (30, 9), (21, 44), (31, 22), (15, 3), (2, 32), (9, 2), (44, 3), (10, 29), (17, 35), (28, 46), (3, 39), (9, 22), (16, 37), (38, 10), (38, 7), (30, 29), (1, 1), (2, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 2), (18, 31), (37, 10), (32, 24), (43, 13), (34, 10), (19, 0), (6, 26), (13, 26), (35, 25), (26, 38), (37, 40), (34, 39), (43, 17), (22, 19), (6, 7), (43, 31), (8, 42), (27, 16), (47, 14), (41, 13), (35, 42), (23, 45), (11, 41), (13, 34), (19, 37), (42, 22), (5, 40), (22, 1), (33, 5), (38, 44), (38, 18), (28, 3), (4, 13), (21, 37), (10, 16), (29, 26), (7, 34), (25, 38), (40, 40), (5, 15), (46, 19), (30, 36), (1, 20), (39, 22), (7, 35), (12, 19), (27, 15), (39, 40), (7, 27), (20, 26), (31, 46), (1, 25), (0, 12), (47, 41), (39, 36), (31, 10), (45, 38), (40, 45), (32, 21), (4, 43), (23, 19), (27, 40), (18, 45), (10, 24), (13, 5), (13, 46), (47, 43), (14, 8), (46, 24), (38, 2), (38, 39), (24, 46), (2, 44), (34, 4), (21, 36), (5, 27), (36, 38), (33, 44), (47, 46), (3, 6), (33, 34), (9, 45), (0, 26), (17, 36), (35, 19), (36, 22), (22, 39), (2, 4), (37, 5), (15, 34), (33, 22), (23, 40), (25, 4), (41, 2), (1, 18), (12, 28), (43, 26), (39, 15), (28, 26), (4, 9), (29, 27), (27, 2), (31, 4), (42, 3), (29, 11), (3, 5), (27, 38), (36, 44), (33, 39), (25, 32), (29, 40), (3, 26), (20, 19), (37, 39), (20, 37), (34, 24), (44, 43), (42, 42), (17, 44), (25, 36), (36, 26), (5, 44), (8, 18), (16, 33), (44, 26), (42, 41), (45, 39), (26, 36), (39, 19), (9, 7), (2, 22), (1, 47), (28, 18), (46, 41), (15, 7), (28, 41), (1, 15), (6, 22), (22, 43), (18, 36), (20, 36), (18, 28), (15, 40), (40, 23), (21, 44), (6, 18), (4, 31), (26, 16), (12, 43), (4, 21), (14, 10), (18, 27), (5, 36), (44, 24), (15, 4), (47, 9), (29, 8), (24, 42), (3, 45), (29, 25), (10, 35), (34, 1), (19, 24), (45, 24), (40, 11), (32, 5), (46, 17), (38, 33), (33, 10), (13, 11), (12, 13), (21, 21), (21, 31), (2, 6), (16, 0), (31, 9), (9, 40), (35, 29), (4, 28), (0, 20), (11, 35), (1, 31), (35, 8), (11, 27), (37, 2), (19, 35), (20, 32), (43, 4), (0, 40), (44, 13), (25, 19), (25, 34), (20, 3), (44, 18), (0, 33), (30, 25), (10, 31), (43, 19), (43, 47), (33, 29), (30, 13), (17, 19), (36, 7), (9, 26), (28, 45), (18, 15), (21, 24), (4, 24), (7, 25), (32, 9), (46, 37), (15, 0), (26, 31), (0, 9), (26, 7), (36, 36), (25, 14), (8, 33), (20, 4), (21, 32), (6, 4), (42, 28), (20, 31), (3, 23), (16, 42), (27, 28), (9, 46), (14, 30), (36, 19), (3, 12), (8, 19), (34, 18), (28, 40), (24, 11), (32, 44), (12, 33), (33, 16), (17, 3), (45, 36), (36, 17), (4, 46), (42, 21), (9, 35), (28, 35), (11, 43), (12, 12), (34, 6), (37, 6), (39, 2), (10, 23), (10, 30), (43, 46), (12, 21), (1, 1), (6, 39), (46, 45), (40, 24), (29, 43), (31, 38), (47, 29), (7, 6), (46, 7), (3, 11), (11, 42), (41, 41), (30, 39), (32, 10), (46, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 29), (34, 11), (28, 17), (28, 5), (10, 24), (46, 35), (34, 7), (32, 41), (16, 17), (17, 6), (10, 32), (42, 40), (23, 29), (41, 19), (26, 9), (4, 26), (12, 24), (37, 13), (7, 4), (45, 5), (34, 30), (4, 4), (19, 11), (13, 24), (16, 36), (23, 15), (7, 18), (5, 12), (41, 15), (26, 0), (9, 16), (26, 8), (29, 24), (22, 19), (16, 19), (37, 2), (29, 1), (4, 7), (16, 38), (33, 38), (0, 41), (16, 16), (19, 0), (0, 13), (22, 32), (29, 22), (15, 12), (10, 28), (23, 33), (39, 27), (26, 18), (32, 3), (27, 5), (21, 23), (20, 7), (31, 39), (41, 30), (42, 4), (4, 23), (35, 33), (6, 1), (16, 39), (29, 34), (47, 10), (11, 0), (14, 39), (6, 18), (37, 41), (14, 36), (6, 11), (10, 41), (10, 23), (22, 10), (45, 42), (24, 18), (42, 15), (19, 34), (32, 25), (28, 15), (26, 22), (6, 27), (34, 24), (0, 38), (22, 16), (43, 24), (10, 9), (28, 22), (7, 40), (14, 16), (27, 40), (0, 27), (16, 7), (47, 4), (24, 14), (12, 11), (41, 14), (46, 15), (5, 6), (20, 27), (1, 4), (41, 2), (29, 11), (5, 36), (44, 23), (41, 1), (42, 18), (40, 5), (19, 5), (16, 35), (25, 30), (34, 3), (18, 23), (16, 25), (19, 38), (47, 6), (13, 23), (2, 31), (30, 1), (34, 5), (12, 18), (21, 8), (31, 34), (0, 16), (37, 1), (31, 13), (20, 5), (28, 31), (38, 6), (15, 40), (16, 10), (13, 27), (14, 42), (25, 8), (47, 40), (0, 32), (23, 42), (22, 20), (36, 0), (3, 14), (16, 27), (40, 20), (37, 3), (36, 4), (46, 24), (43, 23), (5, 26), (4, 39), (27, 16), (0, 17), (2, 3), (20, 28), (39, 5), (2, 20), (42, 37), (8, 11), (4, 13), (47, 8), (17, 32), (30, 5), (25, 33), (19, 35), (1, 8), (27, 22), (38, 30), (16, 11), (27, 0), (8, 33), (0, 42), (25, 19), (33, 14), (5, 11), (24, 9), (37, 33), (1, 42), (13, 17), (11, 33), (0, 7), (10, 10), (10, 1), (42, 19), (21, 32), (45, 27), (24, 42), (24, 35), (38, 38), (37, 32), (26, 24), (29, 19), (42, 27), (40, 33), (46, 9), (40, 11), (39, 19), (3, 12), (28, 26), (28, 33), (33, 40), (17, 24), (28, 19), (46, 23), (5, 14), (46, 14), (24, 30), (22, 21), (41, 17), (23, 10), (11, 10), (41, 22), (35, 3), (13, 9), (42, 10), (7, 7), (26, 16), (27, 26), (18, 4), (7, 31), (25, 31), (21, 26), (14, 26), (1, 29), (44, 25), (10, 21), (28, 27), (45, 30), (2, 39), (0, 1), (46, 8), (44, 41), (32, 24), (1, 36), (0, 21), (23, 39), (29, 9), (30, 36), (6, 26), (9, 18), (13, 12), (38, 4), (36, 26), (7, 24), (13, 26), (3, 25), (26, 23), (21, 3), (47, 37), (16, 28), (31, 41), (35, 36), (31, 36), (22, 28), (11, 34), (32, 26), (40, 42), (39, 36), (45, 20), (19, 20), (33, 23), (22, 3), (22, 26), (31, 28), (34, 19), (29, 6), (8, 5), (6, 21), (24, 20), (21, 21), (34, 14), (33, 7), (19, 3), (22, 33), (9, 31), (18, 36), (18, 26), (28, 11), (43, 15), (36, 15), (28, 42), (14, 12), (40, 14), (24, 23), (0, 4), (47, 27), (18, 15), (35, 23), (24, 25), (43, 6), (12, 37), (20, 42), (13, 38), (8, 16), (34, 10), (22, 40), (5, 21), (47, 13), (27, 36), (14, 0), (41, 3), (40, 30), (13, 41), (31, 26), (34, 22), (43, 21), (11, 40), (44, 34), (18, 37), (28, 30), (3, 30), (6, 9), (44, 32), (29, 32), (40, 7), (22, 39), (37, 11), (45, 7), (6, 36), (39, 15), (6, 29), (27, 27), (21, 17), (1, 26), (38, 19), (9, 8), (35, 42), (35, 27), (14, 8), (43, 18), (14, 5), (32, 2), (45, 36), (10, 8), (30, 26), (12, 0), (40, 22), (46, 29), (5, 30), (34, 27), (3, 2), (7, 21), (28, 2), (15, 11), (8, 37), (5, 25), (38, 7), (2, 24), (45, 1), (14, 24), (33, 21), (11, 35), (30, 3), (29, 12), (29, 27), (46, 34), (8, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 41), (27, 4), (20, 4), (13, 8), (35, 31), (7, 16), (37, 42), (13, 26), (35, 23), (33, 9), (23, 23), (18, 37), (42, 10), (33, 15), (1, 40), (0, 29), (12, 15), (13, 15), (1, 26), (33, 30), (36, 24), (23, 6), (41, 18), (18, 44), (26, 25), (26, 22), (27, 44), (11, 12), (34, 0), (4, 31), (22, 37), (18, 41), (17, 14), (2, 8), (19, 6), (43, 36), (41, 36), (9, 16), (13, 35), (18, 35), (18, 42), (22, 45), (20, 30), (28, 31), (22, 2), (34, 18), (9, 15), (6, 18), (3, 6), (41, 6), (14, 3), (35, 3), (18, 2), (13, 33), (34, 16), (3, 1), (25, 15), (33, 33), (14, 23), (42, 0), (19, 3), (17, 22), (13, 28), (33, 17), (9, 45), (23, 25), (6, 28), (32, 29), (35, 2), (5, 27), (31, 45), (1, 28), (27, 6), (7, 6), (20, 44), (21, 18), (5, 33), (16, 6), (33, 14), (38, 3), (23, 5), (40, 2), (27, 18), (7, 40), (29, 14), (23, 34), (36, 25), (12, 35), (22, 17), (43, 38), (5, 19), (19, 12), (40, 41), (33, 27), (21, 7), (17, 39), (39, 24), (28, 24), (30, 12), (34, 43), (24, 4), (30, 36), (31, 31), (5, 24), (20, 22), (37, 8), (28, 8), (43, 33), (23, 3), (7, 0), (33, 0), (14, 12), (16, 33), (39, 40), (29, 5), (31, 15), (22, 1), (1, 27), (2, 19), (22, 22), (23, 27), (32, 31), (9, 40), (19, 23), (25, 13), (13, 39), (29, 12), (39, 23), (37, 19), (4, 29), (23, 15), (16, 4), (2, 16), (14, 11), (9, 12), (9, 4), (43, 40), (42, 29), (36, 34), (12, 32), (7, 5), (22, 15), (42, 23), (31, 37), (5, 15), (12, 8), (38, 35), (9, 20), (35, 38), (8, 10), (6, 33), (43, 43), (30, 0), (4, 45), (5, 14), (33, 12), (28, 14), (2, 14), (36, 32), (0, 42), (38, 11), (10, 24), (0, 18), (8, 2), (8, 43), (18, 28), (16, 30), (11, 0), (37, 4), (0, 38), (36, 29), (10, 13), (31, 7), (37, 23), (13, 21), (20, 10), (16, 15), (0, 20), (36, 28), (27, 31), (30, 31), (31, 25), (28, 13), (8, 15), (16, 38), (13, 24), (12, 14), (42, 24), (1, 44), (43, 5), (28, 41), (20, 14), (31, 22), (38, 1), (5, 35), (39, 8), (14, 37), (37, 1), (31, 28), (9, 39), (30, 40), (29, 34), (32, 1), (3, 26), (31, 32), (30, 22), (43, 39), (17, 7), (17, 42), (21, 0), (20, 28), (35, 19), (13, 7), (36, 8), (15, 7), (19, 22), (21, 43), (11, 35), (23, 8), (17, 27), (1, 34), (32, 21), (27, 41), (37, 20), (7, 7), (33, 24), (11, 36), (26, 9), (14, 42), (10, 18), (9, 8), (24, 22), (30, 41), (40, 22), (27, 17), (29, 3), (41, 10), (8, 8), (42, 17), (42, 8), (38, 25), (41, 5), (1, 7), (2, 7), (9, 21), (25, 32), (1, 8), (42, 35), (2, 29), (19, 7), (21, 22), (35, 39), (6, 14), (21, 21), (34, 27), (40, 31), (10, 44), (0, 11), (7, 10), (3, 41), (20, 21), (28, 38), (27, 1), (15, 5), (19, 31), (15, 35), (11, 5), (42, 27), (34, 25), (26, 36), (11, 30), (7, 3), (11, 23), (35, 6), (2, 22), (30, 1), (35, 11), (38, 10), (15, 23), (12, 39), (27, 33), (39, 5), (24, 17), (16, 32), (37, 13), (32, 26), (18, 9), (27, 39), (23, 10), (20, 7), (16, 9), (36, 26), (22, 8), (8, 38), (32, 17), (18, 24), (16, 13), (11, 15), (36, 22), (25, 4), (34, 28), (23, 1), (25, 42), (29, 42), (24, 37), (13, 10), (20, 23), (30, 43), (2, 42), (21, 30), (41, 38), (41, 22), (21, 27), (20, 20), (8, 25), (38, 14), (22, 36), (40, 23), (5, 20), (13, 32), (18, 7), (4, 1), (9, 2), (36, 27), (35, 21), (15, 17), (27, 35), (26, 26), (19, 0), (5, 34), (31, 43), (3, 5), (41, 37), (3, 30), (43, 23), (24, 23), (35, 33), (15, 18), (0, 23), (14, 18), (29, 25), (33, 23), (0, 16), (2, 12), (28, 34), (23, 18), (21, 42), (10, 22), (41, 3), (39, 12), (15, 37), (21, 1), (2, 44), (9, 11), (0, 5), (0, 27), (29, 37), (40, 34), (10, 34), (34, 5), (27, 30), (15, 11), (42, 5), (11, 43), (38, 20), (28, 2), (22, 38), (3, 9), (39, 13), (31, 0), (16, 11), (39, 6), (33, 25), (20, 2), (12, 12), (15, 14), (41, 26), (31, 1), (36, 18), (42, 42), (35, 17), (18, 4), (26, 6), (8, 20), (22, 4), (38, 22), (24, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 13), (1, 23), (32, 36), (41, 37), (15, 39), (37, 26), (22, 2), (40, 19), (15, 25), (22, 14), (31, 22), (19, 23), (32, 14), (29, 23), (7, 35), (14, 30), (30, 5), (27, 26), (15, 34), (15, 31), (11, 26), (41, 13), (7, 31), (24, 8), (11, 16), (3, 29), (32, 20), (42, 10), (38, 11), (5, 38), (9, 24), (17, 9), (28, 12), (26, 4), (0, 27), (21, 36), (31, 40), (14, 15), (33, 10), (22, 22), (7, 29), (10, 39), (33, 20), (16, 18), (17, 12), (5, 0), (29, 31), (3, 41), (0, 41), (24, 6), (17, 20), (9, 33), (28, 23), (37, 21), (3, 31), (26, 41), (26, 23), (38, 3), (15, 14), (18, 6), (4, 43), (11, 27), (25, 36), (4, 22), (8, 33), (38, 30), (3, 9), (42, 14), (1, 25), (16, 24), (19, 40), (29, 27), (28, 34), (13, 5), (0, 18), (8, 36), (30, 1), (20, 4), (20, 3), (17, 11), (29, 20), (0, 2), (23, 33), (25, 3), (28, 0), (16, 11), (6, 6), (24, 32), (18, 3), (3, 39), (16, 30), (35, 12), (39, 12), (18, 38), (2, 14), (2, 31), (26, 32), (10, 7), (26, 43), (42, 23), (0, 19), (0, 37), (26, 1), (29, 18), (40, 34), (30, 3), (26, 15), (20, 35), (35, 32), (39, 9), (40, 15), (25, 16), (12, 24), (16, 23), (4, 19), (20, 11), (37, 17), (23, 3), (5, 1), (40, 20), (30, 13), (41, 33), (8, 26), (21, 4), (15, 12), (13, 23), (37, 33), (28, 31), (12, 8), (40, 16), (39, 26), (39, 40), (6, 13), (28, 18), (3, 13), (7, 24), (34, 14), (35, 25), (27, 43), (23, 7), (32, 19), (34, 9), (14, 32), (13, 6), (11, 42), (2, 8), (27, 8), (6, 26), (27, 22), (35, 9), (30, 43), (16, 33), (23, 23), (23, 42), (32, 17), (1, 15), (20, 26), (36, 25), (34, 4), (39, 41), (30, 7), (37, 20), (1, 10), (18, 29), (12, 32), (10, 41), (25, 33), (6, 39), (33, 4), (41, 27), (15, 40), (10, 2), (16, 16), (21, 37), (24, 13), (30, 11), (35, 17), (37, 41), (13, 4), (21, 24), (10, 5), (20, 30), (12, 33), (17, 36), (36, 28), (19, 42), (31, 23), (14, 12), (40, 30), (15, 10), (23, 36), (17, 1), (2, 6), (15, 24), (9, 36), (24, 2), (8, 7), (41, 8), (32, 8), (28, 38), (41, 28), (1, 29), (23, 11), (17, 27), (42, 22), (6, 15), (30, 9), (8, 17), (28, 16), (5, 13), (13, 13), (8, 1), (16, 35), (32, 21), (1, 18), (15, 3), (27, 37), (2, 40), (2, 29), (35, 10), (11, 28), (30, 39), (13, 37), (14, 5), (37, 22), (5, 6), (5, 7), (14, 14), (12, 35), (33, 29), (41, 29), (10, 33), (32, 3), (36, 6), (19, 29), (7, 40), (37, 29), (21, 19), (1, 16), (10, 37), (29, 5), (27, 17), (8, 24), (4, 36), (6, 40), (17, 2), (13, 28), (27, 30), (10, 25), (40, 11), (7, 32), (17, 24), (16, 28), (6, 0), (17, 3), (24, 10), (39, 27), (36, 12), (0, 31), (26, 17), (17, 13), (36, 4), (5, 2), (42, 4), (5, 21), (30, 37), (35, 35), (5, 14), (24, 36), (23, 32), (9, 8), (6, 20), (26, 2), (34, 32), (21, 3), (31, 17), (42, 26), (20, 32), (30, 21), (18, 13), (15, 13), (40, 1), (5, 16), (18, 20), (35, 39), (12, 42), (14, 26), (11, 43), (7, 11), (42, 7), (31, 8), (38, 42), (11, 8), (30, 17), (33, 2), (22, 3), (23, 9), (31, 3), (4, 17), (14, 19), (8, 2), (20, 23), (30, 12), (21, 41), (36, 7), (42, 24), (39, 20), (39, 8), (21, 40), (5, 12), (1, 8), (5, 34), (29, 6), (18, 15), (14, 37), (32, 43), (3, 27), (8, 38), (6, 11), (7, 2), (37, 6), (41, 40), (22, 7), (36, 26), (0, 32), (40, 14), (14, 18), (22, 19), (4, 4), (35, 34), (28, 26), (42, 27), (17, 26), (12, 14), (24, 7), (7, 19), (37, 2), (35, 7), (21, 43), (13, 27), (31, 13), (3, 28), (12, 23), (33, 13), (1, 14), (27, 23), (18, 43), (28, 8), (41, 10), (15, 19), (41, 35), (7, 28), (36, 21), (32, 42), (31, 31), (5, 32), (32, 22), (19, 37), (6, 38), (38, 26), (1, 5), (34, 34), (1, 32), (12, 16), (36, 24), (4, 18), (0, 29), (6, 27), (5, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (39, 25), (24, 18), (36, 12), (41, 20), (16, 2), (15, 37), (37, 11), (41, 12), (11, 10), (20, 7), (29, 22), (0, 16), (4, 27), (11, 4), (20, 35), (32, 38), (27, 28), (21, 20), (39, 22), (20, 34), (4, 12), (43, 31), (9, 33), (20, 3), (44, 4), (44, 24), (42, 37), (10, 3), (11, 11), (15, 41), (24, 19), (44, 38), (34, 27), (4, 3), (15, 7), (26, 4), (2, 24), (32, 8), (30, 29), (12, 14), (2, 19), (7, 33), (39, 28), (8, 27), (39, 0), (25, 14), (18, 9), (16, 16), (29, 21), (32, 31), (43, 25), (29, 38), (38, 1), (35, 34), (10, 38), (23, 6), (6, 24), (23, 10), (4, 9), (24, 6), (42, 38), (27, 35), (23, 22), (38, 16), (21, 5), (40, 41), (15, 38), (36, 41), (40, 37), (11, 5), (32, 25), (37, 22), (2, 16), (2, 3), (29, 34), (12, 38), (8, 39), (37, 1), (18, 26), (1, 23), (39, 3), (1, 7), (10, 35), (29, 3), (9, 23), (41, 8), (25, 19), (8, 6), (41, 31), (10, 41), (6, 41), (20, 4), (1, 19), (26, 29), (39, 9), (2, 12), (26, 34), (20, 10), (32, 40), (31, 30), (28, 1), (9, 17), (28, 31), (17, 6), (38, 37), (9, 18), (32, 22), (9, 19), (19, 40), (36, 11), (38, 7), (17, 26), (10, 34), (42, 10), (29, 6), (25, 37), (10, 20), (1, 40), (39, 7), (3, 24), (29, 9), (1, 28), (12, 5), (25, 20), (8, 32), (41, 26), (44, 8), (8, 24), (40, 3), (19, 33), (2, 37), (11, 0), (14, 23), (21, 0), (4, 10), (1, 24), (21, 25), (13, 30), (41, 32), (35, 3), (33, 20), (26, 31), (6, 25), (39, 12), (6, 1), (33, 23), (21, 11), (6, 27), (28, 41), (41, 24), (22, 40), (23, 3), (2, 30), (13, 41), (21, 29), (4, 6), (25, 36), (33, 2), (2, 26), (17, 25), (42, 27), (18, 20), (15, 30), (12, 20), (20, 2), (31, 11), (29, 17), (37, 9), (41, 25), (43, 15), (36, 24), (38, 11), (5, 20), (3, 11), (21, 31), (12, 7), (6, 15), (28, 22), (16, 27), (31, 38), (7, 26), (3, 2), (14, 6), (0, 24), (28, 20), (4, 17), (25, 8), (41, 23), (0, 20), (20, 40), (22, 3), (31, 12), (32, 3), (19, 32), (39, 2), (7, 35), (28, 8), (8, 38), (31, 35), (39, 36), (16, 41), (35, 23), (13, 35), (34, 14), (38, 30), (25, 24), (27, 5), (0, 2), (17, 24), (16, 19), (20, 30), (17, 17), (4, 40), (2, 15), (37, 0), (36, 3), (25, 29), (17, 9), (37, 39), (28, 0), (42, 9), (32, 26), (13, 14), (19, 31), (40, 12), (9, 36), (15, 31), (42, 33), (26, 12), (17, 23), (37, 26), (41, 4), (17, 8), (2, 11), (33, 40), (41, 14), (22, 0), (13, 0), (25, 17), (2, 2), (30, 11), (44, 36), (34, 26), (44, 17), (9, 9), (32, 4), (38, 4), (38, 15), (14, 1), (28, 19), (40, 14), (7, 10), (11, 19), (32, 23), (19, 39), (35, 5), (13, 32), (20, 13), (34, 24), (40, 16), (31, 9), (29, 33), (34, 28), (6, 26), (44, 13), (2, 10), (1, 33), (8, 11), (11, 40), (38, 8), (6, 4), (27, 29), (7, 28), (43, 20), (31, 20), (13, 13), (9, 37), (27, 22), (41, 38), (43, 27), (13, 6), (24, 26), (40, 34), (22, 37), (35, 8), (1, 21), (10, 29), (12, 3), (12, 1), (4, 0), (28, 9), (40, 29), (3, 35), (19, 14), (5, 26), (35, 35), (11, 33), (12, 15), (5, 35), (26, 35), (11, 6), (40, 31), (36, 26), (28, 14), (5, 29), (39, 18), (0, 14), (33, 19), (7, 40), (20, 11), (27, 30), (28, 6), (5, 34), (3, 28), (19, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 14), (40, 21), (29, 8), (37, 19), (2, 47), (42, 10), (31, 48), (18, 28), (23, 0), (25, 43), (37, 17), (0, 32), (29, 41), (5, 28), (22, 34), (10, 40), (34, 10), (5, 34), (38, 27), (23, 16), (24, 26), (8, 18), (33, 28), (19, 19), (31, 15), (9, 45), (4, 22), (33, 31), (31, 2), (19, 1), (25, 3), (11, 17), (16, 41), (22, 23), (15, 13), (0, 17), (29, 33), (5, 46), (13, 26), (31, 38), (29, 10), (14, 2), (19, 37), (13, 37), (41, 15), (41, 1), (37, 46), (7, 37), (21, 29), (16, 14), (15, 33), (1, 48), (31, 40), (1, 13), (5, 23), (42, 38), (28, 1), (26, 5), (13, 27), (31, 31), (31, 6), (3, 34), (17, 23), (20, 40), (36, 3), (38, 17), (18, 12), (15, 20), (3, 11), (4, 19), (4, 11), (37, 11), (15, 26), (31, 30), (2, 39), (26, 12), (39, 40), (40, 17), (4, 36), (22, 5), (20, 37), (25, 10), (11, 46), (23, 1), (4, 48), (13, 31), (27, 5), (6, 15), (8, 31), (13, 41), (10, 38), (19, 35), (28, 18), (18, 14), (13, 42), (0, 22), (27, 41), (33, 33), (16, 27), (11, 3), (41, 48), (9, 42), (14, 7), (36, 24), (18, 16), (40, 26), (31, 29), (27, 3), (5, 20), (32, 40), (18, 3), (21, 8), (42, 27), (28, 41), (16, 15), (21, 27), (12, 44), (36, 17), (0, 8), (28, 46), (23, 18), (8, 14), (17, 21), (25, 23), (15, 24), (14, 38), (16, 38), (6, 0), (6, 14), (20, 33), (24, 41), (25, 26), (42, 20), (32, 45), (10, 20), (17, 17), (27, 25), (30, 32), (11, 23), (18, 46), (24, 16), (32, 8), (1, 42), (10, 1), (30, 31), (10, 35), (42, 5), (32, 30), (2, 28), (37, 22), (37, 13), (20, 24), (33, 2), (10, 45), (24, 19), (16, 11), (29, 0), (41, 2), (25, 13), (26, 33), (19, 34), (37, 5), (22, 12), (25, 8), (22, 22), (30, 13), (4, 9), (18, 31), (35, 7), (17, 31), (9, 38), (18, 21), (38, 23), (25, 9), (9, 25), (12, 9), (13, 22), (33, 11), (0, 44), (16, 30), (29, 27), (23, 14), (7, 0), (26, 47), (38, 48), (27, 26), (24, 6), (4, 34), (25, 5), (39, 37), (23, 11), (9, 32), (15, 46), (17, 9), (26, 21), (6, 3), (12, 5), (16, 18), (17, 8), (21, 35), (12, 48), (11, 7), (8, 28), (36, 30), (39, 2), (38, 21), (5, 1), (35, 12), (0, 24), (7, 19), (31, 3), (1, 5), (20, 41), (16, 31), (29, 15), (34, 11), (38, 3), (32, 32), (37, 37), (7, 7), (10, 16), (25, 7), (16, 32), (32, 26), (39, 9), (38, 19), (20, 23), (1, 47), (10, 3), (3, 6), (32, 19), (10, 43), (25, 21), (8, 41), (35, 6), (13, 46), (19, 11), (9, 19), (7, 21), (7, 20), (31, 32), (1, 15), (14, 27), (5, 22), (2, 42), (37, 23), (13, 18), (10, 41), (39, 5), (32, 46), (27, 24), (25, 27), (21, 42), (31, 43), (32, 0), (11, 27), (38, 44), (22, 2), (16, 1), (0, 35), (1, 4), (29, 25), (6, 21), (10, 9), (28, 44), (28, 22), (15, 41), (27, 15), (22, 11), (0, 15), (21, 15), (26, 32), (14, 29), (29, 1), (4, 25), (3, 12), (34, 23), (32, 39), (22, 44), (11, 44), (36, 29), (1, 0), (34, 17), (20, 29), (42, 7), (22, 47), (6, 39), (24, 35), (39, 12), (16, 9), (12, 3), (3, 3), (5, 6), (20, 27), (15, 43), (31, 19), (33, 41), (14, 15), (32, 36), (5, 40), (40, 12), (21, 46), (9, 30), (9, 9), (5, 0), (3, 37), (0, 21), (22, 36), (30, 24), (26, 11), (22, 31), (2, 30), (33, 48), (37, 45), (40, 13), (37, 12), (18, 2), (29, 20), (39, 16), (29, 4), (24, 10), (4, 2), (1, 31), (15, 22), (10, 33), (11, 5), (40, 20), (2, 23), (19, 14), (38, 47), (31, 35), (30, 35), (0, 10), (30, 30), (13, 9), (15, 35), (21, 45), (20, 16), (27, 8), (25, 38), (31, 33), (27, 34), (38, 24), (3, 32), (40, 15), (35, 46), (4, 30), (40, 19), (32, 9), (20, 10), (0, 45), (40, 5), (17, 24), (36, 13), (17, 29), (3, 43), (42, 29), (1, 17), (11, 28), (7, 22), (30, 8), (7, 35), (1, 9), (14, 1), (35, 33), (9, 48), (33, 45), (0, 25), (27, 33), (3, 38), (13, 33), (31, 10), (13, 14), (9, 35), (14, 41), (35, 13), (1, 39), (9, 21), (20, 4), (27, 2), (39, 10), (19, 8), (34, 33), (13, 35), (19, 21), (14, 20), (41, 10), (33, 12), (30, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 12), (22, 28), (25, 39), (12, 27), (2, 22), (2, 13), (36, 9), (28, 8), (32, 16), (27, 36), (25, 37), (27, 28), (6, 1), (46, 35), (46, 18), (39, 41), (8, 30), (35, 8), (32, 12), (22, 29), (39, 25), (2, 7), (35, 24), (11, 6), (6, 11), (31, 22), (24, 40), (25, 18), (4, 30), (30, 3), (39, 31), (39, 33), (43, 9), (0, 3), (4, 36), (34, 25), (0, 7), (46, 34), (18, 42), (29, 16), (3, 25), (7, 10), (46, 1), (27, 30), (18, 38), (42, 24), (29, 25), (38, 20), (42, 16), (8, 10), (14, 39), (5, 13), (24, 39), (1, 31), (36, 28), (23, 39), (11, 9), (30, 7), (28, 5), (35, 19), (20, 40), (20, 36), (45, 21), (41, 31), (4, 33), (41, 22), (25, 36), (36, 8), (42, 25), (44, 0), (7, 34), (28, 7), (25, 2), (40, 16), (43, 29), (36, 21), (15, 21), (20, 0), (9, 14), (32, 21), (10, 0), (1, 17), (26, 21), (1, 34), (41, 15), (12, 18), (45, 8), (30, 15), (35, 37), (41, 25), (10, 34), (26, 5), (33, 4), (18, 21), (23, 25), (43, 27), (36, 42), (31, 20), (14, 7), (24, 10), (7, 12), (25, 13), (34, 8), (37, 15), (13, 35), (14, 23), (43, 7), (46, 5), (17, 4), (37, 35), (43, 42), (10, 7), (8, 7), (44, 27), (9, 34), (39, 38), (41, 39), (7, 16), (1, 9), (13, 24), (13, 18), (14, 24), (33, 28), (2, 10), (5, 35), (27, 38), (39, 26), (17, 10), (19, 21), (27, 10), (15, 38), (17, 36), (4, 42), (17, 24), (44, 40), (39, 3), (12, 30), (31, 14), (16, 0), (26, 6), (34, 35), (29, 42), (7, 5), (31, 13), (24, 38), (38, 12), (19, 27), (8, 17), (24, 35), (44, 9), (7, 11), (35, 12), (5, 31), (10, 24), (6, 17), (37, 27), (41, 7), (39, 6), (36, 34), (13, 17), (19, 12), (2, 32), (10, 27), (41, 21), (9, 13), (17, 37), (2, 16), (15, 8), (1, 24), (27, 4), (27, 24), (30, 23), (38, 19), (11, 11), (14, 20), (39, 4), (9, 39), (5, 15), (25, 3), (8, 35), (2, 17), (43, 20), (10, 3), (30, 25), (41, 19), (2, 14), (10, 5), (30, 27), (46, 23), (36, 40), (23, 40), (43, 14), (21, 15), (25, 40), (10, 21), (38, 10), (9, 6), (20, 13), (14, 19), (1, 25), (45, 0), (7, 3), (17, 22), (11, 4), (35, 10), (12, 34), (43, 10), (7, 22), (22, 41), (15, 12), (27, 29), (10, 4), (3, 5), (1, 20), (8, 21), (21, 23), (37, 11), (2, 11), (17, 15), (8, 14), (37, 6), (38, 4), (17, 7), (44, 28), (25, 12), (24, 33), (7, 40), (0, 36), (2, 3), (24, 19), (30, 22), (35, 7), (30, 11), (39, 7), (9, 4), (43, 21), (24, 27), (35, 9), (21, 12), (22, 6), (38, 37), (45, 12), (30, 10), (45, 18), (31, 5), (39, 32), (45, 30), (33, 38), (33, 39), (29, 12), (14, 35), (20, 20), (44, 2), (23, 15), (6, 12), (36, 36), (25, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 34), (44, 22), (17, 40), (45, 14), (36, 12), (28, 18), (10, 27), (0, 3), (15, 16), (29, 40), (32, 46), (37, 41), (11, 37), (0, 29), (19, 3), (36, 5), (43, 16), (44, 4), (4, 27), (10, 45), (45, 9), (38, 19), (8, 3), (18, 4), (30, 8), (28, 2), (24, 46), (14, 29), (42, 9), (33, 30), (14, 42), (32, 22), (19, 35), (5, 14), (7, 24), (19, 12), (28, 14), (39, 18), (18, 7), (38, 16), (12, 44), (34, 5), (22, 33), (30, 46), (10, 32), (37, 21), (6, 27), (25, 38), (17, 18), (37, 27), (19, 16), (3, 0), (2, 25), (25, 3), (22, 20), (41, 40), (12, 11), (10, 15), (30, 44), (11, 40), (31, 29), (32, 0), (14, 41), (12, 38), (27, 16), (0, 41), (18, 25), (44, 15), (28, 24), (28, 42), (3, 29), (41, 6), (36, 40), (19, 41), (21, 44), (13, 23), (20, 33), (30, 22), (42, 1), (15, 20), (13, 6), (22, 28), (26, 14), (42, 18), (32, 3), (43, 14), (43, 10), (17, 39), (24, 35), (2, 18), (21, 37), (31, 32), (20, 17), (27, 7), (10, 37), (32, 39), (9, 1), (22, 39), (32, 1), (4, 6), (9, 25), (33, 43), (12, 43), (43, 5), (43, 32), (34, 2), (25, 41), (13, 29), (35, 35), (10, 16), (39, 22), (12, 36), (5, 8), (0, 1), (30, 16), (15, 5), (7, 20), (44, 14), (25, 42), (42, 0), (8, 34), (39, 36), (28, 6), (41, 0), (31, 8), (45, 3), (38, 23), (1, 35), (41, 43), (16, 34), (9, 6), (3, 45), (16, 40), (44, 18), (18, 8), (24, 30), (1, 23), (3, 9), (38, 0), (33, 16), (30, 36), (41, 10), (39, 12), (33, 35), (42, 7), (34, 42), (8, 32), (0, 26), (44, 16), (39, 14), (5, 7), (31, 46), (31, 18), (31, 34), (7, 7), (18, 29), (0, 11), (42, 43), (14, 44), (22, 25), (20, 8), (45, 22), (34, 25), (0, 47), (21, 42), (10, 19), (40, 42), (3, 40), (1, 11), (5, 46), (14, 38), (33, 38), (9, 23), (15, 41), (7, 14), (38, 43), (3, 19), (3, 3), (9, 17), (34, 6), (22, 0), (42, 20), (44, 38), (42, 31), (45, 17), (45, 8), (11, 36), (15, 28), (37, 35), (29, 23), (12, 23), (11, 24), (25, 37), (10, 36), (36, 19), (23, 27), (4, 32), (16, 5), (5, 21), (7, 8), (23, 8), (34, 4), (37, 4), (13, 18), (40, 9), (20, 28), (14, 18), (10, 1), (14, 15), (26, 5), (33, 27), (30, 32), (5, 30), (28, 29), (42, 21), (7, 38), (31, 25), (4, 0), (29, 24), (21, 9), (9, 19), (10, 35), (37, 32), (44, 5), (30, 11), (39, 43), (10, 11), (40, 7), (16, 46), (18, 30), (45, 41), (15, 45), (34, 8), (18, 27), (20, 7), (31, 0), (45, 21), (19, 2), (28, 0), (29, 5), (37, 47), (17, 6), (42, 41), (12, 25), (35, 39), (12, 35), (43, 20), (0, 21), (14, 24), (9, 4), (33, 18), (1, 6), (26, 21), (8, 17), (32, 28), (0, 2), (30, 30), (39, 7), (1, 24), (41, 20), (12, 12), (24, 1), (18, 3), (13, 15), (18, 12), (18, 40), (24, 13), (26, 47), (26, 46), (8, 39), (1, 38), (30, 19), (43, 34), (16, 7), (27, 30), (39, 17), (6, 45), (39, 6), (31, 33), (0, 14), (30, 23), (28, 39), (1, 1), (6, 44), (8, 18), (40, 13), (28, 36), (25, 40), (17, 14), (44, 6), (29, 6), (8, 33), (19, 23), (36, 45), (27, 21), (13, 21), (33, 45), (35, 47), (0, 38), (41, 26), (16, 44), (3, 13), (14, 5), (10, 47), (10, 7), (13, 3), (36, 4), (17, 28), (30, 24), (22, 7), (0, 35), (44, 46), (41, 36), (31, 27), (16, 42), (27, 39), (25, 21), (45, 27), (35, 20), (15, 18), (33, 0), (3, 34), (41, 38), (29, 17), (21, 32), (14, 14), (42, 38), (1, 36), (41, 35), (7, 41), (32, 18), (19, 29), (39, 15), (42, 8), (37, 31), (27, 32), (16, 0), (4, 41), (45, 20), (19, 10), (29, 25), (20, 39), (6, 19), (34, 29), (11, 30), (10, 18), (24, 21), (11, 19), (42, 28), (22, 29), (18, 13), (34, 14), (15, 36), (35, 46), (0, 15), (20, 38), (24, 40), (25, 1), (44, 31), (4, 11), (0, 25), (45, 30), (22, 6), (40, 47), (29, 19), (45, 34), (38, 15), (42, 42), (7, 33), (25, 46), (41, 42), (38, 8), (3, 16), (10, 43), (24, 20), (1, 26), (38, 39), (5, 2), (18, 28), (39, 35), (0, 45), (34, 46), (43, 43), (8, 5), (16, 1), (4, 45), (40, 2), (45, 13), (29, 3), (29, 41), (9, 47), (31, 12), (0, 24), (31, 4), (2, 29), (14, 27), (23, 16), (44, 27), (18, 20), (3, 2), (9, 38), (26, 4), (10, 6), (30, 2), (30, 18), (7, 2), (43, 15), (31, 21), (14, 2), (28, 10), (4, 37), (25, 25), (13, 0), (16, 18), (15, 22), (40, 1), (32, 29), (26, 8), (45, 2), (27, 13), (24, 37), (13, 12), (14, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 2), (3, 20), (38, 33), (20, 42), (39, 21), (18, 2), (28, 10), (26, 0), (20, 24), (0, 37), (38, 10), (17, 5), (31, 22), (9, 31), (39, 20), (15, 10), (11, 10), (15, 36), (25, 28), (22, 35), (19, 34), (13, 39), (19, 12), (34, 38), (25, 25), (13, 42), (28, 39), (3, 1), (38, 16), (35, 9), (10, 12), (8, 13), (0, 4), (40, 39), (15, 27), (21, 16), (11, 20), (15, 31), (46, 31), (5, 8), (30, 41), (4, 2), (44, 4), (16, 22), (22, 30), (16, 26), (11, 4), (36, 29), (21, 15), (6, 0), (36, 38), (30, 4), (46, 39), (20, 31), (12, 20), (39, 30), (20, 34), (32, 15), (45, 28), (28, 34), (30, 6), (40, 37), (12, 27), (21, 18), (17, 11), (18, 41), (38, 18), (13, 21), (30, 29), (20, 16), (44, 31), (36, 1), (45, 42), (35, 26), (16, 30), (29, 40), (18, 16), (13, 5), (25, 7), (34, 7), (15, 14), (32, 27), (32, 0), (20, 9), (28, 6), (40, 27), (24, 30), (35, 37), (44, 12), (25, 34), (37, 34), (3, 23), (14, 25), (26, 10), (18, 34), (46, 28), (4, 39), (6, 30), (10, 9), (2, 38), (14, 37), (7, 38), (4, 4), (17, 34), (25, 26), (2, 21), (19, 20), (39, 8), (39, 36), (0, 27), (18, 17), (9, 18), (40, 0), (38, 32), (30, 3), (3, 11), (16, 6), (8, 26), (11, 29), (7, 27), (21, 23), (8, 12), (16, 28), (12, 9), (46, 34), (0, 25), (9, 22), (10, 18), (42, 13), (34, 36), (2, 19), (34, 39), (12, 12), (37, 32), (8, 38), (12, 35), (18, 38), (42, 11), (41, 10), (37, 42), (33, 28), (21, 32), (36, 39), (33, 7), (12, 8), (34, 2), (1, 24), (9, 41), (38, 39), (22, 7), (35, 21), (14, 4), (12, 14), (32, 30), (1, 2), (20, 14), (12, 24), (15, 33), (38, 23), (44, 1), (18, 26), (1, 38), (42, 16), (25, 10), (9, 40), (39, 13), (42, 26), (10, 23), (1, 28), (41, 13), (43, 40), (32, 5), (42, 32), (2, 26), (23, 1), (7, 7), (12, 6), (21, 22), (3, 40), (5, 11), (7, 10), (12, 42), (28, 3), (22, 22), (1, 29), (17, 13), (6, 32), (38, 28), (31, 34), (37, 35), (22, 32), (41, 6), (10, 13), (7, 20), (41, 7), (9, 13), (41, 8), (14, 17), (17, 0), (36, 34), (35, 3), (6, 6), (6, 34), (28, 37), (2, 0), (34, 24), (43, 30), (21, 5), (36, 14), (13, 13), (12, 1), (20, 21), (25, 5), (1, 11), (26, 38), (24, 36), (1, 36), (22, 26), (37, 38), (1, 31), (42, 42), (24, 34), (3, 30), (30, 20), (40, 29), (0, 14), (30, 2), (31, 32), (39, 6), (44, 16), (37, 7), (15, 37), (26, 39), (41, 31), (1, 32), (35, 11), (2, 25), (37, 13), (34, 28), (32, 19), (22, 16), (14, 7), (0, 19), (30, 34), (13, 6), (45, 0), (40, 23), (28, 32), (17, 8), (31, 19), (16, 14), (4, 19), (10, 11), (14, 31), (36, 36), (3, 22), (38, 30), (42, 2), (37, 1), (31, 20), (24, 3), (33, 35), (4, 18), (40, 18), (0, 20), (21, 40), (6, 23), (45, 35), (37, 16), (29, 12), (15, 11), (43, 28), (19, 31), (4, 26), (23, 3), (11, 5), (19, 16), (14, 10), (34, 40), (36, 28), (23, 7), (45, 10), (44, 28), (15, 7), (23, 4), (41, 15), (43, 29), (10, 8), (33, 32), (31, 14), (34, 6), (36, 42), (1, 4), (8, 33), (18, 24), (16, 7), (27, 14), (28, 29), (9, 23), (20, 38), (32, 6), (13, 38), (30, 0), (3, 38), (19, 10), (6, 22), (35, 41), (38, 36), (44, 41), (13, 36), (46, 40), (1, 13), (1, 33), (44, 37), (27, 16), (1, 9), (43, 8), (3, 31), (9, 16), (42, 18), (14, 18), (6, 33), (45, 22), (2, 8), (24, 16), (46, 2), (24, 19), (23, 37), (22, 2), (24, 32), (18, 28), (28, 31), (35, 18), (2, 16), (24, 10), (3, 42), (24, 7), (29, 3), (14, 28), (40, 19), (3, 6), (6, 11), (41, 9), (45, 2), (15, 2), (3, 36), (41, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 15), (13, 41), (19, 39), (21, 5), (39, 8), (1, 14), (1, 9), (36, 10), (31, 18), (7, 7), (25, 12), (20, 28), (24, 24), (8, 16), (32, 23), (21, 2), (9, 40), (39, 7), (35, 3), (39, 10), (34, 34), (24, 26), (18, 1), (19, 28), (27, 36), (18, 20), (36, 25), (7, 21), (9, 0), (12, 20), (11, 12), (28, 29), (9, 38), (16, 23), (39, 37), (6, 4), (35, 6), (7, 38), (29, 19), (4, 14), (17, 31), (39, 6), (6, 1), (0, 41), (29, 25), (18, 27), (6, 36), (18, 26), (5, 1), (37, 5), (33, 36), (32, 39), (14, 21), (31, 33), (18, 37), (23, 14), (12, 16), (33, 24), (23, 20), (29, 18), (13, 38), (14, 16), (6, 5), (33, 30), (39, 30), (35, 32), (32, 26), (34, 32), (14, 37), (22, 36), (8, 10), (27, 33), (22, 13), (33, 31), (19, 36), (12, 0), (33, 13), (11, 4), (30, 16), (28, 31), (14, 38), (11, 40), (9, 39), (19, 24), (37, 28), (29, 0), (16, 20), (9, 24), (6, 27), (8, 17), (11, 24), (39, 20), (31, 21), (28, 39), (17, 13), (2, 40), (14, 20), (5, 9), (29, 26), (8, 38), (18, 16), (36, 14), (11, 15), (30, 24), (38, 4), (10, 37), (14, 41), (31, 35), (9, 15), (4, 2), (8, 11), (20, 20), (15, 12), (31, 12), (12, 39), (24, 21), (36, 31), (25, 9), (12, 37), (10, 35), (33, 34), (29, 6), (21, 28), (1, 38), (30, 9), (17, 24), (0, 28), (12, 14), (19, 22), (1, 29), (31, 16), (14, 17), (27, 14), (37, 37), (0, 14), (15, 40), (31, 19), (12, 18), (12, 8), (9, 21), (35, 35), (35, 17), (36, 20), (32, 11), (36, 12), (37, 12), (16, 15), (17, 20), (13, 29), (23, 13), (12, 4), (27, 11), (37, 32), (36, 5), (11, 35), (1, 34), (24, 39), (17, 4), (3, 22), (18, 39), (17, 40), (34, 31), (6, 28), (10, 25), (26, 15), (0, 7), (38, 27), (20, 35), (35, 4), (9, 10), (12, 13), (13, 27), (26, 2), (12, 22), (22, 14), (36, 2), (19, 32), (19, 26), (12, 32), (2, 38), (21, 3), (15, 22), (34, 7), (10, 8), (22, 3), (15, 29), (4, 18), (21, 0), (29, 34), (21, 22), (28, 27), (27, 9), (16, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 42), (26, 23), (32, 21), (0, 11), (32, 35), (6, 13), (11, 20), (22, 20), (20, 33), (9, 40), (1, 36), (30, 26), (35, 17), (23, 40), (21, 26), (41, 34), (36, 15), (37, 39), (41, 41), (25, 39), (17, 21), (15, 28), (0, 29), (6, 35), (7, 21), (28, 35), (0, 6), (11, 34), (32, 16), (22, 17), (8, 32), (32, 8), (18, 26), (11, 11), (0, 23), (36, 14), (19, 29), (6, 21), (15, 38), (30, 28), (22, 5), (23, 12), (15, 4), (14, 37), (25, 16), (29, 13), (23, 30), (33, 6), (8, 35), (17, 32), (37, 12), (7, 42), (28, 38), (0, 41), (25, 19), (27, 41), (21, 29), (21, 12), (30, 17), (36, 17), (15, 12), (40, 1), (38, 9), (31, 30), (37, 38), (24, 39), (4, 17), (40, 31), (34, 26), (36, 37), (37, 20), (10, 30), (25, 17), (26, 24), (25, 1), (2, 36), (2, 29), (14, 16), (32, 14), (8, 11), (2, 31), (28, 23), (13, 8), (32, 0), (31, 39), (25, 31), (24, 35), (26, 30), (43, 21), (37, 24), (3, 27), (25, 10), (12, 32), (31, 29), (37, 19), (36, 31), (19, 22), (26, 28), (36, 34), (18, 6), (6, 23), (33, 0), (3, 37), (36, 5), (1, 10), (40, 17), (22, 32), (37, 2), (2, 14), (34, 40), (37, 7), (40, 18), (9, 42), (21, 19), (30, 34), (43, 1), (1, 4), (3, 16), (35, 31), (1, 18), (30, 5), (26, 27), (12, 7), (23, 36), (4, 19), (29, 18), (22, 10), (34, 41), (33, 28), (30, 30), (17, 40), (21, 25), (8, 28), (7, 7), (26, 18), (43, 29), (30, 19), (18, 37), (4, 21), (38, 41), (32, 33), (12, 28), (16, 26), (33, 30), (31, 3), (1, 32), (16, 24), (3, 29), (12, 36), (12, 33), (18, 25), (41, 0), (26, 36), (0, 8), (25, 9), (43, 34), (38, 12), (25, 23), (8, 20), (5, 36), (32, 28), (4, 5), (27, 30), (39, 13), (0, 19), (30, 3), (27, 2), (33, 29), (20, 35), (14, 1), (28, 8), (35, 40), (18, 20), (4, 12), (1, 8), (22, 13), (18, 24), (22, 21), (8, 31), (17, 22), (33, 2), (7, 35), (13, 9), (38, 2), (16, 32), (24, 25), (9, 3), (40, 38), (23, 16), (42, 1), (24, 26), (27, 7), (28, 29), (18, 12), (8, 40), (10, 18), (26, 3), (10, 12), (14, 15), (6, 5), (17, 14), (23, 19), (26, 33), (28, 10), (4, 1), (2, 23), (28, 40), (7, 31), (6, 20), (24, 21), (40, 30), (30, 40), (12, 35), (34, 18), (25, 7), (15, 29), (11, 42), (7, 16), (23, 15), (10, 36), (43, 35), (21, 8), (34, 28), (25, 2), (41, 15), (41, 31), (0, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 32), (5, 5), (21, 15), (15, 34), (11, 6), (31, 41), (15, 33), (15, 30), (36, 42), (36, 37), (29, 20), (18, 39), (8, 18), (35, 30), (19, 13), (16, 3), (20, 31), (6, 36), (17, 46), (0, 46), (15, 6), (6, 13), (41, 30), (11, 39), (11, 22), (30, 18), (9, 12), (38, 13), (28, 16), (28, 43), (30, 5), (1, 8), (27, 21), (38, 5), (35, 17), (37, 35), (3, 36), (6, 39), (15, 1), (11, 15), (41, 0), (7, 15), (35, 40), (39, 45), (16, 17), (24, 33), (21, 24), (16, 15), (12, 10), (20, 0), (25, 8), (38, 26), (21, 41), (27, 17), (10, 45), (41, 29), (22, 31), (15, 16), (25, 6), (19, 29), (36, 1), (2, 9), (23, 17), (20, 18), (34, 41), (12, 36), (13, 23), (21, 5), (40, 46), (5, 31), (36, 6), (7, 14), (3, 7), (12, 22), (19, 35), (0, 30), (30, 39), (35, 7), (1, 36), (18, 3), (0, 9), (36, 4), (41, 31), (24, 18), (39, 2), (26, 6), (23, 40), (26, 42), (6, 44), (14, 6), (4, 8), (5, 22), (13, 36), (41, 12), (34, 11), (9, 31), (10, 1), (23, 34), (34, 24), (30, 0), (3, 10), (1, 6), (15, 25), (2, 32), (10, 46), (33, 39), (33, 19), (10, 19), (15, 11), (6, 19), (15, 31), (23, 13), (30, 27), (21, 42), (8, 34), (17, 2), (10, 25), (21, 44), (30, 45), (33, 44), (18, 13), (38, 25), (36, 33), (25, 20), (21, 26), (30, 17), (14, 26), (0, 4), (36, 22), (33, 32), (5, 28), (33, 7), (20, 4), (20, 21), (38, 44), (21, 43), (9, 8), (25, 33), (2, 2), (34, 28), (21, 23), (1, 31), (4, 26), (1, 26), (27, 35), (4, 21), (41, 27), (17, 24), (22, 34), (7, 43), (37, 8), (31, 42), (26, 44), (6, 37), (22, 6), (15, 15), (6, 24), (21, 36), (7, 0), (2, 5), (21, 14), (8, 35), (36, 17), (12, 12), (22, 32), (4, 15), (23, 15), (10, 30), (36, 15), (21, 28), (0, 38), (9, 6), (39, 4), (14, 41), (12, 31), (27, 39), (6, 3), (16, 0), (3, 11), (35, 34), (7, 3), (7, 30), (32, 9), (7, 46), (34, 45), (8, 10), (15, 3), (28, 27), (21, 22), (19, 0), (23, 6), (15, 21), (37, 46), (9, 13), (15, 38), (7, 34), (23, 43), (18, 31), (35, 45), (12, 25), (28, 11), (23, 20), (23, 39), (0, 13), (32, 40), (33, 0), (38, 28), (36, 19), (8, 20), (34, 46), (35, 2), (32, 32), (21, 7), (33, 26), (41, 2), (15, 7), (14, 21), (36, 12), (40, 23), (10, 8), (36, 14), (32, 13), (33, 27), (6, 28), (12, 7), (13, 41), (7, 2), (21, 13), (5, 41), (28, 1), (4, 25), (20, 24), (29, 12), (6, 25), (40, 10), (1, 21), (9, 42), (41, 20), (19, 3), (9, 2), (14, 42), (18, 7), (22, 24), (5, 20), (39, 41), (35, 46), (36, 8), (3, 19), (16, 29), (32, 25), (5, 30), (39, 27), (38, 24), (31, 26), (37, 17), (10, 3), (18, 20), (33, 23), (24, 16), (15, 35), (29, 17), (1, 17), (38, 20), (34, 19), (34, 4), (6, 31), (4, 41), (8, 7), (34, 39), (23, 7), (38, 3), (39, 14), (5, 18), (21, 25), (7, 31), (5, 33), (6, 10), (39, 6), (27, 10), (31, 19), (4, 38), (29, 15), (40, 32), (38, 21), (34, 29), (0, 45), (33, 36), (41, 10), (38, 18), (8, 1), (7, 16), (24, 7), (18, 11), (8, 15), (37, 41), (28, 29), (22, 11), (0, 14), (11, 17), (13, 38), (25, 17), (1, 40), (25, 46), (5, 12), (2, 16), (14, 22), (16, 25), (4, 0), (10, 15), (18, 38), (30, 15), (20, 41), (26, 20), (9, 3), (29, 37), (4, 32), (39, 21), (34, 12), (32, 26), (41, 21), (2, 20), (21, 37), (14, 44), (32, 3), (4, 6), (19, 22), (38, 0), (23, 46), (30, 6), (6, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 43), (1, 24), (40, 37), (34, 18), (30, 25), (9, 11), (25, 43), (35, 22), (14, 17), (33, 44), (38, 8), (4, 11), (0, 16), (7, 44), (13, 21), (24, 44), (21, 0), (36, 13), (37, 35), (7, 14), (21, 10), (27, 37), (8, 40), (17, 39), (29, 45), (39, 38), (26, 29), (20, 6), (0, 27), (40, 10), (35, 4), (12, 25), (32, 31), (19, 12), (14, 24), (10, 41), (5, 45), (16, 31), (24, 42), (3, 0), (2, 33), (3, 6), (15, 14), (9, 38), (13, 33), (17, 43), (16, 20), (40, 25), (13, 43), (13, 8), (32, 3), (4, 13), (28, 20), (17, 30), (22, 19), (6, 23), (15, 4), (10, 1), (10, 10), (6, 37), (4, 36), (21, 43), (1, 29), (33, 46), (29, 20), (24, 37), (39, 24), (0, 46), (20, 38), (15, 42), (17, 18), (37, 28), (30, 19), (19, 3), (39, 11), (13, 11), (40, 44), (22, 44), (31, 27), (2, 10), (34, 3), (35, 35), (9, 2), (23, 12), (26, 0), (4, 46), (40, 6), (18, 1), (30, 39), (29, 32), (24, 33), (6, 5), (15, 10), (20, 30), (28, 21), (38, 23), (15, 24), (37, 18), (9, 15), (11, 14), (38, 13), (18, 16), (21, 2), (8, 0), (27, 32), (13, 27), (15, 6), (4, 39), (38, 27), (8, 34), (33, 36), (5, 47), (2, 28), (9, 5), (1, 5), (22, 47), (14, 43), (10, 33), (25, 15), (30, 13), (14, 5), (26, 26), (17, 38), (2, 18), (22, 17), (5, 42), (7, 20), (8, 27), (24, 38), (22, 32), (8, 28), (3, 46), (3, 31), (19, 16), (14, 8), (12, 7), (4, 34), (30, 27), (37, 14), (16, 29), (5, 2), (37, 12), (16, 16), (12, 10), (23, 25), (28, 24), (0, 9), (25, 20), (26, 1), (9, 28), (2, 9), (30, 12), (39, 16), (28, 18), (8, 4), (30, 17), (6, 25), (16, 3), (40, 29), (1, 8), (27, 14), (15, 25), (14, 14), (34, 41), (19, 8), (35, 13), (9, 46), (39, 20), (26, 30), (16, 30), (0, 24), (14, 42), (20, 14), (1, 23), (10, 46), (8, 44), (22, 39), (4, 8), (12, 20), (36, 38), (1, 17), (38, 24), (35, 30), (5, 28), (32, 21), (13, 32), (2, 16), (0, 42), (29, 23), (20, 22), (11, 46), (20, 7), (2, 37), (38, 3), (32, 14), (2, 14), (15, 20), (38, 36), (4, 42), (29, 37), (10, 18), (32, 8), (5, 20), (34, 20), (31, 39), (10, 17), (40, 40), (20, 23), (1, 34), (17, 23), (33, 12), (5, 1), (6, 11), (24, 39), (26, 35), (35, 36), (28, 29), (9, 34), (15, 34), (6, 40), (26, 14), (7, 5), (32, 15), (0, 12), (6, 14), (4, 31), (31, 11), (1, 30), (22, 36), (23, 15), (23, 29), (38, 4), (33, 21), (4, 0), (34, 5), (9, 20), (23, 5), (34, 34), (26, 37), (39, 18), (29, 26), (7, 37), (35, 5), (39, 17), (39, 12), (14, 23), (15, 0), (8, 46), (23, 36), (28, 1), (29, 6), (28, 22), (25, 46), (16, 32), (4, 29), (1, 22), (37, 2), (39, 10), (34, 10), (1, 9), (2, 43), (13, 36), (2, 23), (36, 27), (39, 4), (36, 18), (0, 3), (27, 25), (1, 46), (40, 4), (27, 31), (18, 15), (29, 15), (16, 15), (3, 30), (19, 18), (19, 2), (27, 6), (30, 3), (19, 5), (29, 28), (40, 42), (26, 16), (30, 15), (6, 31), (40, 5), (12, 28), (10, 35), (18, 40), (10, 7), (15, 31), (8, 41), (5, 22), (29, 30), (8, 1), (6, 24), (10, 6), (39, 28), (22, 30), (10, 8), (9, 31), (39, 1), (40, 39), (12, 41), (23, 44), (26, 20), (24, 24), (33, 35), (31, 2), (16, 35), (19, 35), (9, 37), (21, 11), (31, 43), (35, 44), (17, 27), (38, 44), (32, 13), (21, 42), (0, 21), (15, 30), (34, 17), (34, 12), (20, 5), (12, 9), (39, 32), (26, 47), (40, 46), (2, 45), (24, 0), (22, 22), (14, 47), (16, 33), (10, 14), (32, 45), (11, 1), (6, 22), (10, 43), (14, 4), (36, 5), (14, 18), (13, 31), (7, 22), (38, 2), (25, 42), (11, 27), (24, 3), (6, 45), (0, 17), (21, 12), (19, 4), (9, 25), (5, 14), (7, 0), (38, 38), (37, 42), (26, 25), (17, 6), (22, 14), (30, 10), (9, 45), (23, 21), (31, 47), (1, 32), (31, 10), (14, 35), (12, 32), (0, 34), (24, 32), (28, 7), (12, 26), (29, 11), (7, 40), (39, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 15), (29, 22), (13, 41), (3, 40), (31, 21), (26, 31), (16, 41), (26, 26), (34, 0), (30, 10), (13, 31), (18, 5), (12, 28), (11, 6), (26, 6), (5, 13), (21, 14), (33, 29), (5, 36), (25, 0), (7, 27), (22, 18), (33, 41), (21, 35), (39, 21), (16, 40), (7, 31), (37, 3), (30, 0), (17, 36), (33, 42), (2, 27), (36, 0), (22, 25), (34, 30), (29, 41), (31, 40), (9, 39), (26, 10), (35, 6), (36, 8), (30, 39), (32, 30), (22, 42), (12, 13), (33, 14), (35, 32), (15, 5), (19, 24), (43, 23), (4, 18), (4, 24), (30, 24), (23, 14), (1, 15), (14, 19), (32, 10), (20, 14), (30, 43), (41, 18), (1, 19), (14, 4), (29, 42), (35, 35), (4, 7), (10, 20), (1, 33), (8, 18), (43, 9), (9, 9), (10, 16), (8, 24), (4, 15), (9, 7), (29, 35), (13, 16), (28, 43), (23, 34), (31, 2), (17, 34), (23, 35), (11, 17), (12, 1), (24, 14), (9, 5), (35, 31), (18, 16), (8, 29), (1, 16), (29, 33), (32, 33), (36, 7), (20, 3), (22, 7), (25, 19), (5, 40), (5, 14), (41, 1), (23, 1), (29, 14), (15, 13), (6, 1), (7, 15), (19, 3), (6, 37), (21, 30), (25, 10), (19, 12), (22, 35), (3, 15), (40, 14), (0, 25), (33, 26), (32, 25), (14, 14), (28, 35), (2, 11), (28, 12), (42, 10), (1, 30), (34, 5), (19, 17), (18, 13), (19, 25), (31, 30), (3, 22), (30, 13), (29, 21), (32, 11), (6, 12), (25, 7), (5, 22), (31, 41), (36, 3), (13, 14), (40, 8), (15, 2), (37, 13), (9, 24), (21, 34), (13, 35), (43, 4), (24, 42), (39, 24), (13, 2), (43, 39), (7, 3), (31, 11), (32, 5), (6, 16), (15, 42), (0, 13), (39, 14), (24, 29), (1, 37), (31, 7), (11, 3), (33, 6), (4, 29), (33, 1), (35, 19), (6, 7), (6, 3), (40, 38), (31, 0), (34, 31), (24, 22), (3, 25), (42, 22), (37, 33), (7, 21), (31, 17), (10, 43), (27, 27), (37, 42), (34, 34), (5, 32), (34, 37), (18, 40), (37, 16), (6, 8), (23, 19), (1, 29), (9, 37), (26, 36), (4, 26), (38, 13), (12, 32), (18, 34), (42, 11), (28, 3), (1, 31), (11, 8), (23, 37), (39, 33), (30, 15), (42, 29), (37, 30), (24, 43), (3, 4), (35, 17), (26, 0), (8, 5), (15, 27), (9, 42), (8, 23), (10, 3), (38, 29), (18, 38), (18, 26), (0, 17), (37, 18), (17, 22), (8, 43), (0, 6), (35, 24), (16, 12), (0, 35), (10, 5), (36, 27), (18, 1), (32, 17), (16, 4), (24, 6), (11, 20), (39, 11), (20, 38), (25, 12), (29, 19), (23, 42), (43, 24), (43, 21), (8, 40), (6, 11), (38, 27), (20, 28), (22, 0), (9, 29), (3, 10), (11, 36), (35, 1), (5, 27), (33, 35), (43, 32), (19, 22), (26, 28), (10, 40), (35, 28), (21, 7), (26, 41), (29, 1), (5, 11), (7, 42), (3, 31), (41, 15), (9, 22), (17, 23), (5, 3), (31, 43), (5, 18), (7, 14), (38, 2), (2, 36), (2, 21), (1, 3), (1, 11), (31, 9), (37, 34), (24, 36), (19, 15), (24, 1), (36, 32), (26, 3), (3, 6), (31, 22), (27, 3), (40, 11), (14, 13), (2, 30), (26, 38), (26, 29), (15, 16), (22, 9), (40, 35), (13, 34), (32, 38), (26, 34), (40, 10), (8, 42), (14, 28), (11, 24), (37, 5), (27, 6), (15, 7), (41, 4), (22, 3), (24, 40), (14, 38), (31, 18), (30, 33), (16, 16), (18, 28), (22, 29), (37, 40), (5, 30), (29, 18), (6, 2), (19, 41), (3, 11), (41, 3), (39, 28), (4, 2), (1, 5), (24, 38), (23, 18), (0, 41), (10, 34), (36, 42), (3, 18), (29, 29), (32, 34), (3, 43), (21, 10), (4, 1), (3, 9), (1, 27), (18, 25), (31, 5), (17, 29), (14, 7), (36, 28), (27, 19), (37, 39), (11, 35), (5, 43), (7, 13), (33, 0), (6, 20), (26, 32), (18, 6), (0, 30), (18, 3), (14, 16), (30, 1), (21, 41), (30, 21), (9, 40), (11, 37), (16, 7), (18, 9), (7, 25), (26, 43), (12, 25), (43, 42), (41, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 27), (28, 31), (45, 38), (34, 27), (22, 14), (14, 28), (0, 16), (26, 15), (37, 7), (35, 35), (42, 2), (23, 34), (36, 37), (9, 24), (26, 37), (29, 22), (3, 35), (0, 12), (20, 10), (25, 34), (25, 5), (6, 23), (43, 1), (2, 9), (3, 22), (28, 20), (2, 35), (17, 33), (1, 19), (0, 23), (4, 14), (23, 11), (2, 0), (31, 12), (44, 5), (26, 4), (6, 35), (46, 38), (18, 12), (37, 21), (35, 2), (20, 17), (44, 16), (42, 25), (6, 36), (44, 4), (46, 21), (34, 0), (9, 22), (12, 16), (47, 21), (12, 14), (20, 26), (14, 39), (47, 28), (24, 33), (35, 40), (44, 30), (22, 10), (38, 22), (29, 0), (27, 24), (30, 22), (0, 35), (43, 2), (37, 29), (11, 18), (38, 39), (45, 1), (41, 6), (44, 8), (31, 39), (18, 18), (7, 12), (9, 3), (14, 14), (21, 27), (29, 30), (4, 8), (21, 26), (25, 1), (0, 33), (6, 20), (8, 31), (12, 3), (17, 17), (21, 22), (40, 28), (22, 15), (30, 18), (36, 25), (42, 36), (10, 11), (5, 20), (32, 33), (14, 37), (34, 34), (35, 11), (13, 19), (28, 40), (40, 21), (32, 13), (23, 9), (20, 4), (44, 9), (44, 34), (3, 8), (1, 39), (7, 30), (44, 40), (34, 26), (4, 21), (31, 7), (48, 7), (35, 14), (21, 7), (35, 32), (9, 20), (0, 17), (39, 10), (8, 9), (16, 17), (2, 29), (38, 37), (39, 18), (25, 20), (1, 12), (32, 40), (18, 36), (43, 15), (0, 6), (32, 27), (48, 6), (11, 8), (27, 35), (1, 16), (7, 39), (42, 23), (14, 6), (0, 27), (38, 23), (12, 35), (18, 8), (15, 39), (4, 2), (31, 29), (39, 19), (32, 36), (20, 15), (31, 21), (9, 26), (27, 40), (47, 12), (34, 17), (0, 8), (19, 20), (6, 15), (18, 1), (31, 36), (46, 10), (27, 16), (16, 40), (47, 36), (28, 4), (28, 33), (45, 12), (44, 23), (7, 7), (43, 8), (41, 35), (39, 32), (18, 28), (45, 14), (18, 32), (45, 33), (32, 38), (2, 15), (36, 6), (17, 6), (48, 25), (18, 5), (6, 5), (34, 30), (48, 3), (34, 11), (4, 29), (23, 18), (10, 26), (48, 17), (34, 29), (28, 32), (14, 3), (15, 6), (3, 33), (47, 13), (24, 30), (43, 16), (37, 22), (0, 32), (36, 34), (32, 32), (36, 36), (17, 9), (41, 39), (15, 25), (10, 24), (11, 28), (38, 24), (45, 8), (44, 39), (47, 31), (1, 5), (27, 13), (18, 17), (39, 24), (26, 34), (10, 2), (37, 30), (28, 35), (40, 15), (12, 27), (36, 3), (20, 40), (37, 12), (42, 15), (37, 27), (35, 36), (44, 19), (1, 14), (24, 9), (2, 1), (26, 40), (42, 9), (30, 20), (1, 23), (40, 25), (22, 40), (8, 33), (0, 24), (43, 31), (7, 15), (40, 31), (20, 2), (13, 6), (33, 33), (28, 27), (2, 16), (1, 31), (11, 5), (14, 30), (29, 9), (19, 19), (19, 10), (40, 6), (15, 13), (35, 24), (12, 5), (39, 37), (43, 26), (23, 14), (37, 31), (8, 23), (30, 3), (31, 25), (16, 24), (23, 5), (34, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 6), (12, 18), (2, 11), (34, 43), (5, 6), (16, 43), (4, 20), (12, 37), (32, 9), (31, 6), (12, 43), (17, 21), (0, 35), (14, 16), (30, 25), (9, 8), (29, 38), (10, 19), (5, 18), (14, 11), (28, 8), (37, 17), (20, 36), (38, 38), (7, 11), (8, 33), (11, 16), (37, 0), (0, 36), (18, 27), (35, 14), (1, 11), (20, 22), (30, 3), (0, 38), (37, 12), (10, 23), (12, 13), (34, 13), (7, 14), (35, 42), (9, 30), (17, 29), (37, 21), (23, 12), (34, 4), (9, 10), (21, 32), (36, 25), (14, 25), (10, 6), (39, 15), (30, 29), (2, 12), (4, 39), (36, 14), (41, 31), (8, 7), (26, 25), (19, 31), (24, 39), (4, 8), (23, 34), (5, 34), (35, 4), (34, 22), (21, 13), (28, 6), (29, 24), (41, 20), (24, 15), (13, 6), (11, 13), (3, 24), (16, 15), (2, 24), (18, 3), (10, 29), (2, 4), (20, 31), (2, 27), (38, 4), (1, 40), (25, 43), (11, 3), (20, 16), (14, 5), (41, 18), (42, 29), (3, 15), (40, 43), (22, 26), (29, 17), (22, 41), (29, 1), (10, 32), (4, 23), (8, 36), (12, 11), (30, 24), (36, 7), (19, 15), (14, 29), (30, 16), (36, 35), (30, 6), (21, 36), (39, 0), (2, 41), (17, 15), (27, 23), (23, 37), (32, 10), (29, 18), (26, 8), (31, 17), (14, 15), (38, 32), (25, 42), (37, 15), (15, 17), (16, 19), (6, 14), (7, 5), (37, 43), (18, 7), (28, 41), (35, 18), (24, 7), (0, 29), (32, 2), (34, 27), (34, 26), (38, 25), (13, 35), (15, 39), (1, 23), (6, 22), (31, 21), (6, 40), (27, 25), (36, 12), (21, 34), (13, 25), (11, 38), (31, 37), (36, 41), (35, 3), (32, 28), (30, 17), (5, 13), (33, 40), (31, 42), (29, 40), (5, 10), (8, 9), (34, 30), (15, 20), (19, 29), (17, 10), (11, 9), (27, 9), (3, 40), (19, 18), (23, 8), (18, 0), (24, 3), (35, 43), (16, 18), (38, 1), (3, 39), (33, 35), (37, 13), (32, 25), (6, 0), (31, 14), (34, 19), (25, 22), (29, 33), (22, 5), (15, 24), (28, 39), (8, 28), (35, 5), (19, 14), (38, 35), (8, 38), (18, 8), (18, 19), (13, 27), (2, 26), (22, 27), (13, 16), (18, 31), (33, 9), (8, 5), (7, 26), (22, 24), (8, 8), (27, 14), (7, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 8), (0, 16), (37, 29), (13, 8), (4, 43), (39, 9), (36, 32), (30, 11), (4, 28), (36, 10), (38, 29), (29, 27), (37, 22), (37, 35), (2, 41), (29, 31), (27, 16), (38, 24), (36, 3), (24, 28), (45, 31), (16, 37), (23, 35), (0, 30), (23, 41), (21, 23), (23, 13), (36, 18), (15, 40), (37, 33), (26, 12), (2, 31), (21, 5), (41, 9), (4, 33), (20, 24), (9, 0), (26, 8), (2, 10), (17, 20), (31, 24), (14, 38), (31, 27), (12, 35), (44, 33), (40, 30), (40, 34), (6, 6), (11, 39), (31, 19), (11, 2), (14, 21), (22, 30), (39, 11), (8, 36), (20, 12), (22, 8), (23, 16), (21, 11), (9, 27), (25, 13), (26, 15), (14, 23), (35, 12), (2, 15), (36, 29), (21, 18), (35, 11), (17, 15), (14, 3), (45, 18), (19, 44), (10, 0), (39, 7), (20, 0), (30, 36), (32, 42), (33, 8), (12, 9), (31, 38), (11, 10), (30, 44), (0, 35), (28, 20), (39, 39), (7, 21), (30, 22), (41, 20), (25, 40), (42, 4), (5, 4), (38, 36), (2, 1), (30, 39), (45, 1), (23, 24), (14, 29), (25, 2), (34, 23), (9, 14), (40, 32), (6, 9), (39, 0), (24, 6), (41, 18), (27, 26), (14, 2), (17, 10), (24, 5), (31, 41), (2, 39), (34, 27), (3, 32), (5, 40), (27, 37), (20, 5), (15, 0), (18, 31), (36, 36), (6, 40), (3, 1), (40, 3), (1, 30), (41, 29), (24, 19), (21, 27), (33, 22), (16, 35), (42, 26), (11, 35), (12, 12), (26, 23), (23, 42), (6, 13), (12, 29), (22, 27), (31, 37), (0, 34), (28, 44), (30, 19), (25, 37), (29, 30), (5, 21), (14, 35), (42, 13), (31, 22), (36, 17), (39, 30), (17, 4), (17, 19), (40, 42), (41, 15), (38, 1), (32, 33), (34, 2), (32, 38), (26, 41), (41, 42), (40, 33), (12, 43), (8, 34), (21, 36), (31, 32), (32, 10), (44, 36), (40, 15), (39, 13), (2, 18), (16, 8), (18, 33), (9, 33), (4, 10), (19, 33), (18, 16), (30, 40), (20, 23), (45, 43), (43, 10), (15, 30), (0, 5), (37, 1), (14, 34), (40, 9), (15, 8), (14, 32), (0, 43), (15, 5), (33, 26), (2, 25), (33, 12), (13, 42), (28, 34), (39, 14), (33, 11), (14, 9), (8, 0), (39, 37), (24, 39), (18, 4), (26, 5), (19, 30), (38, 18), (18, 9), (17, 2), (26, 40), (39, 20), (37, 38), (26, 20), (35, 19), (40, 10), (44, 21), (22, 16), (9, 22), (26, 7), (15, 14), (17, 17), (10, 4), (16, 27), (35, 17), (6, 2), (2, 16), (4, 19), (9, 40), (11, 28), (2, 17), (34, 40), (42, 32), (3, 13), (20, 37), (30, 30), (7, 6), (1, 25), (20, 22), (16, 4), (34, 4), (40, 0), (2, 2), (7, 37), (40, 19), (2, 34), (41, 17), (14, 28), (31, 34), (26, 13), (39, 8), (11, 13), (40, 28), (43, 6), (4, 22), (10, 22), (34, 5), (26, 31), (11, 9), (35, 0), (34, 14), (45, 40), (30, 21), (41, 36), (19, 42), (37, 10), (28, 1), (20, 21), (8, 8), (40, 13), (10, 16), (31, 1), (26, 27), (18, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 20), (1, 28), (21, 23), (14, 34), (8, 28), (27, 16), (7, 33), (7, 21), (6, 4), (33, 7), (8, 8), (38, 19), (30, 35), (27, 10), (42, 26), (15, 25), (14, 22), (45, 12), (24, 36), (0, 19), (23, 14), (33, 14), (6, 28), (40, 25), (13, 12), (43, 1), (15, 27), (46, 13), (16, 6), (22, 21), (33, 35), (29, 6), (0, 2), (32, 0), (37, 38), (21, 19), (37, 26), (43, 10), (13, 34), (40, 7), (26, 9), (17, 1), (41, 13), (0, 6), (8, 34), (19, 29), (17, 15), (13, 23), (13, 40), (29, 35), (30, 33), (23, 22), (39, 36), (11, 20), (26, 3), (7, 5), (8, 39), (7, 25), (0, 34), (43, 31), (30, 20), (33, 22), (40, 21), (42, 27), (44, 39), (32, 34), (21, 12), (26, 5), (39, 15), (30, 1), (9, 4), (28, 17), (39, 8), (36, 32), (29, 36), (13, 5), (33, 19), (36, 15), (46, 35), (9, 25), (19, 36), (2, 32), (23, 39), (33, 26), (4, 16), (20, 15), (36, 35), (5, 20), (9, 15), (35, 37), (8, 10), (31, 29), (28, 3), (10, 3), (39, 29), (7, 27), (27, 5), (9, 33), (28, 30), (46, 1), (28, 40), (9, 34), (16, 19), (29, 18), (3, 2), (2, 37), (36, 20), (33, 17), (35, 26), (23, 19), (37, 32), (20, 38), (45, 29), (28, 37), (42, 25), (13, 36), (40, 27), (41, 18), (4, 19), (3, 5), (46, 37), (36, 10), (30, 18), (26, 28), (7, 19), (26, 35), (14, 27), (28, 0), (5, 16), (26, 25), (24, 6), (6, 25), (3, 10), (9, 21), (4, 12), (41, 29), (5, 18), (24, 9), (1, 30), (4, 38), (46, 9), (17, 11), (39, 30), (8, 20), (25, 33), (30, 25), (19, 33), (22, 34), (17, 17), (0, 35), (44, 22), (39, 37), (10, 8), (35, 34), (38, 31), (44, 3), (46, 39), (3, 32), (34, 21), (44, 19), (14, 39), (25, 9), (6, 21), (3, 15), (37, 2), (25, 36), (34, 23), (9, 35), (5, 37), (8, 23), (41, 4), (45, 27), (22, 7), (22, 24), (19, 1), (4, 5), (40, 28), (28, 14), (35, 21), (35, 15), (41, 31), (7, 17), (1, 15), (22, 16), (13, 35), (21, 39), (11, 9), (3, 17), (13, 8), (18, 27), (29, 12), (18, 3), (12, 19), (27, 17), (1, 6), (31, 23), (46, 15), (5, 7), (42, 18), (38, 26), (46, 18), (38, 29), (34, 40), (15, 11), (38, 18), (5, 1), (27, 2), (30, 22), (32, 9), (1, 11), (14, 2), (38, 37), (34, 37), (21, 15), (25, 18), (30, 15), (27, 22), (16, 24), (16, 21), (1, 5), (8, 24), (4, 3), (41, 26), (28, 26), (7, 4), (21, 33), (41, 9), (5, 0), (6, 38), (39, 22), (13, 10), (11, 30), (28, 35), (37, 33), (2, 9), (34, 31), (0, 13), (23, 8), (8, 12), (12, 13), (18, 17), (37, 40), (45, 14), (19, 40), (37, 13), (42, 6), (31, 14), (37, 22), (13, 20), (14, 30), (38, 12), (20, 27), (20, 28), (31, 8), (15, 33), (37, 23), (5, 25), (1, 32), (26, 30), (22, 5), (29, 27), (18, 10), (15, 20), (7, 36), (9, 7), (35, 29), (41, 24), (21, 0), (5, 11), (10, 26), (12, 6), (46, 4), (36, 27), (31, 30), (28, 25), (37, 28), (34, 7), (31, 9), (41, 14), (0, 11), (18, 23), (45, 4), (16, 13), (31, 12), (24, 34), (45, 8), (27, 34), (44, 2), (35, 33), (12, 31), (36, 13), (9, 18), (14, 23), (35, 22), (13, 11), (38, 5), (42, 29), (7, 24), (16, 8), (1, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 23), (28, 24), (27, 22), (9, 11), (10, 15), (15, 30), (32, 39), (40, 35), (37, 38), (2, 24), (25, 38), (20, 35), (14, 21), (17, 34), (31, 28), (33, 33), (5, 19), (7, 17), (3, 32), (18, 33), (1, 34), (3, 9), (10, 16), (9, 4), (29, 34), (39, 16), (18, 9), (15, 25), (12, 15), (39, 34), (7, 27), (23, 11), (9, 23), (34, 35), (22, 7), (15, 9), (6, 22), (5, 36), (21, 6), (8, 22), (37, 37), (30, 28), (24, 21), (9, 35), (23, 24), (18, 18), (36, 14), (4, 21), (21, 17), (21, 36), (16, 40), (38, 11), (17, 11), (29, 2), (0, 35), (38, 19), (21, 30), (21, 0), (1, 40), (38, 36), (12, 13), (16, 22), (20, 17), (8, 30), (5, 21), (39, 33), (14, 35), (19, 1), (9, 40), (27, 15), (8, 16), (1, 13), (34, 29), (18, 34), (11, 5), (37, 34), (16, 18), (0, 1), (31, 35), (32, 33), (2, 15), (1, 23), (26, 28), (30, 38), (3, 17), (5, 4), (40, 6), (12, 34), (10, 38), (36, 9), (0, 26), (17, 7), (12, 9), (25, 11), (28, 32), (24, 0), (20, 30), (2, 36), (7, 35), (34, 2), (6, 23), (2, 4), (10, 3), (30, 40), (21, 2), (21, 35), (19, 12), (26, 12), (13, 24), (23, 7), (24, 37), (11, 21), (19, 16), (23, 0), (34, 3), (2, 35), (16, 23), (2, 26), (33, 34), (39, 22), (26, 20), (0, 5), (28, 11), (22, 21), (11, 3), (26, 30), (7, 20), (17, 35), (6, 29), (0, 17), (22, 33), (33, 36), (9, 39), (40, 28), (13, 22), (0, 38), (4, 9), (14, 36), (13, 34), (28, 13), (3, 12), (13, 19), (27, 19), (22, 13), (14, 24), (40, 25), (17, 6), (21, 28), (37, 35), (31, 30), (6, 36), (37, 15), (39, 6), (32, 18), (34, 40), (15, 16), (20, 11), (17, 27), (18, 3), (30, 11), (14, 20), (30, 13), (18, 35), (25, 10), (25, 12), (37, 30), (9, 19), (27, 39), (13, 21), (12, 18), (17, 20), (11, 28), (5, 13), (27, 28), (1, 7), (12, 37), (39, 28), (23, 15), (22, 30), (31, 0), (3, 21), (29, 30), (3, 38), (32, 24), (16, 5), (15, 37), (10, 34), (29, 5), (21, 34), (24, 9), (22, 9), (34, 36), (8, 33), (33, 11), (40, 15), (5, 24), (9, 16), (8, 32), (17, 16), (20, 10), (18, 5), (25, 37), (37, 13), (40, 12), (35, 4), (12, 26), (27, 13), (1, 9), (4, 24), (24, 35), (10, 14), (1, 5), (10, 2), (5, 2), (23, 8), (19, 25), (13, 30), (12, 30), (14, 15), (29, 18), (13, 25), (28, 38), (34, 8), (15, 15), (22, 6), (9, 33), (37, 21), (6, 5), (9, 14), (15, 7), (25, 13), (15, 33), (40, 0), (17, 4), (30, 18), (2, 20), (18, 12), (6, 10), (4, 18), (12, 20), (18, 36), (39, 7), (28, 21), (35, 3), (23, 26), (2, 23), (3, 8), (15, 40), (1, 12), (21, 27), (29, 25), (33, 16), (16, 2), (25, 16), (21, 1), (16, 37), (25, 35), (27, 11), (10, 29), (23, 6), (10, 27), (15, 14), (25, 22), (18, 28), (29, 23), (6, 31), (10, 40), (33, 28), (11, 31), (37, 2), (13, 35), (0, 29), (26, 19), (30, 31), (15, 12), (37, 29), (3, 1), (38, 4), (35, 30), (26, 11), (13, 40), (29, 21), (17, 25), (4, 25), (6, 33), (27, 26), (23, 4), (3, 33), (40, 5), (34, 1), (40, 30), (21, 4), (16, 17), (8, 25), (15, 1), (10, 26), (16, 6), (30, 36), (6, 40), (9, 32), (3, 7), (6, 27), (11, 9), (7, 31), (3, 27), (27, 36), (15, 6), (26, 37), (14, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 1), (13, 46), (8, 40), (9, 37), (33, 10), (14, 21), (3, 12), (36, 8), (36, 11), (13, 3), (38, 43), (38, 10), (15, 42), (33, 17), (19, 19), (23, 2), (15, 7), (34, 34), (33, 34), (4, 29), (0, 15), (18, 36), (26, 41), (1, 32), (9, 34), (9, 38), (12, 2), (8, 3), (16, 14), (25, 44), (36, 16), (19, 41), (14, 5), (31, 33), (41, 29), (1, 34), (8, 7), (34, 27), (20, 13), (30, 24), (25, 3), (29, 1), (35, 22), (24, 18), (37, 7), (36, 15), (19, 38), (33, 15), (5, 15), (31, 37), (39, 14), (22, 26), (24, 45), (0, 12), (27, 15), (4, 15), (18, 44), (12, 12), (4, 8), (37, 32), (30, 39), (20, 27), (5, 32), (25, 16), (0, 18), (36, 29), (6, 26), (0, 4), (12, 42), (31, 13), (20, 23), (10, 41), (29, 30), (22, 16), (11, 16), (37, 29), (1, 7), (33, 0), (37, 14), (40, 13), (40, 39), (21, 10), (16, 26), (20, 45), (8, 32), (2, 43), (11, 9), (41, 42), (32, 21), (17, 30), (8, 12), (14, 4), (10, 36), (37, 12), (41, 11), (35, 42), (26, 43), (21, 3), (14, 32), (36, 1), (19, 36), (21, 33), (27, 42), (5, 10), (7, 6), (31, 25), (23, 41), (41, 20), (19, 24), (10, 12), (40, 34), (10, 18), (18, 32), (21, 19), (36, 21), (28, 35), (15, 20), (9, 30), (7, 28), (24, 23), (40, 6), (16, 43), (34, 17), (30, 23), (7, 46), (28, 0), (16, 23), (34, 11), (19, 29), (9, 26), (24, 22), (7, 41), (25, 43), (37, 13), (0, 39), (7, 36), (27, 7), (8, 30), (31, 43), (12, 20), (29, 41), (7, 1), (32, 4), (1, 13), (29, 0), (14, 33), (31, 9), (32, 15), (1, 23), (4, 42), (3, 0), (3, 24), (5, 34), (12, 16), (34, 19), (15, 1), (16, 46), (12, 21), (1, 30), (28, 30), (37, 4), (3, 2), (25, 42), (4, 24), (39, 35), (2, 6), (20, 4), (31, 0), (15, 33), (22, 41), (15, 22), (30, 9), (31, 46), (18, 9), (13, 17), (12, 27), (0, 16), (22, 4), (22, 14), (26, 9), (16, 21), (41, 10), (11, 7), (36, 0), (22, 33), (26, 5), (27, 2), (28, 25), (23, 22), (38, 33), (35, 12), (37, 18), (34, 20), (8, 29), (6, 23), (6, 4), (34, 26), (5, 28), (9, 43), (11, 24), (34, 21), (13, 25), (12, 45), (6, 18), (34, 16), (16, 17), (11, 44), (18, 28), (31, 39), (27, 28), (27, 25), (34, 2), (14, 23), (15, 36), (27, 46), (33, 43), (27, 39), (0, 26), (21, 35), (28, 19), (41, 31), (35, 11), (22, 30), (8, 26), (4, 41), (31, 16), (17, 32), (8, 22), (28, 18), (3, 17), (37, 24), (40, 29), (0, 1), (26, 21), (23, 13), (24, 24), (25, 45), (28, 36), (0, 8), (8, 11), (41, 33), (31, 10), (4, 32), (25, 23), (38, 2), (29, 19), (0, 43), (12, 44), (6, 24), (39, 24), (25, 30), (5, 2), (6, 9), (5, 19), (18, 37), (39, 33), (3, 1), (39, 45), (24, 12), (19, 45), (23, 31), (11, 21), (9, 32), (30, 2), (34, 30), (9, 21), (31, 44), (1, 46)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 27), (10, 12), (7, 4), (23, 25), (36, 9), (40, 40), (10, 4), (18, 7), (39, 24), (37, 37), (5, 16), (4, 37), (42, 32), (27, 30), (16, 7), (6, 20), (34, 13), (23, 17), (0, 30), (23, 0), (29, 21), (18, 11), (17, 27), (13, 20), (3, 16), (30, 14), (43, 2), (21, 27), (2, 24), (38, 38), (17, 17), (1, 14), (6, 15), (35, 40), (16, 0), (15, 8), (32, 39), (5, 6), (41, 16), (17, 0), (21, 33), (38, 2), (34, 2), (0, 10), (36, 13), (34, 0), (2, 13), (8, 25), (15, 25), (3, 36), (6, 14), (26, 2), (10, 30), (30, 15), (32, 40), (4, 2), (4, 19), (8, 26), (5, 29), (38, 15), (19, 1), (35, 31), (3, 24), (15, 22), (15, 35), (19, 19), (18, 25), (40, 20), (24, 18), (4, 7), (14, 5), (21, 32), (3, 4), (38, 43), (9, 8), (28, 35), (22, 20), (8, 37), (14, 19), (1, 6), (31, 0), (40, 16), (16, 41), (43, 1), (5, 4), (28, 1), (5, 38), (11, 7), (15, 17), (26, 39), (26, 20), (36, 24), (26, 23), (33, 2), (6, 32), (2, 25), (2, 39), (7, 22), (27, 34), (5, 18), (11, 41), (15, 14), (25, 2), (19, 0), (2, 8), (1, 10), (40, 36), (3, 13), (36, 42), (6, 10), (17, 41), (34, 12), (0, 38), (27, 16), (34, 20), (35, 17), (26, 9), (3, 37), (37, 3), (19, 38), (30, 29), (17, 24), (12, 11), (35, 5), (26, 40), (9, 32), (35, 2), (24, 1), (23, 1), (36, 40), (13, 37), (19, 15), (2, 23), (1, 35), (43, 34), (4, 27), (15, 21), (34, 18), (39, 31), (23, 15), (36, 7), (33, 25), (15, 4), (20, 33), (10, 6), (36, 33), (22, 33), (29, 22), (34, 34), (30, 30), (25, 38), (23, 6), (8, 4), (29, 4), (12, 39), (4, 5), (36, 27), (3, 1), (40, 35), (30, 28), (32, 8), (22, 10), (31, 30), (29, 19), (39, 1), (21, 17), (1, 1), (43, 24), (34, 33), (6, 16), (5, 17), (11, 4), (7, 15), (16, 40), (8, 33), (29, 9), (37, 22), (20, 19), (21, 15), (20, 27), (8, 14), (26, 32), (19, 23), (4, 25), (8, 39), (10, 9), (43, 37), (33, 27), (28, 2), (34, 29), (23, 35), (23, 33), (29, 11), (7, 20), (41, 39), (27, 14), (7, 27), (16, 23), (39, 12), (37, 28), (8, 28), (41, 7), (19, 35), (12, 27), (42, 43), (14, 39), (0, 27), (40, 6), (18, 10), (18, 12), (25, 41), (35, 38), (5, 26), (28, 32), (28, 37), (43, 17), (5, 10), (12, 41), (10, 19), (27, 13), (18, 4), (4, 38), (4, 13), (24, 33), (10, 36), (28, 12), (31, 12), (14, 6), (28, 28), (11, 13), (20, 40), (23, 9), (10, 10), (27, 17), (43, 38), (35, 36), (37, 32), (15, 42), (12, 19), (3, 2), (13, 8), (20, 32), (4, 43), (4, 0), (18, 41), (10, 8), (6, 7), (20, 20), (13, 15), (37, 12), (14, 4), (28, 41), (42, 28), (7, 16), (21, 18), (17, 9), (4, 24), (35, 34), (19, 33), (10, 27), (31, 34), (32, 26), (29, 6), (41, 3), (10, 18), (42, 2), (30, 43), (8, 18), (4, 36), (18, 9), (19, 32), (5, 20), (35, 10), (22, 29), (21, 24), (27, 37), (32, 12), (9, 6), (15, 0), (37, 40), (21, 41), (37, 31), (12, 42), (8, 34), (41, 42), (24, 39), (4, 23), (26, 7), (22, 24), (38, 4), (13, 0), (13, 31), (7, 7), (25, 17), (21, 12), (38, 40), (1, 15), (22, 14), (26, 37), (35, 22), (4, 11), (12, 17), (31, 21), (3, 38), (2, 5), (0, 26), (20, 30), (23, 27), (4, 15), (16, 2), (4, 16), (8, 27), (13, 2), (37, 4), (20, 9), (7, 0), (2, 3), (16, 15), (39, 37), (39, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 31), (26, 26), (8, 33), (14, 36), (19, 20), (8, 12), (8, 25), (8, 36), (12, 37), (45, 42), (32, 4), (20, 13), (26, 13), (9, 6), (18, 32), (42, 13), (0, 9), (2, 25), (4, 12), (39, 10), (35, 37), (16, 29), (33, 21), (21, 32), (23, 10), (0, 20), (33, 41), (4, 36), (39, 39), (38, 10), (32, 10), (26, 10), (5, 3), (40, 9), (15, 21), (46, 3), (11, 41), (8, 32), (1, 39), (45, 19), (28, 2), (43, 19), (11, 39), (17, 18), (32, 2), (45, 32), (21, 22), (37, 40), (27, 0), (44, 2), (41, 2), (2, 33), (19, 8), (13, 23), (37, 41), (35, 39), (4, 39), (24, 23), (6, 7), (16, 33), (25, 37), (8, 41), (37, 4), (23, 41), (11, 26), (4, 11), (38, 27), (28, 21), (32, 11), (35, 36), (18, 42), (22, 14), (4, 17), (32, 29), (11, 0), (39, 17), (39, 34), (11, 3), (37, 9), (13, 24), (27, 10), (42, 42), (46, 18), (25, 31), (26, 23), (22, 15), (32, 6), (6, 1), (19, 28), (15, 9), (7, 35), (3, 23), (17, 16), (33, 9), (9, 5), (18, 14), (25, 35), (43, 3), (42, 38), (7, 39), (12, 14), (12, 39), (24, 1), (6, 19), (39, 21), (45, 0), (41, 26), (42, 14), (33, 12), (7, 41), (8, 9), (31, 22), (34, 20), (31, 23), (18, 1), (18, 19), (45, 10), (14, 33), (2, 14), (13, 39), (41, 31), (3, 36), (22, 3), (11, 36), (21, 11), (45, 41), (39, 8), (15, 39), (29, 3), (41, 17), (2, 5), (39, 38), (44, 29), (7, 8), (16, 24), (39, 4), (35, 2), (35, 28), (43, 30), (12, 25), (41, 22), (7, 17), (34, 3), (17, 40), (1, 24), (28, 19), (38, 40), (31, 21), (33, 5), (5, 0), (5, 8), (3, 5), (27, 26), (25, 36), (23, 7), (11, 38), (19, 31), (34, 16), (3, 27), (12, 7), (10, 7), (9, 32), (5, 19), (37, 30), (1, 16), (45, 5), (45, 23), (42, 22), (7, 15), (6, 18), (38, 15), (35, 35), (43, 26), (9, 38), (4, 27), (2, 42), (4, 13), (26, 37), (16, 14), (44, 7), (12, 41), (43, 36), (0, 34), (12, 2), (32, 14), (28, 37), (22, 34), (3, 34), (13, 40), (12, 12), (18, 15), (32, 21), (0, 35), (13, 30), (41, 12), (35, 18), (30, 21), (5, 36), (28, 36), (27, 40), (43, 29), (39, 7), (24, 11), (0, 8), (45, 25), (45, 38), (45, 27), (18, 11), (11, 22), (9, 36), (33, 39), (17, 37), (3, 0), (37, 24), (33, 23), (23, 36), (19, 26), (17, 42), (41, 18), (30, 3), (15, 1), (44, 3), (17, 6), (19, 32), (20, 12), (21, 38), (4, 26), (45, 13), (15, 0), (44, 33), (26, 31), (1, 4), (6, 5), (8, 17), (19, 39), (37, 2), (37, 42), (43, 39), (42, 1), (16, 18), (32, 33), (1, 21), (34, 8), (14, 29), (23, 15), (28, 7), (43, 25), (13, 26), (31, 37), (44, 24), (27, 16), (8, 8), (11, 29), (31, 35), (39, 5), (11, 27), (29, 13), (20, 22), (13, 5), (29, 20), (2, 23), (41, 24), (34, 34), (31, 32), (5, 27), (42, 4), (17, 4), (16, 21), (32, 1), (45, 20), (44, 37), (12, 40), (12, 15), (31, 2), (27, 11), (0, 26), (13, 21), (10, 20), (42, 8), (5, 40), (16, 9), (27, 3), (43, 32), (20, 30), (30, 16), (38, 42), (4, 35), (36, 18), (14, 30), (4, 14), (13, 4), (17, 1), (7, 3), (42, 26), (39, 22), (0, 15), (9, 11), (20, 7), (31, 12), (20, 33), (13, 19), (23, 37), (7, 13), (33, 31), (18, 16), (40, 38), (30, 1), (37, 31), (17, 23), (13, 0), (28, 3), (32, 35), (46, 36), (34, 38), (5, 34), (29, 4), (29, 39), (40, 39), (39, 26), (25, 28), (39, 12), (40, 6), (23, 0), (18, 17), (29, 29), (36, 0), (12, 19), (19, 14), (25, 34), (2, 22), (12, 42), (9, 20), (4, 19), (3, 2), (36, 26), (14, 42), (9, 41), (45, 21), (25, 0), (24, 10), (17, 10), (16, 6), (3, 6), (12, 34), (27, 35), (33, 25), (2, 8), (9, 26), (33, 1), (29, 40), (37, 1), (26, 42), (41, 8), (24, 42), (3, 1), (23, 13), (36, 28), (39, 0), (15, 19), (1, 11), (29, 7), (33, 30), (33, 32), (3, 12), (13, 8), (31, 10), (33, 13), (22, 29), (17, 36), (42, 40), (0, 4), (44, 21), (3, 16), (27, 27), (3, 30), (14, 16), (29, 28), (30, 28), (21, 3), (3, 33), (43, 40), (4, 34), (20, 20), (23, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 40x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 15), (37, 24), (20, 20), (19, 12), (21, 30), (25, 21), (25, 15), (8, 3), (13, 32), (25, 37), (10, 19), (39, 36), (13, 18), (31, 5), (20, 30), (23, 16), (18, 0), (4, 14), (23, 21), (11, 20), (1, 17), (2, 38), (39, 30), (6, 35), (7, 35), (30, 37), (29, 28), (38, 4), (33, 12), (20, 38), (33, 27), (32, 29), (33, 1), (31, 37), (35, 17), (39, 13), (38, 19), (27, 14), (32, 32), (32, 33), (33, 33), (35, 23), (8, 20), (16, 41), (11, 32), (21, 6), (29, 5), (28, 27), (26, 27), (11, 4), (29, 9), (9, 42), (3, 27), (38, 27), (18, 3), (39, 19), (22, 1), (36, 20), (6, 17), (15, 19), (37, 1), (2, 26), (16, 25), (35, 18), (10, 35), (22, 31), (25, 9), (25, 42), (26, 10), (21, 39), (5, 9), (32, 31), (25, 2), (7, 0), (22, 33), (31, 4), (13, 23), (18, 6), (11, 17), (12, 17), (28, 14), (18, 28), (6, 39), (17, 21), (2, 27), (27, 30), (5, 13), (0, 19), (2, 11), (6, 19), (17, 27), (0, 34), (2, 40), (1, 14), (7, 16), (34, 17), (36, 10), (3, 14), (2, 17), (37, 5), (30, 38), (18, 24), (13, 7), (24, 23), (3, 11), (38, 8), (36, 27), (18, 35), (26, 18), (32, 38), (11, 0), (33, 14), (14, 17), (20, 9), (30, 40), (32, 23), (8, 11), (18, 14), (14, 36), (27, 1), (31, 26), (7, 30), (36, 19), (5, 17), (17, 14), (36, 12), (24, 20), (14, 24), (1, 2), (33, 18), (31, 32), (13, 42), (4, 5), (2, 30), (35, 28), (33, 29), (36, 29), (19, 30), (21, 9), (29, 17), (29, 30), (10, 20), (18, 16), (22, 16), (12, 25), (21, 42), (0, 29), (9, 10), (27, 16), (39, 27), (29, 12), (14, 2), (26, 23), (34, 3), (8, 18), (37, 3), (4, 42), (10, 22), (14, 3), (12, 33), (7, 17), (15, 6), (22, 30), (18, 12), (15, 11), (37, 8), (1, 36), (13, 14), (31, 17), (4, 28), (14, 22), (9, 8), (39, 10), (1, 42), (28, 22), (24, 31), (6, 23), (34, 10), (8, 7), (30, 6), (19, 4), (24, 22), (23, 39), (32, 15), (20, 2), (33, 22), (15, 37), (0, 35), (18, 15), (32, 42), (39, 34), (33, 36), (30, 20), (12, 37), (13, 13), (9, 31), (9, 17), (4, 16), (24, 26), (28, 28), (17, 16), (33, 13), (5, 5), (22, 12), (19, 28), (16, 15), (14, 15), (33, 28), (5, 20), (28, 20), (29, 26), (16, 33), (34, 31), (36, 38), (22, 35), (3, 17), (10, 33), (14, 31), (25, 7), (2, 13), (33, 10), (31, 0), (7, 4), (11, 24), (26, 0), (28, 11), (9, 12), (38, 0), (4, 40), (33, 15), (17, 9), (10, 25), (26, 34), (10, 41), (19, 34), (35, 38), (10, 3), (12, 12), (15, 14), (4, 38), (10, 36), (28, 35), (29, 41), (15, 33), (16, 22), (19, 1), (25, 34), (25, 16), (11, 8), (1, 10), (2, 10), (10, 6), (3, 30), (21, 33), (15, 20), (16, 11), (27, 38), (23, 26), (0, 1), (2, 14), (2, 5), (2, 6), (37, 6), (12, 13), (26, 39), (29, 32), (39, 21), (20, 36), (20, 0), (32, 0), (35, 41), (26, 30), (24, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 0), (24, 14), (38, 18), (13, 6), (23, 23), (24, 23), (20, 34), (2, 12), (5, 39), (17, 28), (29, 10), (43, 0), (21, 0), (24, 27), (33, 14), (22, 35), (37, 41), (32, 30), (36, 5), (3, 11), (29, 33), (42, 43), (37, 30), (14, 44), (11, 0), (22, 40), (35, 1), (0, 16), (0, 20), (37, 34), (26, 36), (20, 35), (29, 19), (35, 43), (39, 37), (17, 37), (40, 38), (1, 30), (36, 29), (12, 24), (42, 19), (37, 6), (24, 1), (16, 5), (1, 35), (31, 18), (7, 24), (27, 13), (10, 20), (19, 22), (32, 25), (3, 42), (20, 26), (40, 32), (3, 24), (42, 15), (0, 15), (39, 43), (24, 2), (6, 39), (20, 19), (0, 43), (6, 42), (14, 37), (30, 16), (12, 33), (2, 25), (6, 19), (38, 5), (2, 44), (4, 18), (17, 32), (10, 15), (14, 43), (32, 7), (30, 30), (28, 35), (35, 20), (44, 9), (24, 44), (5, 4), (28, 22), (11, 28), (25, 11), (40, 36), (42, 26), (3, 38), (37, 25), (11, 33), (23, 33), (5, 19), (39, 38), (8, 3), (29, 16), (38, 15), (43, 14), (36, 33), (34, 20), (10, 23), (4, 35), (24, 30), (33, 7), (42, 17), (16, 4), (21, 7), (19, 2), (4, 16), (14, 9), (33, 26), (7, 5), (7, 26), (26, 41), (17, 40), (8, 24), (0, 13), (28, 15), (22, 14), (38, 20), (7, 44), (35, 9), (15, 4), (20, 3), (20, 13), (10, 40), (43, 21), (18, 12), (11, 2), (21, 30), (30, 4), (20, 44), (28, 12), (21, 27), (33, 42), (43, 41), (0, 34), (23, 22), (38, 8), (15, 39), (44, 42), (19, 34), (14, 1), (1, 4), (19, 36), (0, 6), (9, 16), (9, 38), (10, 31), (8, 16), (38, 2), (22, 0), (15, 12), (9, 36), (43, 38), (33, 1), (38, 38), (9, 42), (29, 21), (0, 31), (41, 18), (36, 32), (33, 43), (7, 13), (25, 39), (44, 39), (34, 16), (26, 1), (3, 10), (21, 4), (10, 2), (33, 18), (26, 40), (34, 14), (23, 20), (18, 1), (6, 0), (16, 36), (7, 39), (20, 40), (0, 11), (35, 2), (36, 35), (18, 37), (37, 24), (26, 0), (19, 0), (4, 23), (33, 32), (17, 36), (11, 30), (6, 23), (3, 34), (9, 5), (40, 34), (43, 28), (10, 38), (24, 8), (26, 38), (16, 2), (39, 24), (39, 30), (16, 33), (5, 33), (27, 7), (9, 27), (30, 3), (8, 22), (16, 31), (17, 15), (20, 15), (9, 25), (3, 3), (43, 7), (1, 34), (41, 27), (44, 34), (1, 12), (13, 24), (16, 24), (0, 37), (23, 12), (42, 35), (33, 13), (4, 37), (31, 17), (24, 29), (25, 5), (3, 5), (31, 6), (36, 34), (13, 20), (32, 20), (7, 38), (41, 20), (20, 0), (2, 33), (35, 19), (6, 4), (18, 18), (12, 13), (27, 32), (36, 16), (23, 8), (18, 41), (26, 15), (1, 2), (27, 6), (30, 12), (42, 22), (40, 2), (34, 40), (26, 8), (43, 3), (34, 9), (34, 29), (44, 38), (17, 7), (34, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 36), (37, 25), (39, 34), (37, 2), (11, 1), (2, 13), (14, 16), (38, 36), (38, 21), (8, 5), (36, 36), (28, 39), (31, 18), (21, 16), (16, 21), (39, 0), (20, 23), (18, 6), (12, 18), (37, 30), (40, 32), (37, 27), (12, 17), (23, 6), (28, 4), (23, 39), (4, 8), (28, 15), (9, 33), (36, 1), (25, 7), (36, 29), (32, 31), (3, 25), (6, 18), (9, 14), (10, 21), (35, 12), (2, 18), (6, 3), (15, 22), (15, 32), (1, 13), (13, 9), (24, 13), (27, 0), (10, 23), (36, 32), (11, 21), (28, 3), (16, 18), (34, 37), (24, 35), (5, 27), (27, 32), (40, 37), (13, 2), (33, 35), (13, 35), (37, 0), (25, 28), (29, 24), (0, 28), (36, 23), (9, 18), (10, 30), (8, 9), (29, 0), (16, 10), (4, 16), (32, 22), (12, 11), (7, 38), (26, 25), (12, 21), (28, 36), (31, 25), (37, 37), (9, 5), (25, 19), (36, 9), (2, 37), (2, 2), (38, 34), (19, 14), (2, 15), (5, 8), (30, 27), (37, 33), (22, 39), (0, 22), (24, 32), (39, 21), (34, 32), (17, 5), (13, 22), (39, 19), (31, 2), (11, 32), (3, 17), (19, 23), (29, 9), (7, 26), (3, 2), (25, 9), (26, 23), (12, 14), (30, 2), (17, 35), (40, 6), (40, 27), (41, 31), (33, 21), (20, 26), (35, 35), (3, 0), (23, 22), (30, 9), (27, 3), (0, 27), (0, 3), (16, 9), (37, 16), (8, 7), (10, 20), (1, 9), (22, 29), (36, 22), (13, 17), (2, 17), (40, 14), (29, 34), (11, 31), (10, 33), (38, 23), (28, 26), (10, 12), (20, 25), (10, 38), (12, 12), (4, 38), (20, 16), (16, 14), (20, 20), (10, 16), (4, 12), (23, 35), (34, 2), (13, 3), (10, 8), (1, 36), (28, 16), (17, 26), (21, 22), (22, 31), (31, 22), (20, 22), (22, 12), (21, 8), (39, 30), (21, 15), (5, 24), (28, 27), (20, 9), (17, 9), (27, 29), (25, 17), (26, 14), (26, 12), (30, 36), (31, 5), (40, 39), (5, 5), (20, 8), (0, 14), (35, 15), (29, 32), (26, 19), (5, 33), (36, 19), (3, 1), (26, 36), (27, 2), (25, 5), (33, 22), (5, 18), (29, 1), (39, 7), (4, 11), (37, 31), (35, 7), (41, 16), (20, 12), (41, 13), (26, 39), (33, 8), (0, 35), (2, 12), (32, 15), (1, 27), (28, 32), (15, 15), (21, 25), (16, 6), (25, 32), (3, 23), (33, 38), (8, 11), (23, 11), (28, 23), (10, 24), (39, 4), (6, 30), (33, 16), (27, 38), (6, 36), (9, 29), (35, 5), (26, 8), (22, 7), (1, 19), (41, 28), (7, 17), (24, 4), (24, 14), (41, 15), (24, 8), (26, 3), (31, 34), (15, 28), (8, 26), (35, 26), (28, 1), (17, 22), (3, 20), (32, 39), (29, 31), (7, 19), (9, 34), (41, 22), (10, 0), (20, 27), (18, 31), (9, 39), (9, 10), (25, 4), (15, 35), (22, 23), (11, 7), (7, 32), (11, 22), (0, 5), (40, 23), (38, 33), (10, 9), (2, 1), (2, 33), (25, 3), (24, 38), (40, 15), (1, 17), (26, 2), (7, 27), (33, 9), (14, 5), (30, 4), (22, 0), (19, 25), (13, 31), (3, 26), (21, 24), (3, 35), (24, 30), (2, 25), (10, 18), (31, 16), (31, 33), (33, 20), (9, 28), (19, 17), (31, 21), (40, 36), (15, 0), (7, 5), (21, 3), (36, 3), (22, 18), (27, 19), (17, 19), (14, 37), (17, 16), (20, 14), (13, 12), (35, 0), (19, 3), (8, 2), (6, 25), (18, 10), (41, 8), (3, 39), (24, 27), (1, 0), (9, 37), (18, 21), (17, 31), (18, 33), (22, 2), (29, 12), (14, 1), (2, 22), (39, 25), (10, 11), (32, 19), (12, 33), (18, 12), (25, 6), (39, 33), (16, 0), (37, 36), (10, 7), (32, 20), (36, 2), (33, 1), (16, 13), (41, 12), (16, 29), (38, 7), (13, 1), (12, 6), (1, 8), (12, 38), (4, 25), (29, 11), (7, 2), (36, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 47x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 35), (16, 19), (13, 40), (44, 2), (13, 21), (27, 19), (26, 9), (33, 4), (25, 6), (23, 33), (6, 27), (35, 31), (12, 23), (22, 9), (31, 17), (42, 12), (10, 16), (3, 18), (19, 28), (27, 20), (16, 32), (36, 26), (23, 11), (11, 17), (29, 4), (17, 33), (33, 40), (39, 11), (21, 0), (23, 0), (28, 35), (40, 18), (3, 8), (42, 0), (33, 18), (27, 16), (3, 37), (37, 41), (43, 17), (2, 23), (42, 15), (37, 15), (12, 37), (39, 14), (27, 9), (7, 22), (19, 24), (27, 6), (5, 23), (29, 29), (39, 19), (31, 23), (42, 8), (14, 33), (20, 2), (21, 28), (44, 40), (36, 22), (37, 23), (3, 17), (10, 10), (1, 9), (35, 15), (3, 41), (7, 11), (5, 18), (19, 23), (32, 4), (37, 29), (19, 4), (11, 28), (19, 10), (18, 15), (40, 13), (33, 35), (5, 6), (6, 26), (24, 37), (19, 2), (15, 33), (15, 21), (45, 30), (22, 27), (27, 27), (19, 30), (46, 1), (19, 7), (46, 21), (15, 32), (8, 13), (16, 15), (12, 34), (12, 16), (20, 18), (24, 4), (8, 10), (9, 21), (1, 12), (35, 37), (28, 20), (3, 31), (44, 22), (43, 27), (16, 24), (32, 11), (8, 27), (33, 8), (2, 0), (39, 7), (43, 23), (17, 23), (4, 26), (33, 36), (36, 7), (16, 27), (38, 20), (7, 6), (35, 0), (32, 18), (28, 11), (19, 41), (26, 8), (32, 41), (28, 13), (14, 39), (5, 26), (16, 29), (0, 13), (40, 16), (24, 0), (5, 29), (35, 13), (15, 12), (18, 21), (29, 21), (24, 10), (8, 28), (2, 12), (14, 29), (33, 3), (19, 17), (14, 13), (44, 8), (42, 19), (42, 11), (19, 21), (6, 36), (12, 9), (16, 21), (36, 35), (34, 9), (25, 34), (23, 6), (15, 13), (25, 39), (28, 31), (40, 23), (45, 19), (27, 24), (37, 26), (12, 39), (35, 32), (2, 30), (26, 38), (28, 0), (38, 1), (19, 3), (44, 31), (37, 18), (27, 38), (22, 41), (29, 33), (22, 10), (23, 2), (18, 5), (46, 24), (20, 24), (42, 2), (6, 21), (43, 22), (7, 18), (17, 9), (16, 40), (18, 6), (22, 13), (15, 14), (33, 17), (10, 25), (7, 34), (21, 11), (3, 1), (14, 11), (14, 16), (46, 12), (5, 12), (29, 5), (7, 15), (28, 5), (15, 11), (17, 16), (38, 12), (25, 8), (39, 32), (13, 6), (18, 31), (10, 38), (34, 8), (45, 17), (33, 24), (24, 9), (4, 7), (30, 41), (30, 32), (21, 25), (15, 23), (19, 11), (34, 7), (7, 16), (46, 13), (34, 28), (6, 32), (6, 20), (43, 12), (25, 29), (18, 30), (42, 7), (21, 26), (34, 14), (12, 1), (36, 23), (7, 3), (46, 38), (16, 2), (16, 33), (17, 10), (6, 39), (8, 22), (23, 17), (11, 37), (19, 33), (4, 11), (41, 25), (26, 12), (14, 22), (21, 33), (9, 31), (38, 5), (28, 4), (40, 34), (40, 3), (28, 40), (29, 36), (31, 4), (41, 22), (0, 38), (31, 25), (0, 40), (5, 24), (13, 4), (13, 28), (6, 25), (2, 3), (10, 34), (41, 12), (5, 3), (9, 11), (37, 7), (38, 14), (26, 20), (11, 23), (38, 24), (34, 10), (14, 5), (34, 31), (42, 26), (43, 16), (15, 27), (7, 28), (0, 31), (22, 34), (40, 4), (26, 40), (4, 9), (37, 31), (43, 21), (18, 34), (22, 19), (36, 39), (31, 40), (41, 38), (30, 14), (15, 8), (10, 6), (15, 28), (21, 41), (15, 26), (37, 36), (33, 12), (1, 34), (15, 22), (25, 28), (17, 40), (32, 10), (8, 38), (25, 32), (24, 19), (3, 0), (38, 8), (28, 3), (4, 22), (32, 29), (17, 22), (41, 1), (34, 26), (32, 27), (20, 29), (5, 9), (21, 8), (2, 16), (40, 32), (5, 27), (13, 20), (27, 12), (8, 26), (10, 27), (46, 33), (38, 18), (14, 20), (31, 37), (17, 6), (40, 25), (25, 10), (1, 26), (2, 37), (43, 29), (32, 21), (3, 38), (31, 19), (25, 19), (23, 32), (21, 16), (9, 34), (8, 0), (31, 13), (37, 25), (22, 23), (46, 25), (45, 7), (24, 3), (15, 16), (32, 5), (10, 7), (29, 32), (24, 8), (14, 12), (33, 27), (44, 13), (12, 7), (7, 31), (8, 15), (17, 27), (3, 21), (21, 27), (25, 40), (31, 11), (30, 25), (29, 31), (26, 5), (21, 14), (41, 32), (31, 3), (40, 17), (25, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 4), (19, 26), (37, 33), (8, 35), (28, 35), (18, 0), (29, 12), (10, 34), (3, 4), (45, 40), (19, 28), (29, 10), (4, 20), (39, 13), (9, 1), (45, 32), (39, 26), (6, 27), (19, 11), (32, 16), (35, 22), (11, 19), (31, 44), (40, 7), (31, 36), (14, 19), (34, 3), (5, 24), (24, 33), (34, 41), (33, 10), (43, 22), (47, 9), (35, 13), (37, 28), (25, 21), (31, 43), (17, 5), (29, 41), (20, 17), (26, 4), (8, 12), (11, 12), (45, 26), (11, 30), (2, 24), (36, 23), (19, 2), (4, 44), (26, 43), (5, 16), (14, 9), (3, 21), (1, 19), (30, 21), (14, 26), (13, 10), (42, 11), (16, 20), (20, 18), (20, 2), (34, 42), (24, 29), (31, 37), (27, 5), (24, 43), (27, 26), (35, 31), (25, 4), (4, 29), (33, 0), (24, 7), (1, 37), (44, 33), (16, 14), (28, 28), (12, 16), (13, 0), (25, 10), (11, 41), (29, 16), (28, 34), (10, 38), (22, 33), (32, 13), (45, 42), (29, 7), (33, 40), (0, 14), (0, 5), (22, 17), (14, 28), (9, 39), (27, 38), (34, 17), (32, 35), (17, 29), (20, 12), (38, 9), (4, 14), (39, 9), (12, 33), (22, 15), (8, 9), (29, 6), (13, 3), (2, 37), (6, 7), (15, 25), (14, 3), (40, 29), (9, 15), (31, 25), (0, 27), (22, 26), (37, 18), (20, 1), (4, 11), (3, 17), (10, 21), (2, 14), (17, 11), (21, 11), (33, 28), (31, 41), (10, 28), (28, 29), (28, 24), (16, 29), (13, 4), (9, 8), (23, 12), (10, 24), (23, 0), (43, 25), (29, 30), (36, 35), (31, 33), (37, 36), (39, 41), (1, 10), (7, 33), (10, 6), (42, 44), (3, 30), (9, 17), (35, 19), (33, 33), (27, 41), (16, 19), (45, 14), (39, 11), (43, 10), (33, 14), (14, 5), (20, 16), (42, 33), (18, 30), (34, 19), (11, 0), (1, 24), (44, 32), (2, 44), (30, 44), (27, 14), (4, 34), (41, 10), (43, 38), (41, 30), (10, 16), (14, 7), (2, 20), (35, 0), (27, 36), (4, 9), (41, 11), (25, 14), (5, 41), (40, 17), (13, 20), (2, 1), (24, 13), (6, 13), (14, 38), (17, 15), (47, 15), (24, 17), (24, 34), (15, 20), (15, 11), (14, 24), (0, 26), (2, 2), (20, 4), (17, 23), (41, 22), (24, 31), (19, 18), (22, 23), (2, 7), (39, 39), (24, 1), (5, 23), (24, 41), (10, 22), (11, 32), (0, 9), (40, 36), (8, 25), (34, 25), (11, 34), (7, 10), (38, 33), (24, 37), (24, 22), (30, 19), (15, 18), (29, 31), (47, 23), (4, 16), (21, 26), (27, 6), (12, 14), (15, 39), (20, 41), (33, 6), (0, 20), (2, 27), (25, 9), (27, 0), (35, 6), (6, 17), (9, 30), (47, 6), (19, 17), (41, 16), (37, 3), (41, 15), (29, 40), (46, 39), (6, 14), (5, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 38), (17, 11), (22, 28), (11, 13), (22, 14), (19, 31), (16, 16), (30, 4), (33, 20), (1, 8), (32, 4), (0, 15), (6, 23), (27, 37), (21, 5), (25, 36), (28, 2), (33, 2), (10, 41), (5, 4), (27, 7), (33, 37), (21, 4), (6, 38), (22, 10), (13, 8), (30, 34), (27, 27), (26, 10), (16, 27), (15, 11), (17, 34), (31, 7), (9, 40), (4, 16), (26, 20), (12, 2), (24, 23), (35, 26), (20, 10), (36, 35), (20, 34), (36, 41), (13, 20), (11, 41), (26, 40), (1, 16), (15, 1), (8, 17), (1, 17), (19, 3), (21, 8), (19, 11), (36, 2), (5, 11), (23, 39), (12, 3), (26, 4), (11, 38), (21, 40), (21, 19), (39, 17), (3, 15), (13, 36), (12, 14), (26, 5), (15, 12), (6, 21), (24, 11), (27, 12), (21, 36), (37, 34), (38, 40), (2, 31), (31, 29), (17, 35), (12, 22), (22, 3), (32, 8), (23, 5), (23, 7), (6, 15), (8, 25), (37, 10), (19, 26), (25, 1), (17, 2), (21, 33), (22, 32), (6, 6), (38, 32), (2, 14), (34, 15), (15, 10), (34, 40), (21, 3), (7, 8), (22, 21), (38, 28), (21, 31), (14, 26), (12, 38), (16, 26), (33, 38), (25, 7), (28, 11), (7, 21), (6, 25), (27, 18), (2, 1), (32, 21), (33, 25), (9, 13), (14, 16), (33, 12), (27, 19), (1, 30), (37, 1), (16, 19), (6, 18), (15, 15), (37, 37), (19, 34), (4, 9), (5, 22), (8, 0), (23, 11), (4, 21), (32, 7), (18, 36), (32, 16), (24, 3), (30, 32), (28, 9), (9, 14), (15, 2), (38, 15), (29, 3), (34, 29), (17, 37), (26, 39), (11, 22), (7, 31), (20, 6), (35, 16), (18, 6), (18, 33), (20, 39), (0, 12), (5, 39), (17, 24), (24, 32), (32, 20), (28, 32), (4, 27), (37, 19), (13, 37), (12, 11), (0, 33), (10, 27), (32, 26), (35, 41), (11, 16), (11, 36), (31, 22), (19, 5), (7, 19), (38, 29), (10, 28), (38, 19), (6, 28), (31, 41), (0, 38), (37, 4), (16, 11), (21, 39), (6, 13), (24, 30), (18, 31), (33, 23), (15, 16), (17, 3), (14, 3), (1, 10), (28, 6), (27, 41), (0, 22), (34, 30), (13, 7), (5, 23), (4, 15), (38, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 17), (4, 3), (26, 24), (21, 20), (28, 7), (20, 4), (43, 23), (26, 7), (4, 26), (46, 22), (27, 32), (34, 20), (32, 7), (43, 29), (37, 17), (37, 31), (3, 28), (22, 21), (0, 6), (9, 25), (16, 19), (8, 10), (46, 4), (33, 13), (10, 6), (6, 8), (7, 32), (28, 15), (8, 35), (28, 6), (30, 33), (3, 34), (26, 32), (24, 33), (39, 2), (37, 34), (14, 34), (5, 35), (9, 38), (31, 17), (43, 3), (7, 40), (33, 11), (18, 32), (13, 16), (9, 20), (25, 38), (26, 3), (3, 5), (12, 33), (8, 40), (6, 2), (34, 11), (24, 1), (32, 35), (38, 23), (6, 32), (5, 9), (31, 7), (4, 24), (37, 16), (0, 20), (44, 6), (16, 9), (30, 39), (7, 39), (37, 6), (36, 1), (41, 4), (22, 13), (14, 35), (40, 31), (17, 32), (8, 17), (41, 20), (26, 34), (6, 4), (0, 15), (20, 14), (25, 15), (11, 23), (18, 2), (44, 32), (45, 28), (10, 12), (20, 38), (5, 26), (3, 38), (12, 4), (38, 33), (10, 10), (3, 22), (20, 2), (27, 37), (18, 1), (44, 31), (25, 34), (38, 6), (11, 3), (44, 13), (39, 15), (13, 6), (35, 5), (4, 40), (32, 33), (43, 14), (14, 2), (19, 8), (13, 3), (10, 8), (31, 33), (42, 15), (35, 6), (23, 17), (28, 30), (2, 6), (14, 28), (45, 22), (42, 12), (3, 2), (0, 1), (24, 21), (17, 15), (26, 40), (17, 19), (24, 35), (26, 29), (31, 36), (28, 24), (41, 17), (33, 12), (4, 14), (39, 16), (23, 22), (2, 13), (29, 6), (17, 7), (18, 20), (11, 5), (8, 14), (38, 13), (24, 20), (31, 6), (7, 7), (5, 8), (15, 8), (41, 31), (7, 12), (33, 19), (17, 20), (28, 16), (34, 7), (44, 39), (9, 21), (0, 13), (10, 38), (18, 17), (0, 7), (1, 21), (18, 18), (43, 6), (38, 40), (39, 18), (37, 14), (16, 11), (28, 23), (6, 9), (14, 17), (30, 8), (5, 21), (31, 28), (36, 29), (26, 18), (13, 15), (12, 6), (7, 3), (22, 30), (25, 18), (38, 21), (29, 25), (24, 31), (16, 13), (5, 32), (35, 21), (42, 32), (30, 26), (4, 8), (2, 4), (23, 10), (33, 34), (39, 8), (33, 26), (45, 24), (43, 16), (22, 18), (34, 1), (32, 39), (38, 10), (41, 0), (46, 11), (30, 4), (36, 3), (30, 5), (15, 15), (31, 14), (30, 40), (40, 25), (24, 0), (16, 35), (31, 9), (24, 11), (34, 31), (13, 26), (32, 34), (1, 10), (7, 21), (40, 30), (40, 14), (22, 3), (8, 36), (3, 16), (2, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 29), (3, 17), (28, 4), (2, 42), (23, 20), (23, 26), (23, 32), (34, 29), (38, 19), (42, 28), (12, 18), (15, 20), (0, 7), (0, 22), (39, 1), (4, 41), (38, 25), (12, 16), (35, 18), (13, 35), (30, 32), (25, 38), (13, 30), (15, 17), (33, 13), (1, 7), (29, 17), (0, 37), (18, 23), (37, 4), (39, 34), (6, 3), (19, 45), (39, 29), (5, 24), (22, 44), (5, 46), (36, 30), (35, 6), (37, 25), (17, 45), (36, 29), (9, 18), (24, 31), (22, 14), (26, 44), (12, 3), (1, 44), (24, 23), (13, 32), (27, 31), (7, 36), (18, 36), (25, 33), (6, 5), (31, 39), (31, 40), (21, 37), (24, 5), (18, 41), (26, 4), (40, 7), (13, 45), (16, 28), (19, 38), (4, 27), (14, 38), (43, 27), (42, 25), (6, 36), (42, 26), (42, 15), (0, 13), (28, 15), (12, 33), (30, 34), (24, 14), (19, 7), (6, 34), (5, 15), (9, 8), (22, 28), (30, 2), (7, 23), (40, 19), (5, 11), (2, 11), (36, 12), (6, 10), (21, 38), (18, 46), (11, 41), (9, 25), (20, 13), (32, 41), (15, 24), (22, 0), (33, 5), (35, 41), (41, 27), (2, 41), (8, 2), (24, 29), (16, 7), (19, 43), (6, 13), (27, 32), (40, 3), (2, 1), (7, 22), (40, 32), (19, 17), (7, 20), (38, 17), (35, 40), (34, 0), (24, 26), (21, 23), (38, 26), (24, 27), (15, 2), (22, 8), (7, 32), (17, 39), (34, 46), (35, 38), (4, 4), (39, 10), (32, 31), (39, 25), (43, 7), (14, 1), (26, 35), (42, 45), (29, 4), (35, 23), (35, 22), (41, 23), (18, 45), (37, 13), (42, 4), (7, 38), (31, 25), (13, 26), (12, 37), (27, 45), (32, 21), (26, 42), (25, 5), (16, 40), (30, 30), (0, 12), (26, 10), (16, 21), (42, 13), (30, 7), (4, 37), (23, 31), (0, 44), (2, 12), (10, 30), (17, 12), (31, 11), (18, 10), (15, 44), (37, 40), (3, 6), (41, 22), (41, 10), (10, 40), (37, 28), (17, 32), (5, 37), (43, 2), (35, 47), (36, 45), (43, 24), (22, 24), (8, 27), (0, 33), (33, 30), (15, 36), (42, 16), (17, 25), (40, 29), (26, 20), (4, 22), (15, 21), (14, 24), (8, 3), (13, 20), (25, 22), (12, 41), (16, 4), (34, 18), (12, 14), (26, 19), (3, 47), (26, 16), (11, 14), (40, 5), (29, 6), (4, 36), (32, 23), (11, 2), (19, 26), (25, 16), (30, 16), (35, 36), (19, 21), (1, 29), (27, 40), (37, 12), (29, 3), (5, 9), (31, 6), (25, 6), (28, 28), (12, 35), (34, 16), (18, 43), (12, 1), (11, 43), (4, 19), (10, 31), (21, 42), (33, 8), (21, 30), (30, 28), (14, 15), (0, 23), (5, 43), (26, 24), (18, 34), (21, 36), (12, 20), (29, 33), (19, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 35), (42, 39), (33, 25), (24, 35), (30, 22), (44, 21), (18, 39), (11, 38), (33, 2), (41, 2), (35, 37), (46, 36), (43, 17), (40, 3), (36, 12), (15, 42), (17, 44), (18, 23), (24, 0), (19, 23), (28, 18), (1, 9), (12, 12), (45, 26), (37, 30), (35, 28), (1, 34), (18, 21), (42, 7), (23, 29), (14, 15), (29, 34), (0, 9), (33, 44), (38, 43), (11, 4), (31, 41), (13, 6), (11, 28), (23, 24), (26, 31), (0, 20), (21, 10), (44, 13), (45, 2), (6, 10), (25, 40), (4, 24), (8, 26), (18, 15), (33, 34), (2, 10), (25, 27), (13, 19), (13, 10), (20, 14), (3, 40), (22, 20), (8, 32), (6, 32), (41, 4), (45, 25), (29, 38), (17, 7), (13, 40), (1, 31), (7, 13), (44, 23), (13, 42), (34, 3), (3, 32), (13, 28), (5, 36), (19, 34), (21, 17), (44, 16), (14, 40), (1, 14), (31, 28), (13, 35), (16, 21), (32, 25), (42, 37), (29, 6), (42, 35), (42, 30), (15, 6), (31, 23), (33, 16), (17, 8), (38, 0), (45, 14), (18, 1), (24, 9), (6, 40), (33, 21), (38, 36), (16, 24), (0, 36), (2, 15), (42, 42), (40, 14), (43, 40), (9, 16), (27, 19), (10, 22), (4, 21), (45, 37), (41, 34), (5, 22), (40, 15), (10, 17), (7, 18), (10, 33), (28, 40), (15, 33), (37, 4), (36, 17), (37, 43), (35, 18), (32, 28), (19, 42), (44, 17), (17, 35), (20, 41), (26, 14), (44, 41), (0, 17), (12, 2), (3, 38), (42, 2), (35, 4), (8, 18), (39, 11), (16, 38), (38, 11), (10, 41), (33, 11), (26, 13), (20, 22), (33, 30), (29, 24), (27, 4), (46, 7), (39, 0), (41, 8), (31, 40), (36, 16), (14, 32), (5, 34), (33, 27), (12, 7), (42, 29), (8, 2), (20, 36), (24, 19), (39, 7), (23, 39), (33, 37), (8, 39), (16, 8), (35, 44), (45, 9), (1, 3), (34, 6), (37, 2), (26, 36), (12, 20), (41, 32), (2, 25), (28, 17), (21, 42), (20, 15), (5, 8), (6, 2), (20, 3), (25, 18), (31, 16), (13, 29), (16, 36), (27, 20), (27, 18), (28, 31), (42, 20), (2, 41), (23, 2), (9, 33), (14, 3), (2, 20), (24, 40), (16, 42), (29, 21), (24, 29), (29, 2), (7, 19), (40, 22), (3, 20), (4, 42), (16, 34), (43, 3), (32, 35), (32, 29), (30, 18), (23, 31), (18, 6), (28, 43), (28, 32), (22, 41), (41, 22), (11, 18), (34, 28), (2, 5), (21, 14), (20, 34), (35, 14), (12, 40), (2, 38), (19, 26), (5, 35), (16, 33), (15, 1), (4, 6), (36, 30), (42, 38), (36, 15), (31, 36), (11, 8), (31, 32), (7, 9), (40, 33), (15, 35), (35, 1), (42, 8), (28, 15), (10, 31), (1, 5), (36, 24), (5, 41), (24, 22), (45, 5), (45, 19), (7, 23), (28, 8), (43, 0), (46, 35), (46, 34), (0, 22), (33, 15), (4, 38), (18, 11), (26, 12), (26, 39), (38, 23), (7, 27), (44, 42), (23, 25), (44, 32), (34, 25), (17, 31), (38, 31), (17, 0), (0, 5), (15, 26), (33, 28), (11, 9), (43, 16), (9, 22), (41, 6), (33, 10), (39, 17), (27, 1), (19, 15), (22, 31), (10, 43), (44, 33), (30, 35), (27, 17), (5, 11), (2, 28), (9, 32), (32, 13), (27, 38), (43, 22), (10, 4), (35, 27), (29, 36), (22, 17), (3, 3), (13, 38), (8, 27), (19, 0), (9, 25), (35, 10), (12, 3), (23, 35), (41, 26), (2, 0), (31, 21), (3, 30), (7, 26), (42, 12), (25, 29), (8, 19), (32, 39), (42, 5), (40, 2), (27, 8), (14, 28), (23, 9), (16, 7), (40, 9), (12, 29), (45, 10), (22, 35), (44, 20), (22, 26), (10, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 9), (42, 15), (2, 32), (18, 19), (1, 38), (30, 32), (18, 15), (26, 26), (32, 24), (22, 6), (37, 26), (19, 5), (21, 5), (42, 7), (33, 18), (7, 25), (25, 35), (38, 28), (13, 11), (21, 41), (42, 26), (38, 37), (0, 29), (3, 14), (13, 12), (40, 0), (30, 29), (2, 38), (41, 13), (6, 41), (22, 21), (27, 12), (28, 23), (24, 16), (17, 15), (24, 9), (32, 23), (5, 19), (27, 16), (19, 10), (28, 36), (31, 0), (33, 25), (28, 31), (19, 21), (24, 33), (12, 2), (5, 15), (20, 38), (15, 27), (7, 26), (43, 21), (44, 20), (4, 13), (20, 6), (30, 24), (40, 40), (28, 4), (17, 31), (6, 30), (30, 1), (37, 4), (8, 36), (27, 32), (44, 6), (41, 15), (42, 29), (4, 10), (9, 34), (1, 4), (10, 32), (16, 26), (31, 29), (17, 17), (31, 37), (39, 26), (42, 30), (29, 20), (31, 24), (2, 7), (35, 29), (11, 15), (40, 41), (10, 26), (1, 26), (17, 21), (22, 0), (38, 22), (4, 27), (36, 14), (36, 4), (40, 10), (36, 5), (19, 2), (32, 28), (40, 16), (41, 20), (35, 41), (34, 17), (44, 5), (33, 2), (44, 31), (1, 20), (43, 4), (17, 11), (22, 8), (8, 7), (28, 6), (32, 15), (16, 1), (16, 37), (28, 20), (20, 2), (41, 31), (15, 35), (22, 23), (41, 10), (35, 10), (22, 36), (19, 4), (44, 10), (38, 39), (4, 7), (22, 24), (16, 29), (8, 40), (23, 16), (27, 29), (44, 25), (40, 37), (25, 24), (21, 17), (28, 41), (20, 3), (14, 8), (0, 32), (8, 12), (0, 23), (31, 14), (42, 33), (24, 28), (1, 27), (29, 1), (40, 7), (18, 34), (13, 3), (6, 18), (36, 0), (15, 33), (2, 29), (41, 39), (16, 10), (28, 13), (16, 38), (38, 21), (13, 22), (3, 34), (19, 11), (21, 21), (30, 23), (20, 32), (22, 11), (15, 30), (18, 11), (6, 24), (15, 4), (8, 30), (10, 27), (11, 28), (6, 0), (6, 4), (8, 16), (23, 13), (2, 12), (19, 3), (23, 8), (43, 37), (23, 6), (32, 27), (30, 2), (10, 38), (31, 6), (38, 14), (34, 13), (7, 12), (29, 12), (18, 14), (15, 37), (24, 11), (36, 33), (13, 0), (1, 3), (26, 23), (16, 14), (25, 0), (20, 41), (25, 17), (27, 4), (29, 13), (4, 34), (29, 40), (15, 19), (28, 14), (23, 17), (31, 2), (29, 17), (13, 40), (5, 38), (36, 6), (30, 3), (21, 22), (31, 32), (37, 41), (12, 24), (34, 30), (24, 27), (39, 23), (12, 23), (34, 19), (20, 33), (35, 35), (21, 39), (35, 0), (25, 12), (42, 18), (44, 19), (6, 1), (23, 7), (24, 34), (8, 3), (35, 18), (12, 34), (16, 7), (14, 26), (1, 23), (23, 22), (0, 27), (26, 27), (27, 24), (41, 4), (21, 20), (17, 23), (28, 7), (22, 30), (14, 3), (39, 15), (28, 21), (37, 24), (42, 21), (4, 1), (27, 10), (12, 40), (14, 37), (17, 38), (8, 10), (36, 37), (15, 34), (44, 12), (28, 40), (6, 9), (7, 2), (35, 39), (7, 37), (6, 26), (27, 27), (18, 36), (11, 9), (32, 9), (5, 6), (21, 27), (13, 39), (24, 39), (11, 13), (11, 6), (14, 2), (19, 24), (21, 40), (41, 40), (18, 37), (2, 31), (30, 20), (14, 18), (3, 25), (43, 40), (32, 38), (6, 21), (3, 15), (2, 11), (11, 19), (13, 14), (9, 17), (43, 0), (44, 17), (32, 26), (21, 19), (30, 30), (11, 7), (28, 37), (41, 41), (26, 17), (37, 1), (13, 17), (5, 23), (23, 37), (26, 8), (20, 14), (15, 28), (44, 32), (26, 6), (43, 22), (5, 22), (19, 37), (43, 27), (20, 7), (36, 11), (12, 37), (9, 5), (2, 27), (24, 13), (17, 24), (20, 24), (18, 35), (38, 41), (30, 7), (25, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 20), (6, 0), (46, 31), (26, 24), (17, 9), (41, 1), (20, 40), (3, 28), (32, 11), (23, 38), (25, 32), (12, 46), (31, 28), (8, 35), (18, 4), (44, 39), (6, 28), (47, 25), (2, 25), (39, 23), (27, 32), (26, 10), (37, 8), (12, 8), (33, 14), (18, 34), (26, 18), (45, 37), (3, 29), (5, 23), (22, 12), (26, 21), (32, 20), (15, 43), (15, 44), (10, 25), (21, 9), (2, 27), (19, 22), (45, 43), (33, 45), (20, 23), (39, 39), (28, 4), (15, 25), (36, 17), (35, 33), (48, 21), (41, 12), (44, 3), (17, 30), (15, 32), (9, 12), (25, 11), (11, 13), (11, 42), (45, 0), (47, 35), (11, 38), (11, 12), (24, 9), (4, 42), (42, 11), (13, 5), (18, 12), (29, 8), (47, 44), (47, 20), (10, 5), (34, 32), (11, 37), (28, 23), (9, 39), (20, 43), (9, 0), (2, 16), (3, 14), (29, 34), (24, 7), (24, 8), (21, 39), (43, 33), (45, 29), (40, 24), (18, 37), (30, 30), (18, 17), (44, 33), (5, 37), (11, 16), (29, 32), (14, 34), (21, 6), (38, 37), (39, 33), (45, 11), (18, 30), (11, 17), (7, 0), (12, 41), (15, 13), (26, 43), (17, 7), (36, 12), (29, 17), (27, 10), (44, 38), (29, 18), (34, 5), (4, 28), (4, 9), (17, 43), (37, 44), (9, 1), (45, 35), (19, 44), (43, 43), (25, 12), (20, 14), (43, 23), (35, 22), (38, 11), (3, 44), (2, 43), (18, 20), (41, 10), (13, 0), (17, 19), (0, 38), (13, 15), (42, 28), (31, 7), (21, 44), (47, 11), (27, 25), (14, 31), (0, 34), (38, 31), (4, 38), (46, 7), (37, 9), (23, 0), (25, 27), (26, 40), (41, 43), (13, 42), (27, 0), (12, 19), (27, 23), (24, 5), (45, 10), (48, 35), (3, 9), (22, 44), (42, 17), (34, 44), (28, 10), (12, 10), (21, 5), (18, 42), (32, 27), (12, 31), (47, 21), (4, 27), (31, 37), (19, 10), (16, 20), (31, 25), (30, 39), (2, 11), (46, 44), (30, 29), (35, 5), (27, 11), (24, 42), (11, 35), (40, 23), (0, 46), (46, 35), (6, 4), (10, 6), (31, 4), (22, 27), (0, 40), (28, 7), (35, 29), (19, 29), (27, 38), (32, 2), (39, 7), (5, 20), (41, 34), (10, 2), (43, 15), (45, 38), (24, 16), (14, 40), (19, 1), (30, 43), (21, 40), (8, 37), (8, 30), (27, 8), (9, 44), (13, 7), (22, 17), (15, 2), (43, 32), (5, 30), (37, 37), (37, 36), (39, 25), (15, 17), (16, 9), (7, 46), (10, 43), (23, 40), (40, 30), (40, 28), (28, 46), (47, 37), (6, 9), (12, 23), (41, 20), (10, 46), (45, 30), (6, 40), (0, 18), (23, 24), (32, 9), (21, 17), (29, 2), (44, 7), (38, 4), (12, 29), (35, 34), (43, 3), (47, 36), (21, 37), (19, 25), (6, 24), (0, 35), (2, 21), (32, 33), (39, 34), (46, 27), (15, 23), (16, 36), (27, 6), (25, 1), (17, 40), (13, 30), (37, 25), (2, 13), (17, 46), (1, 17), (5, 16), (8, 22), (44, 23), (43, 20), (31, 22), (19, 35), (18, 13), (18, 1), (43, 16), (20, 46), (19, 6), (22, 36), (16, 14), (37, 41), (0, 3), (45, 20), (7, 12), (12, 37), (34, 38), (22, 10), (18, 43), (4, 5), (3, 39), (13, 1), (39, 15), (34, 34), (2, 14), (33, 44), (45, 45), (41, 35), (48, 1), (13, 8), (9, 17), (16, 12), (13, 18), (42, 35), (46, 0), (35, 39), (15, 1), (38, 17), (16, 40), (25, 8), (21, 11), (21, 28), (31, 43), (22, 29), (44, 15), (35, 41), (30, 8), (13, 27), (24, 23), (33, 38), (30, 36), (46, 18), (42, 8), (45, 42), (5, 36), (13, 40), (43, 36), (37, 24), (15, 11), (46, 28), (30, 35), (18, 29), (30, 38), (2, 33), (7, 39), (26, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 30), (42, 33), (9, 40), (42, 34), (8, 12), (30, 26), (21, 10), (16, 10), (30, 19), (45, 20), (43, 38), (6, 25), (24, 35), (18, 9), (5, 15), (22, 37), (3, 3), (11, 26), (0, 27), (39, 4), (14, 34), (2, 20), (17, 1), (4, 31), (28, 28), (17, 23), (1, 25), (1, 27), (36, 3), (29, 32), (28, 16), (37, 34), (35, 10), (18, 29), (10, 6), (29, 6), (7, 14), (39, 36), (26, 41), (17, 33), (18, 27), (25, 1), (34, 21), (30, 12), (8, 14), (23, 10), (14, 8), (43, 35), (33, 41), (43, 25), (11, 40), (13, 32), (13, 26), (13, 33), (20, 32), (17, 13), (37, 29), (36, 25), (2, 1), (9, 6), (23, 37), (8, 34), (27, 23), (37, 39), (7, 6), (22, 16), (1, 14), (41, 27), (3, 13), (46, 11), (19, 9), (12, 12), (33, 11), (36, 26), (18, 28), (32, 15), (14, 1), (25, 41), (38, 36), (39, 0), (41, 9), (29, 2), (32, 39), (28, 37), (36, 33), (27, 22), (2, 22), (46, 1), (10, 5), (42, 9), (14, 17), (1, 12), (43, 7), (45, 6), (21, 6), (15, 3), (16, 41), (29, 33), (9, 12), (37, 7), (39, 37), (41, 33), (22, 22), (12, 2), (36, 1), (3, 41), (40, 35), (25, 12), (12, 39), (44, 10), (18, 3), (4, 3), (11, 5), (15, 4), (34, 35), (7, 37), (15, 5), (13, 5), (15, 14), (12, 23), (33, 40), (3, 39), (19, 32), (25, 38), (33, 36), (45, 39), (15, 25), (28, 30), (15, 2), (8, 4), (0, 40), (15, 23), (36, 27), (29, 28), (44, 32), (33, 20), (28, 24), (4, 21), (9, 9), (7, 39), (30, 9), (13, 40), (26, 15), (30, 41), (27, 12), (16, 11), (6, 36), (26, 18), (39, 28), (18, 11), (1, 24), (34, 9), (15, 13), (29, 20), (18, 21), (24, 14), (36, 22), (17, 41), (6, 30), (1, 26), (17, 6), (34, 19), (17, 5), (41, 16), (1, 29), (4, 24), (19, 22), (32, 23), (22, 31), (12, 38), (25, 23), (16, 39), (8, 33), (24, 3), (7, 8), (10, 18), (10, 25), (24, 2), (7, 4), (26, 0), (12, 17), (36, 34), (46, 3), (28, 32), (40, 31), (27, 4), (30, 3), (36, 38), (1, 6), (7, 24), (24, 33), (9, 38), (20, 16), (20, 36), (45, 26), (22, 1), (11, 18), (5, 27), (0, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 16), (0, 39), (19, 11), (27, 24), (28, 14), (21, 7), (40, 13), (37, 15), (33, 28), (22, 35), (15, 11), (6, 36), (27, 9), (3, 10), (21, 26), (3, 4), (38, 17), (5, 40), (27, 25), (0, 5), (37, 2), (23, 14), (4, 43), (26, 39), (4, 42), (25, 32), (12, 24), (14, 10), (38, 0), (13, 46), (19, 44), (21, 20), (19, 6), (35, 25), (24, 18), (23, 25), (12, 6), (15, 42), (28, 43), (14, 41), (5, 11), (3, 27), (28, 37), (13, 11), (6, 24), (25, 37), (8, 35), (23, 2), (31, 18), (30, 24), (4, 6), (2, 45), (7, 16), (39, 12), (19, 1), (38, 11), (3, 28), (41, 13), (32, 30), (11, 35), (27, 11), (5, 34), (13, 36), (27, 30), (37, 3), (31, 46), (7, 13), (40, 43), (38, 27), (40, 17), (26, 47), (33, 2), (12, 40), (38, 39), (4, 15), (30, 37), (21, 27), (41, 16), (19, 32), (35, 44), (34, 13), (34, 26), (19, 28), (4, 14), (19, 8), (11, 2), (13, 37), (0, 38), (0, 45), (29, 1), (12, 15), (19, 40), (33, 44), (19, 46), (7, 23), (2, 40), (23, 45), (29, 45), (25, 17), (30, 32), (18, 32), (23, 12), (2, 14), (30, 17), (10, 14), (12, 9), (18, 37), (11, 30), (37, 24), (27, 45), (26, 36), (25, 27), (8, 40), (24, 16), (33, 33), (39, 15), (35, 42), (36, 2), (10, 2), (28, 32), (15, 18), (34, 44), (25, 3), (39, 4), (13, 0), (29, 33), (6, 20), (0, 14), (12, 17), (6, 2), (13, 4), (35, 46), (13, 33), (41, 30), (34, 43), (6, 44), (18, 15), (11, 1), (37, 5), (12, 23), (18, 43), (15, 38), (16, 43), (37, 13), (22, 12), (11, 18), (31, 13), (10, 26), (0, 25), (31, 11), (41, 10), (20, 5), (5, 35), (16, 10), (19, 7), (31, 17), (17, 9), (6, 11), (41, 28), (21, 45), (32, 36), (27, 14), (0, 9), (31, 47), (17, 23), (23, 1), (20, 39), (14, 7), (38, 47), (35, 34), (26, 16), (3, 30), (3, 12), (32, 37), (0, 21), (38, 10), (26, 11), (38, 43), (23, 21), (27, 18), (7, 25), (30, 8), (29, 14), (30, 30), (16, 13), (14, 9), (38, 32), (18, 40), (24, 10), (23, 30), (13, 39), (41, 5), (21, 22), (14, 25), (5, 44), (18, 28), (19, 38), (23, 40), (1, 10), (23, 10), (27, 36), (18, 35), (33, 11), (41, 18), (10, 44), (7, 30), (36, 23), (5, 45), (22, 5), (14, 4), (33, 30), (38, 12), (35, 14), (35, 3), (29, 12), (20, 34), (20, 20), (20, 19), (29, 28), (15, 15), (29, 10), (11, 29), (0, 40), (15, 40), (16, 18), (1, 18), (37, 4), (2, 0), (7, 22), (7, 27), (10, 36), (8, 1), (30, 46), (15, 13), (41, 2), (38, 23), (19, 17), (38, 41), (1, 41), (32, 10), (23, 37), (28, 24), (4, 2), (37, 7), (7, 39), (25, 0), (3, 40), (18, 18), (22, 28), (40, 42), (31, 22), (5, 17), (1, 6), (3, 26), (28, 17), (1, 3), (9, 11), (35, 6), (16, 32), (13, 30), (40, 30), (25, 22), (2, 27), (31, 36), (15, 36), (17, 21), (13, 7), (11, 31), (21, 33), (9, 16), (14, 46), (31, 27), (38, 40), (6, 39), (38, 44), (8, 28), (27, 40), (22, 22), (34, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 6), (4, 26), (24, 25), (33, 41), (37, 36), (26, 32), (3, 19), (28, 34), (26, 31), (13, 29), (6, 19), (28, 22), (13, 0), (31, 0), (7, 31), (6, 37), (25, 12), (16, 33), (3, 34), (38, 23), (20, 26), (22, 30), (6, 3), (0, 13), (24, 14), (2, 36), (5, 33), (8, 6), (15, 20), (25, 5), (20, 41), (26, 34), (9, 31), (24, 6), (23, 27), (23, 39), (8, 13), (32, 10), (34, 20), (16, 11), (14, 2), (18, 28), (19, 6), (20, 10), (30, 2), (22, 14), (34, 9), (3, 9), (11, 10), (28, 10), (37, 24), (36, 15), (16, 30), (4, 28), (1, 27), (24, 15), (18, 24), (15, 15), (15, 8), (37, 3), (22, 26), (39, 19), (39, 14), (8, 23), (8, 8), (39, 13), (3, 17), (36, 42), (22, 28), (23, 18), (28, 28), (26, 28), (25, 38), (8, 40), (24, 18), (38, 12), (15, 23), (28, 19), (13, 22), (38, 31), (27, 7), (30, 39), (31, 10), (10, 37), (31, 31), (31, 35), (5, 0), (17, 14), (17, 9), (10, 10), (34, 27), (23, 33), (40, 38), (12, 41), (25, 13), (32, 25), (39, 11), (8, 35), (6, 31), (8, 15), (15, 30), (19, 5), (4, 16), (40, 40), (18, 6), (32, 1), (23, 9), (31, 6), (33, 6), (26, 5), (31, 42), (20, 20), (13, 18), (29, 41), (22, 1), (2, 8), (11, 25), (14, 20), (2, 33), (24, 0), (21, 8), (16, 38), (39, 41), (10, 3), (1, 23), (28, 4), (39, 9), (4, 22), (40, 3), (23, 19), (8, 38), (31, 3), (26, 27), (27, 10), (6, 33), (20, 16), (10, 31), (21, 25), (35, 40), (40, 39), (23, 11), (21, 21), (39, 17), (18, 23), (20, 36), (23, 8), (30, 6), (30, 21), (1, 26), (34, 42), (26, 33), (40, 29), (27, 27), (12, 8), (17, 23), (39, 3), (36, 19), (10, 7), (33, 36), (29, 29), (29, 3), (7, 9), (16, 10), (38, 3), (19, 34), (11, 32), (13, 20), (12, 22), (33, 37), (40, 16), (8, 21), (29, 34), (6, 39), (11, 16), (32, 3), (26, 21), (12, 11), (2, 26), (12, 26), (0, 7), (2, 24), (29, 18), (35, 13), (30, 8), (12, 4), (37, 37), (26, 22), (5, 36), (40, 26), (14, 39), (9, 19), (32, 42), (20, 29), (17, 19), (4, 23), (35, 9), (3, 32), (20, 24), (11, 28), (12, 0), (33, 39), (13, 24), (24, 19), (24, 29), (33, 16), (10, 5), (8, 22), (9, 5), (32, 41), (0, 28), (30, 24), (18, 10), (13, 21), (36, 35), (6, 6), (5, 35), (15, 32), (34, 13), (2, 3), (22, 32), (37, 40), (18, 20), (40, 13), (38, 39), (3, 35), (17, 40), (1, 7), (8, 37), (17, 6), (6, 11), (26, 25), (10, 11), (28, 38), (6, 7), (17, 15), (34, 36), (29, 16), (6, 13), (5, 15), (35, 1), (2, 20), (0, 19), (17, 36), (5, 23), (5, 5), (1, 8), (40, 4), (24, 37), (31, 9), (28, 40), (35, 24), (10, 32), (36, 4), (8, 9), (31, 18), (39, 10), (26, 26), (23, 30), (3, 6), (22, 31), (3, 15), (7, 5), (40, 10), (25, 15), (25, 33), (38, 21), (17, 10), (21, 31), (9, 0), (25, 31), (13, 25), (39, 1), (21, 26), (40, 27), (13, 30), (16, 28), (16, 25), (24, 3), (38, 35), (14, 38), (33, 7), (34, 14), (33, 13), (25, 34), (7, 35), (12, 31), (13, 37), (20, 9), (12, 30), (22, 38), (20, 27), (3, 36), (34, 8), (14, 5), (28, 29), (13, 33), (33, 14), (31, 22), (38, 38), (16, 17), (2, 11), (8, 3), (8, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 4), (13, 2), (7, 7), (12, 20), (19, 0), (13, 16), (29, 20), (30, 38), (39, 22), (39, 25), (14, 9), (39, 34), (15, 23), (24, 24), (20, 35), (33, 31), (34, 10), (9, 8), (16, 38), (6, 37), (9, 38), (16, 24), (28, 5), (3, 19), (9, 16), (8, 19), (20, 32), (8, 27), (27, 5), (15, 29), (22, 10), (17, 18), (1, 14), (13, 6), (29, 16), (24, 36), (1, 6), (29, 3), (4, 6), (17, 33), (33, 8), (39, 29), (21, 15), (11, 31), (11, 10), (9, 32), (5, 11), (24, 16), (18, 25), (5, 39), (6, 16), (22, 35), (6, 26), (36, 0), (38, 5), (36, 21), (29, 21), (31, 35), (0, 9), (10, 34), (38, 39), (1, 25), (5, 35), (0, 12), (39, 16), (8, 18), (37, 7), (15, 14), (31, 34), (23, 4), (11, 25), (5, 29), (37, 27), (10, 5), (19, 23), (34, 38), (23, 16), (8, 22), (15, 32), (23, 2), (18, 39), (39, 23), (7, 14), (17, 37), (26, 17), (9, 30), (13, 10), (24, 11), (25, 10), (5, 5), (0, 17), (36, 11), (38, 35), (28, 2), (7, 30), (36, 20), (33, 9), (6, 0), (18, 32), (15, 10), (33, 7), (3, 18), (0, 3), (14, 5), (2, 1), (0, 1), (5, 38), (19, 25), (4, 11), (7, 1), (9, 37), (39, 28), (12, 19), (29, 19), (24, 12), (17, 9), (37, 16), (27, 27), (33, 6), (31, 19), (38, 23), (11, 29), (37, 18), (11, 18), (35, 5), (20, 24), (20, 4), (9, 18), (27, 38), (33, 12), (7, 5), (23, 5), (6, 31), (37, 9), (27, 0), (16, 30), (4, 15), (17, 7), (22, 20), (7, 32), (1, 17), (20, 37), (26, 18), (26, 2), (2, 29), (3, 36), (38, 0), (35, 0), (5, 27), (0, 34), (27, 2), (8, 11), (36, 18), (0, 16), (35, 16), (25, 14), (3, 30), (22, 8), (0, 38), (13, 32), (18, 18), (39, 6), (16, 12), (30, 28), (22, 2), (31, 33), (15, 5), (15, 3), (33, 19), (16, 6), (9, 2), (1, 2), (22, 27), (38, 13), (4, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 23), (4, 12), (6, 21), (25, 24), (22, 31), (6, 6), (14, 10), (31, 7), (42, 10), (20, 11), (23, 35), (14, 14), (27, 41), (4, 8), (19, 24), (20, 31), (28, 3), (14, 24), (3, 4), (42, 7), (15, 5), (5, 15), (7, 18), (10, 29), (20, 19), (41, 32), (41, 7), (41, 6), (19, 1), (9, 32), (40, 29), (6, 41), (18, 16), (40, 32), (1, 9), (7, 35), (27, 14), (41, 34), (26, 15), (6, 39), (19, 31), (0, 5), (5, 30), (18, 5), (24, 3), (1, 17), (30, 30), (26, 30), (36, 4), (3, 23), (36, 20), (30, 24), (14, 7), (11, 39), (33, 19), (20, 27), (18, 9), (35, 31), (38, 33), (16, 1), (37, 33), (20, 9), (32, 0), (11, 32), (34, 18), (25, 19), (3, 10), (28, 10), (41, 9), (9, 21), (19, 26), (8, 23), (15, 42), (35, 40), (10, 0), (1, 20), (23, 18), (6, 30), (35, 19), (14, 9), (13, 35), (9, 37), (20, 8), (4, 6), (38, 5), (0, 23), (29, 21), (33, 27), (5, 7), (31, 41), (18, 23), (17, 21), (13, 9), (11, 16), (36, 23), (5, 12), (21, 43), (13, 37), (12, 25), (27, 27), (19, 3), (17, 43), (20, 2), (12, 26), (30, 21), (24, 25), (16, 18), (28, 0), (13, 26), (19, 16), (26, 3), (9, 15), (25, 12), (35, 5), (29, 14), (6, 4), (32, 4), (20, 28), (11, 30), (6, 1), (6, 3), (37, 32), (24, 27), (2, 8), (14, 8), (6, 9), (16, 38), (32, 26), (10, 31), (36, 13), (17, 37), (34, 38), (35, 23), (22, 24), (11, 23), (11, 7), (26, 35), (7, 33), (18, 36), (5, 42), (32, 16), (28, 40), (10, 3), (3, 41), (35, 24), (33, 13), (22, 25), (24, 28), (10, 38), (14, 11), (39, 9), (10, 43), (27, 6), (22, 32), (1, 5), (36, 18), (6, 31), (25, 42), (34, 17), (27, 26), (38, 3), (39, 16), (21, 22), (16, 7), (13, 13), (7, 27), (18, 25), (39, 42), (34, 40), (1, 41), (13, 34), (9, 20), (41, 4), (26, 39), (37, 22), (22, 28), (3, 25), (42, 1), (0, 24), (5, 10), (5, 40), (16, 22), (2, 5), (4, 15), (3, 38), (39, 30), (18, 35), (2, 6), (14, 41), (30, 25), (7, 14), (41, 24), (29, 27), (1, 39), (25, 25), (37, 25), (13, 41), (36, 27), (24, 39), (4, 11), (18, 43), (4, 10), (35, 39), (22, 0), (40, 19), (26, 34), (39, 7), (12, 6), (15, 31), (35, 12), (34, 27), (40, 17), (18, 30), (36, 30), (11, 27), (22, 33), (5, 25), (22, 30), (14, 36), (12, 4), (8, 34), (35, 28), (33, 16), (6, 7), (2, 41), (22, 43), (6, 14), (12, 11), (23, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 10), (34, 12), (21, 20), (24, 20), (5, 19), (22, 12), (34, 36), (8, 33), (1, 13), (13, 16), (28, 26), (24, 26), (9, 17), (14, 31), (10, 38), (14, 8), (36, 32), (40, 21), (21, 42), (25, 5), (35, 28), (25, 41), (14, 5), (6, 19), (7, 17), (10, 10), (13, 38), (17, 1), (37, 12), (33, 30), (42, 33), (20, 21), (39, 38), (43, 23), (28, 36), (18, 39), (39, 43), (10, 26), (22, 8), (23, 9), (37, 23), (37, 6), (38, 34), (18, 31), (20, 17), (34, 7), (3, 5), (23, 35), (34, 28), (18, 42), (38, 2), (1, 32), (31, 9), (10, 42), (15, 17), (35, 27), (39, 6), (6, 42), (10, 19), (16, 9), (24, 43), (38, 3), (44, 17), (36, 33), (2, 26), (40, 1), (26, 35), (18, 41), (4, 24), (19, 27), (2, 32), (43, 19), (20, 16), (12, 31), (9, 20), (36, 21), (5, 22), (33, 36), (0, 42), (23, 15), (37, 16), (21, 27), (38, 41), (12, 32), (28, 41), (12, 14), (0, 6), (26, 2), (7, 35), (12, 35), (15, 42), (43, 25), (0, 4), (9, 36), (44, 5), (43, 0), (30, 43), (3, 1), (5, 38), (13, 3), (34, 8), (16, 15), (23, 21), (15, 30), (11, 19), (5, 3), (2, 12), (32, 20), (23, 1), (22, 38), (14, 13), (34, 41), (35, 3), (9, 19), (29, 35), (4, 31), (37, 3), (37, 38), (7, 30), (41, 14), (13, 13), (28, 1), (30, 37), (6, 41), (11, 40), (6, 8), (26, 38), (22, 13), (0, 14), (17, 19), (13, 24), (38, 4), (35, 33), (24, 3), (5, 8), (10, 41), (12, 33), (40, 33), (36, 4), (0, 8), (3, 4), (5, 17), (5, 41), (27, 4), (40, 36), (9, 37), (12, 8), (42, 18), (24, 9), (26, 1), (42, 37), (28, 12), (17, 30), (24, 29), (43, 20), (10, 25), (14, 43), (34, 6), (9, 32), (24, 15), (12, 23), (5, 20), (27, 35), (43, 16), (9, 18), (3, 31), (42, 11), (36, 0), (14, 10), (1, 0), (40, 5), (26, 23), (6, 25), (18, 16), (29, 19), (12, 6), (7, 12), (42, 28), (1, 34), (17, 25), (10, 8), (35, 25), (19, 31), (41, 16), (20, 12), (15, 7), (32, 0), (25, 39), (10, 33), (33, 5), (26, 37), (15, 15), (12, 27), (44, 8), (30, 29), (27, 39), (11, 3), (16, 24), (40, 40), (28, 30), (22, 14), (42, 19), (31, 16), (5, 25), (1, 33), (21, 30), (43, 31), (7, 22), (38, 38), (13, 34), (7, 34), (41, 2), (37, 14), (18, 28), (17, 8), (38, 11), (33, 38), (28, 11), (3, 34), (37, 2), (15, 19), (20, 5), (1, 22), (1, 15), (15, 9), (33, 28), (14, 32), (28, 18), (32, 17), (21, 29), (8, 41), (20, 30), (22, 15), (27, 14), (7, 5), (24, 37), (31, 6), (8, 10), (30, 20), (44, 41), (36, 34), (36, 23), (33, 29), (34, 27), (42, 26), (22, 19), (21, 32), (9, 25), (38, 37), (4, 23), (8, 8), (18, 32), (22, 35), (0, 32), (7, 24), (11, 26), (37, 32), (0, 15), (30, 1), (11, 1), (19, 1), (35, 43), (20, 13), (6, 27), (7, 6), (38, 6), (2, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 2), (17, 6), (42, 5), (32, 9), (0, 22), (40, 9), (5, 10), (11, 21), (24, 0), (27, 31), (8, 41), (38, 1), (1, 36), (19, 14), (0, 31), (31, 11), (24, 21), (39, 35), (10, 12), (22, 1), (24, 25), (15, 11), (9, 1), (41, 10), (35, 31), (34, 21), (0, 9), (30, 27), (14, 40), (10, 30), (41, 39), (0, 19), (24, 40), (7, 9), (36, 11), (24, 29), (38, 10), (14, 34), (27, 41), (9, 21), (18, 36), (22, 6), (15, 22), (11, 13), (11, 1), (6, 5), (32, 12), (33, 41), (43, 20), (35, 29), (12, 17), (24, 36), (32, 11), (35, 38), (31, 41), (33, 35), (37, 37), (21, 1), (40, 4), (30, 8), (42, 29), (3, 33), (29, 31), (28, 16), (20, 25), (5, 7), (42, 11), (15, 14), (27, 36), (25, 11), (19, 29), (11, 20), (20, 11), (10, 17), (10, 26), (12, 22), (13, 31), (39, 11), (26, 11), (3, 31), (3, 16), (0, 18), (11, 41), (24, 17), (2, 40), (2, 14), (21, 35), (30, 41), (17, 37), (32, 2), (8, 2), (41, 41), (33, 21), (14, 35), (6, 33), (31, 10), (13, 17), (26, 23), (41, 5), (29, 16), (30, 33), (1, 31), (29, 39), (10, 18), (5, 17), (27, 22), (7, 28), (26, 19), (5, 26), (15, 38), (41, 18), (37, 32), (25, 12), (7, 39), (38, 41), (11, 39), (22, 29), (43, 27), (16, 4), (41, 15), (43, 25), (14, 39), (40, 29), (40, 11), (1, 35), (20, 33), (2, 30), (13, 29), (8, 3), (39, 25), (1, 32), (38, 30), (43, 21), (26, 39), (0, 40), (33, 5), (9, 15), (9, 4), (5, 38), (21, 27), (2, 33), (23, 24), (18, 28), (8, 16), (13, 38), (41, 16), (31, 40), (25, 32), (33, 1), (31, 17), (35, 0), (23, 38), (18, 41), (34, 16), (10, 2), (15, 24), (12, 13), (18, 34), (33, 33), (25, 5), (37, 14), (32, 28), (38, 27), (17, 3), (42, 16), (2, 20), (38, 11), (26, 29), (28, 12), (17, 25), (13, 33), (2, 9), (13, 15), (27, 32), (29, 17), (21, 23), (9, 38), (1, 21), (35, 18), (2, 19), (36, 37), (1, 4), (33, 0), (36, 9), (36, 31), (7, 0), (14, 10), (35, 10), (15, 39), (2, 29), (7, 18), (3, 29), (3, 14), (41, 14), (10, 21), (22, 27), (37, 22), (18, 25), (5, 4), (32, 41), (33, 3), (24, 14), (43, 18), (34, 28), (7, 19), (10, 25), (30, 29), (38, 6), (22, 9), (14, 9), (9, 20), (35, 12), (27, 15), (42, 14), (32, 1), (8, 32), (0, 17), (18, 27), (22, 13), (38, 8), (27, 5), (6, 34), (14, 1), (12, 2), (11, 18), (38, 37), (4, 35), (6, 29), (23, 37), (28, 11), (7, 20), (30, 17), (13, 0), (40, 30), (25, 10), (19, 41), (34, 27), (40, 12), (41, 26), (41, 22), (18, 11), (43, 3), (19, 23), (0, 41), (36, 22), (17, 17), (30, 11), (38, 4), (15, 15), (0, 36), (40, 8), (3, 34), (13, 21), (43, 5), (10, 29), (24, 35), (11, 7), (11, 26), (32, 33), (16, 14), (4, 9), (8, 27), (2, 37), (18, 4), (1, 15), (14, 32), (21, 30), (42, 39), (33, 32), (24, 26), (29, 10), (31, 9), (31, 26), (2, 15), (10, 6), (20, 36), (22, 37), (18, 3), (22, 34), (36, 30), (11, 0), (14, 28), (3, 35), (41, 11), (27, 16), (27, 2), (8, 29), (23, 3), (17, 2), (38, 35), (13, 19), (20, 0), (30, 26), (1, 10), (41, 4), (23, 23), (7, 35), (38, 29), (3, 9), (2, 38), (24, 33), (22, 35), (28, 30), (20, 28), (32, 0), (28, 15), (41, 32), (0, 27), (26, 35), (17, 21), (42, 40), (29, 18), (4, 24), (36, 1), (21, 3), (8, 33), (39, 40), (29, 29), (42, 1), (36, 14), (1, 28), (30, 37), (16, 2), (16, 6), (12, 37), (23, 4), (8, 20), (25, 31), (20, 18), (13, 27), (22, 21), (4, 3), (12, 9), (5, 22), (11, 36), (34, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 12), (16, 41), (40, 30), (8, 2), (21, 44), (30, 0), (10, 19), (23, 19), (27, 42), (6, 39), (31, 37), (4, 14), (20, 42), (1, 2), (34, 36), (31, 36), (2, 13), (26, 44), (11, 15), (2, 37), (11, 37), (41, 33), (5, 5), (13, 34), (0, 38), (7, 15), (33, 15), (41, 43), (37, 41), (15, 11), (6, 32), (15, 13), (15, 39), (34, 12), (34, 38), (20, 27), (13, 27), (25, 42), (0, 39), (38, 33), (6, 27), (23, 31), (33, 20), (4, 5), (25, 27), (3, 26), (32, 5), (34, 37), (3, 18), (41, 20), (34, 22), (0, 44), (38, 17), (33, 16), (34, 3), (41, 16), (9, 0), (6, 1), (35, 22), (3, 11), (40, 41), (41, 8), (12, 18), (28, 17), (24, 1), (22, 26), (11, 41), (41, 38), (32, 2), (22, 0), (26, 1), (40, 23), (20, 29), (32, 36), (15, 41), (22, 5), (7, 11), (34, 7), (10, 7), (15, 35), (16, 17), (27, 6), (13, 41), (8, 14), (27, 26), (29, 8), (7, 23), (37, 38), (33, 45), (20, 0), (8, 4), (14, 6), (5, 17), (17, 20), (30, 22), (39, 33), (15, 17), (39, 1), (5, 10), (24, 43), (39, 17), (28, 32), (21, 37), (7, 19), (25, 3), (14, 15), (28, 36), (15, 31), (32, 26), (25, 16), (28, 45), (22, 2), (29, 34), (26, 17), (7, 18), (17, 42), (12, 32), (6, 3), (6, 29), (19, 40), (10, 3), (26, 22), (13, 45), (22, 4), (13, 36), (4, 28), (8, 23), (2, 25), (34, 30), (33, 43), (1, 21), (9, 21), (13, 43), (36, 4), (30, 44), (4, 43), (39, 44), (1, 6), (25, 40), (24, 39), (12, 27), (37, 17), (35, 13), (21, 17), (15, 29), (4, 44), (37, 11), (2, 1), (34, 8), (37, 37), (11, 18), (3, 44), (25, 23), (12, 10), (34, 44), (4, 36), (8, 39), (28, 25), (23, 26), (1, 27), (27, 39), (27, 17), (0, 10), (9, 14), (7, 14), (13, 7), (27, 43), (24, 22), (9, 12), (9, 7), (16, 44), (16, 39), (33, 1), (21, 13), (38, 37), (1, 36), (30, 8), (17, 41), (0, 4), (7, 46), (4, 29), (25, 24), (33, 42), (36, 21), (27, 24), (29, 20), (29, 4), (14, 20), (12, 31), (16, 28), (11, 5), (20, 10), (19, 37), (11, 3), (5, 20), (36, 25), (18, 38), (12, 22), (7, 28), (37, 9), (20, 30), (36, 27), (7, 22), (27, 31), (37, 1), (18, 9), (12, 19), (24, 5), (8, 27), (2, 19), (40, 32), (17, 34), (38, 14), (11, 19), (7, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 30), (12, 34), (29, 32), (48, 6), (8, 16), (12, 12), (39, 25), (42, 37), (45, 18), (21, 15), (45, 15), (25, 22), (26, 11), (27, 36), (25, 12), (37, 16), (14, 11), (15, 33), (17, 0), (18, 24), (44, 23), (36, 15), (25, 14), (2, 27), (6, 31), (17, 11), (12, 24), (40, 8), (12, 13), (40, 6), (5, 3), (24, 3), (5, 35), (4, 34), (17, 19), (24, 40), (43, 24), (6, 34), (46, 18), (6, 14), (1, 17), (32, 16), (24, 38), (12, 3), (27, 39), (17, 35), (27, 3), (48, 26), (0, 16), (15, 11), (33, 11), (7, 17), (30, 29), (47, 15), (2, 5), (42, 16), (9, 12), (39, 9), (32, 39), (22, 13), (19, 36), (36, 16), (5, 39), (19, 11), (41, 21), (16, 15), (2, 21), (13, 24), (10, 31), (33, 30), (37, 3), (42, 15), (0, 39), (20, 26), (45, 34), (16, 0), (14, 34), (5, 1), (40, 0), (8, 29), (32, 11), (18, 10), (6, 8), (26, 6), (41, 33), (5, 31), (33, 26), (25, 33), (8, 19), (35, 13), (32, 4), (0, 22), (11, 28), (41, 15), (38, 17), (0, 17), (29, 14), (26, 28), (36, 22), (11, 26), (32, 18), (29, 37), (3, 22), (16, 4), (7, 16), (39, 21), (4, 39), (31, 15), (9, 27), (16, 40), (6, 15), (19, 21), (7, 8), (19, 27), (18, 23), (29, 40), (19, 24), (6, 13), (8, 3), (7, 1), (44, 40), (11, 11), (40, 23), (17, 12), (36, 29), (42, 39), (0, 9), (10, 5), (3, 25), (2, 6), (14, 18), (38, 37), (14, 6), (36, 24), (28, 36), (42, 29), (47, 13), (24, 37), (15, 40), (24, 16), (47, 38), (8, 18), (15, 30), (2, 38), (27, 19), (10, 37), (48, 30), (7, 21), (18, 17), (10, 6), (14, 31), (7, 30), (19, 16), (44, 2), (5, 20), (17, 23), (37, 21), (18, 33), (16, 11), (11, 32), (6, 22), (27, 32), (46, 34), (38, 22), (36, 40), (13, 38), (13, 40), (15, 22), (25, 35), (7, 26), (8, 5), (38, 2), (5, 5), (1, 24), (19, 2), (31, 1), (2, 24), (1, 3), (39, 1), (17, 13), (13, 34), (20, 3), (2, 20), (25, 10), (33, 31), (29, 25), (42, 26), (35, 15), (26, 29), (27, 31), (39, 14), (39, 17), (31, 9), (19, 1), (31, 33), (42, 31), (33, 12), (42, 5), (43, 14), (30, 12), (15, 14), (32, 3), (25, 27), (45, 19), (13, 30), (45, 7), (46, 15), (1, 8), (34, 16), (42, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 13), (10, 35), (23, 3), (25, 1), (27, 35), (31, 1), (21, 15), (31, 25), (4, 37), (20, 1), (6, 24), (6, 0), (19, 30), (1, 32), (22, 38), (4, 34), (3, 33), (17, 14), (14, 7), (29, 28), (25, 6), (34, 25), (3, 36), (31, 33), (30, 4), (23, 25), (34, 35), (26, 25), (11, 8), (11, 37), (28, 35), (37, 38), (20, 6), (28, 9), (10, 5), (2, 18), (6, 28), (7, 7), (3, 5), (35, 36), (2, 31), (30, 25), (18, 2), (8, 12), (21, 10), (5, 32), (2, 34), (16, 22), (16, 25), (9, 20), (36, 22), (36, 19), (13, 37), (35, 21), (10, 21), (22, 31), (12, 11), (12, 16), (15, 25), (13, 21), (22, 6), (16, 38), (12, 19), (9, 26), (12, 39), (16, 8), (5, 37), (30, 13), (18, 31), (14, 9), (39, 10), (18, 21), (18, 4), (30, 17), (19, 23), (31, 24), (14, 33), (7, 0), (4, 16), (38, 18), (9, 19), (32, 11), (37, 27), (16, 7), (26, 23), (37, 3), (31, 39), (37, 25), (4, 27), (16, 2), (37, 12), (6, 5), (11, 24), (31, 35), (17, 15), (27, 14), (29, 21), (32, 21), (38, 30), (7, 18), (25, 39), (29, 29), (35, 22), (17, 13), (3, 13), (2, 25), (18, 33), (22, 20), (25, 5), (3, 16), (34, 23), (9, 30), (23, 29), (16, 13), (30, 22), (30, 32), (26, 12), (9, 39), (19, 21), (6, 39), (24, 7), (17, 18), (18, 39), (35, 9), (34, 20), (18, 10), (24, 15), (0, 21), (34, 1), (18, 5), (28, 29), (21, 21), (29, 15), (37, 5), (28, 4), (31, 22), (2, 39), (29, 13), (15, 40), (31, 8), (11, 1), (2, 12), (4, 20), (22, 4), (9, 36), (37, 13), (19, 1), (34, 0), (24, 4), (5, 2), (21, 7), (19, 25), (19, 31), (18, 34), (34, 31), (27, 5), (23, 9), (33, 40), (20, 31), (19, 9), (37, 29), (15, 2), (32, 38), (36, 39), (6, 25), (20, 0), (22, 30), (39, 16), (23, 22), (33, 35), (17, 2), (20, 26), (7, 40), (9, 1), (15, 27), (21, 18), (20, 3), (11, 31), (20, 11), (11, 19), (32, 36), (6, 34), (24, 29), (6, 8), (32, 27), (27, 25), (1, 1), (8, 3), (32, 0), (11, 0), (0, 23), (7, 20), (34, 4), (33, 0), (2, 0), (38, 10), (33, 11), (27, 29), (22, 24), (25, 38), (38, 19), (7, 19), (11, 17), (10, 20), (35, 23), (2, 1), (9, 2), (39, 32), (11, 16), (32, 20), (17, 27), (3, 15), (3, 27), (31, 18), (5, 0), (39, 28), (27, 8), (11, 27), (39, 2), (3, 40), (3, 0), (25, 27), (15, 1), (26, 33), (36, 8), (29, 34), (33, 27), (22, 3), (27, 21), (39, 8), (17, 30), (21, 35), (24, 17), (28, 7), (5, 33), (12, 14), (36, 27), (19, 5), (20, 7), (31, 23), (6, 11), (32, 22), (13, 39), (12, 36), (28, 31), (8, 40), (0, 31), (28, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 12), (20, 44), (31, 19), (23, 33), (28, 43), (23, 7), (32, 16), (31, 5), (6, 27), (20, 41), (0, 13), (23, 21), (41, 27), (38, 3), (43, 26), (17, 19), (22, 26), (3, 38), (1, 30), (6, 37), (30, 34), (10, 12), (27, 39), (8, 1), (29, 14), (30, 11), (21, 4), (42, 22), (32, 17), (4, 11), (46, 5), (37, 43), (38, 41), (46, 31), (19, 44), (33, 21), (45, 18), (10, 31), (22, 19), (33, 2), (30, 18), (3, 16), (45, 2), (27, 43), (11, 19), (43, 1), (31, 22), (4, 44), (31, 6), (1, 37), (11, 7), (5, 25), (7, 22), (22, 42), (41, 40), (20, 26), (2, 9), (11, 14), (4, 40), (26, 7), (26, 38), (12, 33), (22, 37), (17, 35), (37, 27), (43, 6), (21, 1), (42, 21), (4, 28), (21, 43), (9, 11), (45, 25), (30, 16), (34, 44), (3, 0), (27, 42), (40, 25), (18, 40), (3, 25), (29, 7), (2, 25), (21, 44), (5, 26), (9, 9), (6, 29), (26, 24), (25, 22), (9, 6), (40, 8), (0, 8), (16, 18), (13, 12), (33, 3), (8, 28), (6, 34), (42, 8), (16, 1), (19, 40), (45, 37), (28, 25), (23, 26), (31, 18), (23, 30), (45, 16), (5, 39), (9, 3), (35, 0), (31, 3), (13, 19), (45, 35), (32, 41), (32, 33), (4, 9), (16, 34), (20, 21), (44, 22), (40, 12), (44, 15), (11, 10), (15, 23), (7, 40), (18, 34), (24, 6), (38, 4), (1, 31), (34, 12), (11, 27), (32, 11), (19, 22), (31, 39), (2, 41), (2, 33), (6, 43), (25, 28), (18, 17), (38, 40), (15, 20), (4, 23), (27, 8), (5, 29), (5, 43), (4, 18), (19, 39), (42, 1), (1, 19), (13, 30), (18, 18), (27, 4), (10, 1), (39, 26), (33, 42), (7, 39), (1, 27), (10, 13), (43, 35), (6, 21), (2, 39), (39, 5), (14, 39), (8, 25), (46, 33), (22, 5), (10, 4), (1, 36), (13, 8), (46, 13), (15, 19), (45, 4), (32, 1), (25, 7), (0, 26), (40, 39), (40, 40), (24, 36), (13, 4), (1, 44), (15, 24), (28, 8), (34, 0), (20, 2), (33, 38), (11, 11), (1, 35), (30, 5), (8, 16), (11, 41), (11, 34), (20, 7), (42, 18), (27, 1), (1, 28), (39, 8), (41, 12), (43, 19), (17, 18), (22, 29), (21, 40), (26, 6), (44, 28), (33, 26), (0, 11), (7, 42), (13, 35), (0, 40), (5, 0), (28, 35), (21, 8), (29, 29), (29, 38), (38, 1), (34, 4), (13, 3), (14, 2), (11, 13), (11, 6), (23, 36), (30, 26), (38, 15), (24, 8), (27, 3), (7, 41), (41, 43), (33, 5), (46, 27), (43, 13), (12, 5), (0, 32), (38, 29), (16, 32), (11, 33), (15, 38), (38, 28), (37, 24), (7, 31), (8, 22), (8, 43), (9, 2), (31, 15), (19, 42), (22, 10), (40, 15), (46, 2), (5, 32), (20, 5), (13, 21), (23, 2), (36, 0), (18, 25), (13, 7), (44, 7), (15, 32), (24, 42), (44, 4), (46, 12), (30, 21), (28, 21), (40, 11), (23, 39), (38, 24), (13, 43), (6, 17), (6, 3), (24, 40), (28, 42), (25, 27), (16, 22), (20, 8), (44, 17), (16, 28), (34, 38), (32, 35), (3, 1), (15, 9), (35, 34), (21, 37), (0, 19), (25, 41), (16, 36), (35, 1), (9, 19), (31, 1), (30, 25), (15, 3), (39, 10), (4, 36), (1, 12), (36, 7), (11, 2), (9, 16), (14, 32), (11, 22), (37, 15), (0, 18), (14, 15), (28, 9), (45, 41), (31, 25), (10, 39), (11, 37), (4, 19), (33, 14), (13, 9), (16, 10), (39, 38), (17, 15), (3, 24), (36, 12), (42, 40), (18, 5), (8, 14), (43, 22), (36, 13), (18, 20), (27, 31), (30, 33), (9, 14), (26, 13), (13, 22), (10, 20), (5, 15), (45, 19), (0, 34), (38, 26), (33, 13), (30, 39), (10, 24), (42, 44), (14, 6), (25, 5), (12, 38), (38, 12), (2, 31), (22, 9), (29, 3), (8, 17), (16, 20), (25, 26), (17, 10), (35, 12), (23, 20), (6, 32), (12, 23), (11, 29), (10, 28), (4, 31), (26, 0), (1, 17), (27, 12), (39, 4), (33, 7), (14, 38), (12, 29), (26, 36), (9, 5), (44, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 38), (28, 29), (18, 1), (0, 48), (14, 1), (37, 5), (14, 5), (47, 33), (35, 19), (19, 7), (8, 12), (21, 40), (47, 1), (9, 2), (42, 44), (20, 19), (34, 1), (17, 44), (23, 43), (38, 17), (10, 39), (20, 14), (33, 16), (6, 45), (9, 47), (43, 22), (25, 45), (29, 37), (36, 33), (30, 48), (48, 11), (13, 11), (39, 36), (24, 48), (46, 46), (26, 36), (10, 42), (47, 41), (0, 19), (0, 28), (28, 42), (34, 7), (34, 9), (29, 33), (9, 37), (47, 28), (30, 24), (14, 15), (47, 34), (37, 24), (12, 44), (42, 48), (11, 22), (46, 22), (45, 13), (18, 19), (13, 24), (27, 27), (6, 42), (16, 36), (25, 35), (13, 15), (8, 19), (8, 38), (37, 42), (14, 25), (38, 7), (5, 30), (24, 27), (8, 28), (27, 1), (11, 11), (40, 26), (20, 17), (3, 9), (46, 15), (9, 32), (39, 24), (37, 21), (30, 7), (39, 7), (24, 29), (6, 21), (23, 18), (43, 12), (2, 21), (7, 12), (13, 41), (14, 10), (35, 20), (14, 48), (0, 11), (14, 40), (45, 7), (32, 18), (10, 44), (7, 18), (32, 43), (28, 28), (24, 20), (25, 36), (34, 40), (20, 31), (39, 13), (17, 47), (29, 35), (39, 16), (35, 32), (24, 23), (40, 4), (23, 38), (41, 1), (40, 40), (36, 32), (31, 25), (38, 34), (44, 16), (5, 18), (44, 39), (15, 10), (8, 43), (45, 25), (35, 35), (45, 11), (30, 30), (3, 3), (45, 16), (28, 24), (22, 48), (11, 26), (14, 13), (26, 14), (19, 6), (45, 3), (29, 3), (17, 32), (23, 6), (44, 13), (36, 1), (43, 17), (23, 4), (7, 38), (13, 39), (42, 21), (26, 27), (10, 11), (18, 42), (20, 25), (45, 43), (31, 38), (40, 17), (21, 18), (4, 10), (1, 35), (48, 34), (14, 44), (22, 3), (6, 27), (24, 19), (48, 5), (28, 10), (7, 1), (2, 16), (37, 37), (16, 27), (26, 41), (18, 14), (26, 13), (21, 39), (4, 12), (26, 5), (25, 39), (26, 7), (38, 21), (27, 40), (25, 41), (12, 25), (46, 1), (6, 44), (18, 13), (46, 38), (24, 17), (46, 29), (6, 4), (3, 39), (20, 27), (10, 2), (21, 0), (35, 45), (37, 48), (26, 31), (19, 4), (22, 27), (19, 41), (24, 5), (39, 9), (43, 19), (3, 32), (47, 7), (31, 14), (9, 35), (19, 31), (32, 45), (33, 42), (42, 19), (21, 32), (31, 16), (38, 20), (8, 36), (44, 0), (25, 44), (19, 34), (18, 36), (9, 48), (47, 42), (2, 11), (33, 34), (6, 16), (18, 8), (48, 8), (28, 25), (10, 6), (7, 10), (47, 6), (4, 1), (45, 37), (46, 20), (6, 9), (12, 14), (36, 9), (43, 18), (24, 46), (16, 15), (5, 32), (34, 26), (11, 34), (12, 42), (41, 23), (25, 32), (43, 26), (29, 4), (47, 44), (29, 24), (30, 31), (43, 43), (44, 4), (19, 15), (22, 6), (30, 6), (32, 48), (38, 1), (8, 17), (28, 37), (1, 42), (44, 15), (2, 12), (46, 45), (37, 11), (21, 10), (12, 39), (17, 17), (35, 17), (4, 38), (16, 28), (22, 39), (36, 18), (44, 32), (37, 3), (33, 17), (45, 21), (25, 21), (33, 43), (20, 13), (14, 29), (29, 25), (4, 18), (43, 45), (27, 25), (38, 11), (9, 23), (29, 16), (20, 11), (38, 35), (24, 31), (12, 22), (28, 27), (37, 35), (35, 47), (46, 26), (18, 15), (26, 21), (3, 46), (35, 18), (8, 16), (28, 4), (4, 27), (40, 25), (5, 31), (23, 20), (24, 22), (19, 11), (18, 18), (29, 21), (12, 37), (37, 30), (20, 18), (19, 37), (39, 28), (48, 21), (17, 21), (45, 30), (15, 32), (7, 30), (48, 41), (9, 46), (25, 15), (7, 37), (12, 43), (24, 3), (5, 42), (41, 13), (1, 26), (16, 10), (31, 44), (35, 23), (9, 43), (20, 43), (37, 40), (30, 20), (27, 21), (34, 39), (12, 3), (17, 19), (37, 1), (8, 1), (13, 29), (3, 34), (13, 28), (1, 3), (33, 44), (28, 33), (38, 16), (12, 13), (39, 37), (22, 10), (46, 37), (38, 42), (16, 23), (36, 5), (4, 46), (46, 10), (34, 12), (12, 15), (33, 47), (10, 22), (27, 43), (19, 14), (4, 31), (10, 37), (27, 3), (14, 33), (2, 5), (8, 37), (41, 36), (7, 3), (32, 34), (8, 29), (23, 45), (39, 32), (32, 27), (15, 38), (1, 45), (16, 22), (2, 17), (21, 41), (38, 39), (29, 30), (7, 5), (40, 2), (8, 46), (26, 43), (22, 15), (8, 9), (48, 16), (28, 30), (5, 29), (22, 7), (33, 41), (23, 29), (33, 27), (4, 19), (7, 21), (17, 18), (20, 44), (30, 35), (39, 18), (37, 23), (48, 12), (0, 33), (32, 21), (40, 27), (33, 46), (46, 3), (48, 9), (4, 17), (18, 47), (1, 44), (10, 48), (25, 46), (23, 17), (25, 37), (18, 30), (12, 4), (11, 47), (21, 8), (3, 43), (26, 26), (34, 43), (20, 6), (45, 24), (17, 16), (26, 25), (1, 37), (18, 10), (8, 34), (7, 27), (22, 40), (18, 21), (23, 46), (9, 12), (34, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 41), (20, 35), (39, 28), (37, 0), (28, 29), (3, 19), (20, 26), (26, 13), (14, 4), (8, 44), (27, 5), (2, 33), (0, 2), (33, 1), (36, 18), (15, 3), (25, 17), (19, 10), (4, 18), (39, 0), (8, 25), (17, 41), (25, 37), (13, 15), (12, 1), (16, 31), (29, 9), (8, 1), (35, 14), (7, 31), (40, 5), (20, 6), (3, 27), (31, 9), (32, 2), (29, 26), (6, 29), (31, 14), (40, 7), (15, 38), (36, 20), (37, 22), (8, 29), (0, 7), (11, 43), (13, 7), (1, 28), (7, 25), (15, 11), (22, 35), (21, 10), (32, 35), (41, 5), (40, 1), (8, 6), (20, 21), (15, 15), (37, 14), (6, 1), (30, 18), (28, 38), (16, 12), (29, 15), (31, 44), (13, 39), (5, 2), (20, 36), (30, 28), (26, 11), (42, 4), (14, 22), (26, 20), (29, 23), (28, 21), (26, 28), (42, 30), (28, 19), (42, 24), (18, 24), (37, 17), (10, 23), (17, 32), (14, 30), (17, 22), (3, 7), (15, 40), (12, 12), (8, 11), (2, 43), (13, 0), (1, 20), (3, 40), (15, 10), (36, 6), (15, 44), (25, 5), (39, 22), (32, 26), (13, 41), (40, 23), (32, 7), (16, 27), (35, 8), (26, 16), (16, 14), (38, 0), (27, 32), (10, 36), (36, 21), (19, 20), (7, 22), (19, 31), (38, 6), (16, 18), (14, 21), (19, 26), (34, 42), (10, 30), (24, 12), (24, 24), (17, 26), (13, 32), (24, 44), (20, 7), (18, 25), (40, 2), (31, 40), (6, 11), (34, 38), (21, 18), (5, 28), (35, 24), (25, 10), (9, 8), (43, 19), (8, 4), (39, 6), (12, 23), (20, 38), (0, 40), (16, 36), (36, 22), (19, 25), (22, 34), (24, 36), (5, 4), (35, 39), (2, 3), (14, 33), (3, 35), (36, 7), (35, 25), (15, 6), (41, 40), (41, 6), (10, 38), (5, 43), (12, 43), (32, 3), (30, 11), (4, 12), (26, 40), (5, 9), (18, 33), (18, 18), (22, 0), (21, 16), (28, 10), (18, 13), (1, 32), (2, 32), (34, 0), (39, 18), (4, 38), (15, 30), (9, 22), (14, 37), (24, 19), (8, 40), (11, 23), (4, 4), (9, 7), (26, 35), (3, 3), (13, 44), (28, 17), (26, 43), (29, 18), (1, 31), (10, 33), (3, 34), (3, 21), (17, 15), (12, 32), (4, 24), (7, 11), (24, 42), (13, 31), (13, 3), (13, 12), (21, 17), (42, 34), (20, 33), (32, 20), (32, 38), (1, 21), (35, 36), (42, 29), (42, 7), (24, 33), (3, 25), (27, 0), (12, 34), (0, 37), (14, 24), (42, 37), (31, 2), (29, 40), (21, 25), (6, 27), (3, 30), (38, 36), (4, 31), (33, 2), (25, 7), (35, 42), (33, 36), (28, 22), (33, 20), (2, 8), (10, 43), (18, 6), (19, 15), (1, 0), (23, 1), (12, 37), (30, 9), (21, 38), (9, 37), (1, 29), (41, 26), (8, 2), (24, 16), (7, 1), (25, 44), (29, 5), (14, 39), (2, 44), (16, 24), (0, 27), (43, 3), (10, 24), (39, 12), (42, 44), (17, 40), (40, 19), (8, 43), (20, 2), (33, 11), (2, 34), (4, 13), (30, 41), (27, 27), (6, 38), (13, 40), (25, 41), (19, 38), (34, 44), (6, 5), (11, 15), (33, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 15), (44, 3), (42, 34), (29, 27), (40, 25), (18, 28), (31, 1), (26, 35), (16, 29), (28, 7), (26, 9), (31, 4), (16, 18), (44, 10), (8, 18), (26, 37), (42, 4), (21, 38), (29, 34), (42, 28), (1, 9), (16, 21), (32, 35), (36, 7), (19, 20), (2, 1), (42, 17), (13, 11), (39, 26), (22, 0), (43, 2), (29, 17), (44, 4), (32, 19), (19, 14), (44, 30), (1, 26), (7, 5), (35, 4), (45, 20), (5, 25), (21, 24), (28, 30), (28, 38), (18, 13), (0, 17), (20, 39), (9, 12), (3, 33), (40, 18), (32, 30), (8, 34), (20, 5), (19, 1), (18, 4), (21, 27), (20, 21), (27, 20), (5, 5), (29, 5), (23, 24), (10, 27), (7, 31), (44, 28), (36, 1), (39, 22), (22, 18), (13, 20), (29, 20), (4, 22), (42, 0), (33, 20), (22, 21), (9, 35), (1, 28), (26, 5), (41, 27), (8, 16), (43, 22), (19, 29), (14, 35), (20, 6), (34, 2), (8, 35), (21, 15), (14, 28), (36, 11), (20, 17), (38, 24), (37, 25), (1, 39), (11, 16), (38, 13), (25, 21), (40, 23), (33, 32), (12, 0), (9, 31), (24, 35), (9, 13), (10, 9), (5, 14), (19, 27), (10, 15), (18, 38), (33, 2), (10, 25), (38, 19), (27, 24), (1, 38), (33, 7), (22, 30), (30, 16), (37, 4), (42, 22), (25, 28), (8, 12), (3, 38), (45, 15), (18, 6), (33, 33), (41, 34), (14, 36), (34, 36), (33, 28), (14, 15), (26, 4), (14, 32), (3, 5), (43, 13), (4, 14), (12, 25), (5, 13), (40, 31), (19, 9), (19, 28), (21, 0), (45, 6), (8, 33), (44, 22), (45, 25), (28, 36), (45, 31), (21, 5), (9, 2), (25, 8), (0, 6), (33, 37), (32, 26), (3, 31), (6, 36), (35, 32), (32, 16), (17, 39), (32, 11), (10, 17), (8, 26), (3, 6), (27, 31), (31, 29), (37, 2), (18, 23), (44, 8), (26, 26), (36, 15), (8, 15), (2, 9), (41, 7), (23, 1), (26, 17), (10, 37), (26, 13), (13, 19), (23, 7), (10, 32), (22, 8), (31, 5), (29, 24), (9, 5), (3, 28), (12, 18), (25, 30), (37, 34), (44, 29), (17, 35), (12, 31), (3, 16), (35, 36), (31, 15), (33, 21), (36, 12), (7, 12), (9, 37), (25, 33), (18, 21), (41, 35), (25, 29), (12, 20), (17, 21), (1, 15), (8, 6), (9, 27), (16, 27), (16, 22), (15, 1), (40, 0), (2, 22), (11, 26), (4, 2), (39, 9), (32, 6), (36, 27), (2, 28), (42, 38), (3, 20), (17, 18), (21, 4), (24, 28), (5, 11), (4, 8), (36, 13), (35, 13), (0, 28), (23, 36), (22, 27), (10, 13), (27, 7), (1, 27), (4, 4), (12, 28), (8, 25), (8, 19), (3, 24), (4, 17), (24, 34), (8, 14), (30, 20), (0, 26), (1, 1), (30, 22), (21, 33), (18, 29), (39, 3), (4, 13), (1, 10), (1, 19), (7, 1), (32, 39), (15, 13), (27, 15), (30, 32), (11, 17), (29, 8), (9, 9), (25, 38), (4, 16), (39, 20), (25, 39), (6, 33), (36, 30), (12, 12), (34, 31), (12, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 5), (12, 19), (10, 9), (30, 29), (18, 32), (1, 33), (26, 16), (26, 20), (12, 7), (37, 40), (18, 34), (30, 19), (24, 7), (42, 15), (38, 9), (6, 13), (2, 9), (24, 32), (20, 9), (30, 7), (45, 24), (47, 41), (2, 37), (31, 39), (28, 39), (17, 41), (18, 38), (7, 39), (17, 13), (25, 4), (20, 36), (21, 30), (9, 37), (40, 36), (11, 0), (41, 33), (19, 19), (27, 24), (38, 7), (16, 6), (1, 11), (5, 28), (43, 29), (40, 39), (10, 26), (45, 38), (0, 5), (37, 31), (34, 34), (39, 16), (45, 16), (39, 38), (11, 9), (29, 18), (6, 37), (23, 3), (18, 8), (48, 27), (6, 40), (6, 22), (23, 24), (43, 34), (36, 11), (12, 14), (23, 18), (14, 1), (43, 7), (45, 34), (37, 15), (42, 30), (22, 8), (14, 18), (22, 10), (16, 0), (29, 6), (14, 33), (19, 26), (6, 5), (15, 25), (44, 14), (15, 15), (36, 3), (38, 11), (9, 15), (34, 0), (24, 14), (16, 31), (2, 8), (16, 3), (19, 15), (40, 12), (20, 24), (35, 35), (16, 26), (41, 29), (38, 13), (29, 13), (31, 35), (5, 18), (33, 27), (28, 23), (8, 8), (44, 20), (37, 7), (2, 24), (3, 41), (0, 17), (2, 40), (14, 11), (1, 29), (3, 38), (34, 6), (4, 32), (11, 19), (47, 12), (18, 26), (17, 39), (9, 6), (1, 30), (18, 39), (3, 14), (18, 17), (12, 5), (3, 33), (6, 24), (47, 1), (38, 33), (19, 14), (21, 27), (4, 0), (10, 10), (43, 5), (47, 18), (26, 35), (41, 27), (47, 36), (34, 1), (3, 27), (3, 20), (45, 40), (29, 20), (6, 21), (4, 20), (1, 18), (25, 26), (31, 36), (30, 31), (21, 4), (24, 38), (23, 8), (14, 2), (47, 31), (41, 13), (26, 37), (24, 40), (4, 24), (40, 35), (47, 3), (39, 7), (16, 34), (32, 4), (22, 12), (10, 31), (34, 16), (8, 32), (10, 39), (14, 12), (39, 8), (40, 9), (45, 2), (28, 35), (41, 39), (5, 23), (1, 26), (41, 9), (1, 39), (34, 25), (27, 1), (20, 17), (12, 17), (31, 12), (48, 0), (4, 19), (20, 30), (13, 3), (37, 14), (41, 3), (23, 38), (7, 5), (3, 30), (32, 32), (42, 4), (17, 40), (34, 23), (37, 13), (41, 31), (8, 33), (20, 39), (40, 1), (38, 32), (13, 41), (11, 2), (11, 12), (21, 10), (35, 15), (26, 9), (11, 36), (34, 18), (1, 5), (44, 32), (37, 17), (26, 31), (9, 28), (34, 8), (4, 18), (38, 28), (27, 17), (42, 16), (3, 23), (26, 27), (9, 32), (32, 17), (16, 15), (7, 0), (12, 13), (8, 27), (40, 37), (16, 33), (28, 8), (28, 3), (32, 24), (39, 23), (3, 40), (26, 12), (4, 5), (28, 7), (29, 32), (24, 34), (12, 41), (46, 31), (22, 27), (23, 1), (21, 32), (38, 4), (29, 9), (37, 25), (46, 9), (24, 12), (11, 3), (31, 6), (38, 27), (11, 16), (45, 5), (12, 21), (25, 28), (5, 1), (11, 41), (39, 2), (2, 25), (24, 1), (1, 8), (23, 13), (38, 17), (34, 30), (18, 36), (5, 10), (35, 34), (4, 25), (41, 15), (2, 26), (39, 22), (48, 2), (23, 32), (28, 40), (30, 5), (32, 6), (31, 11), (3, 28), (15, 35), (17, 5), (11, 30), (35, 30), (42, 8), (7, 25), (12, 35), (8, 21), (46, 14), (7, 1), (45, 17), (19, 10), (23, 19), (14, 3), (21, 18), (8, 7), (31, 14), (39, 32), (29, 24), (27, 18), (42, 34), (43, 21), (43, 9), (32, 3), (26, 33), (44, 30), (33, 33), (46, 19), (22, 29), (24, 8), (26, 14), (21, 21), (12, 38), (14, 30), (19, 41), (41, 24), (7, 7), (8, 22), (12, 26), (47, 0), (32, 25), (33, 12), (39, 27), (2, 32), (38, 22), (8, 0), (29, 40), (11, 5), (2, 6), (23, 33), (10, 22), (48, 31), (14, 28), (18, 23), (8, 18), (25, 9), (17, 36), (20, 11), (32, 2), (6, 34), (37, 33), (20, 33), (5, 4), (28, 30), (0, 36), (9, 19), (43, 0), (46, 11), (37, 22), (39, 5), (11, 8), (45, 41), (21, 3), (2, 10), (40, 17), (7, 18), (37, 18), (22, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 25), (38, 5), (2, 40), (5, 7), (31, 18), (2, 41), (32, 3), (11, 12), (22, 39), (40, 7), (35, 33), (23, 10), (14, 19), (2, 24), (15, 43), (12, 32), (11, 40), (21, 21), (32, 6), (8, 22), (3, 25), (28, 43), (2, 39), (14, 24), (32, 33), (35, 19), (22, 34), (40, 8), (37, 8), (33, 31), (4, 3), (4, 25), (37, 4), (38, 13), (5, 35), (24, 24), (5, 40), (22, 30), (21, 33), (18, 43), (40, 20), (19, 39), (29, 11), (28, 33), (24, 27), (35, 24), (6, 23), (17, 13), (6, 20), (9, 32), (21, 12), (2, 30), (9, 9), (40, 39), (17, 23), (14, 35), (10, 32), (4, 33), (7, 9), (25, 35), (12, 0), (27, 37), (8, 17), (6, 26), (13, 40), (15, 27), (30, 18), (0, 30), (23, 31), (19, 32), (3, 39), (6, 19), (6, 11), (33, 23), (21, 1), (1, 28), (37, 35), (2, 10), (27, 8), (16, 26), (37, 41), (17, 42), (9, 34), (27, 30), (23, 34), (20, 36), (37, 2), (35, 36), (25, 5), (34, 21), (15, 29), (31, 3), (39, 36), (18, 2), (19, 42), (14, 31), (9, 26), (15, 19), (18, 29), (20, 1), (18, 4), (30, 13), (2, 29), (19, 27), (12, 22), (30, 23), (36, 8), (0, 41), (32, 8), (13, 11), (10, 0), (36, 3), (13, 32), (16, 23), (15, 20), (7, 8), (35, 13), (14, 36), (26, 38), (25, 36), (39, 5), (33, 28), (8, 39), (4, 42), (22, 9), (1, 9), (5, 19), (1, 24), (6, 9), (31, 6), (3, 28), (14, 32), (26, 36), (9, 3), (16, 7), (16, 33), (2, 22), (17, 9), (4, 37), (3, 32), (36, 15), (14, 42), (4, 4), (26, 31), (31, 31), (27, 0), (23, 2), (38, 26), (38, 20), (10, 34), (20, 41), (35, 20), (16, 4), (7, 2), (4, 10), (30, 26), (11, 15), (6, 16), (7, 40), (27, 13), (13, 6), (10, 7), (22, 28), (32, 30), (5, 8), (24, 36), (16, 11), (3, 35), (2, 13), (12, 12), (36, 6), (24, 10), (8, 43), (4, 13), (34, 18), (1, 20), (29, 10), (1, 26), (38, 25), (15, 22), (20, 8), (23, 27), (31, 30), (27, 41), (24, 34), (22, 41), (5, 13), (0, 33), (35, 31), (15, 37), (15, 7), (26, 0), (13, 42), (26, 5), (31, 9), (22, 37), (34, 17), (21, 38), (26, 1), (31, 33), (32, 18), (33, 14), (24, 37), (3, 27), (10, 5), (11, 20), (38, 4), (0, 10), (19, 25), (4, 22), (7, 10), (5, 41), (32, 16), (26, 10), (40, 1), (18, 25), (32, 10), (6, 0), (3, 0), (29, 7), (18, 27), (8, 21), (9, 40), (8, 5), (19, 1), (37, 27), (15, 0), (4, 0), (3, 15), (32, 32), (2, 6), (0, 35), (0, 6), (21, 42), (39, 10), (30, 0), (9, 10), (7, 1), (26, 13), (26, 26), (29, 38), (18, 17), (19, 21), (16, 22), (2, 37), (10, 14), (32, 35), (21, 35), (37, 28), (35, 27), (8, 10), (11, 27), (25, 38), (36, 20), (12, 10), (0, 9), (10, 35), (13, 17), (20, 21), (32, 31), (28, 42), (5, 10), (6, 33), (25, 34), (21, 30), (15, 32), (36, 18), (23, 37), (33, 34), (30, 6), (30, 39), (17, 11), (28, 3), (7, 18), (28, 9), (23, 12), (6, 39), (15, 6), (14, 1), (22, 29), (38, 12), (15, 33), (5, 43), (31, 8), (23, 30), (2, 34), (23, 28), (8, 28), (25, 32), (19, 4), (20, 35), (18, 39), (22, 42), (27, 18), (25, 37), (32, 29), (15, 16), (17, 36), (15, 17), (16, 43), (22, 7), (25, 15), (14, 6), (34, 27), (19, 6), (21, 29), (11, 14), (30, 30), (10, 21), (0, 16), (25, 11), (5, 11), (31, 13), (8, 27), (0, 20), (1, 33), (40, 41), (16, 9), (18, 8), (18, 30), (2, 27), (7, 12), (5, 6), (25, 12), (17, 31), (39, 2), (31, 28), (5, 21), (36, 12), (19, 28), (17, 8), (40, 14), (6, 24), (35, 14), (22, 5), (11, 18), (28, 6), (33, 21), (2, 11), (23, 39), (17, 40), (19, 3), (40, 21), (8, 23), (38, 39), (15, 30), (39, 39), (37, 11), (27, 20), (7, 19), (32, 25), (30, 7), (29, 18), (25, 8), (24, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 9), (3, 34), (1, 23), (22, 23), (45, 14), (2, 37), (34, 32), (7, 24), (39, 26), (25, 35), (8, 0), (26, 6), (25, 23), (3, 32), (11, 8), (26, 26), (13, 2), (28, 20), (25, 15), (10, 3), (35, 28), (33, 13), (19, 35), (15, 6), (13, 11), (41, 18), (9, 29), (17, 2), (23, 2), (12, 5), (31, 18), (26, 16), (2, 11), (35, 11), (44, 12), (29, 36), (1, 26), (30, 1), (44, 31), (23, 27), (17, 34), (31, 16), (4, 16), (11, 40), (1, 24), (23, 17), (13, 17), (31, 13), (3, 8), (26, 30), (16, 31), (16, 41), (11, 12), (1, 1), (11, 3), (29, 14), (13, 20), (21, 39), (37, 13), (20, 20), (27, 23), (34, 33), (37, 26), (41, 2), (35, 29), (15, 16), (19, 30), (22, 14), (31, 38), (42, 3), (11, 16), (13, 25), (11, 22), (44, 26), (2, 13), (7, 18), (40, 27), (22, 19), (40, 17), (36, 10), (26, 35), (39, 27), (13, 14), (40, 34), (17, 26), (10, 13), (40, 31), (3, 31), (39, 1), (35, 17), (17, 30), (23, 3), (0, 34), (35, 0), (26, 2), (3, 26), (13, 16), (42, 41), (8, 38), (28, 18), (17, 32), (43, 16), (2, 4), (3, 11), (3, 42), (27, 7), (19, 8), (21, 3), (28, 26), (32, 34), (19, 9), (13, 26), (22, 38), (33, 2), (13, 18), (42, 1), (21, 23), (30, 21), (20, 22), (14, 30), (25, 40), (37, 3), (41, 38), (34, 10), (8, 8), (37, 32), (21, 21), (34, 14), (24, 6), (45, 26), (19, 37), (28, 28), (12, 23), (42, 11), (29, 20), (44, 22), (24, 24), (0, 5), (18, 34), (39, 7), (36, 16), (6, 36), (1, 8), (40, 22), (15, 37), (15, 8), (44, 24), (30, 5), (8, 41), (21, 33), (3, 5), (31, 20), (37, 4), (11, 19), (25, 34), (4, 12), (2, 8), (1, 16), (9, 4), (18, 18), (0, 12), (20, 3), (29, 30), (15, 11), (18, 12), (2, 12), (35, 40), (14, 15), (29, 40), (37, 36), (22, 42), (26, 4), (8, 24), (8, 26), (13, 1), (41, 11), (44, 42), (43, 3), (27, 16), (6, 30), (22, 22), (41, 6), (1, 4), (26, 34), (10, 32), (4, 33), (28, 5), (33, 29), (19, 16), (12, 6), (2, 41), (8, 42), (45, 18), (15, 12), (18, 37), (11, 14), (24, 30), (29, 42), (43, 34), (35, 25), (22, 13), (10, 4), (15, 20), (19, 19), (20, 36), (37, 15), (31, 25), (35, 6), (27, 34), (39, 21), (33, 1), (15, 35), (36, 23), (24, 32), (42, 25), (19, 15), (37, 23), (13, 27), (23, 10), (35, 38), (37, 28), (17, 40), (5, 3), (37, 33), (39, 39), (39, 36), (11, 10), (39, 31), (27, 38), (23, 13), (8, 13), (44, 23), (34, 24), (36, 41), (3, 0), (34, 19), (14, 8), (6, 27), (5, 9), (43, 20), (20, 7), (38, 5), (44, 36), (27, 5), (36, 7), (41, 4), (39, 18), (2, 30), (33, 41), (30, 22), (28, 3), (9, 12), (42, 39), (22, 20), (38, 36), (14, 26), (19, 29), (2, 22), (25, 1), (9, 35), (8, 20), (31, 35), (16, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 38), (23, 21), (13, 9), (17, 3), (16, 16), (38, 46), (21, 2), (27, 4), (42, 28), (41, 15), (32, 13), (27, 20), (48, 38), (21, 18), (45, 26), (22, 18), (40, 36), (46, 35), (46, 18), (23, 11), (37, 22), (40, 28), (23, 8), (42, 37), (46, 9), (25, 23), (29, 42), (39, 27), (15, 9), (42, 26), (33, 0), (15, 31), (42, 46), (26, 23), (4, 11), (30, 3), (18, 41), (1, 8), (29, 33), (8, 9), (35, 22), (1, 4), (18, 27), (43, 22), (3, 0), (37, 46), (3, 22), (39, 22), (40, 0), (48, 39), (40, 22), (26, 6), (6, 8), (47, 3), (23, 6), (17, 18), (7, 30), (32, 30), (20, 28), (17, 0), (24, 19), (12, 6), (17, 2), (39, 13), (12, 9), (41, 1), (38, 29), (33, 6), (3, 10), (26, 0), (19, 7), (29, 40), (4, 27), (47, 11), (2, 2), (30, 39), (21, 11), (27, 13), (5, 19), (23, 0), (42, 6), (26, 20), (39, 9), (43, 7), (1, 44), (22, 44), (29, 37), (21, 7), (38, 0), (4, 0), (31, 7), (44, 38), (8, 37), (36, 46), (7, 32), (42, 27), (27, 18), (10, 26), (42, 35), (12, 18), (35, 36), (20, 12), (32, 21), (2, 31), (20, 13), (9, 0), (22, 30), (15, 40), (34, 29), (11, 14), (13, 39), (34, 41), (32, 12), (37, 19), (48, 28), (25, 44), (36, 22), (23, 43), (13, 43), (29, 9), (37, 17), (34, 0), (14, 31), (3, 23), (35, 32), (5, 45), (9, 45), (39, 44), (29, 3), (12, 5), (41, 22), (40, 9), (2, 6), (8, 24), (31, 44), (22, 25), (9, 27), (6, 38), (36, 8), (45, 22), (34, 45), (30, 41), (22, 37), (11, 19), (4, 37), (46, 42), (39, 30), (32, 16), (27, 38), (29, 35), (38, 28), (23, 37), (14, 14), (15, 32), (37, 45), (6, 42), (27, 30), (30, 1), (8, 29), (9, 11), (44, 18), (24, 38), (22, 22), (7, 39), (38, 34), (10, 16), (30, 9), (29, 0), (10, 3), (18, 8), (1, 38), (27, 23), (45, 14), (29, 45), (0, 30), (6, 27), (14, 25), (22, 16), (35, 3), (13, 42), (31, 17), (11, 4), (1, 0), (43, 43), (32, 42), (2, 25), (33, 42), (34, 26), (21, 6), (18, 42), (24, 35), (4, 43), (39, 45), (36, 20), (3, 19), (19, 39), (1, 37), (45, 37), (21, 44), (48, 46), (4, 15), (1, 12), (35, 18), (20, 38), (23, 35), (42, 20), (17, 8), (14, 12), (27, 34), (37, 31), (13, 12), (48, 16), (42, 47), (26, 21), (41, 18), (17, 24), (35, 1), (11, 45), (47, 17), (48, 11), (18, 6), (11, 8), (11, 18), (35, 13), (28, 33), (42, 33), (8, 16), (42, 14), (17, 23), (28, 27), (48, 42), (29, 38), (16, 47), (7, 42), (11, 25), (14, 24), (12, 36), (9, 20), (5, 47), (41, 3), (6, 35), (23, 33), (35, 4), (6, 46), (27, 12), (25, 25), (5, 17), (19, 41), (10, 30), (31, 24), (31, 28), (5, 9), (21, 29), (40, 13), (27, 0), (19, 18), (46, 40), (26, 18), (7, 40), (31, 29), (11, 21), (13, 29), (40, 17), (19, 2), (7, 43), (15, 38), (8, 0), (14, 28), (43, 45), (46, 29), (47, 33), (12, 16), (33, 5), (36, 35), (44, 3), (0, 27), (18, 40), (39, 26), (36, 26), (47, 46), (46, 32), (31, 33), (1, 30), (13, 5), (18, 20), (9, 17), (13, 25), (23, 2), (28, 46), (29, 6), (26, 15), (10, 25), (18, 18), (10, 14), (15, 6), (30, 26), (28, 30), (3, 24), (33, 22), (22, 41), (45, 8), (15, 15), (30, 8), (13, 2), (48, 10), (10, 45), (21, 47), (30, 24), (35, 9), (30, 2), (5, 5), (43, 8), (0, 31), (6, 32), (37, 29), (6, 13), (43, 6), (15, 2), (45, 40), (44, 44), (30, 35), (2, 12), (5, 4), (0, 22), (48, 27), (4, 22), (8, 34), (33, 40), (29, 16), (25, 33), (27, 35), (35, 45), (9, 47), (42, 15), (1, 19), (45, 41), (11, 38), (9, 9), (16, 37), (46, 6), (35, 34), (43, 11), (37, 43), (18, 12), (5, 25), (34, 34), (2, 22), (39, 16), (5, 15), (40, 43), (16, 28), (42, 40), (1, 17), (33, 26), (34, 24), (48, 40), (38, 32), (8, 19), (29, 29), (26, 35), (29, 32), (43, 5), (33, 43), (21, 19), (30, 47), (6, 2), (20, 11), (41, 41), (38, 27), (29, 27), (17, 6), (1, 18), (38, 47), (38, 25), (20, 45), (10, 37), (42, 1), (43, 36), (42, 3), (1, 13), (28, 44), (40, 5), (46, 15), (25, 45), (16, 26), (13, 17), (4, 32), (14, 3), (43, 17), (0, 21), (9, 14), (18, 26), (37, 38), (36, 42), (32, 45), (6, 34), (24, 16), (10, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 32), (21, 2), (31, 11), (10, 22), (38, 32), (16, 26), (1, 29), (17, 36), (3, 11), (12, 11), (27, 39), (37, 41), (32, 4), (0, 26), (18, 8), (14, 22), (23, 3), (28, 6), (6, 27), (34, 30), (33, 7), (28, 36), (15, 5), (16, 21), (2, 25), (37, 27), (24, 42), (9, 6), (23, 40), (25, 5), (28, 8), (7, 13), (1, 16), (2, 20), (35, 13), (11, 42), (34, 35), (30, 9), (24, 14), (4, 30), (25, 0), (39, 10), (26, 34), (19, 41), (36, 14), (25, 41), (39, 3), (24, 11), (33, 27), (8, 41), (14, 27), (36, 35), (27, 26), (5, 10), (18, 15), (9, 1), (25, 8), (23, 27), (10, 40), (1, 38), (27, 32), (18, 6), (36, 20), (1, 1), (7, 31), (10, 33), (15, 31), (0, 8), (28, 16), (21, 9), (0, 36), (23, 6), (25, 24), (40, 16), (27, 29), (28, 23), (6, 4), (21, 41), (2, 2), (23, 31), (2, 32), (1, 20), (29, 25), (29, 14), (6, 9), (39, 32), (13, 15), (0, 23), (18, 0), (5, 6), (4, 28), (30, 15), (14, 32), (10, 5), (29, 2), (15, 12), (27, 40), (5, 42), (27, 3), (0, 3), (10, 28), (8, 37), (8, 1), (39, 38), (23, 20), (34, 37), (23, 33), (25, 17), (16, 8), (26, 2), (16, 16), (5, 30), (16, 34), (12, 21), (21, 11), (2, 26), (4, 36), (21, 40), (7, 42), (16, 14), (30, 13), (15, 24), (22, 41), (12, 42), (37, 0), (32, 0), (16, 19), (26, 12), (12, 16), (7, 17), (31, 17), (21, 7), (22, 2), (27, 8), (36, 21), (38, 36), (32, 6), (10, 24), (23, 5), (33, 4), (28, 26), (3, 36), (12, 1), (5, 19), (16, 17), (25, 4), (20, 20), (34, 5), (40, 38), (3, 22), (39, 23), (20, 13), (6, 2), (7, 30), (20, 15), (17, 17), (35, 23), (3, 6), (20, 17), (10, 18), (38, 38), (3, 38), (39, 41), (21, 36), (39, 16), (8, 13), (17, 0), (29, 11), (0, 27), (21, 35), (21, 30), (8, 33), (35, 35), (25, 13), (20, 6), (13, 11), (30, 42), (16, 0), (14, 19), (19, 23), (7, 14), (16, 5), (11, 26), (19, 5), (7, 9), (28, 34), (35, 27), (11, 1), (34, 36), (1, 6), (1, 21), (19, 38), (34, 20), (4, 0), (18, 35), (2, 24), (36, 23), (25, 7), (9, 32), (16, 39), (21, 26), (22, 32), (36, 38), (7, 7), (3, 12), (26, 28), (30, 32), (34, 23), (35, 39), (17, 27), (31, 13), (40, 6), (34, 9), (28, 0), (6, 40), (4, 21), (40, 19), (9, 28), (6, 37), (27, 21), (6, 3), (39, 36), (9, 41), (17, 7), (19, 40), (29, 3), (29, 36), (1, 22), (31, 41), (30, 34), (5, 27), (36, 12), (6, 8), (33, 10), (35, 31), (31, 5), (10, 29), (39, 0), (20, 33), (27, 10), (14, 35), (35, 30), (4, 41), (14, 14), (27, 18), (0, 21), (12, 17), (16, 38), (36, 0), (25, 14), (22, 39), (33, 42), (20, 32), (30, 33), (27, 33), (13, 30), (12, 12), (21, 42), (14, 28), (30, 18), (19, 25), (3, 3), (3, 13), (10, 31), (4, 19), (29, 8), (9, 40), (3, 17), (23, 9), (4, 18), (40, 27), (24, 17), (23, 21), (17, 9), (1, 12), (34, 17), (3, 1), (10, 26), (10, 7), (5, 12), (29, 13), (0, 18), (11, 36), (14, 30), (20, 22), (14, 8), (40, 28), (2, 12), (32, 18), (13, 36), (14, 4), (30, 39), (23, 35), (39, 18), (32, 36), (10, 34), (16, 30), (40, 39), (2, 22), (36, 7), (26, 41), (6, 1), (13, 41), (20, 25), (31, 39), (28, 4), (12, 14), (25, 28), (26, 3), (19, 21), (20, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 10), (37, 40), (2, 18), (16, 5), (8, 8), (6, 14), (42, 8), (23, 17), (3, 40), (7, 16), (14, 19), (23, 37), (37, 26), (6, 8), (18, 5), (45, 31), (4, 1), (46, 14), (18, 40), (5, 22), (20, 18), (24, 38), (5, 5), (2, 16), (21, 22), (21, 2), (36, 30), (16, 9), (27, 0), (15, 5), (15, 11), (13, 0), (39, 21), (0, 34), (1, 23), (27, 5), (34, 20), (2, 12), (37, 24), (12, 26), (34, 35), (23, 23), (32, 41), (7, 39), (44, 28), (44, 39), (6, 11), (12, 8), (26, 9), (31, 10), (29, 1), (10, 8), (13, 34), (38, 36), (8, 13), (35, 13), (45, 10), (30, 28), (21, 30), (34, 19), (8, 12), (12, 21), (12, 40), (8, 36), (24, 4), (27, 34), (6, 7), (34, 29), (9, 21), (31, 12), (23, 21), (18, 18), (24, 17), (6, 4), (25, 18), (34, 1), (11, 2), (13, 13), (4, 5), (27, 38), (6, 28), (13, 11), (45, 43), (7, 43), (5, 7), (33, 8), (40, 32), (9, 26), (28, 18), (25, 9), (29, 5), (37, 18), (30, 31), (31, 19), (46, 18), (42, 27), (5, 6), (13, 27), (31, 28), (24, 22), (5, 40), (26, 15), (25, 2), (8, 25), (4, 25), (42, 20), (11, 26), (26, 23), (19, 5), (38, 15), (46, 29), (18, 16), (46, 7), (16, 37), (34, 4), (20, 42), (19, 10), (12, 7), (35, 17), (42, 17), (10, 38), (30, 41), (17, 3), (38, 3), (20, 12), (31, 39), (30, 34), (14, 25), (11, 10), (40, 24), (41, 33), (44, 35), (1, 10), (37, 36), (21, 24), (4, 10), (33, 40), (12, 37), (44, 21), (36, 21), (35, 4), (38, 28), (40, 3), (29, 32), (31, 38), (0, 36), (25, 1), (44, 32), (29, 11), (26, 19), (22, 0), (11, 1), (34, 32), (36, 23), (9, 37), (8, 39), (30, 16), (8, 42), (3, 29), (28, 1), (6, 41), (32, 15), (38, 1), (36, 31), (16, 36), (41, 8), (24, 29), (1, 15), (12, 0), (11, 5), (13, 30), (4, 15), (37, 31), (38, 42), (22, 10), (9, 25), (5, 0), (26, 21), (42, 3), (28, 13), (23, 1), (3, 23), (33, 5), (39, 17), (38, 29), (6, 17), (3, 12), (26, 11), (42, 4), (40, 17), (17, 5), (19, 15), (24, 23), (8, 21), (2, 37), (9, 6), (8, 1), (35, 23), (27, 41), (25, 41), (26, 3), (45, 16), (31, 8), (29, 42), (27, 1), (18, 20), (14, 26), (17, 30), (43, 1), (4, 14), (39, 22), (16, 29), (32, 4), (36, 22), (4, 7), (7, 21), (43, 10), (4, 13), (12, 38), (27, 42), (16, 34), (6, 1), (25, 20), (31, 36), (25, 8), (1, 28), (25, 7), (8, 0), (29, 19), (21, 21), (28, 39), (20, 9), (6, 42), (26, 41), (42, 38), (45, 34), (28, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 37), (34, 32), (4, 40), (14, 6), (17, 19), (3, 12), (22, 42), (5, 33), (34, 7), (25, 34), (41, 8), (1, 6), (21, 11), (9, 37), (28, 26), (15, 29), (11, 27), (38, 20), (14, 0), (38, 17), (27, 37), (23, 6), (40, 43), (39, 41), (16, 12), (10, 12), (10, 32), (43, 17), (7, 23), (22, 15), (16, 5), (16, 21), (17, 37), (21, 17), (36, 43), (15, 5), (26, 43), (23, 20), (37, 20), (29, 10), (31, 10), (17, 22), (2, 11), (9, 33), (37, 21), (11, 6), (4, 0), (39, 24), (27, 14), (18, 14), (8, 2), (20, 16), (35, 45), (41, 28), (39, 35), (34, 44), (26, 24), (10, 41), (2, 23), (28, 32), (12, 28), (25, 40), (41, 0), (34, 37), (0, 43), (35, 18), (10, 3), (28, 42), (11, 4), (2, 0), (33, 33), (3, 19), (3, 4), (10, 1), (39, 29), (11, 14), (33, 40), (13, 10), (30, 5), (12, 14), (22, 40), (19, 37), (38, 33), (26, 20), (3, 21), (36, 8), (10, 31), (24, 18), (10, 25), (29, 33), (1, 25), (16, 6), (5, 19), (27, 15), (17, 0), (13, 3), (35, 21), (41, 5), (3, 35), (11, 33), (2, 4), (35, 38), (17, 16), (41, 13), (42, 30), (14, 44), (36, 7), (21, 24), (14, 27), (19, 12), (15, 21), (0, 29), (37, 9), (21, 19), (23, 33), (24, 41), (33, 6), (39, 43), (15, 26), (13, 37), (10, 20), (31, 36), (31, 39), (8, 9), (24, 9), (36, 6), (18, 33), (17, 40), (14, 29), (33, 9), (22, 43), (18, 22), (10, 23), (40, 28), (9, 34), (31, 1), (4, 10), (36, 2), (37, 37), (15, 43), (38, 2), (21, 33), (32, 6), (21, 27), (42, 26), (24, 45), (24, 44), (30, 4), (0, 41), (18, 42), (3, 30), (13, 5), (1, 13), (42, 39), (27, 10), (40, 20), (19, 42), (24, 1), (3, 0), (40, 4), (0, 18), (35, 24), (32, 13), (36, 14), (35, 1), (37, 15), (15, 34), (15, 11), (18, 13), (25, 19), (16, 43), (1, 20), (7, 44), (5, 1), (43, 41), (18, 25), (7, 9), (6, 30), (37, 0), (37, 28), (41, 40), (8, 12), (34, 15), (5, 0), (41, 33), (0, 9), (27, 13), (42, 3), (43, 23), (12, 15), (11, 30), (12, 17), (2, 27), (29, 1), (23, 13), (37, 4), (16, 3), (14, 14), (14, 38), (42, 32), (33, 17), (11, 29), (9, 2), (24, 42), (25, 25), (29, 16), (31, 37), (12, 34), (14, 45), (18, 45), (18, 32), (42, 37), (43, 1), (41, 25), (28, 40), (34, 27), (14, 22), (11, 3), (38, 37), (30, 6), (12, 35), (19, 30), (11, 43), (36, 1), (27, 9), (17, 27), (8, 8), (25, 36), (14, 40), (0, 15), (33, 25), (26, 30), (8, 3), (42, 29), (20, 18), (43, 4), (41, 34), (5, 29), (8, 42), (21, 2), (2, 18), (40, 44), (3, 29), (32, 5), (36, 24), (41, 42), (13, 29), (7, 31), (9, 21), (34, 12), (13, 11), (1, 26), (9, 43), (15, 41), (15, 20), (14, 41), (16, 13), (38, 0), (38, 31), (1, 23), (32, 42), (41, 4), (20, 32), (10, 33), (11, 40), (38, 39), (32, 44), (0, 38), (41, 14), (12, 20), (17, 11), (40, 42), (41, 38), (32, 45), (35, 33), (39, 16), (13, 0), (29, 31), (37, 11), (2, 5), (21, 44), (28, 27), (25, 3), (26, 17), (3, 10), (39, 18), (31, 44), (11, 16), (35, 3), (9, 3), (23, 9), (4, 5), (38, 6), (43, 10), (6, 34), (18, 15), (40, 26), (22, 17), (26, 19), (14, 13), (16, 26), (31, 15), (18, 5), (37, 44), (35, 11), (31, 14), (9, 29), (23, 15), (26, 5), (6, 14), (6, 0), (27, 4), (7, 25), (9, 44), (29, 44), (29, 0), (39, 7), (39, 2), (27, 39), (25, 4), (26, 2), (37, 3), (35, 26), (7, 32), (28, 12), (2, 41), (38, 30), (23, 16), (34, 42), (2, 12), (33, 31), (16, 25), (33, 21), (41, 39), (10, 9), (26, 38), (43, 29), (23, 35), (36, 15), (19, 32), (29, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 23), (11, 18), (28, 16), (8, 34), (23, 19), (12, 0), (29, 19), (25, 20), (20, 22), (6, 42), (36, 5), (16, 37), (31, 36), (34, 5), (16, 40), (17, 13), (5, 21), (26, 27), (37, 27), (15, 2), (28, 24), (39, 32), (24, 11), (10, 23), (35, 0), (4, 2), (4, 41), (10, 36), (0, 26), (27, 21), (24, 4), (30, 41), (19, 26), (25, 22), (35, 16), (6, 16), (2, 15), (0, 34), (16, 19), (30, 0), (37, 10), (8, 38), (37, 0), (8, 26), (15, 41), (23, 26), (26, 14), (24, 10), (35, 27), (31, 12), (23, 6), (11, 2), (3, 28), (20, 0), (4, 31), (39, 43), (6, 13), (33, 22), (23, 2), (9, 28), (3, 37), (6, 23), (11, 9), (16, 42), (32, 10), (39, 12), (24, 14), (10, 29), (23, 28), (30, 9), (9, 8), (18, 30), (34, 13), (22, 24), (13, 22), (1, 26), (31, 8), (32, 43), (5, 40), (41, 28), (22, 42), (40, 17), (32, 28), (24, 5), (16, 13), (30, 18), (41, 31), (30, 39), (6, 37), (1, 41), (23, 16), (24, 36), (33, 12), (11, 34), (10, 17), (40, 1), (6, 33), (8, 8), (30, 21), (13, 26), (8, 21), (23, 37), (29, 29), (7, 36), (31, 27), (35, 7), (13, 20), (36, 11), (14, 8), (29, 6), (19, 18), (17, 21), (5, 36), (20, 39), (40, 23), (13, 6), (34, 33), (35, 14), (26, 11), (40, 9), (8, 41), (0, 7), (41, 10), (25, 42), (31, 15), (35, 21), (21, 40), (29, 23), (20, 31), (9, 10), (6, 2), (18, 19), (27, 22), (36, 25), (15, 15), (6, 35), (12, 3), (32, 9), (20, 19), (11, 36), (29, 5), (18, 13), (15, 39), (31, 28), (23, 33), (20, 16), (32, 16), (23, 30), (15, 9), (35, 34), (20, 10), (39, 6), (22, 31), (30, 44), (15, 44), (8, 43), (35, 2), (12, 27), (16, 24), (42, 15), (22, 44), (5, 22), (6, 14), (24, 26), (40, 29), (18, 39), (37, 11), (11, 10), (19, 36), (31, 24), (37, 30), (1, 31), (39, 0), (14, 32), (34, 11), (13, 40), (30, 1), (5, 31), (37, 35), (30, 5), (29, 16), (0, 9), (35, 25), (7, 34), (40, 28), (20, 32), (1, 39), (30, 4), (16, 7), (23, 43), (15, 17), (1, 28), (16, 14), (16, 2), (7, 0), (13, 13), (26, 9), (2, 6), (8, 16), (1, 14), (15, 36), (14, 25), (5, 28), (38, 5), (16, 26), (40, 38), (40, 41), (5, 5), (2, 25), (1, 37), (13, 3), (14, 9), (41, 39), (25, 30), (16, 8), (13, 36), (35, 43), (29, 0), (5, 30), (2, 33), (5, 2), (19, 2), (17, 24), (31, 33), (0, 1), (40, 16), (29, 36), (31, 39), (1, 18), (6, 30), (8, 10), (41, 21), (23, 40), (39, 42), (13, 12), (31, 2), (28, 18), (41, 11), (3, 9), (40, 13), (0, 32), (9, 39), (5, 33), (42, 21), (0, 2), (16, 35), (36, 3), (11, 28), (15, 38), (3, 7), (27, 37), (40, 44), (32, 34), (16, 0), (7, 2), (8, 40), (29, 17), (32, 38), (4, 9), (28, 30), (37, 32), (30, 33), (3, 24), (41, 33), (37, 9), (27, 8), (26, 33), (41, 2), (11, 15), (34, 14), (13, 19), (39, 7), (3, 5), (38, 40), (17, 31), (20, 11), (39, 24), (19, 13), (11, 31), (7, 20), (19, 4), (22, 0), (36, 34), (22, 6), (24, 13), (11, 39), (36, 23), (3, 18), (14, 19), (9, 41), (36, 28), (34, 40), (8, 18), (13, 44), (10, 10), (32, 21), (40, 4), (0, 28), (31, 35), (33, 40), (4, 11), (38, 15), (40, 32), (7, 22), (16, 12), (33, 19), (24, 21), (31, 41), (1, 9), (39, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 40x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (32, 33), (2, 16), (38, 30), (38, 15), (16, 22), (31, 31), (13, 32), (6, 17), (27, 41), (36, 5), (35, 41), (39, 26), (5, 8), (10, 17), (30, 1), (24, 18), (37, 4), (23, 24), (27, 5), (29, 28), (26, 41), (19, 29), (21, 23), (12, 42), (4, 2), (12, 19), (25, 2), (5, 27), (15, 39), (31, 24), (32, 37), (3, 27), (1, 43), (28, 41), (32, 39), (6, 35), (27, 30), (0, 34), (6, 16), (20, 38), (11, 9), (27, 14), (26, 22), (8, 17), (22, 23), (21, 31), (26, 14), (0, 5), (23, 9), (21, 22), (17, 22), (29, 41), (14, 10), (16, 3), (14, 27), (10, 7), (34, 27), (5, 6), (35, 31), (30, 29), (33, 21), (20, 3), (11, 25), (11, 18), (7, 18), (10, 28), (35, 17), (2, 43), (36, 15), (9, 42), (17, 17), (21, 20), (24, 6), (15, 38), (13, 22), (13, 35), (38, 11), (38, 42), (24, 29), (37, 21), (5, 19), (6, 4), (23, 32), (39, 30), (0, 27), (8, 11), (12, 22), (33, 2), (19, 41), (37, 25), (23, 33), (20, 13), (3, 30), (34, 38), (13, 41), (21, 8), (39, 25), (7, 1), (29, 7), (23, 36), (4, 39), (16, 5), (36, 43), (19, 39), (9, 2), (30, 42), (9, 26), (17, 1), (12, 14), (11, 41), (7, 17), (23, 39), (22, 14), (11, 43), (20, 23), (30, 27), (22, 21), (26, 4), (0, 1), (18, 29), (0, 20), (22, 10), (12, 5), (38, 14), (26, 23), (14, 28), (6, 12), (14, 37), (30, 3), (22, 31), (22, 18), (6, 31), (31, 37), (35, 35), (38, 37), (32, 11), (26, 0), (12, 10), (0, 32), (30, 35), (34, 26), (29, 25), (26, 5), (20, 15), (32, 13), (11, 34), (3, 17), (0, 40), (17, 5), (21, 3), (9, 39), (1, 17), (16, 13), (18, 20), (11, 19), (34, 40), (10, 39), (9, 30), (18, 38), (32, 2), (30, 15), (33, 17), (23, 6), (33, 40), (25, 38), (30, 33), (10, 33), (5, 12), (14, 34), (28, 20), (0, 37), (16, 14), (24, 14), (26, 13), (28, 28), (5, 43), (5, 24), (9, 27), (27, 19), (31, 33), (37, 7), (31, 38), (22, 27), (7, 21), (39, 14), (20, 34), (23, 18), (20, 4), (13, 9), (0, 13), (27, 28), (15, 0), (6, 19), (7, 29), (27, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 22), (43, 0), (37, 21), (36, 18), (41, 13), (30, 9), (19, 18), (17, 2), (13, 32), (27, 36), (1, 4), (35, 23), (22, 28), (26, 36), (17, 0), (6, 6), (24, 33), (5, 30), (40, 12), (37, 2), (17, 38), (5, 5), (30, 11), (31, 3), (7, 9), (27, 17), (15, 29), (26, 4), (22, 27), (34, 36), (24, 25), (10, 28), (14, 18), (37, 16), (19, 21), (23, 38), (19, 29), (46, 9), (6, 21), (33, 34), (24, 6), (28, 29), (24, 0), (9, 9), (40, 4), (21, 7), (11, 29), (15, 10), (26, 13), (21, 27), (14, 35), (11, 38), (44, 27), (36, 17), (22, 6), (21, 28), (21, 36), (1, 18), (5, 10), (36, 2), (34, 11), (29, 7), (10, 15), (15, 26), (31, 12), (6, 26), (6, 0), (25, 23), (10, 2), (15, 35), (12, 0), (12, 16), (18, 9), (29, 26), (13, 4), (43, 33), (13, 9), (23, 27), (18, 29), (29, 6), (7, 35), (28, 11), (20, 20), (33, 21), (20, 38), (19, 39), (20, 8), (25, 13), (22, 24), (45, 33), (21, 15), (35, 7), (18, 33), (29, 4), (30, 12), (34, 8), (4, 2), (42, 24), (45, 3), (6, 32), (22, 12), (36, 38), (27, 37), (25, 15), (30, 24), (34, 16), (42, 34), (46, 23), (16, 19), (32, 34), (5, 20), (29, 33), (8, 12), (18, 13), (18, 24), (42, 14), (35, 29), (22, 10), (6, 10), (29, 20), (44, 4), (18, 4), (24, 16), (46, 38), (0, 10), (31, 18), (11, 26), (21, 17), (5, 33), (11, 14), (2, 21), (16, 40), (7, 21), (19, 3), (9, 18), (14, 19), (15, 9), (46, 5), (9, 3), (27, 6), (26, 9), (7, 6), (21, 32), (11, 9), (35, 10), (26, 35), (18, 21), (17, 40), (14, 28), (38, 18), (20, 16), (14, 13), (19, 26), (39, 40), (12, 12), (23, 32), (23, 24), (4, 32), (15, 39), (17, 33), (13, 0), (12, 21), (35, 12), (17, 10), (18, 26), (11, 10), (37, 17), (46, 21), (9, 36), (37, 31), (43, 26), (8, 15), (24, 35), (44, 39), (13, 18), (21, 21), (16, 1), (32, 6), (34, 31), (28, 2), (12, 22), (30, 13), (8, 4), (45, 27), (30, 32), (13, 23), (3, 31), (20, 32), (7, 33), (38, 5), (44, 9), (26, 32), (15, 7), (28, 24), (21, 10), (30, 22), (3, 11), (16, 3), (45, 40), (33, 30), (27, 28), (15, 18), (1, 25), (23, 2), (38, 25), (44, 8), (15, 6), (16, 15), (4, 18), (12, 28), (19, 7), (20, 10), (46, 7), (44, 29), (36, 35), (19, 30), (39, 8), (19, 24), (15, 23), (14, 33), (16, 34), (14, 34), (40, 17), (44, 10), (11, 4), (26, 21), (24, 13), (20, 3), (37, 14), (1, 16), (6, 27), (31, 30), (11, 31), (27, 4), (26, 30), (36, 19), (10, 18), (45, 2), (29, 34), (37, 4), (33, 28), (27, 39), (11, 36), (31, 13), (18, 0), (23, 36), (27, 22), (46, 18), (41, 4), (19, 36), (0, 26), (25, 32), (7, 4), (27, 30), (19, 15), (5, 4), (8, 29), (14, 31), (43, 39), (8, 1), (14, 6), (3, 17), (45, 32), (18, 17), (25, 28), (21, 19), (45, 24), (46, 35), (17, 23), (26, 33), (44, 21), (35, 17), (42, 4), (24, 38), (40, 5), (39, 16), (7, 34), (25, 19), (43, 17), (13, 5), (45, 19), (35, 4), (19, 25), (26, 34), (37, 11), (45, 14), (28, 28), (33, 3), (11, 11), (18, 18), (27, 35), (10, 21), (34, 17), (25, 16), (46, 16), (12, 34), (7, 8), (12, 24), (41, 10), (16, 14), (21, 13), (19, 35), (18, 28), (13, 36), (34, 25), (44, 12), (6, 4), (23, 4), (25, 24), (31, 40), (12, 11), (35, 27), (26, 15), (38, 14), (6, 13), (1, 19), (45, 18), (7, 37), (7, 31), (6, 18), (31, 23), (35, 14), (44, 11), (45, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 30), (23, 21), (12, 12), (29, 23), (34, 1), (13, 1), (38, 3), (1, 6), (28, 13), (19, 27), (4, 27), (43, 41), (12, 2), (37, 16), (6, 28), (37, 33), (18, 27), (41, 28), (0, 29), (38, 33), (6, 24), (43, 25), (6, 39), (17, 15), (38, 4), (8, 39), (24, 31), (23, 5), (4, 13), (26, 9), (31, 20), (12, 32), (20, 8), (37, 22), (34, 40), (16, 15), (43, 30), (36, 14), (5, 36), (6, 11), (11, 4), (15, 31), (5, 31), (18, 22), (0, 13), (12, 43), (27, 18), (3, 23), (0, 5), (21, 44), (18, 10), (41, 17), (7, 33), (28, 18), (32, 5), (36, 4), (4, 15), (0, 1), (41, 25), (4, 39), (12, 24), (3, 16), (4, 11), (28, 0), (26, 18), (21, 43), (13, 9), (17, 33), (27, 38), (34, 15), (12, 41), (38, 8), (1, 42), (25, 24), (6, 16), (12, 30), (26, 31), (2, 0), (36, 38), (23, 41), (22, 44), (39, 6), (10, 43), (17, 37), (43, 22), (31, 24), (24, 3), (29, 4), (23, 38), (2, 18), (20, 5), (14, 32), (10, 38), (23, 20), (25, 26), (24, 34), (27, 15), (19, 29), (43, 32), (27, 2), (40, 20), (9, 0), (13, 18), (21, 4), (28, 32), (31, 13), (21, 19), (38, 36), (44, 22), (1, 16), (6, 21), (28, 42), (32, 28), (4, 12), (42, 37), (4, 0), (11, 2), (1, 10), (7, 8), (42, 18), (16, 43), (13, 24), (19, 22), (22, 32), (18, 9), (2, 36), (20, 20), (6, 12), (22, 34), (9, 30), (38, 35), (44, 5), (19, 4), (7, 0), (31, 43), (23, 14), (12, 38), (22, 42), (34, 19), (34, 26), (13, 38), (10, 2), (31, 27), (15, 40), (15, 27), (35, 0), (1, 17), (44, 13), (20, 12), (19, 13), (10, 16), (0, 24), (9, 35), (43, 35), (43, 11), (9, 7), (3, 26), (4, 21), (25, 10), (33, 30), (23, 4), (34, 37), (4, 23), (16, 42), (30, 21), (41, 23), (34, 21), (40, 18), (18, 11), (39, 17), (26, 15), (16, 10), (13, 43), (19, 30), (6, 31), (33, 9), (36, 15), (8, 33), (42, 36), (18, 21), (1, 44), (29, 29), (36, 7), (6, 9), (19, 0), (1, 25), (6, 22), (39, 38), (9, 20), (22, 16), (1, 32), (37, 44), (24, 29), (30, 9), (33, 35), (7, 27), (38, 14), (35, 30), (4, 41), (15, 29), (8, 22), (11, 20), (34, 4), (5, 27), (37, 43), (11, 31), (37, 19), (12, 16), (36, 31), (40, 39), (41, 33), (30, 5), (7, 44), (44, 23), (15, 43), (20, 31), (14, 33), (40, 4), (23, 13), (40, 8), (38, 9), (33, 21), (31, 19), (20, 26), (20, 34), (3, 38), (18, 39), (15, 26), (34, 41), (8, 5), (17, 16), (32, 43), (42, 2), (5, 32), (25, 18), (13, 11), (27, 16), (3, 39), (26, 37), (41, 18), (39, 27), (38, 6), (37, 14), (41, 2), (11, 15), (44, 12), (9, 39), (33, 22), (7, 37), (40, 22), (19, 16), (4, 25), (17, 25), (2, 31), (42, 19), (43, 7), (9, 22), (38, 1), (37, 18), (33, 36), (40, 19), (9, 5), (31, 25), (10, 41), (7, 34), (5, 28), (22, 21), (25, 22), (35, 4), (17, 13), (24, 36), (20, 9), (11, 26), (38, 30), (30, 40), (7, 29), (3, 44), (30, 23), (37, 30), (17, 29), (3, 18), (13, 34), (39, 41), (42, 42), (9, 34), (11, 23), (22, 3), (4, 20), (19, 33), (32, 40), (5, 37), (27, 12), (34, 44), (9, 26), (20, 11), (30, 38), (27, 39), (15, 7), (23, 32), (16, 26), (43, 3), (5, 42), (44, 39), (15, 14), (9, 28), (26, 42), (32, 37), (20, 19), (28, 25), (22, 33), (35, 20), (38, 40), (37, 10), (44, 30), (7, 41), (5, 24), (42, 12), (0, 43), (27, 8), (13, 20), (32, 25), (31, 32), (27, 14), (30, 32), (35, 15), (3, 37), (36, 25), (32, 31), (43, 10), (7, 7), (12, 36), (1, 9), (9, 43), (5, 21), (28, 38), (36, 3), (19, 18), (35, 19), (40, 6), (22, 22), (2, 12), (26, 36), (7, 17), (28, 23), (26, 22), (4, 8), (5, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 10), (36, 21), (4, 26), (13, 2), (16, 31), (25, 18), (11, 39), (24, 9), (39, 8), (1, 19), (16, 11), (47, 34), (5, 21), (14, 37), (11, 20), (8, 30), (5, 37), (37, 2), (14, 7), (3, 27), (41, 32), (32, 5), (21, 29), (16, 7), (43, 20), (44, 29), (40, 10), (25, 23), (45, 18), (37, 3), (11, 2), (17, 21), (40, 18), (38, 36), (22, 34), (43, 32), (4, 4), (20, 20), (27, 25), (37, 21), (6, 32), (11, 6), (27, 23), (28, 37), (6, 14), (2, 17), (47, 13), (23, 25), (10, 8), (2, 40), (25, 20), (20, 1), (0, 27), (5, 7), (15, 14), (40, 5), (15, 41), (45, 22), (2, 1), (19, 11), (11, 12), (41, 35), (44, 41), (2, 35), (20, 40), (1, 6), (31, 16), (42, 29), (40, 6), (34, 32), (45, 14), (17, 16), (4, 40), (39, 19), (46, 16), (1, 33), (40, 26), (39, 1), (15, 38), (2, 26), (34, 33), (41, 27), (27, 15), (31, 33), (32, 38), (25, 22), (16, 13), (6, 27), (21, 15), (15, 25), (5, 12), (38, 28), (18, 37), (17, 30), (37, 5), (37, 38), (32, 39), (3, 32), (7, 37), (37, 31), (44, 14), (45, 23), (23, 20), (6, 25), (18, 3), (14, 36), (3, 33), (33, 36), (3, 30), (44, 12), (7, 0), (22, 7), (23, 5), (29, 10), (20, 41), (7, 19), (38, 23), (32, 25), (37, 1), (35, 12), (39, 23), (39, 40), (23, 30), (0, 36), (42, 6), (34, 38), (30, 37), (27, 1), (33, 0), (29, 24), (14, 23), (40, 20), (27, 39), (11, 9), (7, 17), (15, 6), (7, 25), (23, 12), (32, 30), (10, 5), (15, 28), (39, 0), (41, 26), (34, 12), (33, 10), (31, 10), (5, 2), (20, 35), (42, 17), (9, 6), (6, 24), (17, 14), (32, 28), (3, 7), (28, 23), (44, 2), (16, 20), (47, 40), (21, 22), (36, 29), (8, 11), (15, 35), (41, 11), (32, 20), (21, 12), (2, 16), (9, 4), (45, 40), (5, 17), (2, 24), (9, 38), (44, 7), (40, 34), (2, 27), (5, 39), (38, 26), (39, 38), (8, 12), (46, 24), (47, 33), (36, 9), (21, 32), (27, 7), (29, 16), (33, 1), (26, 0), (35, 23), (42, 10), (13, 18), (25, 36), (10, 33), (19, 18), (45, 39), (13, 7), (10, 17), (40, 23), (27, 16), (38, 35), (0, 9), (9, 3), (17, 26), (19, 38), (43, 1), (26, 20), (4, 10), (26, 12), (4, 16), (0, 20), (15, 7), (21, 14), (38, 9), (26, 4), (45, 37), (28, 13), (2, 32), (0, 38), (1, 40), (4, 34), (33, 2), (21, 35), (23, 9), (19, 21), (36, 14), (0, 17), (39, 16), (39, 28), (19, 27), (40, 39), (23, 10), (22, 12), (47, 19), (43, 39), (41, 22), (35, 19), (20, 28), (6, 23), (6, 29), (17, 0), (28, 14), (1, 37), (27, 2), (5, 32), (4, 37), (2, 39), (41, 0), (14, 1), (8, 4), (44, 9), (18, 39), (0, 28), (18, 27), (6, 36), (42, 25), (35, 4), (41, 29), (28, 20), (41, 23), (1, 36), (22, 15), (31, 37), (3, 3), (21, 11), (31, 36), (9, 11), (12, 8), (26, 25), (0, 39), (44, 13), (34, 25), (3, 24), (19, 40), (36, 11), (15, 12), (3, 31), (40, 36), (40, 3), (11, 23), (35, 26), (15, 15), (28, 29), (6, 6), (12, 2), (27, 19), (46, 21), (17, 37), (44, 16), (38, 34), (37, 17), (12, 3), (34, 27), (24, 8), (12, 7), (3, 10), (24, 12), (30, 5), (42, 28), (13, 30), (1, 38), (14, 10), (42, 13), (13, 20), (44, 8), (28, 27), (20, 38), (5, 0), (11, 17), (4, 23), (47, 39), (18, 13), (15, 29), (39, 26), (40, 4), (29, 3), (32, 34), (46, 27), (12, 0), (6, 17), (15, 1), (9, 26), (41, 17), (18, 11), (27, 3), (3, 37), (21, 16), (12, 31), (38, 11), (39, 22), (34, 21), (8, 25), (38, 33), (25, 14), (43, 21), (32, 6), (12, 15), (30, 36), (3, 39), (8, 21), (38, 16), (35, 5), (42, 30), (24, 6), (20, 21), (21, 18), (36, 36), (38, 27), (20, 39), (29, 19), (21, 41), (30, 28), (9, 29), (34, 16), (43, 17), (45, 33), (0, 19), (1, 0), (7, 22), (46, 17), (25, 13), (25, 4), (46, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 19), (27, 27), (4, 14), (12, 1), (41, 4), (4, 15), (28, 22), (7, 0), (42, 33), (7, 20), (21, 9), (1, 34), (19, 45), (10, 45), (34, 27), (3, 5), (31, 41), (40, 19), (39, 25), (15, 42), (27, 33), (13, 45), (30, 44), (47, 12), (42, 25), (2, 39), (36, 40), (12, 32), (32, 8), (22, 7), (4, 41), (14, 14), (35, 0), (20, 22), (1, 6), (40, 42), (2, 12), (39, 42), (28, 28), (17, 44), (44, 26), (42, 42), (1, 35), (14, 44), (22, 10), (29, 10), (36, 35), (31, 38), (45, 26), (36, 43), (20, 2), (18, 43), (0, 42), (0, 12), (29, 19), (4, 34), (7, 17), (25, 38), (3, 40), (0, 37), (6, 12), (26, 13), (34, 0), (16, 12), (26, 1), (31, 21), (47, 6), (32, 0), (39, 11), (35, 39), (42, 27), (2, 41), (18, 16), (16, 22), (44, 43), (27, 15), (31, 43), (42, 12), (26, 20), (34, 9), (25, 12), (19, 12), (35, 7), (3, 36), (33, 22), (46, 38), (10, 44), (38, 28), (16, 40), (5, 17), (21, 45), (40, 37), (27, 5), (36, 1), (31, 29), (7, 14), (28, 32), (11, 42), (35, 37), (31, 32), (6, 27), (18, 24), (18, 9), (19, 41), (43, 23), (3, 19), (34, 36), (8, 44), (47, 8), (14, 1), (45, 15), (9, 34), (36, 41), (14, 3), (39, 41), (11, 30), (39, 39), (41, 24), (26, 7), (43, 41), (4, 9), (2, 26), (9, 23), (14, 35), (13, 1), (41, 22), (5, 9), (3, 14), (31, 1), (22, 15), (13, 4), (47, 2), (14, 33), (21, 17), (14, 10), (6, 31), (21, 33), (44, 6), (10, 37), (5, 14), (42, 39), (45, 14), (21, 7), (5, 12), (42, 44), (4, 24), (7, 23), (16, 21), (34, 37), (13, 3), (0, 27), (43, 39), (1, 22), (20, 16), (19, 29), (31, 2), (46, 10), (38, 17), (29, 21), (18, 14), (5, 8), (13, 22), (44, 31), (16, 8), (36, 24), (24, 7), (40, 25), (18, 19), (3, 28), (40, 39), (14, 11), (32, 24), (24, 8), (46, 45), (2, 22), (36, 4), (22, 35), (41, 15), (24, 5), (11, 2), (4, 5), (10, 34), (9, 9), (32, 16), (33, 45), (18, 41), (15, 27), (8, 38), (1, 27), (15, 23), (40, 1), (18, 1), (33, 40), (20, 0), (11, 31), (17, 33), (2, 27), (13, 19), (38, 22), (46, 22), (30, 8), (11, 44), (35, 5), (5, 6), (27, 8), (28, 12), (10, 23), (11, 0), (11, 19), (10, 36), (43, 43), (24, 1), (37, 4), (26, 30), (43, 3), (2, 29), (16, 31), (7, 28), (47, 24), (41, 1), (28, 25), (12, 10), (12, 34), (45, 36), (7, 9), (37, 12), (15, 32), (36, 11), (32, 32), (24, 40), (17, 16), (37, 34), (22, 45), (27, 44), (21, 22), (30, 6), (34, 40), (34, 24), (4, 8), (45, 6), (4, 11), (40, 18), (2, 4), (33, 37), (36, 28), (23, 11), (29, 12), (44, 3), (21, 18), (31, 4), (10, 24), (43, 37), (27, 1), (24, 37), (27, 11), (0, 30), (25, 44), (36, 39), (36, 37), (28, 3), (14, 18), (43, 33), (8, 39), (34, 30), (41, 35), (39, 16), (10, 30), (36, 22), (14, 29), (5, 13), (9, 17), (28, 24), (7, 38), (26, 42), (34, 6), (31, 25), (43, 19), (19, 8), (47, 41), (44, 11), (14, 22), (18, 32), (28, 0), (25, 20), (21, 26), (44, 4), (3, 32), (29, 2), (27, 22), (46, 19), (45, 7), (15, 14), (23, 33), (26, 17), (22, 38), (0, 28), (10, 12), (37, 3), (36, 31), (0, 21), (20, 5), (39, 13), (8, 18), (14, 4), (11, 22), (29, 39), (30, 12), (16, 27), (5, 39), (41, 37), (2, 21), (34, 14), (44, 32), (19, 20), (19, 30), (28, 40), (32, 17), (15, 3), (47, 27), (3, 21), (43, 42), (8, 16), (29, 3), (18, 11), (47, 4), (30, 36), (36, 10), (11, 34), (37, 29), (9, 27), (29, 26), (28, 44), (5, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 32), (4, 6), (26, 19), (20, 23), (6, 35), (20, 35), (0, 27), (32, 1), (34, 25), (24, 21), (38, 0), (3, 5), (17, 31), (0, 22), (28, 31), (15, 16), (24, 27), (17, 7), (15, 20), (8, 34), (11, 36), (6, 25), (1, 28), (25, 12), (42, 1), (22, 36), (2, 1), (34, 13), (4, 17), (3, 11), (42, 28), (34, 29), (3, 0), (32, 23), (20, 21), (10, 6), (28, 27), (0, 35), (9, 24), (22, 34), (6, 23), (11, 31), (16, 29), (36, 35), (16, 30), (20, 29), (9, 38), (10, 31), (16, 27), (31, 36), (31, 40), (6, 9), (3, 15), (0, 31), (32, 31), (7, 18), (43, 12), (10, 24), (39, 33), (37, 26), (10, 39), (2, 15), (35, 4), (11, 33), (12, 39), (13, 17), (1, 6), (25, 7), (32, 21), (37, 2), (1, 5), (13, 12), (19, 16), (1, 21), (29, 40), (1, 40), (41, 25), (4, 8), (13, 3), (40, 30), (40, 28), (21, 38), (43, 27), (36, 8), (27, 1), (18, 40), (7, 23), (11, 4), (39, 17), (0, 37), (28, 39), (35, 2), (39, 15), (3, 20), (36, 39), (14, 39), (16, 22), (25, 27), (42, 11), (7, 2), (38, 17), (25, 16), (28, 2), (5, 7), (8, 26), (23, 3), (19, 29), (13, 30), (8, 1), (5, 15), (42, 20), (29, 32), (23, 6), (27, 39), (28, 15), (8, 38), (1, 30), (12, 20), (33, 21), (4, 21), (29, 31), (1, 38), (6, 3), (34, 6), (38, 20), (27, 22), (20, 18), (9, 17), (34, 19), (31, 26), (19, 22), (32, 15), (12, 17), (20, 28), (14, 17), (6, 2), (24, 25), (5, 28), (5, 17), (15, 30), (31, 25), (25, 23), (19, 12), (15, 24), (36, 19), (42, 4), (8, 17), (26, 27), (40, 3), (22, 24), (19, 23), (1, 33), (9, 3), (21, 31), (3, 37), (27, 35), (11, 28), (15, 13), (26, 22), (33, 11), (3, 36), (14, 34), (34, 22), (39, 11), (28, 34), (43, 3), (10, 27), (39, 5), (30, 11), (36, 29), (6, 30), (0, 25), (27, 30), (1, 18), (5, 24), (20, 26), (42, 10), (10, 13), (19, 8), (17, 17), (30, 15), (42, 22), (2, 26), (22, 10), (28, 5), (26, 37), (13, 37), (11, 24), (8, 25), (28, 7), (28, 17), (0, 14), (8, 30), (17, 2), (28, 37), (1, 20), (42, 27), (40, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (45, 11), (13, 26), (6, 16), (38, 38), (18, 8), (32, 41), (38, 11), (10, 2), (3, 20), (8, 32), (4, 21), (29, 22), (1, 45), (7, 24), (20, 12), (39, 18), (39, 16), (18, 11), (4, 42), (30, 24), (44, 43), (7, 1), (29, 1), (19, 45), (12, 12), (17, 6), (31, 25), (10, 1), (24, 21), (5, 34), (0, 40), (5, 38), (37, 16), (47, 5), (38, 44), (19, 10), (17, 44), (4, 15), (42, 5), (5, 33), (21, 25), (44, 16), (36, 34), (6, 35), (34, 31), (43, 24), (2, 45), (24, 42), (14, 28), (2, 38), (29, 8), (15, 17), (24, 5), (20, 17), (16, 33), (13, 11), (22, 22), (27, 31), (6, 36), (3, 5), (4, 6), (32, 29), (4, 37), (33, 42), (26, 39), (31, 35), (43, 18), (13, 12), (27, 4), (34, 26), (45, 19), (9, 39), (39, 3), (35, 32), (13, 38), (3, 24), (6, 20), (37, 1), (25, 13), (29, 2), (37, 0), (18, 38), (22, 32), (3, 43), (3, 27), (36, 32), (47, 23), (42, 18), (0, 21), (24, 13), (23, 7), (1, 22), (4, 0), (46, 21), (33, 40), (8, 8), (36, 16), (20, 40), (33, 3), (23, 12), (17, 8), (12, 10), (23, 17), (31, 16), (39, 6), (18, 14), (25, 40), (36, 3), (22, 8), (41, 19), (1, 43), (45, 45), (6, 0), (23, 19), (15, 29), (25, 32), (28, 10), (32, 7), (5, 11), (35, 25), (36, 28), (22, 23), (23, 13), (7, 32), (23, 11), (14, 34), (20, 39), (42, 16), (11, 15), (34, 17), (26, 19), (31, 28), (36, 44), (47, 40), (38, 36), (5, 18), (24, 39), (46, 9), (31, 31), (37, 41), (40, 2), (0, 44), (7, 11), (1, 3), (8, 4), (13, 28), (36, 40), (35, 4), (10, 6), (11, 0), (9, 20), (26, 5), (20, 30), (32, 25), (35, 21), (16, 35), (40, 5), (17, 38), (28, 44), (29, 43), (40, 25), (6, 25), (31, 0), (28, 34), (30, 41), (30, 27), (21, 38), (22, 43), (12, 44), (12, 43), (46, 29), (14, 2), (32, 43), (25, 41), (29, 21), (40, 21), (24, 7), (40, 13), (46, 33), (36, 11), (1, 24), (8, 14), (13, 21), (38, 7), (19, 25), (42, 20), (31, 44), (46, 28), (29, 0), (42, 32), (5, 23), (39, 7), (35, 5), (20, 24), (40, 44), (28, 9), (15, 15), (37, 26), (5, 7), (11, 2), (15, 22), (15, 36), (7, 43), (3, 8), (14, 12), (11, 21), (1, 21), (28, 37), (43, 8), (31, 19), (15, 33), (45, 38), (21, 32), (22, 34), (25, 14), (16, 9), (27, 45), (25, 35), (19, 34), (11, 20), (18, 4), (7, 3), (13, 13), (38, 39), (30, 4), (47, 1), (21, 0), (1, 9), (17, 27), (24, 29), (33, 26), (46, 1), (28, 0), (23, 41), (35, 40), (42, 22), (35, 39), (17, 43), (2, 10), (8, 18), (12, 33), (10, 23), (1, 42), (30, 38), (45, 4), (17, 39), (17, 19), (6, 33), (43, 30), (5, 36), (29, 7), (10, 28), (36, 39), (43, 3), (0, 45), (42, 2), (33, 45), (15, 41), (26, 37), (3, 45), (41, 21), (8, 27), (8, 37), (31, 17), (10, 38), (4, 19), (28, 24), (36, 45), (12, 27), (7, 0), (16, 3), (47, 15), (20, 27), (9, 35), (26, 2), (42, 13), (19, 40), (13, 9), (45, 9), (19, 27), (3, 38), (33, 5), (5, 26), (36, 26), (22, 18), (2, 35), (21, 43), (5, 4), (43, 27), (10, 40), (11, 27), (6, 28), (33, 44), (17, 42), (19, 19), (14, 23), (6, 22), (43, 33), (31, 42), (22, 17), (39, 42), (34, 44), (18, 32), (25, 33), (0, 23), (24, 38), (28, 30), (18, 9), (13, 23), (32, 33), (46, 37), (21, 1), (0, 3), (25, 1), (12, 25), (46, 4), (16, 43), (15, 3), (16, 16), (26, 45), (2, 14), (34, 14), (1, 44), (14, 30), (45, 6), (21, 19), (47, 2), (29, 26), (34, 39), (27, 25), (22, 7), (41, 32), (44, 8), (32, 1), (2, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 40), (39, 2), (28, 15), (18, 6), (15, 29), (12, 33), (17, 16), (31, 1), (3, 25), (9, 2), (0, 11), (24, 16), (24, 30), (0, 8), (16, 9), (8, 9), (23, 24), (9, 5), (19, 4), (9, 33), (23, 6), (7, 24), (42, 37), (41, 27), (39, 19), (19, 5), (23, 26), (6, 4), (12, 6), (25, 34), (1, 9), (8, 30), (38, 1), (29, 29), (25, 18), (21, 3), (40, 32), (27, 6), (34, 37), (2, 34), (19, 24), (36, 35), (32, 33), (17, 17), (16, 18), (36, 6), (32, 19), (38, 22), (2, 14), (18, 25), (11, 35), (8, 24), (4, 10), (25, 16), (28, 3), (7, 36), (38, 4), (2, 5), (9, 12), (16, 35), (40, 26), (25, 11), (15, 0), (1, 26), (11, 15), (6, 39), (9, 39), (25, 3), (27, 25), (2, 32), (10, 4), (26, 1), (42, 32), (34, 18), (24, 5), (9, 13), (12, 12), (13, 28), (0, 19), (23, 19), (12, 8), (40, 9), (38, 19), (33, 6), (16, 11), (15, 35), (39, 6), (13, 13), (12, 7), (33, 22), (10, 23), (8, 6), (26, 40), (3, 27), (10, 38), (8, 26), (30, 27), (29, 3), (1, 36), (6, 14), (19, 15), (31, 36), (36, 36), (6, 5), (41, 9), (3, 3), (4, 20), (2, 29), (15, 5), (5, 30), (1, 34), (7, 14), (7, 4), (7, 2), (33, 5), (3, 38), (33, 19), (32, 7), (10, 10), (11, 34), (25, 19), (13, 41), (33, 28), (6, 34), (32, 30), (34, 11), (21, 28), (38, 13), (17, 26), (6, 29), (27, 27), (35, 27), (30, 40), (34, 2), (42, 11), (40, 33), (21, 15), (30, 3), (36, 24), (13, 7), (22, 37), (28, 33), (20, 1), (18, 33), (14, 21), (42, 36), (2, 39), (34, 27), (38, 41), (4, 23), (7, 13), (5, 11), (13, 32), (30, 18), (23, 32), (20, 17), (12, 20), (30, 37), (17, 28), (19, 8), (36, 21), (17, 4), (32, 8), (34, 41), (41, 16), (3, 31), (8, 35), (23, 15), (12, 39), (14, 9), (2, 24), (26, 10), (30, 13), (18, 34), (10, 40), (30, 38), (27, 18), (13, 9), (6, 41), (34, 32), (36, 12), (14, 14), (24, 41), (7, 34), (11, 33), (18, 4), (6, 38), (18, 36), (17, 35), (29, 23), (38, 20), (18, 5), (16, 30), (8, 40), (30, 22), (14, 10), (8, 3), (37, 5), (21, 11), (0, 29), (31, 39), (21, 27), (39, 10), (17, 14), (18, 8), (1, 22), (6, 9), (41, 17), (17, 12), (31, 21), (15, 15), (22, 16), (40, 16), (36, 8), (5, 22), (39, 26), (20, 29), (39, 4), (36, 15), (22, 22), (32, 29), (33, 10), (22, 3), (31, 15), (16, 16), (38, 3), (35, 35), (35, 8), (9, 25), (31, 35), (10, 22), (42, 29), (39, 8), (13, 0), (2, 23), (19, 25), (28, 30), (5, 33), (0, 31), (11, 20), (41, 13), (6, 36), (24, 9), (23, 2), (2, 26), (34, 20), (3, 18), (18, 32), (28, 13), (19, 21), (22, 4), (5, 18), (18, 41), (22, 36), (41, 25), (28, 9), (39, 11), (40, 4), (42, 16), (33, 25), (19, 39), (34, 24), (3, 36), (39, 22), (1, 23), (9, 32), (24, 21), (30, 12), (39, 17), (19, 34), (13, 39), (19, 36), (24, 14), (5, 41), (23, 0), (26, 34), (13, 22), (15, 39), (27, 7), (15, 6), (26, 25), (0, 33), (26, 39), (25, 32), (31, 5), (32, 13), (26, 9), (35, 34), (36, 25), (4, 19), (42, 34), (32, 39), (30, 17), (37, 22), (40, 40), (34, 6), (5, 2), (9, 18), (20, 3), (40, 8), (7, 16), (12, 32), (0, 9), (23, 27), (28, 23), (20, 9), (30, 36), (34, 31), (25, 25), (13, 38), (25, 17), (25, 6), (26, 3), (38, 35), (33, 21), (41, 20), (21, 19), (22, 33), (24, 0), (3, 32), (5, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 24), (15, 15), (6, 1), (31, 37), (19, 17), (7, 37), (17, 23), (27, 4), (16, 25), (16, 12), (36, 30), (25, 36), (30, 19), (39, 35), (41, 17), (38, 22), (33, 28), (19, 9), (17, 2), (35, 33), (1, 33), (30, 1), (27, 7), (41, 35), (24, 19), (23, 29), (24, 0), (18, 27), (21, 7), (3, 7), (5, 11), (1, 6), (13, 28), (19, 13), (1, 2), (2, 36), (29, 3), (2, 6), (38, 12), (34, 30), (17, 14), (40, 27), (34, 1), (13, 40), (33, 40), (35, 26), (21, 13), (39, 16), (37, 28), (1, 34), (21, 14), (38, 2), (26, 32), (31, 7), (5, 10), (33, 17), (14, 40), (11, 12), (29, 2), (7, 8), (15, 13), (39, 1), (10, 23), (17, 37), (36, 33), (36, 32), (2, 8), (2, 17), (39, 29), (30, 22), (4, 25), (14, 12), (43, 32), (16, 14), (24, 10), (5, 20), (25, 34), (8, 9), (21, 8), (41, 21), (1, 31), (29, 37), (36, 35), (5, 13), (4, 0), (23, 19), (18, 4), (38, 16), (18, 28), (6, 14), (17, 4), (0, 4), (18, 25), (25, 15), (2, 39), (1, 20), (5, 33), (41, 39), (16, 9), (14, 16), (42, 11), (36, 1), (32, 35), (24, 13), (41, 4), (17, 31), (36, 21), (26, 23), (3, 34), (12, 6), (10, 35), (42, 23), (12, 3), (3, 2), (27, 33), (30, 24), (27, 31), (36, 2), (4, 21), (44, 40), (39, 18), (25, 33), (44, 6), (39, 2), (4, 26), (41, 26), (44, 4), (28, 35), (17, 12), (44, 5), (35, 8), (26, 17), (21, 6), (36, 15), (32, 15), (4, 40), (33, 41), (40, 3), (39, 21), (6, 4), (27, 3), (1, 8), (44, 34), (39, 39), (33, 12), (28, 29), (4, 30), (30, 16), (21, 27), (29, 21), (14, 27), (38, 36), (31, 25), (44, 11), (27, 18), (23, 7), (35, 1), (3, 39), (2, 1), (29, 40), (40, 28), (37, 21), (40, 38), (10, 8), (19, 15), (22, 4), (31, 4), (13, 35), (23, 16), (9, 18), (21, 32), (6, 21), (32, 24), (22, 35), (41, 1), (35, 7), (3, 36), (9, 35), (23, 40), (27, 30), (44, 3), (30, 6), (12, 9), (19, 32), (4, 13), (15, 2), (44, 29), (4, 9), (24, 3), (5, 3), (22, 7), (23, 21), (36, 18), (0, 36), (32, 26), (3, 18), (12, 11), (28, 16), (13, 16), (32, 41), (2, 11), (16, 19), (38, 6), (39, 19), (30, 39), (14, 18), (20, 22), (16, 29), (30, 34), (13, 19), (14, 8), (32, 4), (0, 19), (7, 41), (0, 13), (29, 28), (36, 6), (42, 0), (31, 41), (29, 25), (34, 23), (42, 4), (37, 35), (44, 23), (44, 17), (35, 32), (43, 8), (41, 12), (19, 18), (34, 22), (42, 5), (28, 2), (16, 1), (42, 2), (31, 40), (3, 40), (24, 15), (18, 7), (32, 6), (8, 36), (8, 12), (10, 21), (30, 4), (37, 32), (13, 34), (16, 37), (2, 5), (29, 22), (22, 12), (40, 15), (9, 33), (14, 39), (17, 0), (11, 25), (15, 32), (21, 30), (40, 23), (2, 19), (31, 30), (0, 10), (1, 26), (5, 5), (23, 11), (8, 4), (2, 38), (40, 24), (23, 37), (39, 37), (21, 18), (29, 39), (20, 36), (22, 27), (37, 25), (38, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 25), (11, 31), (20, 27), (25, 45), (35, 34), (27, 15), (35, 6), (0, 1), (39, 28), (28, 42), (33, 3), (6, 25), (16, 39), (13, 24), (12, 7), (21, 5), (37, 1), (15, 5), (12, 27), (40, 29), (39, 37), (35, 44), (26, 35), (4, 33), (23, 48), (39, 8), (13, 34), (1, 26), (19, 15), (4, 44), (45, 46), (31, 31), (18, 10), (0, 39), (45, 36), (33, 39), (22, 26), (9, 38), (48, 41), (27, 14), (41, 36), (33, 2), (26, 4), (44, 37), (25, 28), (45, 28), (21, 44), (6, 46), (31, 21), (17, 33), (26, 32), (6, 30), (4, 45), (12, 28), (8, 44), (31, 48), (30, 14), (20, 8), (37, 16), (24, 33), (41, 35), (32, 10), (31, 35), (6, 26), (16, 26), (28, 33), (46, 14), (11, 26), (14, 16), (25, 29), (33, 19), (43, 32), (41, 32), (46, 4), (23, 46), (20, 46), (17, 2), (25, 33), (28, 26), (2, 31), (8, 25), (33, 34), (12, 34), (42, 19), (4, 39), (23, 39), (46, 45), (9, 35), (42, 21), (42, 36), (48, 31), (20, 40), (44, 4), (34, 11), (39, 33), (10, 32), (38, 23), (37, 10), (24, 17), (1, 10), (40, 2), (27, 23), (39, 12), (34, 2), (32, 2), (17, 23), (0, 21), (6, 10), (0, 4), (38, 33), (47, 12), (17, 19), (39, 14), (28, 25), (9, 0), (37, 30), (22, 11), (5, 5), (37, 0), (22, 25), (26, 41), (34, 42), (42, 5), (28, 35), (35, 10), (23, 38), (15, 19), (31, 11), (35, 25), (18, 19), (7, 44), (14, 33), (9, 25), (5, 33), (9, 21), (14, 20), (3, 22), (11, 9), (22, 32), (25, 43), (16, 7), (16, 45), (31, 30), (6, 44), (25, 11), (35, 46), (26, 45), (16, 25), (26, 33), (5, 19), (14, 17), (10, 7), (12, 8), (34, 43), (16, 40), (14, 44), (8, 17), (17, 6), (19, 34), (24, 24), (38, 8), (48, 19), (47, 39), (35, 12), (38, 46), (1, 47), (12, 10), (42, 33), (1, 19), (32, 4), (45, 6), (25, 26), (36, 40), (7, 27), (47, 0), (11, 46), (22, 42), (35, 22), (4, 1), (33, 21), (20, 34), (48, 34), (29, 27), (20, 14), (31, 4), (26, 34), (37, 36), (10, 15), (39, 10), (0, 44), (16, 17), (32, 28), (38, 1), (11, 24), (31, 19), (41, 3), (17, 35), (40, 6), (13, 2), (20, 22), (29, 10), (15, 9), (8, 30), (9, 47), (5, 21), (26, 40), (4, 40), (44, 35), (33, 11), (18, 2), (40, 40), (34, 19), (17, 10), (38, 35), (23, 5), (32, 32), (27, 44), (32, 44), (2, 41), (48, 42), (29, 17), (44, 0), (11, 21), (19, 36), (29, 1), (38, 12), (36, 13), (28, 47), (43, 38), (35, 48), (44, 15), (36, 32), (16, 44), (31, 41), (46, 1), (18, 7), (45, 30), (17, 26), (35, 23), (19, 4), (24, 25), (18, 16), (44, 48), (37, 27), (27, 19), (11, 25), (25, 3), (4, 8), (25, 7), (32, 48), (24, 21), (13, 46), (46, 42), (12, 4), (34, 5), (24, 1), (22, 1), (9, 43), (44, 9), (42, 26), (14, 3), (16, 31), (29, 39), (33, 46), (45, 17), (23, 4), (19, 3), (45, 12), (1, 9), (1, 29), (15, 38), (46, 0), (36, 6), (42, 47), (3, 46), (27, 46), (27, 29), (33, 14), (42, 32), (20, 33), (35, 4), (37, 6), (41, 30), (12, 20), (31, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 32), (2, 39), (3, 45), (13, 13), (22, 38), (15, 6), (7, 19), (8, 1), (4, 8), (34, 7), (29, 18), (37, 30), (33, 13), (16, 23), (14, 36), (36, 41), (7, 36), (33, 8), (13, 8), (40, 23), (23, 22), (13, 15), (23, 5), (7, 33), (32, 46), (33, 19), (31, 39), (3, 3), (38, 15), (40, 36), (39, 11), (1, 6), (36, 8), (42, 24), (32, 3), (0, 45), (0, 41), (7, 15), (22, 10), (7, 12), (32, 9), (36, 46), (21, 22), (6, 15), (41, 17), (20, 34), (39, 19), (31, 22), (19, 0), (2, 13), (25, 22), (35, 5), (8, 37), (31, 15), (36, 12), (27, 5), (8, 22), (5, 46), (17, 21), (25, 34), (39, 0), (26, 41), (37, 41), (6, 5), (41, 15), (39, 4), (4, 46), (35, 4), (15, 27), (33, 21), (28, 44), (30, 3), (42, 9), (32, 38), (34, 45), (5, 17), (26, 46), (18, 44), (10, 18), (36, 31), (11, 36), (16, 36), (39, 9), (10, 20), (2, 41), (22, 20), (22, 11), (33, 39), (42, 40), (24, 16), (7, 29), (6, 35), (41, 4), (34, 8), (15, 13), (28, 45), (21, 45), (39, 39), (10, 26), (41, 22), (11, 23), (7, 27), (32, 0), (25, 37), (18, 17), (32, 31), (22, 9), (35, 32), (41, 34), (23, 15), (19, 11), (38, 46), (8, 14), (28, 36), (12, 9), (7, 14), (32, 35), (42, 4), (16, 27), (16, 22), (20, 7), (10, 37), (15, 45), (19, 37), (22, 24), (19, 23), (25, 29), (8, 42), (6, 2), (11, 19), (39, 32), (24, 1), (17, 26), (11, 40), (32, 5), (23, 18), (33, 44), (12, 26), (17, 23), (17, 19), (33, 3), (29, 6), (13, 38), (37, 4), (18, 46), (33, 43), (11, 31), (4, 21), (42, 5), (36, 2), (14, 23), (19, 16), (17, 9), (20, 4), (16, 24), (18, 2), (13, 35), (19, 31), (38, 12), (14, 37), (38, 25), (17, 1), (39, 33), (20, 44), (22, 28), (20, 22), (29, 2), (24, 12), (28, 38), (3, 21), (0, 43), (2, 4), (12, 28), (1, 33), (19, 5), (39, 12), (32, 19), (30, 20), (33, 35), (8, 47), (39, 35), (12, 41), (4, 24), (22, 42), (7, 2), (12, 5), (22, 43), (21, 24), (38, 40), (14, 29), (22, 15), (30, 0), (6, 3), (30, 2), (12, 19), (12, 6), (41, 43), (33, 5), (31, 46), (24, 18), (6, 31), (5, 36), (16, 30), (14, 44), (40, 4), (9, 16), (2, 0), (16, 9), (17, 18), (13, 44), (17, 16), (14, 19), (20, 25), (2, 28), (35, 25), (18, 43), (38, 36), (21, 0), (20, 3), (2, 42), (29, 31), (9, 25), (33, 20), (42, 31), (41, 9), (38, 2), (40, 44), (3, 19), (11, 33), (20, 30), (18, 9), (41, 18), (41, 26), (24, 22), (20, 27), (2, 18), (40, 24), (0, 47), (34, 0), (22, 34), (29, 30), (32, 7), (25, 25), (21, 30), (19, 44), (14, 27), (18, 36), (17, 38), (37, 12), (28, 5), (34, 10), (16, 26), (23, 20), (1, 8), (35, 9), (31, 18), (35, 15), (21, 47), (22, 25), (29, 36), (6, 34), (12, 24), (1, 32), (29, 20), (41, 37), (41, 39), (19, 6), (14, 17), (10, 16), (0, 12), (6, 47), (36, 5), (2, 1), (41, 40), (36, 15), (34, 11), (26, 3), (22, 3), (23, 43), (16, 0), (25, 44), (31, 35), (25, 18), (2, 8), (6, 42), (3, 17), (25, 2), (12, 25), (8, 0), (23, 19), (7, 30), (23, 27), (7, 16), (17, 5), (28, 26), (16, 46), (13, 33), (17, 24), (5, 30), (30, 19), (11, 12), (14, 40), (4, 29), (33, 2), (26, 43), (2, 38), (14, 0), (37, 6), (9, 6), (13, 26), (12, 30), (6, 25), (26, 30), (37, 37), (35, 26), (20, 39), (24, 15), (7, 18), (34, 1), (13, 11), (27, 12), (1, 46), (0, 37), (35, 6), (18, 40), (37, 33), (12, 35), (33, 10), (30, 37), (42, 11), (18, 30), (26, 2), (4, 19), (30, 46), (25, 15), (22, 46), (39, 3), (39, 42), (30, 36), (19, 8), (4, 22), (25, 0), (22, 22), (27, 42), (40, 39), (36, 47), (22, 18), (6, 1), (3, 5), (1, 44), (17, 20), (42, 2), (4, 16), (39, 2), (1, 9), (28, 22), (17, 46), (23, 33), (29, 15), (27, 40), (33, 31), (36, 16), (41, 44), (9, 4), (4, 27), (23, 1), (17, 37), (2, 17), (32, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 42), (37, 42), (7, 5), (2, 41), (22, 25), (5, 39), (17, 17), (39, 5), (28, 15), (13, 1), (25, 27), (24, 23), (14, 5), (7, 29), (18, 32), (11, 24), (28, 31), (20, 23), (22, 8), (37, 4), (20, 1), (13, 9), (3, 18), (2, 31), (28, 14), (30, 47), (28, 41), (13, 14), (14, 27), (19, 44), (42, 30), (14, 18), (16, 6), (10, 41), (3, 36), (29, 44), (6, 9), (37, 45), (1, 3), (17, 8), (41, 15), (19, 43), (8, 16), (26, 13), (23, 1), (43, 44), (10, 8), (39, 19), (36, 15), (35, 9), (23, 14), (32, 40), (17, 20), (11, 7), (5, 12), (20, 35), (14, 4), (4, 40), (12, 40), (17, 42), (32, 0), (17, 29), (14, 15), (9, 35), (35, 45), (2, 40), (38, 6), (33, 23), (15, 6), (31, 13), (42, 31), (10, 28), (38, 43), (39, 18), (22, 47), (35, 3), (16, 1), (32, 2), (0, 27), (7, 42), (5, 28), (31, 3), (14, 28), (26, 24), (9, 40), (42, 17), (19, 28), (26, 35), (23, 19), (14, 16), (21, 7), (6, 0), (32, 20), (6, 47), (37, 18), (4, 20), (19, 41), (37, 7), (32, 17), (29, 9), (3, 28), (20, 43), (18, 45), (17, 38), (33, 18), (40, 20), (3, 37), (39, 34), (38, 14), (24, 4), (14, 25), (41, 1), (32, 36), (30, 25), (29, 6), (40, 0), (40, 4), (43, 11), (40, 8), (30, 29), (40, 17), (13, 43), (8, 33), (13, 19), (36, 46), (10, 4), (23, 45), (15, 13), (29, 31), (18, 43), (21, 8), (34, 45), (39, 47), (43, 8), (30, 44), (7, 45), (19, 30), (38, 38), (31, 39), (43, 17), (8, 10), (31, 10), (8, 0), (13, 23), (26, 4), (30, 22), (15, 47), (36, 21), (5, 21), (4, 18), (6, 8), (41, 4), (15, 33), (36, 17), (30, 48), (29, 22), (19, 4), (1, 31), (35, 8), (35, 11), (38, 3), (43, 47), (14, 34), (24, 24), (18, 10), (36, 7), (33, 41), (2, 9), (41, 22), (9, 7), (15, 19), (3, 34), (14, 1), (26, 46), (3, 41), (8, 26), (0, 48), (33, 47), (30, 40), (4, 0), (16, 34), (14, 36), (7, 8), (38, 1), (24, 16), (25, 40), (19, 3), (39, 39), (30, 28), (9, 34), (13, 27), (16, 13), (40, 11), (18, 9), (4, 39), (14, 42), (28, 24), (43, 6), (17, 39), (6, 6), (29, 48), (34, 12), (42, 47), (19, 9), (36, 16), (33, 28), (40, 42), (19, 26), (17, 40), (10, 7), (15, 31), (35, 46), (25, 18), (11, 40), (21, 45), (11, 31), (20, 33), (28, 11), (3, 43), (33, 15), (9, 37), (19, 2), (36, 8), (12, 47), (0, 21), (25, 35), (23, 37), (30, 6), (14, 6), (28, 34), (43, 37), (36, 39), (17, 31), (31, 2), (16, 24), (9, 19), (9, 18), (43, 5), (43, 30), (5, 35), (39, 48), (42, 32), (29, 42), (33, 16), (6, 33), (3, 21), (16, 48), (24, 29), (38, 24), (0, 39), (23, 33), (24, 41), (20, 31), (10, 1), (37, 48), (17, 6), (4, 41), (25, 13), (11, 42), (7, 22), (3, 27), (6, 7), (8, 24), (37, 20), (39, 27), (4, 5), (31, 19), (26, 43), (27, 18), (24, 2), (7, 14), (13, 29), (28, 39), (6, 27), (14, 19), (39, 31), (9, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 7), (6, 27), (13, 14), (33, 1), (25, 40), (33, 14), (39, 3), (24, 3), (20, 17), (24, 19), (42, 11), (18, 32), (9, 31), (43, 27), (0, 26), (14, 14), (20, 43), (21, 17), (14, 8), (7, 33), (10, 15), (25, 35), (38, 39), (29, 14), (18, 37), (15, 28), (11, 30), (34, 42), (13, 37), (9, 39), (15, 40), (29, 10), (13, 43), (33, 19), (35, 14), (2, 8), (0, 31), (16, 7), (0, 8), (41, 9), (15, 24), (38, 29), (42, 25), (8, 2), (7, 29), (38, 12), (23, 14), (2, 31), (43, 32), (22, 43), (37, 25), (6, 30), (27, 28), (0, 12), (32, 3), (15, 33), (23, 11), (24, 13), (5, 4), (24, 21), (17, 15), (23, 32), (24, 18), (40, 5), (42, 16), (34, 11), (10, 26), (7, 17), (17, 31), (24, 10), (25, 30), (37, 1), (8, 1), (30, 40), (21, 8), (31, 42), (13, 18), (20, 38), (33, 21), (18, 27), (38, 36), (9, 38), (43, 23), (16, 26), (10, 21), (33, 36), (7, 7), (21, 13), (21, 40), (13, 41), (17, 1), (42, 9), (4, 34), (33, 7), (10, 13), (43, 17), (27, 11), (26, 3), (17, 9), (43, 25), (31, 30), (13, 30), (22, 31), (7, 8), (9, 37), (19, 31), (7, 6), (10, 9), (34, 13), (10, 7), (14, 13), (17, 36), (9, 30), (30, 3), (38, 41), (2, 23), (14, 15), (21, 42), (28, 22), (13, 39), (7, 22), (17, 30), (39, 13), (31, 8), (35, 4), (4, 7), (36, 34), (29, 30), (41, 26), (19, 13), (25, 6), (35, 3), (23, 21), (6, 9), (10, 41), (0, 25), (16, 36), (19, 15), (39, 29), (2, 16), (6, 23), (31, 40), (11, 4), (36, 39), (21, 18), (33, 11), (17, 14), (19, 20), (32, 15), (30, 24), (35, 26), (31, 29), (39, 24), (20, 26), (0, 15), (11, 2), (2, 29), (34, 40), (41, 31), (28, 33), (22, 10), (5, 26), (25, 0), (6, 38), (29, 3), (16, 40), (12, 19), (3, 34), (4, 2), (23, 31), (10, 30), (36, 10), (20, 39), (39, 35), (25, 25), (15, 30), (38, 43), (6, 42), (26, 28), (38, 42), (12, 26), (37, 29), (5, 1), (19, 21), (22, 2), (33, 32), (29, 25), (32, 16), (33, 9), (15, 9), (18, 10), (30, 38), (33, 13), (9, 1), (32, 19), (16, 4), (30, 9), (0, 37), (2, 19), (8, 34), (25, 11), (34, 4), (3, 18), (30, 14), (6, 24), (6, 25), (4, 43), (20, 29), (34, 21), (36, 4), (34, 17), (39, 34), (1, 42), (3, 5), (17, 25), (35, 11), (24, 32), (18, 43), (20, 14), (17, 43), (0, 21), (19, 5), (26, 35), (38, 38), (15, 3), (39, 39), (17, 0), (10, 29), (12, 16), (7, 24), (6, 39), (34, 36), (26, 20), (26, 5), (27, 32), (7, 32), (37, 32), (42, 32), (37, 34), (26, 42), (37, 5), (22, 1), (13, 12), (15, 41), (27, 15), (28, 14), (34, 2), (39, 33), (31, 27), (7, 18), (5, 36), (32, 13), (26, 37), (9, 42), (42, 41), (28, 29), (10, 11), (14, 18), (26, 2), (29, 31), (31, 23), (7, 0), (37, 36), (1, 5), (37, 18), (41, 30), (43, 0), (9, 6), (14, 40), (9, 34), (37, 4), (23, 19), (36, 20), (19, 36), (41, 1), (31, 37), (26, 1), (4, 31), (42, 35), (1, 8), (25, 4), (31, 5), (11, 6), (27, 23), (34, 16), (17, 8), (14, 12), (1, 26), (26, 30), (11, 39), (28, 38), (12, 35), (19, 12), (2, 32), (17, 40), (26, 21), (7, 4), (36, 6), (25, 24), (25, 10), (7, 19), (21, 31), (9, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 29), (24, 29), (4, 0), (32, 16), (3, 20), (6, 0), (5, 14), (12, 20), (36, 38), (9, 10), (3, 25), (10, 24), (29, 28), (37, 10), (21, 46), (0, 27), (32, 9), (5, 43), (15, 42), (3, 0), (6, 19), (8, 30), (5, 10), (18, 42), (2, 18), (33, 26), (32, 15), (40, 30), (22, 21), (12, 36), (26, 16), (0, 16), (26, 38), (34, 7), (20, 11), (36, 33), (30, 22), (3, 31), (6, 34), (21, 8), (10, 0), (18, 3), (18, 14), (40, 42), (39, 24), (19, 34), (27, 10), (11, 43), (25, 45), (28, 46), (8, 9), (9, 42), (37, 26), (24, 26), (26, 22), (8, 43), (34, 21), (38, 31), (14, 37), (16, 12), (7, 11), (36, 30), (5, 31), (31, 42), (2, 14), (1, 34), (39, 38), (14, 45), (26, 24), (0, 39), (10, 20), (37, 16), (32, 34), (38, 9), (30, 18), (28, 20), (21, 34), (23, 43), (27, 45), (5, 8), (8, 27), (1, 14), (15, 43), (31, 24), (8, 41), (28, 30), (15, 17), (13, 33), (10, 44), (33, 43), (24, 40), (13, 31), (32, 45), (40, 45), (13, 43), (21, 7), (22, 32), (26, 20), (4, 14), (8, 39), (23, 10), (1, 1), (26, 17), (4, 7), (25, 30), (15, 34), (35, 24), (2, 4), (13, 28), (3, 43), (5, 15), (31, 16), (23, 0), (21, 13), (37, 11), (24, 46), (20, 3), (37, 6), (34, 3), (33, 22), (26, 32), (18, 1), (9, 34), (38, 22), (12, 33), (30, 26), (0, 42), (37, 29), (9, 38), (19, 28), (16, 37), (16, 39), (40, 4), (30, 36), (2, 20), (39, 39), (40, 6), (22, 23), (13, 11), (0, 24), (23, 20), (29, 29), (2, 17), (37, 23), (7, 12), (35, 4), (6, 14), (27, 29), (33, 20), (12, 24), (30, 45), (23, 41), (12, 43), (7, 33), (31, 27), (39, 34), (21, 19), (37, 36), (10, 36), (21, 41), (35, 13), (14, 21), (40, 2), (21, 9), (18, 32), (3, 19), (35, 1), (32, 1), (8, 25), (9, 18), (35, 39), (20, 15), (11, 22), (20, 45), (28, 13), (10, 27), (18, 28), (13, 2), (40, 7), (39, 16), (36, 25), (30, 27), (40, 43), (17, 11), (35, 0), (5, 19), (22, 11), (27, 8), (33, 9), (1, 17), (35, 22), (36, 22), (14, 13), (18, 6), (2, 37), (34, 4), (19, 40), (18, 0), (27, 30), (1, 45), (13, 35), (33, 4), (6, 29), (32, 39), (40, 34), (29, 6), (22, 43), (11, 11), (17, 1), (9, 35), (12, 5), (23, 3), (10, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 31), (25, 33), (8, 42), (14, 29), (34, 6), (42, 20), (27, 16), (35, 27), (23, 28), (1, 27), (31, 8), (44, 6), (41, 18), (22, 32), (44, 11), (26, 0), (7, 1), (7, 19), (33, 41), (10, 28), (26, 1), (3, 12), (44, 7), (30, 20), (10, 18), (3, 33), (39, 27), (36, 14), (35, 34), (13, 2), (46, 13), (33, 36), (27, 13), (3, 30), (15, 12), (44, 31), (11, 10), (36, 28), (16, 42), (43, 5), (34, 40), (4, 30), (0, 5), (12, 25), (34, 2), (16, 39), (18, 32), (35, 32), (28, 9), (30, 37), (11, 3), (10, 5), (2, 14), (40, 39), (28, 8), (28, 40), (27, 25), (44, 13), (2, 26), (9, 18), (8, 25), (14, 28), (34, 12), (1, 41), (29, 16), (33, 35), (1, 36), (22, 37), (3, 34), (5, 32), (10, 6), (5, 1), (44, 15), (29, 4), (17, 6), (9, 29), (28, 42), (12, 36), (40, 7), (21, 30), (2, 12), (25, 3), (23, 31), (10, 12), (37, 17), (43, 21), (24, 36), (3, 3), (26, 11), (34, 10), (41, 16), (45, 25), (11, 4), (40, 26), (34, 42), (37, 15), (30, 12), (46, 22), (26, 39), (20, 6), (35, 19), (33, 0), (35, 40), (26, 20), (33, 30), (10, 27), (29, 26), (11, 35), (31, 15), (43, 42), (13, 9), (30, 13), (46, 26), (37, 18), (23, 39), (36, 11), (24, 24), (18, 30), (8, 11), (41, 12), (4, 34), (3, 1), (10, 42), (41, 29), (15, 9), (16, 6), (4, 9), (6, 37), (18, 18), (38, 37), (21, 7), (38, 33), (21, 15), (37, 34), (28, 16), (9, 36), (26, 27), (9, 20), (6, 18), (11, 2), (24, 10), (28, 2), (6, 10), (42, 33), (46, 21), (22, 31), (29, 21), (28, 41), (11, 8), (13, 41), (46, 11), (31, 14), (4, 25), (42, 2), (9, 10), (2, 33), (38, 11), (18, 42), (41, 14), (15, 23), (7, 32), (31, 35), (40, 35), (14, 31), (12, 6), (20, 37), (28, 10), (6, 33), (44, 22), (15, 2), (32, 17), (26, 36), (40, 21), (11, 0), (5, 13), (4, 40), (29, 15), (18, 1), (46, 39), (3, 41), (42, 7), (22, 18), (16, 2), (45, 11), (40, 38), (43, 34), (5, 23), (39, 16), (34, 25), (24, 5), (44, 29), (13, 8), (27, 40), (9, 24), (18, 4), (20, 28), (38, 10), (6, 27), (19, 17), (42, 0), (14, 8), (36, 39), (9, 40), (4, 18), (33, 24), (4, 5), (24, 28), (0, 37), (37, 22), (37, 40), (4, 39), (16, 26), (38, 8), (9, 27), (41, 31), (45, 36), (9, 38), (25, 13), (4, 0), (25, 27), (10, 37), (46, 15), (42, 8), (29, 41), (0, 22), (25, 11), (31, 4), (36, 42), (16, 18), (25, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 23), (41, 41), (5, 19), (44, 26), (30, 19), (21, 18), (27, 47), (18, 43), (29, 0), (13, 6), (23, 29), (4, 11), (39, 18), (32, 3), (46, 19), (6, 45), (32, 13), (42, 29), (23, 13), (8, 42), (17, 38), (20, 46), (14, 33), (40, 46), (6, 35), (31, 21), (12, 21), (24, 22), (26, 28), (45, 26), (29, 28), (14, 36), (10, 20), (10, 2), (32, 20), (46, 15), (36, 43), (17, 42), (24, 15), (31, 27), (38, 26), (18, 46), (13, 29), (25, 27), (0, 11), (7, 39), (26, 20), (10, 31), (30, 40), (21, 3), (46, 10), (36, 3), (41, 6), (23, 7), (32, 38), (10, 41), (46, 36), (44, 38), (47, 23), (3, 40), (23, 0), (36, 24), (0, 26), (36, 18), (33, 41), (31, 30), (16, 25), (23, 26), (0, 46), (28, 26), (1, 19), (36, 14), (31, 9), (22, 6), (28, 1), (25, 44), (31, 20), (22, 4), (6, 16), (42, 8), (15, 35), (32, 24), (14, 20), (7, 26), (47, 19), (43, 26), (22, 45), (43, 45), (12, 31), (41, 24), (38, 10), (15, 40), (1, 29), (37, 34), (4, 30), (9, 2), (8, 19), (13, 12), (24, 46), (28, 30), (16, 14), (31, 43), (28, 10), (17, 28), (1, 22), (20, 43), (15, 5), (14, 19), (35, 35), (6, 42), (15, 31), (8, 23), (25, 10), (21, 42), (45, 7), (4, 34), (36, 19), (24, 45), (26, 15), (8, 36), (44, 13), (35, 37), (13, 39), (0, 9), (28, 23), (19, 39), (42, 34), (40, 24), (25, 22), (19, 28), (11, 27), (28, 7), (1, 3), (39, 47), (19, 30), (31, 45), (16, 11), (42, 6), (38, 7), (5, 42), (4, 15), (29, 42), (1, 36), (5, 22), (24, 40), (34, 7), (19, 43), (12, 42), (41, 11), (35, 32), (47, 42), (33, 47), (21, 40), (11, 17), (47, 24), (13, 22), (13, 20), (11, 8), (44, 23), (47, 30), (21, 33), (11, 25), (6, 27), (11, 0), (1, 37), (5, 0), (31, 12), (22, 24), (36, 20), (24, 39), (32, 37), (8, 5), (22, 33), (20, 24), (31, 3), (43, 0), (19, 8), (38, 21), (14, 10), (38, 24), (0, 33), (38, 38), (12, 18), (34, 45), (13, 38), (4, 35), (33, 10), (37, 33), (12, 44), (12, 19), (28, 11), (33, 4), (0, 14), (20, 17), (1, 23), (44, 42), (21, 4), (16, 5), (33, 45), (26, 35), (17, 8), (45, 40), (18, 23), (18, 20), (6, 44), (25, 41), (6, 33), (20, 35), (15, 11), (44, 1), (3, 39), (13, 42), (43, 20), (28, 20), (26, 40), (42, 23), (12, 46), (11, 35), (37, 46), (38, 20), (35, 31), (8, 2), (10, 45), (2, 10), (32, 31), (26, 21), (0, 38), (30, 45), (43, 17), (13, 25), (43, 43), (16, 37), (32, 39), (38, 19), (28, 40), (23, 38), (28, 36), (14, 31), (11, 4), (24, 34), (3, 19), (9, 19), (20, 2), (4, 12), (23, 39), (24, 11), (26, 7), (8, 26), (39, 39), (26, 29), (15, 32), (25, 35), (47, 1), (41, 20), (11, 11), (19, 25), (3, 4), (3, 30), (19, 10), (28, 41), (3, 1), (25, 45), (27, 26), (21, 24), (47, 21), (39, 13), (11, 2), (15, 36), (13, 9), (34, 11), (34, 5), (14, 0), (23, 43), (20, 10), (8, 22), (8, 10), (47, 20), (41, 2), (30, 14), (8, 25), (5, 4), (7, 20), (21, 46), (17, 4), (15, 17), (18, 27), (27, 35), (3, 3), (46, 41), (45, 17), (7, 6), (33, 33), (32, 21), (33, 20), (43, 46), (47, 22), (41, 10), (9, 44), (16, 10), (46, 32), (47, 14), (6, 39), (27, 21), (39, 45), (16, 34), (0, 4), (23, 17), (27, 27), (9, 18), (17, 12), (25, 23), (37, 19), (10, 44), (28, 4), (7, 8), (15, 29), (40, 39), (43, 41), (7, 45), (28, 16), (13, 7), (34, 29), (42, 26), (19, 32), (34, 25), (33, 6), (10, 4), (2, 37), (8, 0), (47, 25), (43, 3), (0, 27), (31, 41), (45, 32), (25, 7), (34, 33), (37, 25), (24, 12), (41, 30), (36, 34), (30, 2), (31, 7), (29, 20), (1, 20), (19, 46), (10, 23), (42, 32), (6, 14), (39, 37), (45, 3), (47, 39), (16, 8), (0, 24), (5, 41), (42, 18), (37, 39), (9, 43), (38, 34), (29, 38), (12, 43), (26, 26), (4, 39), (6, 37), (9, 13), (15, 10), (44, 4), (2, 2), (45, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 7), (15, 39), (19, 16), (34, 35), (32, 28), (24, 20), (11, 25), (9, 8), (28, 32), (38, 23), (33, 21), (28, 37), (32, 4), (34, 8), (31, 7), (32, 11), (16, 37), (37, 9), (38, 36), (20, 33), (10, 8), (9, 22), (4, 15), (27, 22), (33, 25), (37, 14), (3, 12), (11, 7), (33, 4), (8, 22), (33, 22), (1, 18), (24, 33), (19, 21), (2, 39), (11, 1), (20, 28), (22, 2), (3, 30), (2, 36), (14, 5), (26, 36), (39, 1), (1, 33), (38, 16), (0, 19), (7, 24), (4, 10), (12, 36), (8, 35), (12, 20), (24, 4), (31, 36), (15, 2), (16, 33), (19, 39), (15, 5), (19, 31), (21, 6), (18, 27), (36, 24), (37, 19), (18, 17), (11, 16), (11, 14), (18, 9), (23, 23), (24, 34), (27, 40), (40, 24), (41, 34), (17, 21), (14, 3), (25, 29), (17, 29), (9, 9), (32, 19), (0, 1), (33, 35), (21, 14), (34, 14), (22, 33), (19, 10), (6, 22), (23, 29), (31, 34), (18, 37), (21, 34), (34, 4), (2, 26), (2, 37), (23, 39), (37, 23), (40, 16), (18, 30), (38, 10), (32, 21), (13, 5), (5, 39), (10, 7), (34, 0), (9, 35), (42, 1), (24, 32), (0, 26), (8, 23), (34, 6), (39, 13), (13, 14), (36, 38), (0, 13), (10, 30), (19, 20), (5, 12), (33, 12), (4, 20), (7, 7), (10, 21), (29, 34), (23, 20), (31, 2), (20, 6), (24, 18), (30, 33), (8, 18), (27, 28), (14, 20), (6, 13), (10, 31), (12, 28), (15, 9), (17, 20), (4, 12), (7, 3), (1, 28), (5, 32), (2, 23), (40, 7), (41, 11), (4, 39), (38, 12), (37, 33), (36, 36), (4, 33), (33, 24), (5, 2), (3, 16), (12, 39), (26, 6), (37, 25), (0, 11), (38, 34), (1, 32), (14, 18), (16, 16), (26, 1), (4, 0), (5, 17), (27, 1), (1, 35), (0, 33), (22, 23), (11, 19), (10, 17), (5, 40), (40, 29), (12, 16), (26, 19), (38, 14), (40, 21), (40, 22), (17, 24), (3, 10), (36, 35), (36, 37), (4, 34), (16, 34), (33, 27), (21, 22), (30, 10), (22, 0), (11, 12), (26, 38), (35, 19), (16, 15), (9, 6), (41, 0), (38, 0), (14, 24), (20, 10), (15, 14), (22, 26), (9, 28), (31, 38), (42, 0), (38, 22), (19, 29), (37, 36), (30, 9), (2, 20), (22, 25), (5, 5), (13, 31), (23, 31), (41, 30), (4, 30), (39, 10), (6, 29), (6, 8), (33, 19), (39, 32), (20, 3), (38, 28), (4, 32), (28, 10), (34, 31), (37, 3), (4, 6), (6, 31), (16, 4), (41, 21), (16, 40), (25, 14), (17, 5), (10, 38), (21, 3), (20, 40), (41, 20), (2, 9), (12, 9), (9, 16), (10, 34), (17, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 44), (40, 45), (38, 44), (22, 3), (32, 27), (3, 37), (26, 27), (21, 40), (33, 29), (5, 11), (18, 29), (22, 39), (40, 35), (17, 9), (8, 31), (10, 13), (29, 9), (41, 12), (36, 22), (17, 15), (32, 20), (6, 4), (20, 22), (10, 45), (1, 7), (21, 2), (33, 36), (13, 6), (39, 11), (39, 32), (30, 14), (11, 38), (0, 5), (27, 9), (13, 46), (12, 22), (9, 22), (28, 9), (41, 9), (20, 34), (6, 39), (40, 11), (2, 33), (11, 16), (24, 18), (28, 31), (15, 6), (26, 36), (23, 0), (11, 31), (31, 14), (6, 1), (2, 32), (6, 2), (14, 30), (27, 16), (26, 7), (11, 14), (21, 5), (41, 1), (0, 33), (1, 36), (15, 45), (16, 13), (22, 31), (29, 18), (37, 15), (23, 32), (39, 38), (38, 17), (41, 40), (19, 20), (24, 39), (20, 12), (33, 33), (4, 11), (9, 8), (4, 16), (36, 8), (34, 32), (31, 32), (40, 23), (13, 33), (17, 0), (30, 25), (15, 13), (13, 35), (37, 29), (2, 10), (8, 12), (24, 38), (33, 3), (38, 14), (33, 7), (8, 29), (9, 3), (18, 11), (27, 15), (33, 16), (8, 27), (32, 25), (21, 23), (40, 24), (14, 10), (34, 21), (28, 2), (9, 14), (41, 4), (13, 25), (36, 26), (29, 37), (23, 25), (35, 11), (36, 16), (16, 24), (32, 11), (26, 35), (39, 37), (36, 41), (31, 17), (10, 4), (9, 40), (27, 14), (38, 45), (20, 17), (7, 46), (35, 20), (35, 33), (27, 7), (32, 24), (35, 24), (27, 2), (22, 12), (1, 30), (17, 35), (19, 8), (4, 18), (23, 40), (17, 11), (33, 28), (39, 14), (40, 15), (28, 14), (32, 22), (8, 25), (21, 1), (34, 39), (8, 37), (23, 21), (7, 15), (0, 1), (32, 35), (26, 23), (13, 12), (13, 11), (1, 44), (0, 39), (6, 16), (2, 4), (32, 2), (35, 7), (9, 11), (36, 7), (21, 15), (4, 38), (37, 16), (32, 1), (19, 18), (17, 29), (5, 9), (28, 24), (26, 31), (22, 25), (35, 39), (20, 18), (13, 39), (16, 38), (2, 28), (7, 36), (15, 30), (21, 9), (16, 42), (7, 41), (32, 18), (0, 12), (40, 16), (30, 3), (26, 43), (23, 20), (34, 28), (36, 13), (8, 20), (19, 6), (37, 30), (0, 11), (25, 9), (0, 37), (11, 25), (9, 31), (36, 19), (34, 26), (4, 24), (1, 2), (5, 18), (21, 4), (31, 1), (10, 27), (19, 0), (31, 21), (11, 20), (19, 38), (34, 46), (24, 31), (11, 42), (7, 24), (15, 26), (5, 34), (9, 17), (29, 40), (32, 30), (10, 2), (9, 26), (41, 23), (26, 21), (11, 37), (3, 29), (13, 17), (18, 42), (40, 20), (39, 41), (33, 24), (18, 8), (40, 30), (25, 22), (18, 16), (33, 45), (10, 10), (12, 10), (36, 1), (8, 17), (12, 16), (40, 18), (27, 43), (2, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 22), (12, 41), (4, 29), (37, 10), (15, 24), (29, 30), (39, 5), (17, 33), (18, 33), (28, 5), (13, 5), (30, 26), (20, 13), (41, 11), (41, 6), (33, 43), (15, 35), (45, 16), (30, 34), (5, 36), (5, 13), (13, 8), (25, 22), (3, 23), (4, 26), (9, 24), (14, 35), (43, 8), (31, 40), (2, 30), (35, 38), (40, 33), (18, 47), (17, 35), (37, 29), (12, 18), (12, 45), (14, 7), (36, 14), (36, 39), (19, 21), (22, 26), (16, 41), (37, 28), (28, 42), (24, 36), (33, 29), (38, 5), (9, 8), (24, 10), (45, 8), (34, 9), (16, 7), (10, 2), (15, 41), (38, 33), (30, 17), (35, 26), (20, 40), (4, 33), (12, 46), (38, 16), (3, 19), (2, 10), (37, 44), (2, 43), (36, 0), (2, 46), (12, 24), (8, 2), (7, 22), (7, 42), (26, 8), (10, 11), (14, 2), (22, 2), (13, 13), (42, 31), (10, 26), (32, 38), (45, 32), (17, 46), (10, 44), (8, 5), (38, 7), (28, 46), (16, 1), (7, 1), (41, 5), (38, 17), (20, 20), (2, 33), (37, 35), (36, 38), (26, 21), (34, 5), (34, 26), (35, 9), (11, 46), (9, 28), (44, 21), (16, 8), (32, 22), (43, 42), (13, 23), (27, 41), (22, 35), (30, 3), (2, 32), (22, 17), (42, 29), (7, 13), (24, 33), (42, 16), (35, 10), (34, 1), (34, 21), (2, 27), (25, 32), (19, 32), (20, 33), (13, 34), (14, 1), (30, 30), (15, 10), (19, 15), (43, 7), (18, 21), (39, 2), (16, 40), (26, 25), (42, 12), (39, 25), (42, 46), (22, 47), (0, 32), (4, 35), (9, 21), (33, 37), (44, 33), (26, 11), (27, 20), (8, 47), (15, 11), (6, 35), (21, 20), (42, 20), (28, 41), (16, 5), (15, 19), (10, 24), (31, 44), (11, 30), (32, 40), (9, 41), (19, 31), (4, 31), (10, 25), (42, 32), (33, 4), (10, 12), (33, 22), (19, 20), (33, 30), (25, 45), (39, 4), (5, 20), (44, 36), (25, 6), (15, 27), (28, 35), (29, 40), (35, 18), (9, 16), (13, 35), (8, 26), (28, 21), (33, 3), (13, 22), (24, 21), (34, 43), (37, 18), (45, 5), (11, 2), (23, 12), (9, 43), (19, 35), (31, 47), (4, 22), (7, 16), (4, 46), (28, 8), (34, 40), (3, 10), (1, 2), (45, 25), (23, 35), (19, 9), (27, 31), (0, 35), (8, 6), (32, 43), (20, 4), (32, 32), (22, 42), (1, 47), (15, 13), (31, 32), (25, 26), (44, 27), (22, 12), (35, 19), (34, 38), (12, 39), (37, 8), (6, 23), (31, 27), (11, 23), (30, 2), (23, 37), (22, 0), (36, 37), (9, 17), (19, 22), (11, 1), (23, 39), (38, 8), (28, 38), (2, 12), (28, 1), (25, 46), (22, 10), (32, 15), (14, 27), (39, 29), (0, 7), (34, 6), (18, 5), (29, 7), (32, 4), (25, 7), (26, 47), (39, 12), (8, 13), (3, 43), (18, 24), (19, 33), (21, 6), (25, 1), (3, 29), (15, 44), (42, 7), (22, 4), (24, 9), (14, 41), (25, 14), (45, 23), (1, 38), (33, 28), (7, 40), (22, 9), (27, 13), (28, 40), (28, 25), (33, 23), (35, 24), (18, 23), (23, 28), (17, 31), (27, 34), (17, 19), (1, 28), (39, 35), (4, 15), (2, 11), (17, 44), (1, 13), (11, 40), (21, 35), (40, 26), (5, 42), (26, 7), (44, 46), (45, 35), (21, 41), (10, 19), (13, 38), (8, 43), (40, 5), (28, 19), (31, 5), (7, 9), (26, 20), (27, 2), (15, 7), (39, 10), (35, 17), (32, 10), (24, 32), (27, 14), (0, 44), (11, 35), (40, 12), (31, 41), (25, 21), (14, 18), (28, 33), (6, 19), (39, 23), (7, 15), (38, 44), (15, 5), (40, 6), (35, 29), (16, 22), (20, 3), (38, 26), (21, 13), (40, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 14), (39, 45), (12, 26), (16, 21), (26, 37), (26, 32), (8, 8), (9, 22), (2, 43), (13, 10), (32, 36), (7, 38), (12, 30), (19, 44), (23, 21), (16, 14), (15, 23), (37, 15), (30, 24), (8, 11), (39, 4), (4, 28), (0, 25), (19, 26), (38, 0), (37, 12), (28, 47), (33, 6), (41, 14), (12, 20), (12, 11), (32, 44), (10, 15), (25, 27), (13, 26), (23, 28), (24, 42), (33, 1), (1, 46), (3, 44), (39, 18), (20, 34), (14, 37), (37, 7), (28, 33), (33, 38), (27, 12), (11, 22), (17, 32), (6, 12), (40, 27), (17, 31), (6, 5), (18, 21), (18, 45), (21, 5), (22, 9), (27, 43), (34, 44), (13, 28), (31, 11), (27, 31), (33, 44), (31, 26), (21, 8), (7, 12), (36, 2), (27, 7), (32, 9), (18, 20), (4, 46), (17, 36), (42, 25), (2, 12), (19, 37), (20, 7), (26, 6), (32, 10), (5, 23), (30, 5), (22, 21), (8, 25), (1, 42), (37, 21), (40, 16), (12, 17), (34, 15), (28, 16), (31, 9), (41, 30), (19, 47), (11, 42), (20, 19), (4, 27), (2, 36), (22, 44), (27, 13), (37, 29), (31, 31), (20, 40), (28, 30), (5, 15), (20, 9), (34, 25), (10, 34), (3, 20), (23, 39), (9, 33), (20, 0), (37, 31), (26, 2), (27, 19), (39, 37), (42, 37), (24, 15), (33, 37), (27, 17), (14, 3), (15, 45), (29, 3), (4, 12), (24, 1), (11, 16), (7, 32), (18, 29), (0, 45), (19, 31), (34, 3), (30, 11), (10, 47), (5, 8), (1, 17), (25, 26), (38, 41), (32, 34), (18, 42), (8, 7), (8, 42), (29, 24), (33, 15), (33, 27), (31, 29), (26, 1), (18, 41), (24, 19), (19, 34), (27, 27), (19, 33), (19, 25), (16, 25), (7, 14), (3, 42), (5, 37), (1, 29), (27, 3), (30, 25), (42, 33), (19, 1), (33, 14), (0, 20), (17, 44), (24, 32), (20, 20), (11, 26), (32, 16), (40, 10), (38, 12), (29, 47), (40, 18), (16, 11), (28, 29), (25, 40), (36, 23), (25, 19), (36, 3), (22, 8), (23, 20), (39, 36), (37, 32), (11, 45), (36, 27), (3, 1), (30, 45), (21, 45), (10, 19), (39, 16), (29, 34), (40, 36), (4, 23), (0, 37), (35, 12), (10, 41), (31, 3), (23, 24), (8, 6), (39, 10), (11, 2), (14, 5), (1, 36), (31, 22), (27, 24), (2, 26), (8, 27), (8, 9), (3, 0), (5, 1), (21, 29), (2, 34), (21, 15), (15, 43), (41, 11), (11, 34), (42, 12), (21, 17), (5, 0), (35, 37), (25, 3), (12, 10), (18, 7), (20, 17), (21, 22), (42, 13), (37, 8), (13, 35), (3, 18), (25, 6), (6, 0), (16, 7), (42, 28), (23, 12), (34, 26), (40, 21), (23, 47), (17, 16), (38, 7), (8, 44), (32, 0), (11, 43), (13, 36), (28, 8), (19, 41), (22, 20), (0, 3), (15, 18), (11, 14), (7, 16), (33, 47), (18, 9), (15, 42), (22, 10), (7, 9), (38, 42), (8, 17), (4, 11), (38, 36), (10, 32), (21, 27), (6, 24), (31, 4), (24, 12), (14, 2), (28, 26), (8, 1), (29, 43), (38, 18), (22, 31), (28, 37), (21, 26), (4, 32), (18, 16), (21, 18), (38, 2), (4, 43), (12, 0), (4, 13), (34, 8), (40, 13), (2, 8), (33, 42), (29, 30), (3, 19), (36, 32), (17, 39), (42, 32), (21, 10), (0, 41), (2, 7), (17, 14), (10, 24), (7, 19), (4, 9), (25, 43), (11, 17), (12, 25), (26, 25), (6, 42), (27, 34), (26, 14), (9, 15), (26, 45), (12, 46), (32, 33), (19, 30), (1, 39), (20, 10), (40, 9), (10, 31), (33, 12), (29, 11), (32, 4), (36, 45), (5, 16), (35, 20), (15, 2), (36, 6), (19, 45), (17, 27), (3, 2), (42, 44), (40, 23), (20, 5), (40, 37), (19, 13), (39, 40), (37, 42), (31, 7), (19, 16), (39, 38), (18, 46), (5, 40), (34, 0), (26, 30), (37, 3), (11, 31), (5, 47), (19, 15), (16, 20), (3, 43), (20, 27), (26, 3), (13, 9), (19, 6), (18, 12), (6, 1), (40, 44), (38, 15), (13, 16), (35, 0), (39, 3), (5, 31), (10, 12), (6, 8), (32, 25), (18, 26), (12, 7), (22, 22), (7, 33), (25, 14), (30, 12), (29, 27), (8, 28), (10, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 21), (33, 45), (19, 38), (33, 22), (12, 25), (16, 37), (25, 2), (7, 41), (22, 29), (26, 5), (32, 9), (3, 39), (25, 8), (14, 16), (39, 23), (27, 34), (34, 40), (31, 5), (8, 33), (22, 43), (2, 13), (11, 22), (22, 20), (39, 18), (30, 35), (36, 14), (4, 28), (41, 32), (44, 25), (30, 42), (40, 38), (30, 3), (15, 38), (14, 4), (8, 32), (9, 38), (14, 26), (43, 37), (29, 26), (33, 19), (42, 32), (7, 14), (7, 16), (11, 9), (24, 2), (29, 18), (12, 46), (27, 6), (0, 38), (18, 17), (35, 37), (37, 19), (22, 22), (7, 36), (36, 7), (27, 3), (21, 19), (14, 8), (29, 13), (16, 45), (0, 8), (25, 42), (42, 37), (44, 44), (6, 22), (2, 0), (25, 20), (11, 28), (5, 40), (9, 25), (34, 28), (13, 40), (15, 23), (14, 24), (17, 43), (15, 43), (29, 25), (14, 11), (13, 32), (20, 37), (4, 20), (21, 40), (17, 26), (16, 38), (38, 43), (16, 22), (43, 6), (34, 7), (10, 7), (3, 31), (32, 3), (21, 2), (31, 20), (40, 45), (33, 33), (16, 31), (21, 28), (25, 34), (19, 37), (11, 43), (10, 26), (24, 19), (36, 9), (20, 8), (14, 46), (44, 4), (30, 41), (40, 20), (14, 2), (3, 16), (44, 18), (26, 2), (10, 17), (16, 1), (5, 13), (19, 18), (14, 0), (29, 22), (1, 43), (13, 45), (28, 39), (16, 21), (2, 19), (28, 31), (4, 7), (22, 9), (16, 44), (11, 25), (29, 41), (19, 3), (29, 6), (34, 5), (31, 3), (8, 11), (42, 28), (21, 38), (10, 43), (5, 24), (25, 40), (17, 4), (43, 16), (28, 11), (22, 11), (5, 43), (1, 16), (35, 14), (33, 20), (19, 42), (2, 11), (43, 32), (14, 34), (28, 8), (25, 15), (4, 35), (16, 43), (33, 32), (9, 30), (37, 41), (36, 39), (2, 1), (32, 43), (38, 19), (43, 36), (32, 32), (14, 6), (20, 31), (6, 27), (38, 14), (21, 9), (26, 7), (26, 14), (15, 37), (39, 11), (38, 25), (33, 11), (9, 4), (28, 36), (39, 43), (4, 6), (19, 30), (1, 37), (32, 35), (23, 44), (15, 18), (29, 12), (13, 42), (19, 32), (37, 6), (27, 46), (24, 10), (12, 30), (29, 4), (36, 29), (1, 3), (36, 23), (20, 11), (16, 36), (1, 33), (18, 9), (42, 2), (30, 24), (42, 11), (2, 45), (40, 1), (39, 46), (8, 27), (28, 46), (23, 1), (5, 37), (21, 1), (5, 5), (1, 8), (23, 6), (11, 27), (27, 36), (35, 5), (42, 45), (36, 20), (27, 13), (13, 25), (23, 11), (21, 10), (30, 44), (38, 26), (41, 20), (25, 23), (15, 36), (33, 6), (4, 43), (18, 5), (27, 42), (37, 32), (16, 17), (37, 37), (21, 5), (33, 5), (39, 5), (12, 12), (31, 1), (37, 23), (26, 23), (26, 37), (23, 43), (31, 43), (38, 0), (24, 8), (29, 27), (33, 46), (43, 45), (28, 17), (13, 41), (7, 34), (32, 0), (18, 16), (40, 10), (28, 15), (34, 21), (41, 2), (22, 10), (7, 10), (44, 39), (20, 30), (3, 22), (29, 8), (40, 33), (35, 29), (35, 36), (3, 25), (35, 19), (36, 18), (41, 0), (26, 16), (29, 39), (29, 15), (1, 0), (44, 40), (38, 33), (35, 33), (7, 7), (40, 13), (18, 37), (0, 28), (30, 27), (43, 42), (10, 16), (12, 1), (6, 35), (40, 24), (34, 38), (31, 45), (18, 35), (21, 8), (43, 44), (0, 45), (18, 38), (24, 13), (4, 30), (14, 13), (35, 25), (16, 25), (3, 14), (34, 9), (21, 20), (24, 35), (18, 29), (20, 4), (31, 34), (17, 18), (8, 23), (0, 11), (40, 9), (0, 4), (13, 28), (18, 3), (33, 13), (24, 34), (26, 27), (31, 36), (22, 32), (8, 43), (39, 20), (20, 28), (32, 31), (22, 0), (17, 15), (40, 41), (10, 28), (34, 22), (3, 21), (25, 10), (18, 34), (5, 20), (15, 29), (44, 33), (36, 35), (25, 36), (36, 44), (29, 14), (24, 38), (26, 15), (5, 22), (29, 28), (18, 11), (9, 17), (4, 14), (5, 44), (13, 12), (4, 37), (42, 27), (20, 0), (25, 7), (13, 21), (41, 24), (13, 6), (39, 32), (2, 24), (29, 16), (14, 30), (8, 15), (5, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 41), (31, 38), (36, 48), (7, 34), (13, 3), (39, 10), (23, 1), (1, 20), (13, 40), (26, 10), (10, 37), (23, 44), (2, 13), (18, 38), (39, 27), (27, 40), (27, 28), (2, 40), (30, 1), (21, 18), (1, 35), (8, 40), (16, 23), (37, 12), (19, 22), (11, 38), (26, 40), (27, 1), (20, 47), (29, 0), (6, 4), (8, 0), (22, 1), (14, 42), (2, 19), (28, 27), (22, 39), (15, 47), (18, 24), (31, 45), (2, 11), (29, 25), (2, 5), (38, 12), (31, 24), (14, 18), (15, 36), (24, 29), (34, 21), (29, 43), (32, 33), (36, 42), (35, 45), (34, 11), (21, 13), (10, 6), (26, 27), (30, 33), (10, 19), (3, 7), (21, 43), (39, 26), (24, 35), (28, 0), (26, 35), (6, 26), (5, 12), (24, 3), (34, 25), (30, 17), (24, 36), (33, 5), (10, 43), (10, 44), (36, 26), (10, 41), (30, 23), (20, 14), (13, 15), (3, 20), (34, 17), (12, 36), (25, 5), (15, 27), (10, 45), (7, 19), (19, 10), (22, 36), (16, 39), (25, 34), (30, 32), (12, 29), (22, 38), (1, 43), (19, 17), (35, 14), (7, 15), (27, 11), (18, 48), (14, 1), (34, 37), (39, 29), (29, 17), (21, 29), (21, 28), (25, 44), (11, 31), (28, 3), (33, 15), (33, 1), (0, 7), (1, 7), (22, 17), (23, 46), (38, 39), (18, 16), (35, 12), (14, 11), (38, 46), (31, 39), (28, 24), (3, 14), (17, 15), (1, 40), (16, 3), (12, 30), (39, 21), (33, 43), (39, 36), (21, 23), (9, 10), (2, 29), (5, 1), (34, 44), (32, 47), (18, 10), (1, 34), (30, 21), (4, 0), (17, 20), (31, 7), (23, 43), (12, 45), (24, 30), (4, 12), (37, 36), (30, 41), (30, 5), (22, 8), (7, 6), (35, 27), (32, 1), (31, 14), (19, 15), (23, 10), (23, 9), (37, 8), (12, 4), (15, 37), (30, 43), (28, 6), (9, 21), (36, 43), (23, 14), (5, 46), (20, 26), (1, 15), (29, 16), (7, 17), (3, 28), (2, 31), (9, 39), (38, 22), (0, 13), (10, 12), (39, 0), (0, 34), (31, 26), (25, 16), (39, 12), (5, 41), (5, 29), (11, 41), (31, 25), (10, 14), (38, 10), (1, 12), (19, 16), (20, 23), (31, 13), (34, 42), (34, 35), (26, 26), (23, 12), (23, 4), (38, 1), (12, 16), (1, 10), (25, 37), (6, 36), (32, 24), (35, 19), (15, 30), (31, 20), (13, 18), (2, 36), (26, 15), (21, 25), (8, 17), (26, 2), (11, 43), (24, 45), (26, 38), (12, 24), (16, 31), (34, 8), (3, 40), (4, 14), (24, 32), (9, 26), (17, 48), (13, 22), (16, 5), (2, 32), (19, 2), (39, 30), (26, 19), (31, 12), (12, 27), (21, 10), (7, 8), (20, 8), (27, 33), (27, 37), (30, 18), (24, 34), (25, 47), (7, 40), (16, 18), (22, 4), (24, 31), (13, 36), (35, 2), (25, 30), (20, 34), (0, 29), (5, 25), (13, 6), (1, 26), (31, 48), (31, 22), (26, 16), (27, 15), (27, 0), (32, 42), (18, 22), (10, 36), (20, 3), (28, 20), (29, 19), (26, 34), (19, 13), (18, 15), (17, 26), (6, 20), (35, 21), (18, 1), (23, 18), (4, 5), (33, 2), (34, 0), (2, 12), (11, 19), (15, 39), (16, 35), (27, 44), (8, 46), (16, 17), (36, 6), (32, 30), (22, 0), (14, 15), (36, 39), (29, 13), (1, 11), (3, 35), (27, 48), (2, 26), (20, 39), (4, 2), (7, 31), (12, 31), (37, 26), (26, 33), (31, 40), (30, 11), (35, 23), (21, 22), (24, 7), (1, 36), (4, 28), (29, 4), (4, 36), (17, 30), (5, 35), (4, 32), (1, 25), (25, 19), (14, 0), (29, 33), (0, 9), (17, 42), (8, 30), (12, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 34), (31, 19), (45, 9), (28, 34), (47, 12), (9, 32), (34, 2), (38, 11), (5, 14), (11, 46), (47, 25), (11, 0), (19, 24), (38, 22), (8, 37), (48, 37), (2, 19), (39, 7), (4, 28), (45, 41), (7, 30), (24, 5), (30, 9), (30, 45), (34, 13), (32, 33), (11, 41), (29, 32), (41, 30), (9, 48), (23, 41), (43, 16), (13, 19), (41, 45), (37, 47), (12, 45), (14, 48), (32, 25), (14, 47), (13, 29), (26, 27), (3, 40), (21, 7), (34, 30), (6, 31), (27, 25), (0, 33), (23, 34), (39, 6), (30, 34), (7, 19), (33, 46), (5, 2), (18, 10), (46, 3), (33, 26), (38, 4), (21, 6), (35, 48), (31, 5), (43, 19), (40, 39), (45, 23), (46, 31), (9, 29), (30, 25), (47, 37), (17, 23), (39, 12), (33, 15), (10, 43), (39, 37), (5, 40), (9, 37), (45, 10), (20, 32), (44, 31), (9, 28), (5, 33), (7, 11), (28, 21), (48, 23), (3, 44), (45, 35), (46, 10), (38, 12), (27, 36), (37, 45), (27, 7), (13, 0), (39, 14), (44, 14), (43, 32), (8, 28), (19, 11), (36, 7), (19, 2), (47, 29), (38, 30), (16, 14), (22, 2), (24, 37), (14, 32), (19, 30), (12, 22), (46, 38), (29, 6), (36, 23), (32, 27), (5, 39), (27, 5), (6, 23), (11, 36), (35, 25), (22, 22), (32, 5), (8, 13), (48, 31), (35, 35), (11, 20), (31, 36), (3, 45), (29, 10), (27, 10), (42, 2), (24, 44), (31, 13), (33, 7), (32, 29), (23, 28), (7, 6), (47, 34), (14, 9), (32, 47), (21, 48), (43, 8), (19, 8), (3, 43), (10, 11), (38, 3), (38, 48), (3, 26), (22, 6), (21, 5), (23, 3), (32, 26), (20, 11), (26, 40), (30, 14), (14, 7), (39, 23), (47, 13), (14, 0), (17, 30), (13, 35), (46, 9), (46, 12), (25, 22), (7, 42), (5, 20), (19, 16), (15, 7), (15, 41), (24, 19), (35, 6), (2, 33), (23, 25), (17, 31), (7, 45), (18, 19), (26, 37), (12, 19), (30, 11), (24, 32), (5, 13), (27, 3), (13, 47), (37, 36), (25, 14), (33, 41), (28, 10), (45, 14), (10, 3), (44, 42), (30, 32), (1, 36), (21, 16), (33, 48), (46, 1), (23, 19), (10, 35), (16, 41), (36, 4), (43, 22), (5, 10), (33, 25), (9, 8), (26, 45), (36, 3), (21, 47), (12, 15), (36, 32), (8, 38), (43, 18), (18, 2), (14, 31), (22, 20), (34, 9), (10, 14), (30, 27), (44, 46), (29, 8), (34, 7), (9, 41), (44, 10), (11, 11), (43, 7), (2, 39), (41, 33), (22, 38), (25, 47), (25, 9), (14, 4), (16, 33), (36, 43), (1, 43), (6, 27), (4, 32), (38, 35), (48, 21), (24, 45), (17, 9), (45, 22), (14, 18), (38, 44), (6, 10), (9, 5), (26, 47), (26, 12), (28, 8), (17, 47), (1, 35), (40, 35), (4, 12), (23, 23), (0, 11), (38, 39), (35, 37), (17, 39), (17, 17), (31, 4), (0, 23), (26, 2), (33, 27), (11, 9), (13, 1), (3, 2), (45, 42), (1, 26), (3, 21), (3, 7), (8, 20), (12, 2), (18, 47), (1, 31), (30, 7), (34, 8), (13, 28), (43, 3), (44, 7), (12, 44), (19, 25), (39, 36), (30, 41), (19, 13), (7, 16), (19, 18), (27, 14), (42, 1), (40, 28), (12, 1), (11, 14), (37, 33), (23, 42), (8, 43), (15, 39), (39, 4), (31, 23), (6, 45), (40, 15), (48, 10), (11, 28), (0, 13), (42, 0), (46, 14), (25, 16), (33, 35), (48, 40), (45, 29), (21, 20), (40, 0), (28, 27), (9, 22), (23, 39), (22, 36), (2, 37), (0, 43), (29, 29), (25, 41), (25, 32), (29, 2), (2, 1), (35, 33), (30, 46), (27, 35), (19, 31), (41, 36), (9, 9), (16, 0), (8, 29), (4, 18), (41, 17), (35, 18), (22, 16), (11, 31), (21, 21), (12, 34), (13, 20), (39, 28), (34, 19), (37, 4), (31, 34), (5, 16), (23, 29), (31, 0), (20, 22), (40, 3), (10, 36), (27, 47), (6, 22), (36, 10), (24, 47), (17, 26), (22, 39), (47, 14), (21, 2), (7, 41), (23, 37), (20, 2), (44, 33), (14, 44), (17, 16), (2, 35), (27, 39), (45, 27), (38, 45), (9, 18), (19, 9), (32, 38), (38, 7), (21, 41), (11, 33), (8, 42), (20, 10), (28, 11), (0, 7), (24, 15), (14, 37), (12, 24), (32, 19), (46, 36), (45, 18), (14, 25), (48, 6), (37, 14), (6, 0), (16, 6), (16, 4), (31, 37), (29, 3), (28, 5), (23, 36), (26, 46), (17, 11), (17, 32), (33, 36), (32, 2), (31, 43), (43, 34), (44, 12), (45, 16), (9, 43), (29, 28), (9, 19), (23, 12), (7, 43), (20, 17), (5, 31), (48, 22), (39, 24), (33, 19), (15, 27), (20, 27), (15, 29), (18, 7), (32, 3), (20, 4), (15, 25), (21, 13), (48, 18), (30, 24), (3, 3), (39, 18), (2, 48), (0, 21), (38, 36), (5, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 21), (7, 13), (29, 3), (4, 15), (6, 33), (13, 8), (17, 26), (21, 45), (24, 26), (37, 37), (5, 2), (29, 18), (9, 36), (17, 33), (42, 9), (41, 2), (7, 0), (42, 5), (20, 47), (6, 15), (1, 6), (38, 17), (27, 3), (34, 43), (6, 4), (20, 33), (16, 32), (23, 26), (33, 20), (9, 17), (16, 41), (32, 33), (18, 37), (21, 0), (41, 7), (32, 31), (23, 47), (5, 25), (22, 7), (29, 47), (11, 13), (8, 42), (17, 8), (41, 30), (17, 27), (11, 40), (27, 21), (14, 32), (3, 14), (25, 47), (28, 17), (32, 42), (39, 11), (16, 38), (5, 43), (14, 14), (38, 47), (10, 30), (26, 42), (18, 46), (17, 5), (42, 41), (0, 46), (24, 45), (40, 42), (42, 27), (16, 11), (33, 39), (25, 37), (15, 22), (31, 11), (20, 14), (35, 26), (32, 28), (42, 17), (39, 1), (18, 17), (4, 1), (12, 30), (30, 28), (33, 22), (18, 29), (7, 33), (15, 25), (11, 27), (12, 48), (31, 8), (21, 10), (9, 35), (40, 13), (21, 20), (27, 1), (0, 6), (38, 4), (4, 22), (13, 30), (36, 11), (23, 39), (30, 26), (4, 30), (39, 18), (31, 23), (11, 25), (38, 20), (27, 9), (25, 46), (34, 15), (1, 28), (9, 6), (2, 31), (39, 12), (22, 25), (16, 27), (39, 7), (37, 21), (2, 14), (5, 13), (3, 44), (34, 10), (1, 12), (20, 23), (37, 29), (30, 39), (13, 12), (20, 15), (37, 28), (17, 32), (23, 7), (23, 11), (11, 21), (11, 45), (11, 39), (15, 38), (13, 16), (1, 15), (1, 41), (14, 45), (0, 36), (31, 18), (20, 38), (0, 19), (33, 23), (16, 35), (25, 2), (4, 8), (5, 31), (15, 13), (14, 12), (41, 21), (35, 36), (0, 13), (11, 26), (21, 5), (13, 6), (17, 41), (41, 29), (14, 13), (11, 5), (41, 4), (17, 4), (11, 37), (36, 26), (19, 10), (19, 38), (17, 31), (19, 37), (21, 48), (4, 27), (41, 43), (16, 40), (0, 48), (17, 23), (39, 28), (26, 35), (34, 5), (28, 41), (30, 46), (19, 18), (11, 4), (18, 39), (6, 1), (32, 37), (42, 3), (19, 24), (27, 23), (29, 41), (18, 47), (19, 36), (26, 31), (22, 23), (12, 34), (40, 41), (8, 21), (6, 19), (13, 0), (40, 30), (10, 41), (7, 14), (23, 9), (25, 4), (22, 34), (5, 3), (15, 39), (20, 26), (16, 43), (22, 40), (23, 48), (25, 13), (22, 8), (41, 13), (9, 26), (39, 13), (34, 44), (13, 45), (10, 22), (0, 34), (18, 31), (29, 42), (20, 24), (21, 35), (39, 43), (18, 38), (24, 17), (10, 2), (34, 3), (14, 4), (4, 24), (40, 28), (34, 35), (2, 48), (8, 35), (25, 10), (4, 38), (27, 28), (7, 38), (17, 16), (5, 34), (13, 34), (30, 22), (3, 48), (14, 18), (33, 28), (24, 20), (32, 27), (14, 29), (15, 33), (17, 18), (35, 19), (26, 8), (19, 5), (12, 22), (41, 1), (40, 8), (36, 5), (33, 2), (22, 13), (35, 44), (25, 11), (33, 16), (19, 20), (29, 32), (15, 41), (32, 8), (33, 33), (0, 16), (23, 30), (2, 33), (36, 17), (35, 37), (37, 24), (38, 38), (39, 21), (17, 17), (22, 35), (6, 32), (0, 18), (6, 2), (16, 34), (26, 39), (7, 10), (25, 45), (39, 17), (1, 46), (7, 11), (12, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 38), (47, 15), (11, 20), (11, 8), (19, 5), (22, 14), (5, 29), (5, 20), (35, 4), (44, 15), (46, 11), (14, 0), (2, 36), (17, 35), (10, 16), (10, 30), (37, 26), (1, 11), (3, 27), (21, 17), (21, 30), (32, 18), (1, 32), (7, 2), (12, 23), (44, 7), (41, 5), (13, 21), (3, 29), (14, 25), (9, 28), (8, 8), (17, 27), (19, 10), (19, 36), (17, 3), (12, 27), (31, 9), (13, 22), (44, 31), (7, 36), (38, 24), (36, 24), (35, 6), (34, 4), (2, 27), (22, 18), (15, 12), (38, 36), (30, 28), (12, 22), (34, 23), (5, 2), (43, 35), (25, 15), (0, 27), (7, 38), (28, 3), (6, 5), (47, 28), (6, 25), (40, 1), (18, 14), (33, 32), (20, 29), (47, 13), (41, 38), (0, 28), (30, 10), (13, 35), (21, 6), (30, 36), (36, 8), (40, 24), (21, 1), (25, 11), (14, 13), (29, 15), (25, 12), (19, 28), (2, 15), (39, 8), (36, 16), (22, 38), (38, 31), (24, 7), (17, 39), (33, 16), (30, 8), (46, 25), (1, 19), (34, 27), (1, 22), (14, 21), (40, 18), (17, 18), (11, 13), (3, 8), (25, 1), (39, 2), (6, 4), (26, 4), (48, 13), (19, 17), (28, 8), (39, 33), (37, 28), (27, 28), (20, 38), (4, 24), (40, 2), (36, 7), (22, 12), (20, 10), (42, 2), (15, 27), (27, 2), (29, 31), (23, 24), (27, 13), (22, 35), (7, 10), (44, 33), (31, 16), (2, 21), (27, 32), (29, 3), (48, 21), (12, 34), (45, 19), (37, 4), (5, 25), (4, 30), (42, 24), (39, 13), (45, 6), (40, 37), (7, 9), (39, 37), (47, 3), (18, 13), (48, 14), (27, 16), (40, 21), (0, 38), (18, 2), (5, 33), (10, 29), (5, 8), (36, 23), (45, 30), (30, 21), (17, 19), (7, 13), (32, 4), (24, 3), (45, 23), (48, 24), (30, 24), (19, 33), (44, 37), (27, 19), (33, 21), (35, 29), (2, 32), (32, 13), (46, 34), (29, 34), (24, 17), (16, 35), (21, 8), (29, 12), (9, 10), (30, 31), (16, 20), (20, 6), (29, 37), (7, 14), (31, 15), (34, 20), (46, 18), (40, 34), (46, 1), (33, 30), (45, 13), (43, 0), (0, 1), (37, 38), (22, 29), (8, 33), (21, 2), (16, 38), (44, 20), (37, 34), (12, 15), (20, 3), (16, 31), (6, 13), (8, 38), (21, 36), (32, 30), (44, 9), (47, 14), (11, 30), (43, 24), (25, 8), (27, 14), (22, 23), (8, 12), (9, 23), (17, 32), (10, 23), (34, 16), (40, 33), (26, 5), (17, 31), (34, 13), (35, 35), (41, 8), (4, 10), (21, 27), (22, 11), (2, 29), (34, 36), (28, 28), (31, 18), (39, 1), (24, 8), (5, 13), (28, 27), (48, 31), (33, 1), (11, 5), (1, 35), (39, 24), (32, 19), (21, 24), (20, 12), (26, 37), (25, 38), (3, 32), (18, 23), (5, 12), (46, 28), (12, 12), (45, 18), (20, 16), (23, 15), (31, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 13), (5, 25), (39, 24), (21, 4), (6, 3), (10, 18), (34, 42), (7, 9), (19, 32), (21, 36), (24, 17), (29, 26), (1, 19), (15, 24), (20, 13), (15, 21), (35, 1), (4, 31), (2, 22), (6, 18), (34, 35), (24, 20), (12, 43), (34, 19), (37, 2), (21, 20), (20, 14), (35, 38), (24, 39), (39, 3), (12, 44), (17, 39), (32, 10), (32, 38), (7, 45), (11, 18), (11, 31), (15, 27), (4, 35), (20, 17), (2, 24), (33, 43), (11, 39), (34, 6), (37, 45), (29, 0), (32, 7), (0, 26), (6, 16), (35, 15), (16, 40), (40, 32), (3, 3), (13, 27), (25, 42), (4, 16), (41, 17), (20, 40), (0, 34), (31, 28), (25, 37), (8, 24), (28, 33), (19, 11), (41, 18), (39, 30), (34, 45), (33, 30), (9, 43), (29, 24), (1, 21), (19, 31), (14, 13), (1, 2), (39, 42), (3, 25), (8, 8), (37, 1), (2, 38), (12, 2), (8, 4), (16, 6), (7, 29), (12, 21), (31, 45), (27, 30), (20, 36), (26, 22), (15, 5), (0, 18), (19, 6), (7, 8), (31, 19), (38, 9), (32, 4), (20, 35), (8, 16), (6, 11), (1, 29), (6, 40), (29, 1), (3, 20), (19, 12), (17, 45), (38, 44), (4, 41), (20, 42), (0, 17), (36, 26), (6, 12), (6, 28), (16, 1), (20, 32), (18, 24), (32, 23), (12, 25), (16, 22), (22, 17), (14, 2), (13, 9), (31, 35), (30, 43), (36, 42), (17, 24), (39, 15), (26, 14), (15, 6), (34, 14), (31, 25), (28, 43), (30, 24), (23, 18), (21, 22), (37, 7), (2, 37), (32, 36), (9, 34), (17, 31), (23, 28), (0, 31), (27, 39), (35, 24), (21, 9), (5, 2), (3, 34), (11, 9), (9, 0), (5, 9), (3, 0), (24, 34), (9, 29), (8, 23), (15, 43), (11, 28), (19, 45), (24, 7), (35, 31), (17, 22), (17, 19), (6, 37), (9, 26), (27, 24), (7, 20), (32, 29), (38, 19), (19, 3), (18, 40), (5, 36), (1, 33), (3, 14), (33, 13), (19, 42), (26, 6), (30, 14), (19, 5), (1, 17), (6, 35), (14, 8), (26, 24), (30, 44), (14, 24), (38, 25), (18, 32), (32, 0), (9, 45), (28, 11), (10, 34), (5, 27), (20, 44), (11, 32), (21, 10), (0, 45), (27, 2), (36, 38), (14, 12), (11, 25), (9, 20), (32, 14), (33, 25), (8, 19), (22, 26), (0, 10), (14, 28), (25, 18), (19, 38), (13, 43), (5, 13), (12, 19), (10, 32), (19, 44), (24, 23), (12, 8), (29, 10), (35, 44), (27, 23), (38, 29), (8, 40), (21, 14), (0, 33), (25, 1), (37, 42), (23, 11), (26, 41), (27, 4), (4, 5), (31, 39), (32, 19), (30, 7), (18, 5), (33, 29), (37, 6), (6, 36), (32, 13), (38, 18), (20, 26), (35, 41), (13, 1), (24, 25), (28, 24), (12, 30), (31, 16), (8, 33), (15, 33), (29, 27), (36, 40), (2, 16), (9, 33), (4, 14), (41, 20), (3, 37), (7, 1), (27, 28), (37, 36), (16, 18), (4, 36), (14, 16), (23, 25), (17, 2), (15, 44), (12, 3), (5, 17), (31, 22), (10, 10), (19, 9), (13, 6), (12, 15), (1, 26), (8, 13), (31, 26), (6, 21), (17, 44), (29, 20), (19, 21), (23, 17), (25, 24), (4, 8), (3, 11), (27, 27), (39, 14), (21, 3), (7, 33), (37, 44), (40, 9), (7, 12), (30, 6), (4, 43), (24, 3), (38, 40), (35, 25), (4, 17), (33, 37), (1, 35), (18, 42), (25, 9), (23, 23), (19, 18), (3, 19), (28, 22), (17, 33), (16, 7), (8, 5), (13, 39), (16, 42), (21, 31), (0, 16), (36, 10), (26, 20), (23, 21), (9, 4), (5, 1), (17, 43), (23, 16), (12, 11), (8, 30), (33, 17), (24, 10), (19, 15), (12, 29), (0, 24), (9, 19), (28, 7), (2, 43), (39, 7), (10, 28), (0, 25), (9, 12), (28, 19), (10, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 29), (26, 40), (19, 27), (19, 19), (1, 19), (38, 21), (30, 1), (1, 31), (34, 37), (30, 21), (21, 36), (37, 1), (33, 22), (22, 10), (40, 20), (15, 8), (29, 12), (5, 28), (17, 18), (2, 27), (16, 38), (40, 37), (6, 26), (22, 22), (3, 33), (28, 20), (15, 47), (18, 30), (20, 15), (38, 6), (20, 32), (42, 41), (20, 43), (21, 34), (41, 17), (39, 25), (31, 22), (34, 20), (27, 13), (27, 17), (32, 22), (36, 32), (22, 40), (14, 8), (42, 13), (38, 34), (25, 23), (29, 44), (24, 10), (31, 36), (13, 4), (4, 41), (35, 0), (39, 28), (34, 47), (14, 21), (18, 18), (34, 43), (41, 24), (24, 37), (34, 7), (14, 47), (36, 34), (16, 15), (21, 24), (41, 27), (2, 3), (38, 3), (24, 2), (42, 4), (2, 20), (6, 30), (23, 46), (3, 18), (15, 20), (39, 1), (27, 38), (17, 35), (9, 31), (31, 19), (5, 18), (3, 24), (9, 17), (13, 30), (21, 30), (1, 9), (22, 44), (42, 6), (0, 37), (39, 44), (13, 25), (19, 37), (37, 6), (24, 41), (14, 40), (36, 16), (2, 29), (6, 7), (33, 18), (1, 42), (21, 35), (13, 23), (36, 29), (21, 47), (2, 17), (12, 44), (30, 18), (38, 41), (21, 31), (16, 31), (6, 16), (7, 13), (7, 23), (4, 39), (16, 27), (10, 23), (8, 34), (41, 45), (3, 31), (21, 43), (20, 27), (6, 42), (26, 33), (41, 10), (35, 26), (32, 6), (29, 47), (6, 6), (29, 42), (28, 9), (12, 21), (8, 22), (8, 30), (1, 40), (1, 14), (10, 43), (10, 34), (39, 26), (0, 40), (23, 44), (16, 3), (25, 6), (0, 27), (36, 30), (2, 7), (36, 22), (15, 38), (32, 44), (29, 27), (1, 33), (28, 21), (19, 34), (36, 35), (34, 41), (16, 46), (24, 28), (30, 5), (14, 35), (19, 32), (10, 10), (0, 11), (32, 10), (26, 20), (11, 10), (0, 36), (14, 13), (6, 14), (31, 9), (37, 29), (7, 17), (1, 20), (20, 28), (34, 15), (14, 12), (25, 16), (19, 31), (32, 45), (3, 45), (22, 2), (16, 5), (32, 23), (20, 12), (33, 47), (5, 20), (8, 28), (31, 41), (8, 3), (1, 18), (26, 2), (9, 9), (37, 25), (33, 9), (8, 15), (7, 30), (19, 15), (16, 7), (38, 8), (36, 8), (14, 10), (28, 39), (32, 24), (41, 13), (38, 37), (32, 26), (32, 0), (12, 37), (20, 25), (7, 4), (12, 25), (7, 22), (10, 14), (21, 13), (8, 38), (16, 40), (2, 45), (6, 17), (20, 8), (7, 14), (14, 26), (16, 37), (7, 38), (13, 13), (3, 3), (3, 20), (19, 41), (41, 2), (24, 13), (14, 18), (23, 1), (31, 17), (39, 38), (32, 35), (39, 31), (5, 19), (13, 17), (6, 47), (14, 34), (6, 33), (25, 33), (18, 31), (29, 40), (18, 25), (37, 42), (38, 16), (29, 3), (32, 18), (17, 34), (22, 47), (37, 46), (27, 32), (27, 27), (10, 40), (39, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 28), (34, 40), (12, 19), (15, 36), (23, 10), (44, 4), (25, 2), (44, 39), (9, 30), (16, 14), (34, 21), (43, 37), (43, 39), (43, 30), (43, 28), (2, 26), (36, 26), (9, 13), (11, 0), (8, 41), (20, 7), (4, 39), (11, 17), (13, 30), (39, 18), (12, 16), (14, 13), (39, 27), (0, 5), (0, 14), (33, 9), (1, 11), (4, 30), (33, 16), (24, 3), (19, 12), (26, 5), (33, 34), (5, 3), (12, 18), (45, 40), (9, 39), (36, 24), (39, 23), (34, 31), (31, 25), (14, 32), (32, 5), (25, 16), (40, 20), (12, 27), (6, 26), (26, 10), (23, 40), (34, 23), (13, 13), (25, 7), (39, 39), (15, 8), (0, 34), (43, 5), (27, 41), (37, 10), (0, 7), (30, 2), (41, 22), (21, 22), (8, 36), (14, 25), (4, 22), (39, 20), (20, 37), (18, 4), (37, 30), (32, 11), (23, 41), (0, 36), (33, 31), (38, 18), (39, 31), (4, 37), (42, 18), (26, 35), (8, 13), (12, 10), (36, 32), (7, 22), (22, 14), (27, 3), (27, 38), (10, 32), (33, 38), (32, 17), (12, 13), (21, 11), (35, 12), (42, 19), (37, 26), (15, 28), (34, 35), (9, 26), (11, 38), (1, 13), (15, 2), (19, 27), (12, 38), (30, 41), (30, 14), (22, 11), (37, 16), (31, 35), (0, 33), (15, 22), (17, 37), (8, 6), (26, 4), (39, 34), (14, 31), (1, 12), (43, 7), (41, 39), (5, 0), (10, 15), (28, 9), (33, 18), (40, 30), (7, 27), (17, 12), (23, 37), (35, 36), (24, 6), (40, 2), (23, 35), (9, 25), (15, 39), (7, 33), (26, 37), (17, 14), (45, 9), (27, 6), (36, 10), (7, 2), (40, 38), (20, 2), (19, 2), (11, 3), (22, 13), (5, 33), (5, 28), (18, 36), (40, 23), (21, 12), (3, 24), (30, 3), (24, 1), (0, 1), (30, 9), (36, 29), (36, 40), (26, 18), (45, 32), (7, 12), (17, 39), (5, 11), (20, 17), (20, 18), (7, 39), (12, 4), (39, 40), (44, 31), (24, 28), (38, 34), (27, 9), (8, 29), (21, 21), (16, 19), (35, 22), (45, 28), (29, 28), (41, 2), (0, 26), (20, 10), (26, 27), (6, 7), (0, 32), (20, 33), (13, 36), (16, 2), (22, 19), (40, 21), (27, 31), (37, 39), (20, 40), (37, 35), (25, 25), (4, 7), (9, 4), (11, 21), (20, 5), (34, 13), (41, 41), (24, 25), (32, 15), (23, 31), (26, 38), (37, 36), (30, 21), (9, 29), (21, 34), (44, 22), (28, 5), (14, 4), (39, 30), (28, 23), (31, 30), (33, 7), (24, 38), (34, 1), (43, 22), (20, 31), (42, 22), (12, 33), (38, 17), (28, 28), (36, 17), (1, 19), (30, 1), (18, 23), (16, 37), (19, 14), (40, 34), (43, 35), (6, 37), (27, 36), (19, 13), (27, 18), (13, 34), (41, 0), (42, 11), (4, 24), (44, 14), (35, 8), (12, 40), (23, 33), (13, 18), (26, 0), (2, 4), (29, 16), (0, 19), (26, 21), (2, 28), (14, 20), (12, 31), (3, 14), (38, 13), (12, 5), (13, 26), (41, 20), (17, 2), (30, 17), (26, 24), (16, 23), (42, 10), (34, 33), (29, 15), (38, 33), (5, 5), (22, 17), (5, 18), (6, 23), (1, 18), (17, 33), (23, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 4), (24, 21), (13, 12), (43, 3), (28, 40), (9, 6), (3, 5), (20, 6), (21, 32), (43, 13), (38, 2), (21, 38), (19, 13), (17, 27), (41, 25), (32, 2), (31, 39), (25, 6), (10, 16), (31, 6), (9, 8), (30, 23), (24, 27), (28, 31), (32, 13), (4, 8), (30, 35), (10, 24), (34, 19), (36, 23), (38, 33), (36, 40), (5, 11), (32, 33), (32, 40), (2, 20), (39, 15), (42, 29), (32, 25), (10, 3), (28, 29), (0, 20), (20, 20), (25, 35), (13, 6), (30, 29), (19, 12), (20, 34), (33, 15), (34, 24), (30, 1), (37, 38), (29, 28), (20, 2), (18, 19), (18, 25), (35, 26), (7, 0), (2, 35), (30, 40), (11, 23), (3, 19), (27, 3), (8, 12), (39, 42), (17, 29), (42, 39), (40, 12), (39, 32), (6, 38), (37, 34), (30, 37), (28, 39), (26, 5), (20, 12), (44, 0), (21, 43), (22, 17), (6, 18), (7, 8), (39, 4), (4, 14), (7, 15), (39, 19), (2, 2), (21, 22), (36, 31), (6, 11), (7, 20), (25, 33), (9, 25), (20, 3), (20, 42), (7, 19), (41, 21), (23, 26), (40, 28), (5, 3), (32, 16), (35, 41), (9, 17), (39, 2), (4, 10), (38, 3), (28, 30), (4, 12), (11, 3), (28, 28), (10, 2), (4, 20), (10, 7), (13, 24), (25, 11), (14, 27), (16, 42), (2, 36), (10, 25), (20, 31), (36, 21), (14, 15), (11, 13), (29, 21), (44, 7), (5, 42), (7, 26), (32, 7), (17, 25), (33, 30), (34, 9), (22, 43), (17, 42), (42, 34), (30, 32), (9, 14), (20, 22), (23, 1), (41, 2), (6, 29), (37, 23), (38, 27), (23, 36), (6, 21), (0, 7), (44, 36), (12, 17), (16, 20), (40, 11), (40, 21), (2, 37), (5, 7), (32, 22), (22, 35), (34, 22), (7, 10), (34, 10), (39, 6), (5, 4), (3, 43), (9, 9), (23, 31), (12, 12), (37, 8), (24, 43), (11, 40), (36, 15), (0, 13), (34, 31), (36, 5), (1, 15), (8, 43), (33, 34), (33, 14), (41, 23), (25, 3), (41, 1), (24, 2), (10, 22), (27, 21), (32, 10), (18, 3), (21, 35), (5, 16), (27, 9), (22, 40), (40, 1), (7, 39), (2, 34), (23, 19), (4, 22), (38, 36), (33, 36), (38, 29), (14, 18), (35, 18), (43, 0), (34, 4), (2, 25), (13, 11), (29, 9), (16, 27), (7, 38), (15, 5), (39, 39), (28, 2), (43, 8), (14, 22), (8, 2), (27, 13), (17, 6), (36, 29), (1, 37), (29, 4), (20, 18), (11, 21), (12, 33), (23, 25), (40, 30), (11, 39), (11, 26), (10, 9), (25, 24), (39, 36), (10, 36), (15, 29), (20, 35), (20, 41), (41, 15), (25, 5), (26, 20), (31, 18), (3, 0), (42, 17), (29, 18), (42, 2), (43, 15), (38, 43), (43, 28), (40, 4), (27, 32), (22, 1), (21, 24), (12, 27), (23, 9), (28, 14), (8, 29), (43, 5), (8, 9), (15, 43), (11, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 0), (14, 18), (18, 41), (38, 2), (9, 23), (27, 39), (15, 15), (41, 0), (41, 5), (18, 15), (35, 20), (34, 13), (30, 40), (22, 28), (36, 6), (5, 5), (18, 9), (9, 33), (29, 42), (14, 29), (40, 27), (34, 9), (16, 9), (5, 20), (22, 0), (25, 7), (28, 0), (11, 25), (40, 32), (24, 1), (25, 24), (30, 15), (26, 21), (9, 20), (39, 20), (38, 31), (33, 38), (19, 35), (1, 10), (3, 34), (16, 38), (4, 9), (27, 3), (27, 2), (12, 22), (37, 10), (1, 39), (6, 16), (5, 21), (17, 8), (30, 42), (0, 35), (12, 41), (13, 18), (5, 6), (30, 39), (23, 17), (2, 28), (38, 20), (11, 2), (11, 0), (32, 4), (3, 7), (3, 40), (0, 30), (8, 8), (24, 21), (36, 38), (18, 32), (4, 32), (12, 6), (21, 16), (16, 36), (3, 22), (13, 22), (25, 23), (2, 41), (6, 37), (14, 20), (17, 22), (2, 4), (6, 3), (5, 17), (7, 24), (25, 0), (25, 43), (14, 41), (27, 17), (3, 42), (19, 7), (8, 28), (5, 25), (39, 29), (36, 18), (37, 3), (22, 31), (29, 2), (12, 38), (15, 37), (5, 2), (2, 31), (30, 6), (20, 8), (2, 6), (32, 43), (20, 43), (22, 26), (32, 39), (31, 26), (6, 34), (30, 9), (0, 8), (24, 9), (33, 42), (39, 41), (23, 37), (37, 16), (15, 20), (36, 14), (32, 8), (10, 35), (2, 39), (29, 1), (12, 20), (34, 26), (1, 32), (26, 40), (14, 42), (8, 25), (39, 43), (23, 0), (8, 6), (7, 37), (21, 17), (14, 6), (10, 8), (18, 22), (39, 40), (28, 20), (6, 21), (30, 17), (9, 10), (24, 19), (12, 34), (13, 21), (28, 28), (39, 42), (15, 24), (35, 10), (21, 20), (40, 42), (19, 24), (22, 9), (27, 35), (19, 26), (31, 1), (11, 43), (34, 7), (3, 33), (14, 15), (31, 15), (13, 11), (8, 14), (33, 14), (34, 38), (29, 41), (37, 34), (17, 18), (30, 26), (15, 30), (36, 30), (13, 39), (25, 12), (2, 43), (29, 18), (24, 24), (3, 39), (22, 39), (26, 29), (9, 22), (23, 10), (37, 41), (9, 5), (16, 22), (25, 17), (23, 5), (18, 17), (5, 33), (2, 25), (20, 23), (11, 40), (13, 17), (36, 28), (25, 38), (20, 17), (1, 26), (20, 26), (21, 33), (40, 43), (30, 24), (9, 18), (10, 26), (13, 14), (0, 18), (11, 16), (28, 40), (37, 21), (37, 17), (19, 3), (32, 13), (38, 10), (22, 5), (7, 23), (4, 27), (40, 20), (5, 14), (22, 14), (3, 15), (25, 28), (36, 10), (40, 8), (12, 7), (30, 25), (39, 9), (21, 39), (10, 27), (36, 39), (33, 36), (26, 42), (36, 5), (10, 42), (40, 0), (16, 25), (27, 20), (38, 8), (19, 36), (36, 21), (16, 16), (13, 23), (24, 31), (20, 1), (16, 35), (37, 31), (11, 7), (2, 11), (17, 15), (14, 10), (39, 5), (3, 43), (26, 12), (26, 1), (4, 1), (7, 5), (36, 15), (40, 23), (8, 32), (23, 35), (10, 28), (1, 6), (26, 14), (26, 2), (6, 12), (10, 19), (34, 10), (33, 2), (38, 43), (40, 33), (10, 23), (41, 25), (9, 36), (24, 23), (9, 13), (35, 40), (24, 18), (28, 4), (35, 11), (26, 30), (32, 23), (23, 27), (37, 4), (1, 43), (5, 22), (20, 21), (41, 23), (34, 6), (5, 15), (25, 8), (40, 35), (41, 13), (15, 22), (8, 7), (28, 2), (24, 20), (0, 22), (38, 18), (25, 1), (24, 37), (6, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 0), (15, 33), (41, 20), (19, 23), (25, 12), (40, 11), (1, 6), (23, 25), (38, 21), (8, 21), (32, 22), (7, 5), (25, 19), (22, 9), (42, 10), (28, 15), (7, 3), (37, 6), (12, 27), (2, 6), (8, 14), (15, 22), (15, 38), (25, 1), (12, 7), (9, 12), (46, 34), (45, 18), (14, 5), (10, 24), (7, 14), (30, 18), (12, 25), (37, 34), (18, 19), (5, 15), (19, 28), (39, 14), (43, 13), (14, 13), (24, 36), (24, 37), (33, 10), (10, 23), (41, 39), (6, 7), (32, 7), (15, 6), (4, 29), (17, 24), (45, 3), (6, 11), (14, 6), (34, 21), (16, 7), (27, 0), (4, 13), (25, 13), (17, 21), (28, 35), (18, 27), (17, 4), (34, 15), (21, 29), (23, 5), (13, 5), (17, 9), (27, 37), (14, 8), (8, 22), (41, 35), (8, 35), (39, 39), (42, 24), (7, 8), (11, 26), (26, 38), (7, 11), (9, 10), (5, 7), (13, 7), (26, 23), (43, 20), (37, 37), (29, 21), (35, 10), (24, 5), (4, 22), (28, 14), (38, 11), (37, 26), (8, 1), (21, 34), (23, 32), (14, 22), (40, 9), (18, 25), (41, 16), (46, 19), (12, 8), (7, 7), (18, 12), (45, 34), (16, 4), (14, 4), (6, 9), (11, 2), (21, 5), (21, 0), (16, 34), (5, 37), (11, 9), (12, 34), (23, 24), (1, 0), (24, 25), (41, 27), (41, 3), (40, 5), (20, 34), (13, 18), (12, 13), (25, 10), (3, 39), (3, 7), (24, 33), (11, 8), (8, 12), (22, 35), (23, 38), (15, 10), (13, 33), (37, 32), (34, 6), (24, 27), (33, 5), (34, 0), (10, 17), (35, 22), (13, 9), (12, 20), (3, 1), (28, 36), (43, 34), (24, 12), (25, 18), (4, 34), (20, 31), (35, 25), (9, 3), (38, 12), (5, 16), (39, 29), (43, 27), (5, 23), (35, 3), (18, 9), (35, 26), (7, 38), (10, 4), (20, 6), (40, 32), (16, 36), (30, 3), (12, 24), (45, 12), (30, 34), (17, 17), (11, 19), (35, 37), (36, 37), (19, 3), (21, 20), (20, 11), (1, 1), (15, 31), (38, 9), (37, 2), (34, 26), (25, 38), (6, 10), (8, 30), (46, 26), (22, 2), (23, 10), (7, 33), (3, 2), (11, 16), (1, 21), (36, 1), (4, 5), (31, 0), (11, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 16), (35, 3), (31, 43), (18, 10), (7, 11), (15, 19), (24, 11), (17, 43), (38, 9), (41, 5), (12, 7), (21, 31), (12, 27), (21, 43), (36, 36), (24, 22), (29, 27), (18, 4), (0, 2), (19, 36), (6, 22), (28, 5), (27, 10), (4, 16), (21, 3), (13, 6), (31, 37), (27, 7), (20, 36), (8, 30), (4, 19), (41, 42), (18, 22), (20, 43), (40, 46), (36, 32), (16, 26), (13, 8), (24, 43), (2, 20), (15, 34), (14, 4), (28, 18), (7, 13), (14, 8), (31, 38), (9, 26), (41, 3), (2, 13), (22, 30), (18, 8), (3, 20), (38, 41), (20, 34), (12, 26), (16, 40), (3, 26), (13, 11), (7, 30), (18, 23), (10, 6), (39, 42), (0, 7), (16, 34), (37, 19), (24, 33), (23, 2), (31, 2), (39, 0), (35, 20), (11, 43), (24, 44), (25, 4), (28, 9), (24, 26), (1, 22), (8, 23), (25, 35), (32, 19), (5, 38), (21, 32), (16, 43), (41, 41), (8, 33), (25, 23), (40, 10), (2, 30), (15, 11), (2, 23), (30, 24), (3, 37), (28, 34), (18, 42), (25, 20), (7, 9), (32, 41), (20, 32), (27, 14), (3, 42), (37, 18), (18, 37), (27, 42), (35, 34), (13, 45), (41, 30), (21, 41), (22, 13), (4, 33), (4, 9), (23, 40), (5, 4), (13, 20), (37, 42), (15, 2), (27, 25), (30, 28), (19, 43), (34, 29), (21, 34), (26, 38), (29, 6), (36, 43), (22, 15), (16, 35), (5, 6), (1, 18), (20, 40), (19, 26), (30, 37), (27, 3), (19, 3), (32, 30), (37, 43), (11, 31), (17, 5), (23, 1), (39, 6), (2, 9), (5, 8), (4, 5), (35, 37), (3, 15), (36, 26), (41, 34), (0, 30), (5, 23), (9, 29), (1, 20), (15, 12), (3, 29), (3, 10), (0, 33), (21, 21), (17, 21), (5, 7), (39, 12), (12, 32), (22, 0), (12, 24), (14, 30), (24, 10), (14, 16), (2, 39), (22, 4), (6, 44), (18, 5), (39, 44), (19, 8), (10, 10), (1, 8), (17, 9), (41, 32), (37, 39), (26, 42), (36, 34), (33, 13), (32, 34), (40, 12), (2, 6), (8, 2), (19, 44), (24, 32), (33, 21), (28, 13), (2, 19), (29, 10), (27, 8), (31, 40), (0, 45), (25, 29), (2, 11), (24, 45), (35, 10), (26, 45), (4, 25), (14, 21), (24, 23), (38, 12), (38, 27), (36, 33), (14, 29), (0, 29), (3, 16), (28, 10), (13, 0), (2, 24), (0, 27), (2, 42), (25, 6), (16, 12), (39, 32), (40, 2), (25, 34), (23, 30), (8, 5), (13, 10), (11, 7), (38, 20), (32, 2), (26, 26), (24, 34), (4, 17), (8, 17), (11, 33), (3, 39), (1, 37), (14, 5), (24, 19), (4, 45), (1, 0), (8, 28), (15, 41), (35, 14), (23, 33), (36, 20), (11, 45), (37, 41), (14, 10), (24, 5), (33, 34), (7, 20), (14, 15), (29, 18), (31, 25), (12, 42), (37, 16), (10, 35), (35, 1), (17, 41), (23, 43), (30, 39), (7, 43), (27, 45), (30, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 33), (11, 1), (16, 15), (10, 38), (38, 0), (17, 19), (15, 12), (0, 45), (22, 12), (21, 5), (34, 16), (22, 33), (23, 15), (14, 24), (40, 18), (5, 43), (6, 3), (7, 22), (40, 13), (21, 12), (20, 46), (39, 26), (38, 35), (19, 48), (18, 9), (30, 12), (40, 41), (27, 21), (39, 9), (8, 30), (36, 11), (26, 38), (17, 7), (9, 22), (23, 8), (19, 4), (39, 24), (8, 41), (41, 2), (5, 19), (38, 18), (10, 4), (0, 26), (11, 5), (10, 18), (13, 27), (40, 38), (41, 10), (19, 31), (33, 41), (26, 44), (11, 14), (8, 6), (24, 42), (15, 40), (40, 20), (37, 15), (0, 44), (10, 20), (21, 21), (24, 1), (8, 29), (33, 10), (18, 5), (3, 18), (6, 24), (15, 31), (26, 6), (21, 34), (10, 0), (28, 16), (18, 43), (38, 17), (7, 45), (5, 25), (34, 33), (5, 29), (28, 24), (15, 10), (11, 19), (22, 9), (27, 29), (42, 37), (17, 4), (15, 26), (32, 8), (12, 32), (0, 28), (8, 39), (30, 41), (35, 15), (29, 36), (16, 21), (33, 30), (38, 7), (24, 44), (13, 25), (15, 46), (19, 2), (42, 45), (24, 21), (11, 48), (19, 14), (9, 48), (10, 33), (42, 31), (5, 13), (24, 35), (31, 21), (13, 0), (33, 13), (7, 27), (20, 11), (6, 17), (5, 30), (39, 46), (20, 36), (22, 14), (16, 20), (13, 28), (2, 0), (42, 27), (24, 32), (11, 47), (14, 3), (18, 32), (29, 38), (19, 18), (26, 39), (42, 41), (38, 34), (26, 45), (24, 5), (40, 29), (10, 14), (19, 15), (17, 16), (12, 14), (26, 46), (8, 4), (31, 30), (29, 45), (8, 15), (26, 16), (15, 34), (14, 1), (8, 28), (23, 48), (7, 38), (1, 12), (25, 47), (29, 0), (11, 20), (38, 24), (38, 39), (31, 9), (17, 15), (6, 5), (30, 42), (29, 8), (28, 21), (24, 41), (38, 43), (25, 35), (21, 8), (3, 34), (35, 4), (14, 9), (37, 14), (11, 23), (40, 27), (28, 31), (8, 47), (2, 25), (23, 46), (7, 7), (8, 37), (30, 10), (14, 14), (15, 4), (28, 9), (8, 32), (25, 1), (38, 23), (40, 8), (13, 21), (5, 3), (21, 48), (13, 3), (11, 46), (11, 38), (22, 32), (24, 22), (32, 28), (36, 2), (28, 34), (42, 13), (29, 43), (23, 19), (21, 14), (42, 20), (27, 45), (3, 13), (23, 31), (4, 15), (30, 44), (29, 42), (16, 10), (30, 31), (33, 20), (14, 35), (6, 36), (10, 37), (29, 34), (41, 16), (32, 1), (21, 33), (25, 19), (42, 5), (32, 38), (22, 39), (9, 1), (6, 1), (6, 30), (39, 34), (6, 35), (27, 38), (4, 48), (39, 42), (41, 22), (29, 4), (1, 40), (20, 17), (17, 40), (33, 36), (4, 35), (31, 28), (4, 21), (36, 28), (19, 11), (34, 32), (10, 7), (16, 27), (15, 19), (8, 26), (18, 3), (30, 38), (13, 32), (27, 42), (27, 19), (19, 16), (9, 29), (29, 11), (0, 14), (18, 23), (12, 48), (36, 12), (14, 20), (8, 23), (0, 21), (13, 14), (35, 42), (39, 36), (2, 36), (2, 20), (20, 5), (29, 13), (5, 4), (4, 37), (9, 45), (29, 9), (10, 41), (35, 34), (5, 44), (36, 0), (36, 14), (36, 48), (25, 25), (28, 47), (30, 21), (11, 15), (20, 15), (6, 38), (10, 6), (38, 36), (40, 47), (27, 32), (42, 16), (8, 14), (18, 17), (34, 0), (16, 1), (17, 29), (13, 44), (6, 12), (7, 32), (26, 3), (34, 41), (31, 13), (21, 3), (33, 40), (11, 27), (2, 2), (5, 16), (31, 0), (34, 31), (7, 14), (30, 1), (33, 42), (15, 21), (8, 34), (42, 29), (31, 16), (36, 30), (39, 6), (5, 34), (22, 3), (6, 44), (13, 12), (33, 32), (37, 36), (37, 2), (5, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 32), (23, 31), (8, 17), (43, 19), (36, 12), (9, 21), (33, 20), (28, 26), (8, 24), (26, 4), (14, 7), (20, 10), (15, 26), (10, 3), (25, 24), (0, 40), (24, 3), (16, 6), (35, 13), (9, 28), (19, 28), (11, 7), (19, 40), (37, 9), (19, 42), (37, 16), (24, 13), (10, 22), (22, 34), (2, 11), (40, 9), (33, 43), (3, 20), (24, 1), (23, 2), (45, 41), (18, 17), (34, 28), (28, 38), (35, 11), (10, 13), (42, 18), (18, 37), (2, 30), (13, 6), (38, 9), (23, 27), (7, 42), (5, 14), (29, 19), (43, 40), (37, 3), (37, 27), (14, 29), (4, 27), (24, 20), (16, 42), (30, 10), (3, 13), (36, 42), (32, 17), (6, 0), (1, 35), (3, 18), (36, 7), (14, 0), (0, 5), (35, 37), (22, 30), (14, 16), (30, 41), (28, 9), (18, 39), (19, 5), (41, 18), (29, 40), (9, 40), (22, 29), (15, 16), (42, 43), (17, 21), (37, 2), (25, 21), (30, 26), (20, 44), (45, 33), (17, 12), (35, 18), (14, 25), (29, 6), (24, 27), (34, 5), (19, 19), (18, 12), (28, 31), (43, 44), (40, 40), (38, 13), (36, 44), (33, 6), (34, 37), (8, 40), (18, 26), (23, 39), (34, 13), (1, 16), (28, 30), (32, 39), (40, 34), (2, 41), (41, 42), (13, 35), (44, 17), (45, 29), (15, 9), (11, 43), (11, 44), (20, 27), (41, 12), (40, 13), (24, 11), (13, 41), (5, 39), (16, 37), (3, 1), (5, 33), (31, 19), (23, 29), (18, 25), (18, 31), (9, 41), (4, 13), (7, 25), (19, 2), (8, 8), (0, 19), (8, 19), (29, 26), (18, 3), (11, 34), (41, 39), (1, 31), (4, 40), (3, 35), (36, 15), (14, 4), (36, 13), (28, 32), (39, 24), (23, 25), (11, 39), (25, 42), (8, 28), (41, 13), (25, 44), (4, 42), (28, 3), (40, 39), (4, 26), (23, 8), (32, 25), (13, 2), (9, 15), (10, 11), (8, 44), (40, 24), (20, 43), (20, 17), (4, 10), (33, 38), (9, 33), (18, 10), (33, 19), (26, 36), (32, 44), (27, 23), (23, 26), (18, 42), (23, 24), (31, 4), (30, 14), (6, 12), (33, 8), (19, 25), (7, 26), (8, 33), (4, 12), (23, 20), (0, 7), (2, 7), (25, 27), (6, 23), (17, 32), (33, 24), (43, 9), (34, 0), (34, 38), (14, 43), (27, 32), (1, 2), (5, 8), (10, 39), (32, 15), (45, 13), (31, 11), (45, 8), (5, 38), (45, 18), (15, 35), (42, 34), (0, 22), (3, 26), (22, 35), (1, 36), (20, 15), (32, 16), (8, 38), (29, 7), (13, 38), (39, 3), (30, 33), (18, 40), (13, 20), (10, 9), (39, 17), (14, 9), (28, 5), (5, 37), (42, 13), (38, 8), (21, 32), (21, 40), (12, 22), (34, 23), (11, 5), (12, 7), (21, 0), (3, 8), (31, 40), (11, 41), (39, 16), (2, 34), (25, 39), (27, 44), (17, 11), (34, 30), (6, 35), (18, 28), (9, 35), (16, 17), (7, 37), (0, 21), (9, 27), (19, 22), (36, 9), (20, 12), (21, 8), (42, 12), (28, 1), (38, 15), (26, 31), (34, 3), (22, 6), (1, 33), (40, 4), (36, 24), (39, 44), (8, 22), (11, 2), (1, 0), (29, 33), (16, 3), (21, 43), (28, 40), (30, 17), (42, 6), (44, 22), (35, 38), (44, 13), (17, 0), (7, 31), (10, 19), (39, 15), (36, 14), (36, 33), (31, 30), (13, 25), (9, 42), (2, 42), (4, 14), (41, 1), (8, 11), (3, 25), (45, 27), (28, 7), (25, 7), (33, 29), (29, 16), (9, 5), (37, 26), (2, 40), (8, 10), (21, 23), (37, 38), (12, 13), (40, 27), (3, 12), (0, 9), (25, 41), (29, 31), (9, 24), (36, 41), (32, 38), (29, 25), (24, 10), (21, 33), (39, 13), (44, 1), (26, 24), (36, 23), (26, 10), (32, 1), (43, 43), (28, 21), (21, 37), (43, 22), (15, 36), (19, 7), (12, 5), (18, 7), (34, 14), (21, 17), (10, 32), (38, 42), (28, 34), (25, 13), (7, 8), (22, 11), (2, 33), (3, 14), (24, 30), (43, 30), (5, 25), (31, 1), (30, 12), (40, 12), (20, 39), (37, 35), (5, 15), (36, 18), (36, 35), (9, 43), (29, 5), (44, 3), (36, 16), (40, 33), (15, 43), (21, 12), (16, 38), (4, 31), (3, 19), (12, 27), (18, 27), (4, 30), (5, 0), (18, 8), (11, 0), (11, 9), (19, 32), (43, 34), (27, 33), (43, 27), (43, 33), (43, 10), (25, 6), (0, 8), (15, 2), (29, 37), (17, 30), (34, 17), (38, 3), (21, 36), (45, 31), (33, 44), (41, 35), (25, 43), (15, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (39, 29), (13, 18), (28, 30), (33, 21), (8, 14), (7, 1), (26, 39), (33, 2), (35, 1), (13, 22), (31, 25), (29, 10), (42, 26), (16, 19), (7, 34), (34, 29), (15, 37), (10, 40), (37, 22), (4, 15), (32, 5), (30, 19), (15, 36), (22, 14), (18, 8), (3, 2), (0, 19), (11, 38), (25, 11), (13, 7), (18, 24), (19, 3), (1, 25), (22, 39), (41, 7), (33, 22), (1, 35), (35, 36), (16, 18), (22, 24), (12, 19), (40, 38), (1, 5), (40, 33), (32, 19), (37, 25), (32, 18), (3, 21), (12, 21), (40, 1), (21, 23), (3, 17), (0, 27), (30, 23), (10, 14), (18, 32), (44, 39), (19, 4), (18, 34), (7, 33), (6, 6), (19, 39), (15, 6), (2, 36), (27, 20), (30, 3), (37, 9), (26, 17), (28, 33), (31, 4), (15, 23), (30, 27), (31, 31), (9, 5), (22, 8), (36, 16), (3, 37), (20, 22), (30, 10), (14, 14), (6, 16), (0, 35), (4, 11), (4, 28), (4, 25), (19, 32), (19, 35), (23, 31), (12, 37), (22, 0), (15, 10), (23, 33), (16, 40), (16, 39), (13, 29), (29, 19), (22, 34), (21, 36), (30, 37), (41, 0), (14, 35), (12, 9), (4, 19), (17, 25), (34, 23), (9, 31), (5, 32), (23, 11), (17, 23), (39, 12), (15, 14), (32, 11), (12, 2), (5, 30), (20, 20), (9, 15), (26, 36), (26, 20), (30, 17), (16, 20), (31, 5), (25, 2), (32, 15), (25, 33), (42, 29), (11, 14), (40, 32), (23, 26), (16, 6), (28, 9), (24, 8), (20, 1), (43, 11), (22, 7), (3, 29), (5, 25), (34, 8), (41, 28), (12, 17), (2, 35), (0, 37), (23, 32), (35, 19), (4, 1), (13, 40), (31, 28), (8, 24), (20, 31), (10, 25), (18, 35), (20, 40), (13, 17), (32, 17), (40, 35), (32, 38), (9, 26), (34, 33), (13, 30), (18, 33), (8, 26), (1, 32), (21, 14), (5, 14), (28, 7), (21, 17), (8, 12), (18, 26), (43, 33), (43, 18), (37, 1), (4, 33), (40, 36), (41, 4), (35, 26), (26, 27), (7, 3), (25, 13), (31, 20), (6, 24), (38, 18), (25, 38), (9, 28), (39, 15), (39, 2), (1, 34), (27, 1), (35, 23), (10, 36), (11, 25), (6, 34), (27, 9), (19, 34), (27, 7), (26, 6), (2, 11), (5, 12), (23, 15), (11, 4), (32, 9), (11, 21), (34, 16), (32, 25), (25, 40), (0, 23), (19, 17), (39, 36), (13, 15), (16, 13), (7, 11), (8, 32), (12, 11), (16, 14), (16, 25), (9, 8), (24, 22), (33, 7), (39, 26), (27, 13), (13, 5), (8, 6), (38, 7), (36, 39), (43, 20), (34, 24), (21, 13), (31, 14), (17, 10), (29, 33), (5, 15), (15, 8), (13, 14), (0, 34), (23, 14), (10, 12), (10, 35), (31, 7), (6, 0), (34, 1), (41, 36), (32, 34), (38, 4), (33, 6), (44, 8), (36, 31), (30, 6), (24, 34), (32, 2), (24, 13), (1, 30), (39, 14), (43, 0), (16, 8), (27, 19), (4, 36), (28, 20), (3, 9), (0, 36), (24, 26), (29, 17), (5, 36), (20, 26), (34, 14), (7, 39), (34, 20), (2, 14), (43, 32), (23, 9), (39, 23), (31, 8), (34, 28), (20, 10), (42, 22), (25, 16), (29, 38), (13, 0), (37, 2), (19, 24), (36, 3), (32, 24), (41, 40), (4, 16), (40, 40), (1, 19), (30, 33), (12, 25), (37, 4), (30, 4), (18, 17), (17, 17), (13, 19), (40, 31), (33, 10), (25, 36), (7, 22), (18, 10), (25, 28), (4, 12), (17, 39), (21, 22), (44, 24), (28, 26), (2, 6), (3, 19), (22, 11), (0, 20), (4, 5), (12, 38), (18, 39), (18, 20), (25, 6), (6, 15), (6, 4), (25, 5), (31, 0), (39, 28), (8, 8), (4, 40), (38, 13), (42, 3), (17, 29), (24, 29), (2, 18), (42, 23), (32, 26), (25, 0), (38, 29), (9, 23), (7, 0), (18, 9), (31, 16), (16, 4), (41, 30), (40, 12), (33, 19), (15, 5), (44, 6), (18, 12), (19, 30), (40, 25), (38, 12), (41, 3), (32, 21), (22, 33), (31, 35), (17, 8), (6, 21), (23, 37), (38, 14), (3, 34), (31, 18), (5, 23), (3, 20), (42, 28), (8, 39), (3, 11), (31, 1), (15, 16), (10, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 30), (10, 8), (12, 27), (17, 33), (38, 10), (29, 9), (46, 34), (5, 14), (41, 36), (25, 15), (42, 4), (39, 7), (27, 40), (18, 2), (21, 39), (44, 10), (31, 1), (15, 42), (34, 6), (14, 39), (10, 18), (18, 25), (11, 6), (39, 41), (8, 2), (16, 21), (42, 24), (18, 30), (37, 22), (4, 18), (7, 11), (2, 15), (13, 31), (41, 25), (37, 13), (5, 3), (37, 30), (14, 23), (16, 5), (23, 4), (35, 19), (37, 28), (12, 5), (3, 20), (15, 10), (39, 29), (22, 32), (41, 1), (21, 10), (31, 22), (9, 25), (36, 11), (27, 29), (16, 1), (27, 37), (35, 28), (10, 25), (6, 33), (4, 12), (16, 14), (38, 30), (34, 13), (45, 37), (45, 40), (6, 36), (40, 10), (24, 19), (45, 5), (38, 22), (38, 38), (19, 33), (3, 4), (19, 35), (1, 20), (7, 22), (42, 30), (1, 30), (7, 18), (35, 17), (40, 38), (32, 39), (29, 38), (18, 36), (25, 23), (0, 8), (6, 10), (38, 17), (20, 20), (41, 16), (0, 24), (37, 4), (1, 8), (19, 36), (6, 4), (6, 0), (45, 7), (30, 19), (45, 42), (36, 16), (29, 2), (38, 9), (34, 17), (0, 13), (13, 4), (44, 8), (0, 38), (1, 39), (18, 8), (17, 10), (18, 1), (24, 20), (43, 43), (40, 5), (10, 23), (44, 37), (36, 43), (35, 23), (45, 44), (15, 6), (35, 34), (0, 20), (40, 11), (29, 18), (38, 32), (14, 26), (11, 14), (11, 28), (32, 37), (46, 8), (44, 6), (24, 0), (37, 24), (10, 20), (33, 16), (42, 40), (41, 19), (20, 37), (8, 22), (43, 3), (0, 39), (33, 9), (10, 14), (22, 43), (34, 38), (11, 40), (26, 25), (10, 9), (12, 37), (1, 13), (18, 34), (17, 15), (22, 19), (30, 10), (44, 13), (20, 32), (6, 17), (6, 1), (39, 8), (27, 34), (21, 18), (8, 8), (3, 29), (20, 36), (15, 21), (25, 40), (28, 13), (32, 23), (25, 17), (44, 39), (0, 10), (44, 1), (24, 34), (30, 28), (42, 29), (0, 40), (15, 33), (10, 7), (8, 20), (29, 27), (22, 15), (10, 26), (2, 36), (46, 25), (43, 20), (30, 35), (26, 23), (16, 13), (39, 22), (11, 11), (5, 8), (18, 10), (4, 35), (17, 19), (44, 25), (18, 43), (0, 31), (19, 31), (15, 19), (42, 12), (3, 1), (21, 14), (34, 34), (24, 18), (31, 10), (35, 15), (36, 23), (39, 36), (33, 27), (9, 17), (31, 32), (14, 31), (16, 29), (44, 44), (16, 15), (0, 33), (41, 22), (8, 10), (23, 41), (22, 8), (38, 41), (34, 20), (25, 24), (6, 39), (23, 27), (30, 37), (37, 7), (15, 40), (32, 10), (31, 0), (32, 21), (2, 10), (1, 23), (26, 12), (15, 28), (20, 43), (31, 25), (7, 35), (21, 40), (45, 9), (41, 39), (43, 7), (10, 43), (44, 7), (45, 17), (19, 1), (31, 35), (6, 25), (32, 7), (8, 3), (1, 19), (37, 3), (32, 14), (7, 12), (40, 29), (15, 37), (19, 5), (38, 39), (46, 28), (24, 2), (16, 44), (12, 18), (20, 40), (19, 11), (17, 36), (17, 30), (43, 41), (18, 5), (8, 29), (32, 26), (42, 28), (13, 35), (23, 9), (18, 3), (35, 36), (46, 42), (20, 41), (26, 39), (6, 12), (31, 30), (27, 39), (46, 21), (6, 43), (2, 19), (28, 14), (43, 26), (8, 28), (26, 14), (28, 32), (20, 18), (8, 30), (24, 8), (11, 41), (33, 43), (45, 31), (23, 32), (16, 31), (16, 33), (30, 31), (0, 4), (28, 36), (30, 8), (38, 11), (0, 7), (19, 14), (30, 17), (31, 14), (41, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 39), (37, 15), (41, 36), (33, 27), (35, 0), (20, 20), (20, 7), (26, 36), (8, 2), (25, 29), (21, 28), (17, 3), (26, 32), (21, 21), (38, 30), (7, 16), (38, 9), (2, 37), (29, 10), (27, 26), (19, 37), (27, 8), (29, 8), (32, 34), (42, 35), (11, 34), (33, 5), (22, 17), (6, 33), (8, 12), (4, 4), (15, 5), (0, 20), (3, 36), (29, 34), (19, 34), (36, 27), (30, 21), (1, 21), (15, 37), (17, 28), (5, 21), (8, 31), (12, 0), (4, 13), (30, 16), (23, 31), (2, 24), (35, 29), (16, 38), (0, 21), (40, 33), (15, 16), (0, 2), (35, 12), (6, 4), (2, 18), (27, 1), (13, 26), (15, 24), (4, 10), (42, 2), (23, 33), (7, 25), (19, 14), (35, 11), (23, 6), (42, 8), (11, 16), (19, 11), (25, 21), (18, 4), (33, 39), (33, 21), (26, 8), (5, 33), (18, 10), (31, 38), (42, 25), (10, 8), (15, 33), (39, 11), (1, 38), (7, 24), (8, 33), (22, 0), (19, 17), (35, 5), (22, 15), (37, 22), (29, 18), (23, 20), (32, 28), (32, 25), (4, 20), (36, 11), (16, 17), (8, 20), (15, 17), (33, 9), (29, 36), (19, 3), (22, 36), (30, 27), (35, 19), (15, 19), (28, 8), (27, 13), (2, 0), (42, 22), (35, 13), (6, 21), (33, 37), (1, 39), (33, 22), (32, 8), (24, 25), (24, 13), (24, 35), (0, 18), (28, 10), (40, 34), (21, 27), (39, 32), (2, 29), (30, 34), (20, 36), (39, 27), (4, 0), (42, 5), (31, 20), (28, 38), (17, 15), (9, 6), (23, 12), (34, 32), (9, 32), (37, 9), (30, 4), (33, 35), (19, 36), (3, 32), (16, 9), (34, 16), (29, 19), (19, 16), (0, 1), (6, 13), (36, 3), (14, 33), (21, 3), (21, 1), (16, 18), (12, 7), (39, 20), (38, 2), (17, 34), (10, 15), (23, 38), (17, 2), (23, 35), (2, 9), (19, 30), (23, 37), (3, 11), (16, 20), (11, 7), (41, 25), (19, 8), (42, 19), (18, 13), (11, 12), (31, 19), (29, 5), (1, 27), (27, 25), (31, 21), (35, 17), (21, 31), (35, 24), (1, 14), (24, 14), (38, 23), (13, 31), (20, 24), (22, 20), (2, 10), (35, 35), (6, 11), (38, 34), (21, 9), (20, 29), (27, 6), (14, 38), (38, 14), (28, 18), (33, 3), (11, 29), (17, 7), (37, 0), (5, 25), (25, 9), (8, 14), (22, 24), (14, 18), (7, 1), (32, 0), (36, 17), (31, 17), (18, 2), (30, 26), (16, 28), (13, 15), (37, 10), (0, 29), (39, 36), (36, 6), (13, 29), (24, 33), (10, 9), (28, 17), (9, 25), (4, 24), (5, 35), (24, 28), (39, 26), (15, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 20), (24, 30), (9, 2), (33, 38), (37, 24), (5, 9), (11, 14), (13, 15), (19, 19), (16, 17), (19, 29), (38, 31), (13, 22), (10, 7), (36, 18), (1, 10), (21, 3), (8, 1), (31, 11), (12, 26), (12, 19), (13, 13), (0, 4), (18, 21), (30, 24), (1, 2), (9, 17), (7, 6), (8, 23), (36, 31), (28, 35), (35, 44), (31, 24), (8, 30), (37, 13), (22, 26), (19, 12), (29, 31), (7, 42), (32, 3), (0, 40), (30, 13), (7, 29), (15, 8), (30, 0), (26, 22), (14, 42), (20, 31), (9, 38), (39, 29), (11, 19), (18, 16), (24, 11), (8, 35), (4, 2), (0, 1), (21, 6), (18, 13), (13, 3), (36, 23), (23, 16), (32, 21), (20, 25), (20, 38), (32, 43), (20, 44), (10, 6), (9, 4), (35, 0), (33, 39), (29, 6), (4, 9), (27, 32), (3, 6), (28, 16), (3, 29), (30, 43), (38, 21), (14, 9), (39, 21), (19, 38), (19, 16), (30, 44), (27, 43), (30, 29), (32, 29), (32, 39), (4, 18), (32, 31), (26, 4), (18, 28), (2, 31), (26, 34), (33, 7), (23, 15), (29, 32), (38, 17), (28, 1), (7, 30), (1, 29), (34, 40), (36, 44), (37, 43), (6, 36), (4, 6), (34, 6), (4, 10), (26, 9), (0, 7), (17, 3), (7, 36), (22, 16), (3, 43), (5, 10), (16, 42), (19, 26), (14, 31), (18, 30), (22, 35), (18, 7), (19, 13), (2, 43), (4, 31), (32, 2), (24, 23), (17, 34), (36, 16), (9, 34), (27, 0), (23, 35), (16, 15), (33, 35), (38, 3), (8, 38), (6, 28), (15, 12), (20, 4), (21, 16), (26, 38), (4, 29), (13, 36), (11, 25), (24, 41), (17, 1), (2, 20), (18, 35), (23, 1), (7, 27), (33, 12), (38, 32), (11, 43), (39, 23), (4, 13), (20, 8), (6, 39), (31, 44), (39, 35), (39, 18), (5, 29), (20, 40), (6, 11), (8, 18), (24, 25), (8, 32), (7, 4), (12, 25), (37, 16), (2, 7), (14, 24), (29, 4), (12, 31), (38, 19), (6, 30), (30, 10), (1, 18), (0, 24), (21, 8), (18, 2), (25, 10), (32, 1), (20, 10), (1, 37), (39, 41), (14, 8), (31, 12), (30, 15), (32, 6), (13, 5), (37, 30), (11, 4), (30, 33), (20, 16), (40, 24), (11, 35), (22, 18), (25, 16), (21, 12), (17, 29), (24, 16), (8, 13), (23, 33), (2, 4), (11, 26), (6, 10), (20, 22), (28, 37), (22, 30), (29, 35), (19, 2), (28, 23), (27, 42), (29, 44), (20, 30), (40, 28), (30, 8), (13, 19), (8, 26), (27, 34), (27, 3), (27, 11), (40, 11), (16, 34), (10, 8), (8, 20), (30, 31), (12, 34), (10, 39), (30, 34), (39, 15), (19, 44), (34, 10), (38, 25), (32, 24), (0, 25), (20, 23), (12, 44), (39, 6), (26, 13), (10, 11), (36, 29), (2, 36), (18, 26), (9, 8), (13, 41), (10, 35), (13, 10), (32, 8), (38, 30), (22, 4), (23, 9), (27, 38), (9, 6), (23, 37), (38, 15), (25, 23), (28, 22), (10, 24), (37, 22), (13, 14), (3, 37), (28, 20), (3, 1), (24, 33), (23, 23), (36, 12), (18, 6), (15, 3), (4, 24), (8, 0), (13, 0), (6, 2), (28, 25), (31, 39), (30, 20), (6, 34), (25, 13), (21, 22), (28, 31), (40, 31), (25, 44), (10, 44), (32, 27), (33, 9), (40, 30), (27, 2), (28, 41), (0, 21), (18, 3), (29, 14), (24, 22), (18, 12), (29, 2), (37, 40), (26, 26), (30, 27), (9, 26), (10, 5), (24, 19), (40, 33), (17, 36), (8, 33), (13, 8), (35, 31), (23, 13), (26, 16), (21, 1), (18, 19), (12, 8), (2, 24), (15, 25), (35, 17), (1, 15), (21, 34), (1, 5), (5, 35), (2, 33), (33, 20), (38, 2), (28, 12), (15, 37), (9, 1), (5, 15), (7, 22), (10, 33), (18, 23), (23, 10), (4, 26), (39, 22), (39, 16), (24, 39), (31, 6), (14, 19), (27, 13), (3, 42), (29, 42), (22, 25), (16, 41), (35, 39), (30, 21), (35, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 21), (42, 37), (23, 29), (33, 39), (25, 9), (33, 23), (26, 6), (9, 15), (10, 35), (14, 26), (8, 29), (30, 1), (20, 5), (38, 5), (39, 0), (8, 27), (15, 26), (17, 5), (17, 15), (3, 26), (9, 8), (14, 6), (9, 34), (22, 32), (21, 6), (14, 30), (7, 37), (13, 40), (6, 30), (11, 5), (3, 0), (37, 37), (11, 36), (17, 10), (32, 21), (2, 19), (19, 1), (5, 34), (26, 13), (38, 29), (12, 39), (30, 0), (6, 40), (32, 0), (33, 0), (13, 4), (37, 29), (38, 40), (3, 30), (23, 33), (6, 19), (32, 13), (26, 5), (23, 37), (17, 12), (39, 25), (21, 16), (31, 29), (19, 22), (7, 30), (30, 10), (18, 12), (21, 17), (4, 22), (28, 23), (6, 29), (21, 5), (37, 26), (24, 27), (19, 25), (5, 20), (14, 14), (16, 18), (21, 36), (12, 27), (26, 2), (3, 34), (23, 8), (8, 7), (28, 17), (27, 5), (24, 36), (28, 11), (12, 1), (12, 37), (13, 9), (4, 20), (16, 7), (23, 15), (33, 18), (6, 0), (36, 36), (39, 36), (42, 23), (19, 38), (7, 33), (16, 13), (39, 1), (22, 33), (35, 27), (13, 39), (22, 25), (2, 39), (16, 27), (25, 31), (30, 3), (23, 32), (12, 13), (16, 29), (10, 38), (21, 39), (16, 12), (4, 18), (20, 27), (14, 12), (36, 9), (0, 5), (40, 30), (17, 2), (16, 32), (22, 9), (7, 19), (34, 3), (4, 3), (9, 33), (20, 28), (35, 34), (12, 24), (6, 15), (25, 40), (22, 2), (23, 19), (21, 38), (19, 8), (3, 11), (40, 27), (9, 4), (18, 39), (39, 14), (4, 10), (16, 34), (38, 26), (34, 35), (21, 14), (12, 31), (42, 27), (22, 36), (18, 36), (6, 13), (30, 6), (15, 8), (21, 29), (28, 22), (11, 23), (18, 32), (28, 19), (33, 36), (42, 21), (7, 34), (18, 30), (19, 24), (22, 18), (22, 21), (25, 12), (30, 37), (35, 35), (26, 24), (40, 25), (34, 23), (26, 11), (22, 16), (15, 7), (35, 15), (23, 0), (28, 16), (36, 28), (13, 2), (11, 38), (30, 17), (34, 26), (27, 31), (19, 4), (20, 6), (25, 1), (41, 16), (30, 26), (7, 39), (12, 22), (17, 29), (5, 24), (39, 9), (16, 36), (34, 15), (4, 39), (40, 14), (17, 3), (39, 22), (37, 3), (0, 22), (15, 10), (25, 36), (36, 23), (20, 9), (10, 34), (0, 2), (12, 10), (41, 33), (23, 25), (20, 26), (38, 18), (1, 3), (31, 21), (13, 12), (41, 34), (22, 30), (30, 40), (14, 15), (6, 20), (39, 28), (29, 29), (17, 19), (31, 16), (37, 24), (0, 20), (19, 33), (5, 22), (4, 27), (39, 40), (11, 9), (15, 4), (32, 16), (36, 21), (15, 30), (30, 20), (39, 7), (27, 7), (35, 1), (39, 4), (20, 37), (18, 34), (3, 33), (35, 30), (34, 1), (16, 40), (4, 14), (21, 10), (42, 18), (16, 20), (19, 14), (12, 15), (13, 36), (8, 18), (29, 22), (11, 33), (17, 25), (2, 22), (23, 36), (9, 26), (37, 13), (7, 11), (28, 8), (5, 25), (16, 16), (6, 34), (11, 14), (1, 40), (0, 23), (9, 0), (5, 26), (26, 3), (33, 26), (37, 7), (21, 4), (24, 21), (10, 18), (13, 7), (3, 5), (42, 28), (11, 8), (37, 15), (41, 22), (42, 34), (42, 12), (3, 18), (14, 29), (38, 32), (26, 4), (3, 37), (8, 15), (4, 30), (7, 14), (21, 15), (38, 3), (32, 40), (31, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 12), (1, 14), (2, 2), (28, 6), (12, 14), (37, 7), (7, 8), (1, 1), (35, 22), (5, 3), (14, 8), (14, 33), (16, 32), (9, 38), (7, 42), (31, 24), (5, 5), (5, 29), (12, 39), (6, 26), (30, 28), (35, 7), (11, 8), (24, 21), (21, 43), (25, 21), (36, 26), (12, 2), (4, 30), (14, 13), (29, 37), (18, 3), (34, 33), (22, 17), (19, 24), (7, 5), (19, 25), (5, 31), (24, 11), (39, 25), (19, 38), (9, 13), (8, 26), (31, 23), (0, 15), (21, 27), (14, 27), (29, 38), (33, 10), (38, 31), (38, 26), (5, 8), (12, 0), (26, 7), (17, 10), (19, 32), (17, 0), (40, 19), (34, 12), (30, 7), (29, 21), (23, 17), (18, 12), (22, 19), (22, 39), (34, 40), (22, 26), (35, 24), (28, 21), (38, 13), (35, 34), (29, 10), (30, 18), (17, 16), (32, 1), (37, 5), (12, 37), (23, 16), (23, 2), (11, 13), (8, 8), (20, 38), (28, 40), (13, 16), (21, 32), (8, 31), (4, 36), (36, 39), (5, 43), (18, 17), (22, 29), (11, 35), (12, 19), (34, 22), (31, 7), (19, 31), (37, 22), (36, 17), (26, 9), (38, 6), (23, 35), (26, 20), (4, 1), (20, 17), (32, 37), (38, 28), (29, 22), (22, 31), (35, 25), (15, 11), (18, 25), (8, 6), (30, 12), (22, 34), (39, 3), (5, 36), (5, 39), (31, 17), (36, 14), (34, 13), (33, 26), (35, 5), (2, 43), (38, 29), (25, 13), (3, 34), (2, 14), (34, 21), (26, 36), (23, 24), (9, 22), (5, 28), (25, 16), (24, 43), (9, 40), (28, 12), (19, 1), (27, 42), (18, 33), (40, 25), (40, 9), (28, 39), (18, 18), (13, 15), (1, 34), (0, 16), (10, 36), (4, 40), (17, 33), (12, 23), (8, 4), (33, 28), (11, 28), (16, 41), (7, 21), (0, 18), (7, 23), (29, 16), (7, 18), (22, 18), (39, 30), (37, 33), (14, 12), (9, 28), (40, 23), (29, 40), (12, 8), (5, 10), (39, 10), (26, 39), (26, 42), (2, 41), (11, 17), (26, 21), (29, 39), (4, 7), (38, 25), (36, 29), (38, 2), (30, 16), (26, 10), (4, 10), (20, 36), (16, 42), (16, 34), (2, 28), (37, 19), (37, 34), (2, 33), (33, 2), (11, 40), (4, 41), (24, 25), (27, 13), (4, 27), (33, 3), (2, 13), (34, 32), (28, 28), (9, 23), (11, 1), (19, 27), (5, 22), (31, 4), (10, 21), (10, 33), (10, 31), (6, 2), (16, 3), (10, 7), (16, 7), (28, 23), (22, 6), (23, 42), (28, 19), (10, 5), (19, 0), (27, 4), (7, 35), (40, 13), (35, 9), (6, 15), (17, 1), (30, 36), (22, 24), (0, 30), (11, 30), (9, 7), (34, 26), (38, 37), (25, 32), (13, 31), (35, 10), (34, 18), (16, 24), (38, 14), (12, 26), (32, 25), (0, 10), (25, 1), (8, 35), (22, 12), (35, 20), (22, 4), (12, 7), (32, 41), (1, 12), (20, 28), (29, 31), (3, 37), (1, 39), (21, 11), (6, 21), (30, 30), (24, 18), (26, 34), (9, 9), (36, 5), (7, 37), (6, 25), (4, 11), (0, 3), (24, 8), (38, 38), (18, 38), (16, 16), (8, 17), (17, 17), (13, 27), (18, 15), (37, 30), (1, 6), (0, 33), (30, 4), (11, 36), (21, 40), (10, 3), (29, 27), (5, 38), (11, 26), (37, 36), (28, 33), (7, 13), (13, 8), (15, 32), (17, 22), (39, 26), (2, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 47), (1, 35), (42, 7), (18, 25), (44, 21), (43, 25), (5, 21), (17, 1), (14, 5), (40, 38), (0, 14), (12, 33), (0, 24), (16, 22), (14, 10), (17, 12), (25, 34), (34, 13), (5, 23), (2, 38), (28, 26), (26, 2), (32, 38), (43, 23), (8, 39), (5, 25), (6, 41), (8, 28), (25, 44), (9, 15), (12, 40), (1, 37), (26, 36), (13, 9), (19, 40), (46, 12), (39, 22), (39, 35), (11, 37), (39, 24), (15, 24), (12, 34), (28, 12), (0, 17), (5, 12), (10, 10), (7, 28), (44, 36), (20, 28), (31, 0), (32, 35), (14, 48), (44, 12), (1, 48), (21, 41), (27, 0), (41, 46), (17, 9), (26, 43), (39, 29), (40, 3), (34, 21), (14, 28), (15, 21), (7, 4), (14, 45), (7, 10), (19, 19), (12, 1), (2, 21), (41, 24), (41, 39), (43, 35), (33, 11), (38, 22), (35, 24), (0, 23), (44, 23), (2, 0), (33, 23), (2, 13), (12, 44), (4, 25), (6, 11), (22, 2), (21, 35), (29, 24), (39, 42), (32, 4), (30, 36), (12, 27), (22, 47), (10, 42), (20, 41), (29, 2), (10, 12), (31, 22), (18, 23), (3, 22), (25, 17), (23, 13), (39, 32), (3, 6), (31, 39), (12, 11), (42, 17), (28, 40), (18, 32), (25, 5), (13, 8), (6, 45), (40, 4), (44, 16), (32, 9), (28, 0), (8, 9), (11, 38), (18, 39), (20, 38), (45, 32), (30, 24), (10, 38), (6, 35), (17, 48), (6, 20), (44, 19), (29, 6), (3, 7), (41, 45), (16, 44), (11, 5), (23, 33), (8, 37), (16, 32), (12, 36), (17, 38), (23, 34), (24, 20), (11, 18), (11, 42), (29, 7), (4, 10), (16, 3), (13, 14), (5, 42), (16, 19), (36, 36), (13, 47), (12, 17), (46, 42), (30, 3), (36, 7), (20, 6), (41, 37), (40, 16), (46, 35), (33, 46), (1, 16), (46, 17), (10, 19), (46, 37), (24, 24), (11, 48), (41, 23), (25, 32), (3, 3), (13, 1), (18, 4), (8, 0), (11, 44), (20, 48), (28, 47), (0, 9), (23, 1), (24, 30), (36, 26), (27, 30), (44, 43), (7, 27), (4, 22), (6, 26), (39, 10), (17, 31), (26, 21), (38, 1), (24, 27), (1, 40), (45, 38), (23, 46), (12, 8), (22, 5), (37, 8), (7, 47), (32, 36), (37, 22), (32, 18), (44, 9), (3, 46), (45, 24), (5, 18), (7, 33), (2, 26), (18, 7), (32, 40), (10, 29), (10, 0), (40, 26), (13, 40), (24, 47), (46, 41), (20, 43), (44, 7), (23, 45), (2, 47), (43, 32), (35, 27), (17, 29), (10, 34), (42, 33), (0, 27), (26, 8), (43, 4), (14, 26), (0, 35), (34, 47), (19, 26), (15, 30), (1, 7), (23, 32), (40, 1), (16, 13), (33, 48), (35, 18), (17, 26), (43, 16), (28, 11), (9, 46), (28, 30), (34, 25), (23, 17), (26, 48), (8, 38), (8, 45), (8, 32), (28, 5), (7, 7), (41, 26), (44, 15), (30, 37), (38, 36), (28, 33), (5, 11), (19, 47), (5, 31), (6, 46), (32, 27), (9, 11), (45, 31), (24, 41), (10, 18), (1, 47), (21, 31), (7, 15), (0, 20), (7, 21), (36, 19), (10, 20), (13, 23), (18, 11), (0, 30), (1, 1), (16, 25), (15, 39), (40, 18), (35, 10), (14, 21), (17, 27), (25, 36), (37, 35), (44, 28), (29, 36), (11, 25), (32, 33), (12, 2), (46, 5), (8, 3), (33, 15), (32, 7), (16, 43), (37, 2), (32, 24), (44, 35), (24, 13), (20, 27), (4, 17), (44, 25), (16, 9), (11, 2), (45, 4), (19, 29), (39, 17), (20, 22), (4, 39), (43, 15), (9, 27), (7, 48), (4, 27), (19, 5), (1, 20), (21, 22), (31, 29), (42, 24), (11, 33), (35, 7), (16, 33), (23, 14), (28, 42), (25, 26), (35, 8), (46, 47), (23, 28), (31, 30), (28, 36), (22, 17), (33, 38), (31, 9), (0, 12), (23, 27), (39, 44), (29, 21), (28, 1), (13, 46), (44, 11), (31, 43), (22, 41), (21, 40), (16, 42), (42, 46), (21, 28), (45, 45), (36, 44), (28, 25), (34, 22), (13, 36), (11, 29), (9, 31), (15, 1), (38, 26), (10, 13), (9, 37), (18, 26), (20, 4), (12, 18), (29, 44), (43, 0), (32, 12), (35, 32), (0, 6), (1, 27), (46, 15), (44, 45), (3, 27), (31, 15), (36, 11), (33, 28), (13, 0), (46, 31), (4, 12), (4, 8), (6, 34), (28, 9), (13, 2), (31, 47), (23, 48), (39, 8), (40, 10), (44, 26), (14, 35), (44, 41), (40, 17), (44, 4), (28, 27), (23, 47), (40, 14), (5, 7), (16, 14), (9, 44), (32, 16), (18, 37), (16, 12), (10, 8), (15, 33), (26, 29), (3, 44), (8, 47), (33, 43), (40, 45), (40, 24), (1, 10), (40, 27), (11, 31), (41, 0), (30, 1), (12, 41), (44, 14), (46, 22), (33, 2), (44, 10), (22, 24), (2, 20), (28, 20), (15, 32), (24, 36), (12, 28), (36, 27), (4, 36), (3, 47), (38, 0), (19, 7), (22, 9), (27, 43), (40, 36), (32, 6), (25, 20), (10, 37), (22, 33), (42, 31), (24, 46), (18, 33), (26, 38), (8, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 14), (41, 10), (7, 23), (38, 44), (11, 45), (30, 29), (24, 3), (43, 2), (23, 8), (22, 12), (41, 4), (16, 15), (5, 34), (26, 45), (10, 41), (37, 38), (38, 8), (25, 19), (43, 6), (32, 33), (31, 40), (7, 16), (28, 24), (14, 23), (20, 5), (26, 41), (23, 24), (26, 10), (11, 15), (32, 21), (35, 22), (41, 23), (9, 29), (33, 26), (36, 0), (18, 40), (5, 35), (29, 45), (35, 37), (23, 29), (12, 4), (10, 35), (36, 2), (32, 7), (0, 39), (36, 40), (43, 12), (3, 32), (4, 42), (42, 16), (10, 43), (45, 33), (45, 19), (25, 28), (21, 33), (9, 32), (9, 3), (3, 42), (26, 40), (21, 3), (16, 6), (39, 15), (6, 14), (41, 22), (2, 35), (28, 45), (42, 14), (43, 45), (10, 6), (4, 35), (9, 15), (35, 6), (33, 45), (44, 2), (37, 19), (40, 43), (40, 8), (5, 42), (7, 15), (35, 5), (44, 26), (5, 32), (39, 25), (6, 40), (20, 38), (15, 41), (1, 11), (32, 46), (44, 36), (13, 17), (10, 9), (6, 18), (26, 36), (40, 35), (23, 19), (25, 23), (10, 22), (33, 1), (0, 6), (40, 11), (45, 26), (40, 34), (44, 16), (10, 44), (24, 2), (12, 36), (4, 10), (37, 40), (5, 41), (38, 11), (29, 43), (31, 10), (40, 16), (1, 36), (37, 5), (16, 35), (29, 4), (18, 21), (14, 32), (1, 41), (20, 4), (1, 16), (6, 39), (3, 12), (1, 27), (3, 35), (28, 21), (16, 44), (24, 1), (15, 34), (27, 29), (27, 23), (36, 38), (12, 14), (37, 9), (11, 4), (7, 17), (9, 21), (3, 38), (31, 0), (18, 23), (4, 44), (20, 25), (39, 13), (18, 20), (42, 17), (15, 3), (35, 30), (33, 36), (40, 18), (37, 0), (27, 14), (44, 41), (6, 34), (0, 15), (21, 44), (9, 16), (7, 24), (45, 6), (30, 9), (42, 18), (16, 40), (11, 44), (13, 10), (45, 35), (33, 30), (9, 45), (45, 13), (21, 18), (21, 40), (27, 6), (32, 38), (10, 33), (15, 17), (27, 36), (2, 22), (24, 13), (18, 45), (38, 26), (20, 42), (38, 0), (9, 2), (21, 39), (26, 22), (41, 8), (29, 19), (28, 25), (9, 39), (13, 36), (29, 0), (4, 40), (34, 2), (5, 5), (35, 40), (44, 25), (10, 5), (43, 30), (40, 42), (2, 23), (35, 18), (24, 11), (8, 16), (40, 46), (27, 0), (18, 12), (31, 23), (20, 33), (15, 39), (29, 42), (21, 11), (25, 6), (7, 7), (39, 44), (8, 11), (45, 32), (42, 40), (38, 12), (41, 35), (24, 31), (9, 25), (33, 5), (9, 12), (1, 42), (6, 28), (16, 17), (1, 23), (12, 43), (23, 38), (2, 16), (3, 11), (19, 25), (33, 14), (32, 32), (18, 25), (14, 45), (38, 43), (42, 27), (3, 41), (1, 21), (13, 19), (37, 20), (35, 9), (11, 39), (18, 4), (45, 42), (15, 18), (38, 20), (34, 26), (42, 42), (28, 34), (31, 4), (12, 0), (22, 9), (38, 2), (17, 8), (0, 2), (6, 43), (26, 37), (32, 18), (19, 9), (36, 21), (12, 41), (17, 33), (16, 2), (13, 44), (21, 34), (21, 16), (29, 8), (35, 16), (37, 12), (39, 3), (42, 45), (30, 15), (28, 28), (0, 28), (0, 46), (20, 44), (31, 22), (17, 1), (17, 4), (33, 28), (5, 20), (3, 27), (22, 23), (23, 21), (44, 44), (31, 18), (12, 28), (27, 42), (11, 33), (14, 24), (5, 25), (12, 21), (6, 2), (22, 37), (3, 5), (41, 18), (44, 18), (17, 6), (10, 20), (36, 8), (2, 45), (12, 34), (17, 20), (38, 45), (30, 18), (26, 19), (30, 6), (34, 46), (35, 3), (8, 27), (16, 31), (42, 11), (25, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 16), (43, 37), (9, 17), (18, 32), (1, 11), (16, 41), (10, 22), (5, 21), (37, 29), (38, 38), (41, 0), (44, 17), (45, 39), (39, 0), (38, 1), (18, 40), (41, 22), (34, 43), (25, 11), (14, 5), (38, 12), (6, 41), (13, 43), (39, 28), (9, 3), (34, 7), (30, 11), (15, 25), (25, 15), (14, 43), (21, 12), (1, 10), (23, 5), (42, 4), (41, 38), (18, 17), (19, 5), (29, 10), (44, 32), (25, 2), (31, 24), (11, 14), (36, 5), (16, 38), (5, 24), (11, 28), (11, 1), (10, 28), (41, 27), (19, 27), (41, 30), (37, 16), (45, 1), (28, 39), (9, 6), (9, 21), (23, 30), (44, 16), (22, 16), (43, 27), (14, 34), (26, 4), (4, 38), (20, 13), (11, 3), (7, 8), (1, 27), (21, 26), (20, 3), (47, 6), (46, 35), (33, 22), (32, 17), (18, 0), (19, 44), (19, 25), (46, 11), (21, 25), (6, 3), (19, 20), (33, 7), (4, 26), (6, 27), (8, 23), (20, 43), (12, 3), (43, 1), (12, 42), (3, 38), (11, 21), (4, 41), (41, 42), (5, 0), (34, 39), (24, 41), (35, 12), (34, 10), (43, 7), (45, 19), (19, 42), (12, 14), (19, 6), (23, 8), (7, 0), (16, 16), (26, 13), (20, 30), (14, 14), (4, 39), (8, 43), (13, 44), (7, 37), (32, 22), (2, 31), (28, 32), (6, 29), (25, 32), (31, 8), (18, 31), (17, 41), (23, 37), (33, 12), (19, 33), (8, 18), (24, 33), (26, 29), (4, 9), (30, 44), (0, 8), (31, 25), (11, 27), (11, 15), (14, 19), (42, 2), (46, 39), (45, 17), (17, 30), (31, 41), (21, 5), (12, 16), (38, 3), (25, 19), (15, 0), (44, 4), (20, 23), (20, 32), (37, 35), (40, 35), (45, 30), (10, 26), (4, 35), (27, 10), (43, 5), (35, 22), (33, 24), (31, 20), (2, 3), (23, 42), (47, 41), (43, 23), (40, 5), (17, 0), (22, 42), (42, 6), (20, 0), (40, 25), (0, 34), (15, 4), (26, 42), (1, 29), (33, 15), (39, 41), (26, 41), (42, 34), (39, 35), (43, 13), (42, 1), (4, 20), (1, 19), (41, 2), (27, 0), (19, 15), (1, 14), (36, 35), (11, 42), (22, 8), (18, 7), (36, 3), (33, 20), (22, 36), (1, 38), (12, 7), (14, 18), (7, 27), (20, 39), (45, 14), (5, 14), (11, 25), (17, 1), (5, 5), (34, 5), (3, 30), (1, 30), (37, 13), (34, 14), (36, 30), (41, 32), (15, 7), (22, 23), (15, 14), (26, 32), (3, 33), (3, 2), (32, 20), (46, 8), (43, 26), (8, 41), (2, 20), (6, 12), (16, 32), (35, 13), (12, 6), (19, 21), (5, 13), (5, 29), (8, 25), (39, 34), (30, 21), (22, 26), (36, 8), (6, 22), (17, 13), (19, 34), (21, 4), (34, 21), (45, 12), (38, 21), (12, 5), (33, 11), (42, 24), (22, 25), (44, 29), (29, 17), (45, 36), (46, 19), (8, 8), (27, 19), (25, 24), (43, 39), (25, 9), (17, 12), (0, 2), (13, 24), (21, 15), (38, 16), (21, 31), (17, 38), (43, 10), (18, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 1), (44, 1), (2, 31), (28, 38), (20, 27), (37, 6), (45, 11), (15, 34), (4, 1), (43, 8), (3, 27), (34, 17), (33, 22), (20, 39), (22, 26), (39, 41), (39, 26), (32, 4), (19, 31), (30, 10), (38, 34), (7, 38), (26, 17), (46, 28), (46, 33), (43, 0), (9, 34), (30, 3), (44, 13), (26, 19), (1, 15), (9, 29), (36, 38), (38, 27), (31, 42), (34, 40), (6, 42), (21, 11), (43, 39), (17, 18), (47, 22), (17, 36), (48, 28), (15, 13), (14, 12), (24, 16), (31, 6), (10, 18), (34, 12), (21, 35), (7, 28), (1, 22), (20, 31), (24, 10), (5, 5), (19, 38), (19, 11), (2, 37), (7, 26), (8, 14), (17, 0), (22, 22), (31, 41), (41, 10), (23, 32), (32, 30), (47, 34), (0, 15), (18, 3), (41, 39), (6, 34), (8, 17), (38, 3), (14, 11), (27, 25), (11, 41), (4, 9), (2, 38), (40, 22), (11, 21), (26, 9), (22, 12), (15, 17), (11, 22), (41, 40), (48, 33), (38, 11), (39, 40), (15, 37), (12, 5), (0, 31), (45, 31), (33, 5), (19, 18), (30, 31), (37, 4), (37, 18), (47, 16), (40, 37), (13, 0), (20, 16), (22, 20), (28, 41), (17, 7), (18, 11), (8, 13), (4, 18), (44, 11), (9, 33), (23, 38), (47, 36), (5, 6), (32, 42), (32, 21), (43, 42), (35, 12), (14, 18), (18, 2), (3, 5), (6, 41), (42, 30), (24, 19), (30, 42), (37, 37), (6, 30), (45, 42), (16, 3), (41, 43), (15, 38), (47, 3), (35, 38), (39, 37), (47, 38), (4, 17), (30, 19), (2, 6), (45, 18), (48, 7), (13, 10), (43, 40), (28, 5), (29, 4), (27, 11), (19, 33), (17, 24), (20, 26), (0, 32), (24, 6), (42, 17), (14, 36), (0, 20), (9, 28), (19, 7), (17, 32), (46, 39), (41, 2), (44, 26), (24, 25), (21, 17), (31, 8), (46, 41), (30, 35), (37, 32), (23, 28), (4, 24), (12, 21), (13, 34), (8, 3), (16, 0), (36, 32), (20, 37), (16, 25), (33, 23), (23, 40), (35, 25), (6, 19), (6, 36), (4, 42), (10, 34), (39, 38), (34, 43), (37, 10), (32, 16), (19, 39), (3, 23), (8, 33), (48, 21), (48, 25), (18, 14), (14, 28), (21, 40), (44, 0), (38, 19), (5, 17), (48, 27), (17, 13), (37, 40), (13, 20), (5, 11), (25, 8), (35, 24), (46, 21), (22, 25), (33, 31), (17, 34), (43, 16), (45, 43), (27, 39), (43, 22), (6, 39), (12, 24), (41, 34), (6, 2), (16, 2), (48, 10), (25, 19), (4, 43), (36, 4), (40, 35), (22, 23), (21, 14), (20, 12), (25, 35), (3, 7), (39, 34), (23, 41), (13, 14), (42, 29), (33, 24), (44, 41), (12, 22), (46, 22), (9, 14), (11, 12), (25, 40), (41, 38), (23, 23), (21, 1), (10, 27), (2, 11), (44, 3), (4, 41), (30, 29), (46, 34), (9, 36), (6, 17), (30, 33), (15, 31), (10, 8), (14, 4), (35, 34), (9, 27), (32, 14), (45, 1), (7, 15), (37, 7), (33, 27), (20, 42), (1, 11), (20, 17), (21, 20), (12, 15), (27, 20), (9, 18), (44, 9), (34, 39), (38, 2), (38, 43), (34, 34), (23, 5), (3, 30), (15, 28), (24, 41), (4, 20), (11, 4), (36, 43), (2, 34), (39, 42), (34, 36), (37, 1), (44, 19), (37, 38), (29, 41), (45, 25), (8, 20), (20, 38), (45, 6), (48, 40), (22, 32), (48, 23), (14, 13), (4, 30), (15, 40), (48, 37), (26, 32), (25, 29), (1, 19), (21, 41), (43, 35), (3, 37), (45, 27), (5, 20), (4, 19), (8, 37), (17, 15), (9, 30), (12, 1), (0, 43), (15, 43), (24, 11), (30, 25), (45, 19), (42, 37), (22, 27), (41, 8), (2, 27), (12, 18), (17, 17), (29, 22), (35, 29), (16, 43), (3, 40), (7, 29), (13, 17), (29, 34), (7, 40), (5, 25), (12, 12), (3, 28), (11, 24), (11, 40), (9, 22), (36, 35), (23, 29), (25, 37), (26, 14), (7, 33), (40, 5), (38, 25), (12, 7), (35, 28), (31, 5), (22, 8), (43, 21), (37, 19), (29, 7), (28, 24), (48, 26), (34, 28), (32, 41), (19, 10), (18, 1), (21, 19), (22, 11), (6, 43), (23, 20), (42, 24), (24, 38), (34, 19), (8, 41), (23, 35), (40, 9), (46, 10), (30, 24), (40, 39), (31, 13), (28, 19), (7, 34), (22, 36), (30, 18), (37, 31), (25, 5), (48, 18), (40, 15), (40, 34), (41, 42), (46, 43), (24, 18), (9, 7), (31, 40), (40, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 17), (25, 10), (28, 41), (8, 37), (38, 14), (18, 21), (28, 12), (0, 38), (19, 22), (11, 28), (25, 39), (35, 3), (12, 29), (1, 23), (29, 0), (30, 15), (18, 9), (21, 41), (32, 5), (2, 27), (10, 17), (32, 10), (8, 33), (20, 34), (12, 7), (35, 18), (41, 19), (10, 16), (40, 26), (30, 40), (23, 37), (34, 39), (41, 18), (4, 10), (2, 16), (18, 36), (44, 37), (12, 38), (1, 29), (19, 30), (24, 7), (1, 43), (16, 32), (23, 0), (4, 4), (39, 8), (21, 7), (6, 23), (44, 27), (29, 19), (18, 4), (0, 28), (21, 38), (37, 16), (16, 10), (20, 30), (31, 40), (31, 9), (14, 16), (11, 23), (33, 27), (15, 15), (3, 17), (40, 1), (15, 10), (5, 29), (8, 9), (13, 2), (43, 21), (1, 26), (18, 39), (1, 6), (31, 41), (18, 37), (26, 40), (4, 12), (27, 38), (32, 8), (4, 6), (13, 37), (36, 19), (43, 25), (12, 14), (37, 14), (20, 28), (13, 40), (1, 41), (13, 13), (25, 14), (2, 37), (4, 22), (8, 36), (8, 26), (18, 7), (22, 26), (38, 6), (35, 13), (29, 1), (12, 5), (16, 14), (19, 29), (19, 14), (41, 20), (33, 31), (18, 28), (8, 8), (23, 3), (17, 10), (22, 27), (36, 42), (6, 5), (9, 35), (34, 9), (22, 24), (23, 15), (17, 2), (31, 30), (7, 14), (8, 17), (37, 11), (8, 32), (26, 7), (9, 19), (12, 35), (16, 13), (26, 9), (10, 4), (4, 21), (24, 42), (14, 21), (23, 40), (44, 15), (22, 40), (37, 3), (37, 38), (11, 39), (5, 35), (1, 30), (0, 19), (1, 11), (35, 22), (14, 17), (21, 20), (12, 33), (12, 10), (10, 7), (2, 22), (18, 25), (9, 28), (23, 30), (11, 11), (14, 35), (15, 38), (19, 25), (31, 11), (13, 24), (2, 43), (23, 43), (15, 4), (24, 9), (43, 33), (44, 38), (20, 1), (36, 10), (7, 20), (42, 5), (6, 37), (44, 40), (38, 34), (30, 25), (5, 12), (21, 10), (31, 31), (29, 22), (29, 26), (42, 19), (28, 34), (25, 22), (5, 25), (7, 22), (27, 39), (2, 23), (10, 42), (2, 15), (8, 3), (39, 15), (32, 22), (7, 11), (43, 17), (27, 19), (15, 24), (19, 0), (22, 39), (37, 25), (29, 42), (36, 39), (31, 27), (27, 33), (27, 0), (39, 22), (43, 35), (8, 21), (39, 3), (9, 6), (20, 39), (40, 29), (30, 36), (42, 12), (42, 31), (7, 5), (35, 11), (25, 41), (32, 26), (19, 16), (7, 18), (5, 39), (13, 12), (5, 3), (7, 7), (34, 42), (44, 16), (11, 6), (8, 4), (3, 39), (18, 1), (43, 26), (5, 31), (42, 4), (9, 44), (40, 2), (37, 26), (34, 0), (40, 23), (42, 23), (20, 3), (40, 36), (10, 30), (40, 32), (44, 41), (38, 21), (27, 18), (13, 32), (37, 42), (13, 0), (36, 11), (22, 15), (15, 1), (10, 19), (3, 19), (35, 24), (36, 24), (18, 3), (5, 34), (13, 25), (19, 32), (11, 22), (15, 14), (9, 20), (11, 44), (26, 5), (24, 33), (15, 39), (35, 16), (15, 34), (24, 16), (7, 25), (42, 33), (32, 32), (22, 9), (34, 22), (25, 20), (27, 32), (13, 14), (3, 10), (25, 9), (22, 19), (17, 15), (38, 29), (21, 13), (15, 8), (26, 24), (13, 36), (36, 5), (35, 39), (27, 23), (37, 24), (24, 26), (41, 17), (5, 0), (13, 30), (24, 11), (25, 32), (26, 13), (7, 32), (16, 16), (31, 3), (27, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 38), (27, 26), (32, 22), (25, 9), (34, 22), (28, 37), (29, 4), (12, 15), (33, 15), (45, 38), (7, 17), (20, 7), (42, 30), (32, 1), (43, 33), (39, 16), (24, 39), (10, 24), (0, 5), (45, 9), (45, 32), (18, 13), (40, 25), (39, 20), (36, 17), (21, 18), (10, 21), (27, 13), (24, 31), (45, 21), (15, 9), (18, 38), (0, 37), (8, 39), (12, 0), (30, 40), (8, 8), (40, 26), (33, 2), (29, 33), (27, 1), (26, 25), (12, 29), (33, 37), (43, 9), (36, 31), (38, 15), (25, 14), (15, 11), (10, 20), (7, 8), (37, 39), (10, 17), (31, 7), (27, 18), (29, 13), (11, 5), (45, 12), (29, 32), (4, 22), (18, 40), (29, 18), (11, 35), (20, 20), (6, 0), (18, 20), (42, 15), (5, 38), (44, 15), (13, 19), (11, 15), (15, 34), (30, 3), (9, 9), (21, 7), (42, 2), (30, 21), (18, 14), (13, 39), (44, 31), (34, 20), (33, 27), (6, 20), (19, 9), (42, 40), (23, 40), (14, 23), (36, 14), (39, 34), (36, 8), (38, 12), (26, 29), (17, 24), (34, 12), (5, 29), (34, 32), (41, 36), (10, 13), (37, 11), (16, 37), (31, 40), (7, 1), (20, 33), (7, 12), (21, 13), (10, 1), (43, 23), (22, 35), (45, 19), (12, 25), (22, 0), (32, 27), (45, 22), (14, 1), (27, 38), (8, 36), (40, 33), (29, 23), (6, 36), (42, 29), (38, 6), (11, 19), (3, 10), (39, 33), (7, 15), (24, 37), (3, 29), (42, 24), (40, 10), (23, 26), (35, 2), (32, 21), (15, 0), (40, 4), (28, 28), (28, 13), (30, 5), (23, 5), (9, 36), (18, 32), (26, 24), (20, 32), (12, 20), (29, 12), (24, 11), (3, 7), (14, 29), (26, 35), (29, 38), (5, 36), (42, 31), (23, 25), (20, 27), (31, 17), (18, 22), (10, 5), (1, 30), (17, 38), (23, 16), (14, 40), (20, 12), (8, 24), (4, 34), (28, 5), (17, 11), (16, 39), (35, 35), (41, 14), (5, 21), (8, 12), (34, 40), (25, 23), (4, 36), (22, 32), (36, 1), (37, 20), (45, 33), (21, 31), (5, 8), (6, 40), (25, 8), (41, 5), (14, 32), (41, 9), (18, 10), (39, 32), (0, 7), (33, 35), (41, 32), (34, 28), (15, 19), (41, 10), (19, 39), (4, 3), (37, 34), (37, 17), (36, 0), (15, 32), (2, 17), (21, 33), (4, 4), (38, 25), (13, 25), (10, 33), (45, 11), (25, 11), (16, 31), (10, 23), (30, 8), (5, 39), (16, 33), (32, 26), (8, 7), (10, 8), (1, 32), (8, 33), (41, 16), (41, 6), (1, 25), (35, 21), (13, 14), (30, 24), (7, 5), (4, 16), (14, 28), (20, 28), (3, 5), (0, 14), (9, 11), (11, 14), (5, 27), (24, 16), (43, 8), (14, 8), (16, 18), (42, 16), (33, 31), (29, 6), (6, 30), (43, 40), (13, 30), (36, 24), (44, 18), (11, 40), (33, 12), (19, 33), (6, 15), (24, 1), (6, 8), (11, 27), (32, 33), (42, 28), (38, 22), (11, 39), (21, 23), (17, 39), (10, 15), (7, 40), (2, 21), (28, 32), (45, 23), (44, 8), (36, 28), (16, 14), (38, 10), (40, 15), (13, 31), (19, 28), (35, 6), (27, 4), (16, 4), (26, 7), (25, 40), (1, 19), (41, 25), (23, 8), (29, 29), (9, 38), (21, 8), (9, 27), (39, 8), (4, 11), (18, 9), (13, 6), (13, 36), (30, 11), (14, 20), (42, 33), (38, 33), (5, 1), (27, 23), (10, 26), (24, 32), (17, 25), (8, 32), (15, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 22), (7, 7), (7, 28), (40, 39), (45, 31), (25, 40), (25, 36), (15, 26), (38, 16), (42, 30), (6, 25), (44, 23), (26, 4), (0, 42), (28, 10), (4, 34), (37, 11), (19, 17), (34, 8), (1, 4), (36, 10), (1, 28), (25, 15), (25, 0), (19, 13), (41, 39), (16, 23), (5, 17), (37, 15), (1, 1), (27, 37), (2, 29), (26, 18), (24, 32), (42, 4), (8, 32), (39, 7), (18, 34), (39, 9), (24, 14), (43, 18), (14, 28), (46, 20), (25, 20), (7, 11), (23, 7), (45, 41), (32, 37), (17, 35), (27, 2), (8, 11), (41, 41), (37, 19), (35, 17), (44, 16), (29, 37), (7, 39), (17, 8), (11, 39), (38, 14), (11, 18), (32, 39), (37, 3), (46, 30), (41, 16), (32, 8), (30, 2), (37, 35), (0, 39), (46, 16), (29, 5), (8, 14), (14, 4), (13, 0), (12, 23), (25, 3), (34, 30), (17, 37), (14, 6), (13, 19), (7, 0), (29, 26), (36, 16), (7, 26), (30, 28), (36, 29), (5, 0), (1, 41), (29, 21), (18, 17), (12, 8), (24, 15), (43, 27), (22, 5), (14, 41), (3, 35), (35, 12), (37, 36), (35, 6), (13, 8), (19, 30), (8, 0), (15, 18), (24, 21), (31, 38), (46, 18), (26, 13), (45, 8), (36, 27), (43, 14), (27, 6), (15, 39), (23, 24), (44, 4), (8, 22), (45, 42), (24, 30), (5, 30), (39, 14), (39, 25), (25, 34), (11, 0), (46, 35), (19, 18), (38, 6), (21, 25), (43, 3), (38, 13), (13, 22), (43, 21), (6, 33), (28, 17), (7, 20), (33, 38), (40, 38), (12, 2), (26, 39), (1, 32), (38, 5), (40, 40), (40, 17), (39, 0), (13, 24), (25, 31), (41, 18), (15, 31), (21, 26), (44, 2), (6, 12), (32, 21), (22, 32), (46, 5), (31, 6), (4, 31), (28, 37), (2, 25), (43, 40), (0, 41), (21, 36), (17, 4), (16, 4), (39, 32), (33, 40), (46, 37), (24, 42), (17, 17), (8, 20), (34, 37), (10, 14), (23, 38), (30, 13), (22, 41), (42, 40), (24, 6), (26, 36), (1, 2), (39, 2), (31, 10), (22, 13), (42, 8), (43, 23), (9, 9), (42, 11), (18, 9), (25, 30), (6, 41), (14, 3), (5, 18), (34, 13), (30, 41), (2, 30), (9, 25), (33, 17), (28, 28), (41, 8), (41, 20), (43, 17), (34, 36), (33, 14), (12, 36), (4, 22), (7, 6), (11, 35), (33, 10), (29, 14), (13, 9), (2, 9), (27, 29), (9, 38), (24, 35), (12, 11), (29, 10), (6, 7), (39, 13), (10, 38), (44, 17), (19, 14), (40, 24), (36, 9), (22, 39), (25, 39), (40, 21), (37, 8), (37, 24), (33, 3), (36, 17), (42, 25), (26, 12), (22, 25), (8, 36), (39, 30), (40, 41), (15, 7), (20, 25), (23, 26), (41, 7), (19, 38), (25, 2), (5, 36), (1, 37), (22, 34), (38, 8), (0, 31), (30, 37), (3, 20), (39, 24), (14, 27), (10, 20), (29, 40), (44, 41), (16, 25), (27, 41), (40, 20), (34, 22), (45, 30), (29, 12), (37, 39), (45, 21), (35, 40), (34, 25), (31, 14), (38, 20), (33, 24), (34, 5), (33, 0), (37, 18), (27, 32), (12, 1), (11, 5), (35, 19), (16, 39), (44, 22), (25, 33), (10, 8), (20, 11), (26, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 20), (39, 35), (1, 1), (25, 27), (8, 39), (19, 30), (36, 28), (43, 31), (20, 32), (17, 16), (24, 20), (45, 47), (25, 35), (7, 18), (27, 25), (33, 44), (24, 17), (29, 39), (17, 26), (18, 16), (39, 34), (7, 43), (14, 33), (43, 28), (38, 5), (45, 45), (45, 33), (34, 17), (46, 4), (36, 4), (28, 33), (31, 9), (20, 46), (10, 10), (7, 41), (27, 18), (36, 37), (2, 23), (43, 37), (46, 5), (10, 14), (37, 8), (32, 30), (16, 40), (11, 40), (38, 21), (9, 6), (41, 31), (18, 20), (1, 15), (12, 10), (39, 6), (6, 21), (24, 35), (14, 31), (35, 22), (11, 23), (0, 33), (15, 7), (22, 24), (2, 3), (37, 9), (42, 2), (1, 40), (11, 19), (32, 37), (20, 15), (16, 37), (40, 14), (23, 28), (7, 29), (39, 14), (30, 42), (18, 13), (30, 44), (43, 7), (35, 12), (3, 7), (12, 36), (9, 15), (40, 7), (0, 26), (26, 6), (34, 30), (18, 5), (40, 5), (40, 35), (4, 10), (22, 20), (3, 13), (37, 13), (16, 46), (3, 37), (2, 43), (7, 34), (45, 44), (43, 11), (15, 17), (34, 35), (1, 33), (32, 46), (0, 27), (14, 15), (44, 3), (20, 12), (34, 23), (3, 25), (33, 1), (23, 45), (44, 46), (14, 14), (29, 23), (42, 30), (19, 31), (3, 39), (13, 19), (20, 19), (3, 5), (16, 29), (18, 39), (29, 2), (35, 32), (38, 28), (27, 14), (38, 41), (20, 27), (13, 18), (5, 20), (0, 3), (39, 12), (40, 31), (33, 45), (2, 21), (34, 13), (28, 1), (13, 37), (42, 32), (7, 36), (21, 38), (11, 39), (24, 41), (22, 22), (12, 43), (14, 17), (16, 33), (0, 41), (0, 1), (23, 31), (19, 8), (30, 5), (22, 43), (16, 22), (42, 26), (22, 30), (3, 45), (42, 16), (16, 41), (42, 14), (11, 46), (28, 45), (22, 2), (40, 3), (30, 46), (43, 22), (33, 33), (15, 4), (16, 5), (12, 47), (34, 3), (41, 2), (23, 22), (7, 28), (42, 5), (39, 45), (34, 34), (25, 11), (15, 27), (28, 14), (13, 45), (44, 23), (0, 43), (3, 38), (39, 36), (21, 39), (21, 36), (5, 16), (13, 13), (42, 38), (46, 39), (31, 38), (16, 13), (14, 9), (29, 47), (41, 17), (1, 34), (33, 6), (44, 19), (26, 5), (42, 24), (25, 41), (10, 39), (36, 16), (12, 23), (6, 31), (6, 29), (38, 11), (18, 32), (37, 33), (16, 25), (12, 24), (33, 22), (13, 46), (46, 28), (4, 42), (21, 17), (26, 28), (11, 32), (15, 23), (44, 28), (2, 20), (25, 23), (26, 15), (34, 6), (8, 26), (44, 20), (8, 38), (26, 45), (6, 2), (19, 29), (27, 39), (40, 17), (7, 7), (44, 33), (4, 7), (18, 28), (25, 0), (25, 10), (14, 22), (43, 30), (28, 6), (28, 12), (45, 39), (39, 46), (15, 20), (1, 9), (4, 0), (35, 34), (31, 14), (9, 20), (36, 46), (15, 14), (41, 30), (37, 27), (7, 39), (32, 6), (36, 25), (38, 8), (14, 25), (3, 15), (20, 23), (11, 37), (40, 34), (15, 31), (4, 27), (21, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 2), (2, 39), (21, 9), (44, 6), (22, 24), (24, 6), (24, 24), (22, 35), (18, 15), (8, 4), (27, 36), (14, 25), (1, 29), (31, 29), (10, 23), (25, 24), (21, 16), (21, 2), (44, 32), (7, 5), (35, 12), (1, 34), (44, 30), (9, 12), (30, 4), (14, 14), (22, 9), (14, 34), (24, 3), (29, 12), (33, 8), (21, 20), (35, 19), (27, 3), (38, 16), (15, 9), (5, 10), (32, 36), (44, 11), (11, 1), (1, 17), (38, 19), (17, 24), (11, 8), (22, 27), (15, 1), (2, 37), (6, 23), (26, 27), (6, 21), (20, 29), (14, 23), (14, 18), (5, 20), (43, 27), (21, 6), (10, 18), (17, 40), (17, 30), (21, 11), (35, 23), (14, 5), (40, 3), (37, 39), (4, 4), (22, 32), (10, 31), (33, 4), (26, 5), (7, 11), (1, 30), (40, 25), (25, 13), (37, 21), (38, 33), (24, 36), (23, 37), (17, 25), (9, 1), (35, 2), (32, 32), (25, 7), (0, 40), (31, 12), (34, 27), (32, 9), (18, 37), (12, 2), (20, 11), (34, 24), (24, 39), (27, 40), (27, 25), (6, 40), (26, 0), (10, 37), (39, 2), (36, 21), (9, 3), (44, 14), (21, 37), (22, 21), (6, 20), (25, 6), (13, 32), (4, 10), (26, 29), (11, 28), (10, 33), (33, 12), (21, 17), (38, 32), (28, 34), (8, 25), (37, 22), (15, 17), (17, 35), (18, 25), (17, 12), (10, 32), (5, 22), (33, 30), (32, 25), (40, 34), (8, 2), (11, 40), (33, 16), (4, 27), (38, 21), (16, 10), (28, 21), (33, 33), (37, 16), (39, 0), (1, 1), (8, 40), (25, 2), (19, 12), (28, 19), (37, 31), (34, 34), (23, 10), (7, 32), (41, 11), (17, 0), (18, 39), (38, 22), (30, 37), (19, 40), (8, 9), (39, 21), (38, 28), (41, 27), (3, 18), (5, 11), (32, 30), (7, 20), (6, 29), (16, 22), (41, 2), (14, 10), (29, 39), (41, 9), (29, 3), (40, 24), (1, 25), (31, 10), (8, 31), (37, 26), (44, 25), (12, 6), (16, 34), (4, 28), (35, 10), (37, 18), (24, 5), (24, 7), (8, 23), (22, 37), (20, 24), (34, 32), (36, 20), (13, 16), (13, 39), (25, 14), (6, 2), (0, 26), (13, 4), (21, 35), (20, 27), (20, 35), (24, 14), (41, 35), (39, 29), (26, 30), (8, 8), (36, 3), (34, 21), (7, 2), (43, 18), (12, 3), (19, 0), (32, 12), (15, 37), (34, 11), (23, 33), (30, 30), (33, 19), (25, 12), (9, 30), (29, 7), (9, 38), (9, 14), (0, 18), (6, 1), (42, 15), (40, 9), (40, 15), (26, 16), (20, 4), (23, 21), (16, 40), (15, 3), (0, 21), (4, 24), (3, 22), (37, 35), (6, 8), (18, 36), (28, 31), (27, 8), (43, 24), (13, 28), (7, 22), (41, 4), (34, 15), (21, 31), (12, 39), (12, 20), (0, 17), (39, 11), (7, 24), (0, 2), (17, 28), (35, 25), (38, 26), (27, 27), (31, 21), (1, 28), (17, 39), (30, 28), (21, 21), (12, 1), (35, 20), (10, 5), (26, 31), (44, 7), (31, 27), (16, 9), (35, 36), (18, 0), (41, 23), (4, 17), (39, 34), (4, 15), (38, 37), (20, 17), (16, 13), (28, 36), (39, 13), (37, 40), (42, 5), (0, 10), (43, 5), (10, 10), (41, 10), (7, 8), (33, 3), (38, 2), (10, 36), (40, 32), (3, 27), (7, 31), (2, 15), (7, 28), (8, 39), (6, 13), (14, 0), (8, 0), (27, 21), (41, 7), (34, 25), (15, 40), (34, 13), (40, 28), (19, 22), (7, 12), (35, 0), (8, 5), (8, 7), (38, 14), (14, 8), (24, 13), (5, 5), (41, 28), (1, 19), (6, 12), (14, 27), (42, 35), (7, 1), (14, 9), (31, 19), (11, 17), (7, 34), (11, 7), (17, 19), (21, 8), (14, 31), (9, 36), (26, 32), (2, 26), (20, 13), (12, 31), (7, 10), (33, 40), (22, 39), (16, 27), (32, 8), (17, 37), (44, 37), (22, 5), (20, 6), (10, 38), (16, 26), (4, 7), (37, 1), (4, 40), (22, 14), (26, 24), (24, 22), (26, 15), (15, 34), (28, 12), (29, 15), (23, 32), (33, 32), (9, 15), (34, 18), (30, 1), (1, 40), (30, 31), (14, 33), (39, 39), (20, 25), (10, 13), (21, 13), (25, 16), (22, 18), (43, 35), (5, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 32), (14, 39), (26, 25), (12, 35), (10, 8), (34, 17), (6, 3), (18, 12), (20, 33), (16, 18), (5, 16), (23, 15), (5, 32), (32, 11), (1, 21), (25, 35), (23, 16), (31, 38), (16, 31), (27, 24), (26, 30), (31, 26), (7, 20), (3, 35), (38, 13), (7, 19), (0, 30), (15, 10), (15, 13), (31, 9), (31, 23), (32, 1), (0, 29), (36, 17), (16, 3), (29, 10), (23, 14), (17, 7), (14, 31), (38, 16), (15, 2), (14, 24), (16, 14), (36, 5), (32, 34), (18, 31), (38, 15), (8, 35), (35, 35), (28, 26), (2, 2), (17, 34), (32, 5), (1, 7), (31, 37), (2, 37), (27, 35), (27, 28), (13, 32), (8, 21), (17, 38), (9, 12), (12, 19), (8, 37), (31, 22), (39, 8), (8, 16), (28, 27), (35, 8), (24, 21), (19, 38), (16, 13), (25, 26), (2, 26), (6, 17), (26, 6), (0, 8), (17, 0), (1, 41), (18, 6), (32, 0), (35, 34), (28, 22), (12, 4), (10, 1), (31, 18), (18, 11), (2, 13), (32, 21), (0, 40), (32, 13), (33, 0), (12, 8), (18, 42), (35, 1), (37, 4), (14, 15), (39, 22), (21, 32), (3, 26), (36, 34), (27, 1), (37, 40), (35, 25), (6, 37), (14, 25), (29, 6), (11, 22), (37, 9), (33, 10), (4, 6), (30, 31), (8, 3), (20, 23), (2, 35), (4, 39), (28, 30), (34, 9), (3, 5), (17, 12), (11, 26), (9, 29), (23, 7), (20, 16), (37, 5), (39, 34), (26, 35), (32, 17), (4, 11), (10, 19), (17, 20), (8, 22), (25, 6), (6, 1), (0, 21), (40, 37), (37, 25), (30, 9), (15, 19), (3, 30), (21, 8), (24, 38), (36, 10), (29, 42), (0, 23), (10, 29), (17, 30), (22, 38), (5, 35), (3, 34), (6, 20), (13, 17), (27, 8), (7, 22), (13, 39), (27, 22), (14, 10), (23, 33), (26, 39), (7, 35), (35, 19), (27, 4), (9, 42), (10, 2), (35, 6), (10, 21), (31, 39), (17, 26), (16, 24), (30, 25), (0, 24), (30, 33), (3, 21), (30, 15), (16, 4), (28, 1), (17, 21), (2, 21), (40, 2), (12, 24), (22, 41), (22, 21), (15, 29), (13, 21), (36, 16), (14, 7), (19, 41), (12, 10), (35, 39), (21, 24), (12, 2), (12, 25), (10, 4), (33, 27), (7, 18), (3, 27), (35, 27), (20, 32), (16, 35), (1, 39), (0, 39), (21, 12), (25, 15), (36, 36), (17, 32), (36, 2), (17, 10), (15, 14), (39, 15), (1, 31), (13, 24), (1, 17), (27, 37), (27, 17), (28, 23), (30, 30), (29, 16), (11, 10), (28, 38), (16, 30), (20, 20), (5, 25), (31, 30), (38, 34), (19, 18), (0, 20), (16, 34), (10, 9), (16, 37), (6, 21), (39, 4), (24, 27), (11, 13), (13, 10), (10, 22), (13, 9), (10, 27), (19, 1), (24, 2), (7, 8), (8, 24), (38, 30), (12, 42), (21, 31), (8, 30), (25, 3), (19, 21), (8, 31), (16, 6), (15, 3), (25, 18), (31, 42), (5, 37), (37, 38), (3, 7), (28, 25), (0, 31), (7, 7), (18, 29), (4, 27), (20, 37), (11, 37), (6, 28), (30, 42), (20, 24), (25, 38), (24, 40), (9, 22), (39, 37), (24, 29), (33, 20), (11, 30), (9, 37), (7, 39), (6, 0), (18, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 12), (24, 23), (14, 35), (39, 25), (39, 1), (11, 35), (30, 2), (20, 10), (14, 12), (0, 9), (38, 18), (28, 7), (21, 12), (20, 32), (36, 41), (24, 34), (12, 15), (3, 6), (37, 33), (35, 6), (18, 19), (1, 9), (5, 4), (13, 10), (3, 1), (31, 32), (16, 31), (10, 4), (43, 16), (26, 10), (17, 42), (19, 34), (28, 23), (22, 27), (16, 32), (33, 0), (23, 8), (33, 23), (43, 11), (15, 9), (14, 21), (33, 26), (13, 39), (11, 2), (12, 21), (36, 13), (43, 20), (6, 6), (25, 42), (7, 20), (3, 22), (24, 39), (43, 1), (28, 6), (4, 17), (3, 33), (40, 25), (39, 22), (2, 7), (33, 42), (28, 37), (37, 39), (12, 22), (29, 5), (9, 15), (17, 33), (7, 26), (34, 33), (15, 11), (37, 6), (30, 11), (33, 20), (2, 0), (33, 25), (6, 19), (21, 28), (39, 26), (16, 34), (5, 1), (39, 12), (0, 1), (2, 5), (31, 42), (14, 3), (7, 39), (34, 16), (27, 14), (28, 25), (26, 34), (18, 21), (8, 35), (26, 32), (38, 36), (42, 10), (14, 26), (18, 13), (34, 21), (33, 41), (2, 25), (21, 3), (27, 19), (6, 1), (13, 17), (0, 20), (22, 2), (21, 18), (5, 0), (34, 20), (32, 25), (6, 40), (0, 14), (0, 5), (12, 9), (9, 33), (43, 30), (26, 21), (10, 38), (10, 33), (40, 3), (17, 11), (40, 6), (22, 29), (10, 31), (26, 15), (30, 21), (8, 13), (6, 24), (27, 22), (3, 16), (12, 1), (10, 5), (16, 33), (43, 41), (14, 11), (18, 1), (11, 8), (18, 40), (36, 35), (10, 19), (30, 0), (25, 34), (8, 39), (35, 33), (7, 15), (25, 37), (1, 25), (2, 3), (21, 16), (41, 28), (21, 5), (2, 38), (31, 31), (20, 36), (33, 15), (33, 35), (34, 2), (21, 27), (37, 37), (33, 3), (1, 18), (14, 38), (25, 1), (25, 6), (12, 3), (20, 17), (4, 0), (33, 17), (41, 34), (22, 38), (26, 23), (21, 36), (1, 26), (43, 25), (13, 21), (7, 22), (30, 34), (7, 8), (4, 16), (10, 7), (40, 0), (7, 40), (14, 32), (28, 3), (20, 1), (42, 14), (32, 19), (14, 4), (23, 35), (43, 22), (9, 7), (11, 30), (29, 28), (22, 9), (33, 33), (15, 40), (12, 37), (38, 42), (40, 27), (5, 23), (28, 8), (4, 34), (22, 16), (32, 34), (28, 18), (2, 24), (11, 1), (5, 11), (6, 32), (40, 31), (8, 21), (31, 40), (33, 10), (39, 8), (7, 12), (9, 18), (42, 9), (15, 17), (8, 37), (42, 6), (15, 10), (25, 19), (27, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 45), (33, 38), (16, 17), (35, 43), (3, 1), (6, 46), (2, 43), (31, 33), (8, 10), (5, 29), (25, 42), (36, 13), (1, 42), (23, 36), (38, 29), (37, 13), (9, 24), (24, 42), (7, 16), (43, 38), (5, 7), (25, 15), (18, 42), (24, 0), (10, 6), (39, 1), (25, 7), (37, 36), (17, 36), (4, 31), (23, 15), (7, 13), (25, 4), (2, 5), (3, 21), (9, 14), (10, 15), (10, 13), (29, 44), (10, 35), (30, 46), (18, 10), (37, 22), (24, 46), (30, 36), (26, 34), (6, 31), (19, 47), (29, 32), (12, 19), (24, 13), (27, 40), (41, 19), (6, 26), (25, 31), (3, 29), (32, 22), (42, 28), (5, 38), (28, 38), (36, 5), (19, 0), (18, 24), (33, 4), (7, 3), (14, 38), (7, 31), (42, 11), (32, 28), (36, 30), (9, 17), (2, 41), (34, 20), (27, 42), (0, 22), (0, 15), (31, 5), (6, 7), (29, 21), (0, 4), (30, 33), (30, 5), (20, 23), (33, 21), (3, 4), (42, 25), (40, 32), (0, 2), (30, 41), (5, 47), (11, 1), (12, 7), (24, 12), (7, 4), (22, 38), (11, 13), (43, 3), (2, 35), (9, 45), (39, 31), (31, 42), (15, 14), (40, 28), (32, 46), (8, 3), (26, 26), (14, 27), (7, 42), (13, 38), (39, 33), (9, 11), (16, 20), (40, 36), (41, 45), (26, 8), (40, 26), (2, 0), (42, 42), (21, 17), (21, 1), (30, 7), (20, 47), (2, 26), (40, 2), (43, 16), (11, 24), (28, 25), (25, 0), (23, 24), (17, 0), (13, 28), (18, 4), (9, 41), (26, 21), (41, 7), (4, 32), (2, 10), (28, 11), (34, 2), (37, 47), (38, 9), (12, 20), (33, 26), (1, 25), (36, 4), (27, 35), (23, 34), (22, 16), (17, 28), (14, 35), (31, 23), (32, 40), (1, 6), (26, 43), (6, 29), (29, 43), (13, 23), (2, 44), (35, 1), (39, 25), (30, 11), (31, 21), (39, 14), (9, 12), (28, 26), (7, 0), (42, 7), (30, 4), (43, 8), (37, 46), (20, 10), (18, 30), (14, 4), (9, 39), (23, 30), (40, 1), (4, 19), (29, 4), (41, 33), (15, 39), (18, 28), (1, 24), (32, 32), (40, 8), (6, 30), (32, 43), (24, 19), (3, 6), (4, 3), (26, 25), (27, 36), (6, 44), (42, 27), (17, 22), (9, 13), (9, 23), (20, 17), (29, 9), (20, 25), (15, 27), (31, 45), (39, 43), (1, 16), (41, 47), (1, 37), (16, 14), (43, 18), (30, 3), (13, 20), (18, 13), (35, 34), (29, 1), (11, 16), (3, 26), (28, 44), (0, 27), (9, 5), (3, 23), (43, 34), (41, 1), (37, 6), (19, 22), (5, 37), (33, 37), (21, 15), (33, 23), (26, 6), (6, 3), (35, 2), (42, 23), (17, 18), (12, 25), (16, 27), (17, 3), (18, 20), (43, 43), (6, 21), (0, 45), (7, 15), (23, 12), (13, 44), (34, 1), (0, 28), (8, 45), (42, 41), (36, 34), (27, 46), (33, 45), (21, 35), (18, 5), (17, 41), (32, 47), (12, 42), (25, 30), (30, 42), (0, 31), (17, 5), (27, 38), (25, 41), (9, 19), (1, 7), (20, 3), (20, 36), (41, 18), (19, 31), (17, 13), (33, 32), (32, 12), (32, 39), (8, 28), (21, 39), (24, 20), (4, 45), (30, 8), (3, 35), (43, 27), (8, 34), (14, 17), (36, 46), (13, 15), (27, 39), (28, 9), (40, 41), (18, 26), (40, 16), (12, 8), (40, 7), (24, 28), (19, 17), (38, 28), (26, 17), (6, 32), (25, 37), (17, 43), (26, 1), (22, 5), (36, 20), (19, 41), (13, 46), (16, 22), (29, 24), (23, 43), (24, 36), (0, 12), (5, 9), (35, 3), (31, 32), (30, 14), (21, 38), (6, 4), (22, 0), (14, 34), (15, 12), (43, 37), (14, 42), (39, 2), (26, 3), (19, 42), (12, 1), (42, 6), (0, 21), (9, 22), (11, 20), (25, 12), (7, 40), (14, 26), (26, 47), (32, 37), (33, 9), (12, 3), (30, 19), (37, 32), (38, 38), (21, 37), (42, 12), (31, 37), (24, 30), (11, 40), (43, 11), (43, 44), (22, 8), (34, 5), (16, 36), (37, 1), (26, 29), (13, 21), (3, 45), (37, 23), (4, 13), (41, 24), (41, 44), (0, 39), (17, 34), (42, 40), (20, 12), (34, 33), (20, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 33), (18, 23), (24, 32), (3, 14), (17, 32), (0, 18), (18, 35), (22, 12), (39, 0), (32, 10), (17, 0), (14, 26), (6, 31), (11, 9), (14, 23), (38, 33), (13, 14), (7, 32), (2, 37), (12, 17), (0, 11), (44, 39), (4, 10), (11, 19), (24, 3), (42, 14), (13, 11), (30, 24), (3, 31), (26, 0), (28, 4), (26, 38), (16, 23), (21, 21), (23, 7), (21, 25), (4, 35), (28, 29), (14, 14), (17, 17), (23, 28), (38, 39), (0, 31), (5, 33), (28, 30), (7, 27), (29, 13), (43, 32), (9, 23), (2, 26), (3, 30), (0, 22), (3, 8), (26, 3), (25, 5), (30, 0), (44, 3), (18, 33), (18, 16), (19, 15), (31, 5), (14, 9), (24, 7), (22, 30), (16, 1), (8, 36), (29, 5), (11, 14), (34, 35), (14, 15), (15, 9), (9, 13), (37, 19), (28, 38), (4, 29), (35, 20), (37, 21), (29, 24), (8, 6), (35, 28), (26, 14), (39, 13), (5, 3), (33, 24), (17, 7), (19, 9), (10, 28), (26, 32), (8, 9), (5, 23), (45, 29), (7, 11), (13, 37), (14, 20), (45, 16), (14, 21), (3, 24), (33, 25), (4, 37), (13, 35), (11, 11), (24, 25), (30, 3), (24, 34), (32, 21), (40, 9), (27, 29), (42, 12), (9, 19), (0, 36), (12, 13), (17, 1), (13, 28), (4, 28), (0, 4), (33, 31), (19, 0), (45, 7), (39, 39), (19, 11), (30, 1), (0, 26), (7, 6), (36, 22), (37, 34), (33, 20), (31, 24), (31, 15), (15, 0), (26, 21), (1, 17), (35, 6), (36, 10), (3, 23), (12, 8), (40, 12), (22, 3), (17, 13), (22, 6), (19, 6), (33, 30), (21, 33), (28, 26), (22, 9), (7, 12), (40, 33), (31, 11), (2, 20), (0, 8), (24, 10), (43, 3), (42, 39), (44, 11), (23, 5), (33, 21), (2, 29), (6, 26), (19, 24), (19, 25), (2, 15), (6, 11), (19, 35), (4, 33), (20, 9), (38, 18), (15, 14), (23, 8), (8, 30), (28, 18), (3, 28), (22, 20), (43, 13), (12, 33), (8, 39), (36, 6), (16, 36), (4, 7), (29, 16), (26, 19), (21, 9), (13, 3), (31, 34), (34, 37), (35, 22), (34, 14), (31, 38), (42, 35), (29, 30), (34, 13), (23, 6), (17, 38), (3, 18), (11, 30), (25, 24), (30, 14), (27, 34), (17, 35), (1, 32), (44, 38), (6, 33), (15, 2), (32, 6), (20, 28), (25, 37), (20, 37), (5, 38), (18, 37), (25, 27), (16, 19), (30, 9), (4, 31), (37, 38), (17, 29), (2, 30), (18, 18), (39, 34), (3, 5), (0, 15), (42, 1), (17, 19), (25, 15), (24, 28), (25, 30), (41, 35), (42, 3), (19, 36), (12, 4), (19, 5), (45, 9), (5, 9), (34, 25), (17, 5), (29, 29), (12, 14), (19, 3), (14, 34), (26, 36), (37, 12), (22, 37), (1, 6), (9, 30), (35, 7), (30, 39), (31, 27), (21, 32), (44, 4), (39, 18), (33, 37), (25, 20), (0, 17), (5, 0), (19, 39), (30, 30), (20, 24), (20, 10), (12, 1), (1, 7), (22, 35), (25, 36), (41, 31), (35, 18), (0, 35), (44, 35), (34, 27), (23, 26), (38, 10), (9, 34), (19, 38), (17, 34), (29, 33), (10, 12), (30, 23), (3, 16), (33, 3), (33, 13), (44, 12), (13, 27), (16, 17), (35, 9), (15, 20), (42, 17), (40, 21), (10, 32), (30, 2), (15, 31), (27, 30), (38, 5), (23, 0), (10, 18), (10, 31), (4, 11), (41, 14), (40, 15), (21, 20), (17, 11), (30, 36), (9, 3), (0, 1), (24, 11), (8, 37), (10, 27), (44, 6), (8, 5), (33, 33), (2, 16), (22, 11), (35, 23), (16, 31), (14, 30), (27, 20), (28, 6), (35, 38), (38, 28), (33, 35), (26, 20), (39, 8), (30, 27), (12, 37), (30, 28), (2, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 39), (1, 4), (42, 38), (17, 12), (27, 17), (35, 4), (6, 41), (33, 9), (23, 24), (19, 23), (34, 30), (27, 1), (41, 21), (31, 4), (37, 36), (39, 7), (31, 3), (5, 14), (1, 28), (31, 35), (5, 43), (22, 35), (41, 34), (26, 34), (7, 7), (27, 43), (14, 34), (13, 30), (26, 26), (22, 33), (37, 29), (14, 33), (11, 25), (31, 7), (29, 31), (19, 22), (5, 33), (29, 21), (14, 0), (8, 6), (5, 5), (29, 7), (17, 11), (14, 14), (33, 28), (7, 41), (17, 35), (25, 11), (2, 5), (7, 18), (27, 10), (32, 15), (8, 5), (25, 34), (9, 4), (31, 42), (1, 2), (10, 11), (41, 25), (5, 26), (39, 4), (0, 31), (4, 3), (3, 8), (26, 39), (11, 22), (35, 5), (29, 24), (13, 0), (2, 22), (34, 14), (14, 2), (6, 16), (13, 14), (26, 25), (16, 22), (7, 16), (31, 36), (36, 27), (9, 29), (6, 0), (15, 15), (11, 2), (21, 3), (38, 34), (21, 36), (0, 42), (36, 7), (10, 28), (39, 39), (30, 17), (28, 41), (42, 36), (7, 29), (10, 31), (4, 6), (27, 19), (36, 34), (36, 3), (17, 4), (13, 16), (35, 31), (2, 42), (15, 21), (34, 10), (7, 43), (29, 18), (17, 20), (34, 5), (9, 20), (8, 7), (24, 16), (24, 34), (20, 18), (18, 21), (24, 33), (18, 16), (34, 2), (36, 11), (22, 37), (33, 1), (12, 7), (21, 19), (26, 37), (24, 1), (19, 41), (16, 23), (27, 29), (30, 10), (41, 30), (24, 8), (4, 27), (14, 6), (9, 42), (39, 29), (24, 0), (37, 25), (32, 12), (24, 37), (9, 39), (26, 6), (14, 41), (36, 29), (10, 22), (34, 39), (1, 20), (4, 12), (42, 5), (4, 22), (20, 1), (21, 42), (11, 13), (10, 8), (3, 3), (42, 1), (17, 41), (5, 19), (5, 37), (40, 28), (33, 4), (30, 15), (24, 29), (7, 35), (31, 31), (13, 36), (10, 14), (35, 20), (21, 2), (21, 18), (41, 12), (30, 38), (4, 35), (12, 27), (3, 36), (9, 11), (11, 34), (3, 42), (11, 37), (41, 8), (23, 27), (35, 32), (20, 32), (22, 15), (18, 3), (10, 41), (19, 4), (5, 27), (27, 31), (24, 10), (30, 35), (14, 30), (16, 5), (9, 32), (4, 4), (13, 28), (34, 22), (33, 36), (11, 41), (7, 20), (3, 12), (24, 28), (41, 35), (37, 30), (42, 27), (5, 40), (4, 19), (22, 7), (42, 33), (2, 40), (25, 25), (29, 16), (37, 37), (21, 13), (30, 30), (7, 2), (15, 19), (28, 25), (17, 31), (0, 2), (9, 16), (34, 9), (3, 15), (27, 27), (21, 41), (40, 15), (21, 22), (19, 36), (38, 37), (22, 19), (32, 29), (31, 21), (5, 39), (27, 3), (8, 2), (28, 36), (10, 6), (2, 30), (9, 0), (19, 39), (13, 1), (16, 36), (29, 37), (17, 26), (1, 27), (12, 2), (18, 12), (25, 36), (34, 35), (4, 8), (0, 25), (37, 3), (35, 24), (24, 7), (5, 28), (35, 26), (36, 28), (2, 18), (16, 4), (17, 5), (12, 40), (32, 32), (6, 25), (33, 2), (28, 23), (27, 8), (7, 19), (25, 29), (27, 12), (3, 39), (22, 13), (31, 19), (41, 41), (22, 10), (17, 16), (38, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 35), (39, 23), (38, 31), (25, 31), (0, 6), (6, 16), (8, 21), (36, 12), (5, 44), (42, 21), (0, 9), (38, 18), (3, 44), (28, 17), (43, 10), (18, 26), (10, 42), (32, 4), (28, 11), (1, 45), (37, 29), (43, 31), (22, 23), (17, 28), (14, 43), (0, 41), (15, 28), (31, 34), (14, 9), (9, 36), (1, 3), (24, 33), (6, 28), (22, 39), (36, 32), (26, 34), (22, 20), (28, 43), (19, 27), (30, 1), (19, 10), (16, 27), (14, 11), (34, 14), (33, 38), (33, 5), (24, 39), (21, 35), (13, 2), (25, 39), (43, 5), (1, 35), (9, 32), (0, 30), (38, 41), (8, 16), (31, 4), (24, 31), (18, 16), (28, 14), (34, 30), (13, 7), (37, 23), (25, 2), (32, 36), (20, 27), (19, 4), (41, 17), (42, 16), (22, 25), (0, 29), (9, 28), (22, 28), (25, 29), (24, 37), (26, 24), (0, 39), (9, 27), (31, 13), (6, 12), (10, 20), (30, 21), (36, 19), (21, 7), (1, 15), (40, 9), (11, 12), (17, 17), (41, 7), (24, 0), (23, 25), (12, 2), (17, 0), (16, 21), (1, 42), (39, 36), (23, 24), (1, 32), (35, 39), (18, 43), (44, 42), (28, 4), (5, 17), (29, 1), (22, 34), (38, 13), (13, 17), (2, 4), (5, 1), (17, 39), (34, 2), (2, 37), (0, 31), (32, 21), (42, 25), (11, 43), (3, 33), (28, 28), (19, 33), (9, 37), (42, 38), (38, 3), (31, 16), (19, 2), (12, 43), (3, 27), (37, 37), (29, 21), (26, 19), (41, 10), (24, 29), (14, 16), (11, 40), (32, 7), (27, 15), (39, 37), (20, 34), (20, 21), (29, 43), (16, 7), (34, 29), (9, 0), (12, 16), (18, 36), (12, 30), (7, 32), (44, 35), (40, 30), (41, 2), (36, 30), (14, 37), (33, 25), (15, 32), (26, 32), (11, 21), (10, 40), (18, 10), (19, 15), (16, 44), (33, 36), (25, 20), (25, 4), (29, 31), (13, 26), (14, 1), (33, 24), (12, 44), (31, 35), (37, 25), (32, 24), (19, 20), (33, 40), (34, 37), (15, 42), (4, 6), (14, 25), (20, 18), (34, 10), (28, 30), (37, 9), (38, 9), (1, 16), (22, 11), (11, 33), (20, 30), (31, 2), (3, 14), (7, 8), (40, 10), (5, 19), (37, 13), (24, 28), (28, 13), (27, 20), (44, 27), (31, 1), (34, 9), (44, 31), (36, 38), (14, 18), (4, 38), (39, 1), (27, 23), (32, 15), (8, 12), (35, 37), (3, 42), (14, 20), (9, 45), (10, 10), (17, 14), (10, 27), (19, 42), (2, 44), (24, 8), (39, 17), (38, 30), (32, 42), (36, 39), (8, 29), (26, 22), (37, 32), (43, 23), (25, 10), (39, 15), (30, 45), (19, 22), (3, 9), (1, 36), (20, 22), (37, 26), (8, 11), (4, 15), (10, 7), (16, 30), (13, 13), (14, 7), (18, 0), (36, 8), (3, 19), (6, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 20), (30, 27), (22, 30), (33, 3), (6, 24), (24, 1), (2, 39), (18, 40), (29, 11), (18, 16), (9, 24), (35, 27), (25, 5), (12, 14), (34, 35), (34, 22), (28, 19), (5, 29), (2, 6), (12, 6), (27, 13), (6, 8), (19, 35), (8, 25), (25, 35), (27, 11), (29, 13), (28, 36), (42, 22), (33, 15), (39, 27), (36, 17), (37, 39), (3, 14), (10, 1), (13, 18), (32, 16), (18, 22), (3, 32), (40, 13), (40, 25), (31, 21), (20, 11), (15, 40), (20, 8), (33, 12), (41, 1), (6, 22), (29, 15), (4, 13), (31, 27), (42, 16), (25, 33), (14, 22), (3, 19), (18, 28), (30, 30), (11, 19), (9, 12), (1, 30), (26, 12), (35, 33), (32, 29), (10, 6), (16, 10), (38, 37), (14, 17), (15, 3), (25, 26), (25, 20), (29, 8), (3, 7), (26, 25), (6, 4), (5, 21), (28, 24), (34, 2), (39, 39), (9, 19), (20, 5), (11, 10), (36, 35), (2, 40), (17, 39), (39, 15), (6, 39), (1, 35), (30, 23), (32, 38), (35, 18), (20, 10), (21, 15), (20, 9), (14, 13), (11, 27), (34, 38), (41, 8), (24, 17), (23, 2), (29, 4), (31, 14), (15, 18), (31, 8), (32, 37), (21, 31), (21, 38), (7, 21), (34, 32), (43, 23), (22, 18), (32, 27), (30, 18), (40, 16), (26, 20), (24, 12), (0, 9), (30, 40), (4, 23), (1, 6), (40, 30), (25, 15), (5, 18), (17, 4), (17, 13), (33, 34), (8, 33), (3, 28), (31, 34), (38, 36), (12, 21), (33, 11), (13, 4), (17, 31), (22, 17), (10, 3), (12, 37), (18, 14), (0, 36), (10, 10), (7, 1), (22, 0), (36, 13), (21, 22), (18, 2), (9, 16), (14, 5), (22, 29), (0, 5), (38, 29), (33, 32), (3, 27), (32, 3), (6, 33), (13, 3), (9, 27), (31, 36), (22, 7), (19, 33), (9, 7), (31, 16), (32, 7), (12, 13), (11, 1), (20, 32), (32, 14), (30, 29), (35, 20), (41, 14), (36, 20), (7, 11), (32, 31), (5, 11), (38, 10), (7, 19), (11, 20), (7, 0), (11, 4), (38, 35), (12, 35), (8, 1), (25, 22), (35, 34), (4, 32), (29, 23), (12, 23), (2, 33), (37, 24), (1, 25), (42, 6), (12, 5), (4, 25), (33, 19), (33, 0), (12, 26), (41, 22), (37, 11), (32, 19), (1, 28), (33, 31), (0, 40), (7, 10), (3, 15), (15, 24), (34, 3), (19, 30), (36, 32), (32, 35), (16, 18), (13, 11), (41, 29), (0, 21), (2, 7), (14, 28), (16, 39), (29, 5), (6, 23), (33, 25), (13, 20), (24, 2), (31, 20), (35, 39), (10, 17), (12, 3), (5, 38), (25, 37), (0, 37), (1, 10), (34, 12), (31, 31), (29, 31), (30, 16), (6, 34), (35, 31), (32, 1), (27, 38), (35, 3), (27, 18), (7, 13), (35, 2), (11, 25), (31, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 28), (18, 2), (7, 15), (9, 29), (4, 2), (37, 17), (16, 23), (7, 40), (17, 6), (38, 35), (20, 44), (41, 45), (0, 29), (23, 46), (18, 25), (22, 14), (43, 8), (32, 24), (32, 18), (38, 30), (22, 42), (13, 13), (5, 45), (7, 43), (13, 10), (21, 36), (23, 4), (25, 40), (11, 40), (36, 16), (26, 44), (36, 46), (21, 43), (41, 21), (29, 37), (26, 20), (23, 31), (3, 2), (18, 34), (13, 40), (41, 43), (27, 36), (39, 21), (2, 20), (18, 43), (7, 1), (20, 20), (11, 31), (36, 5), (0, 41), (40, 1), (6, 2), (1, 23), (30, 25), (23, 3), (13, 0), (4, 31), (39, 16), (21, 17), (26, 22), (21, 0), (6, 6), (37, 40), (32, 28), (39, 8), (2, 32), (42, 40), (16, 25), (29, 43), (40, 10), (17, 25), (42, 0), (10, 9), (19, 17), (10, 26), (19, 27), (43, 12), (14, 29), (42, 7), (35, 23), (34, 15), (37, 32), (35, 45), (25, 27), (1, 0), (5, 18), (22, 24), (43, 1), (20, 18), (7, 6), (5, 21), (9, 45), (31, 27), (24, 36), (38, 7), (23, 28), (42, 15), (36, 27), (28, 21), (32, 0), (40, 3), (17, 31), (29, 10), (37, 13), (12, 3), (16, 33), (18, 30), (39, 13), (40, 5), (38, 33), (9, 30), (22, 44), (38, 3), (33, 26), (24, 10), (39, 23), (18, 18), (11, 37), (9, 27), (5, 6), (23, 24), (41, 5), (36, 25), (36, 35), (27, 8), (42, 23), (14, 16), (5, 23), (0, 32), (6, 26), (37, 8), (4, 7), (5, 31), (3, 23), (34, 2), (18, 10), (29, 42), (42, 22), (15, 24), (24, 40), (6, 28), (9, 44), (43, 20), (4, 1), (11, 19), (15, 37), (1, 42), (5, 29), (30, 14), (15, 30), (36, 6), (13, 18), (30, 24), (7, 26), (31, 5), (38, 44), (37, 23), (6, 40), (2, 5), (41, 7), (12, 37), (40, 14), (14, 2), (10, 42), (22, 22), (25, 11), (15, 19), (41, 22), (40, 15), (0, 31), (9, 8), (6, 41), (22, 5), (10, 28), (10, 4), (16, 17), (17, 14), (24, 42), (28, 26), (12, 19), (22, 15), (27, 0), (22, 31), (9, 39), (8, 44), (43, 35), (23, 1), (24, 34), (22, 33), (0, 12), (21, 31), (14, 15), (10, 0), (7, 20), (15, 15), (39, 34), (7, 3), (43, 45), (39, 37), (16, 37), (29, 30), (42, 8), (27, 40), (21, 32), (27, 14), (8, 0), (0, 20), (23, 30), (34, 35), (0, 16), (40, 2), (28, 17), (27, 44), (24, 4), (9, 24), (34, 42), (12, 33), (40, 44), (11, 20), (18, 40), (30, 10), (6, 21), (1, 41), (33, 11), (14, 20), (40, 37), (16, 26), (14, 19), (36, 34), (34, 37), (16, 0), (42, 43), (31, 33), (10, 40), (29, 22), (19, 26), (43, 0), (38, 31), (27, 15), (36, 10), (27, 37), (23, 5), (24, 29), (31, 6), (16, 36), (19, 7), (37, 22), (3, 15), (4, 18), (43, 22), (14, 24), (8, 17), (19, 1), (20, 22), (2, 1), (18, 33), (5, 11), (39, 18), (13, 25), (11, 22), (41, 29), (33, 35), (25, 3), (14, 26), (43, 37), (23, 43), (28, 9), (5, 17), (30, 29), (6, 20), (0, 27), (28, 36), (8, 31), (26, 24), (30, 33), (33, 10), (8, 29), (26, 32), (29, 27), (11, 32), (21, 22), (7, 18), (15, 6), (0, 7), (23, 36), (12, 18), (24, 13), (29, 34), (2, 6), (35, 32), (27, 20), (10, 25), (8, 13), (13, 39), (19, 30), (30, 34), (12, 34), (29, 4), (37, 33), (27, 35), (22, 9), (4, 44), (29, 38), (28, 2), (6, 0), (5, 27), (28, 35), (12, 5), (36, 43), (9, 36), (26, 41), (13, 1), (24, 30), (38, 14), (11, 10), (15, 18), (9, 21), (19, 22), (8, 8), (15, 5), (33, 20), (41, 25), (22, 4), (3, 21), (17, 37), (32, 40), (31, 4), (22, 11), (17, 16), (21, 28), (40, 45), (37, 12), (40, 30), (34, 31), (23, 22), (19, 35), (2, 29), (2, 22), (9, 6), (5, 9), (17, 28), (10, 10), (36, 29), (23, 0), (0, 13), (31, 41), (28, 5), (4, 40), (35, 2), (11, 6), (33, 33), (15, 25), (12, 39), (11, 36), (16, 4), (1, 20), (35, 26), (41, 18), (27, 2), (25, 37), (22, 36), (36, 45), (24, 37), (20, 27), (21, 42), (31, 21), (32, 33), (11, 5), (33, 42), (37, 4), (9, 33), (43, 24), (37, 0), (2, 4), (33, 15), (15, 16), (0, 28), (37, 36), (3, 32), (41, 32), (0, 33), (42, 12), (40, 8), (3, 5), (14, 34), (39, 28), (1, 31), (10, 22), (21, 10), (13, 44), (16, 22), (23, 10), (22, 23), (7, 10), (40, 43), (4, 22), (35, 16), (38, 43), (12, 21), (17, 1), (3, 45), (25, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 36), (39, 22), (23, 27), (38, 12), (18, 5), (16, 35), (6, 5), (30, 12), (38, 11), (34, 28), (10, 33), (3, 35), (18, 22), (20, 18), (14, 34), (7, 27), (8, 25), (38, 2), (10, 24), (12, 5), (18, 10), (17, 24), (12, 17), (14, 26), (40, 24), (34, 29), (7, 3), (39, 1), (34, 2), (6, 39), (18, 15), (31, 26), (10, 29), (5, 24), (11, 35), (40, 34), (19, 1), (11, 22), (27, 9), (30, 10), (38, 33), (9, 26), (2, 19), (25, 28), (33, 19), (26, 41), (36, 29), (38, 3), (39, 25), (27, 16), (33, 38), (13, 16), (34, 18), (0, 33), (0, 29), (36, 28), (3, 28), (10, 7), (39, 28), (6, 29), (25, 20), (11, 26), (19, 18), (38, 16), (6, 15), (6, 35), (36, 33), (8, 18), (14, 7), (15, 40), (34, 32), (22, 4), (2, 0), (24, 34), (6, 13), (26, 38), (14, 33), (33, 35), (33, 34), (38, 13), (15, 21), (29, 14), (16, 13), (25, 12), (16, 26), (6, 18), (6, 11), (12, 12), (19, 21), (14, 5), (28, 6), (28, 15), (27, 2), (32, 26), (28, 1), (32, 15), (31, 27), (40, 25), (19, 23), (14, 0), (3, 12), (4, 27), (15, 36), (35, 1), (1, 12), (27, 14), (20, 23), (15, 18), (24, 24), (25, 6), (8, 6), (2, 29), (17, 27), (24, 27), (0, 14), (25, 1), (35, 16), (18, 27), (24, 8), (37, 29), (18, 41), (19, 11), (13, 25), (12, 34), (14, 23), (31, 28), (13, 12), (35, 34), (36, 40), (18, 26), (29, 28), (5, 9), (40, 37), (13, 39), (4, 13), (7, 32), (25, 25), (28, 13), (34, 22), (15, 32), (0, 12), (26, 3), (18, 14), (19, 40), (2, 14), (10, 4), (29, 34), (17, 35), (12, 2), (7, 10), (33, 12), (32, 28), (38, 30), (33, 16), (26, 30), (4, 15), (0, 41), (5, 32), (10, 9), (27, 17), (16, 9), (36, 37), (24, 6), (18, 29), (30, 29), (0, 13), (4, 31), (19, 8), (19, 27), (29, 19), (37, 11), (14, 35), (12, 40), (21, 22), (1, 14), (28, 0), (40, 32), (7, 4), (6, 34), (29, 22), (32, 14), (7, 26), (18, 25), (9, 16), (3, 19), (36, 15), (31, 33), (40, 7), (32, 27), (27, 18), (33, 26), (28, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 25), (14, 3), (16, 40), (26, 9), (10, 21), (32, 7), (39, 14), (0, 26), (1, 46), (31, 8), (35, 5), (38, 6), (40, 21), (26, 1), (12, 15), (22, 45), (16, 23), (3, 14), (14, 35), (36, 6), (3, 42), (22, 32), (30, 33), (5, 31), (9, 40), (34, 3), (17, 6), (41, 26), (27, 36), (23, 42), (2, 42), (34, 25), (40, 40), (19, 9), (18, 39), (6, 24), (27, 32), (4, 37), (30, 36), (26, 45), (21, 14), (29, 41), (30, 7), (25, 39), (29, 6), (19, 19), (18, 32), (9, 31), (41, 28), (28, 13), (39, 30), (3, 21), (31, 0), (38, 35), (7, 30), (27, 2), (8, 45), (13, 29), (4, 28), (31, 21), (31, 31), (33, 9), (31, 18), (4, 2), (31, 39), (18, 14), (7, 23), (5, 1), (30, 9), (9, 19), (14, 46), (25, 16), (22, 24), (25, 14), (5, 0), (17, 10), (39, 38), (10, 28), (2, 16), (24, 39), (4, 45), (41, 33), (4, 22), (9, 35), (11, 16), (7, 40), (3, 27), (24, 13), (25, 22), (6, 32), (4, 5), (24, 22), (19, 40), (36, 18), (26, 21), (0, 21), (20, 4), (18, 36), (2, 45), (2, 44), (8, 22), (38, 29), (21, 33), (26, 18), (9, 24), (28, 33), (28, 10), (11, 26), (26, 44), (16, 24), (5, 12), (25, 33), (13, 24), (11, 23), (19, 32), (1, 43), (8, 16), (41, 17), (25, 10), (8, 33), (7, 12), (33, 37), (7, 35), (27, 8), (1, 16), (21, 0), (24, 45), (13, 4), (8, 21), (12, 37), (14, 11), (7, 7), (12, 1), (33, 17), (12, 3), (41, 5), (35, 37), (36, 1), (31, 36), (4, 25), (9, 29), (8, 26), (16, 1), (5, 28), (24, 27), (11, 13), (25, 17), (31, 40), (35, 35), (20, 5), (17, 45), (22, 31), (35, 9), (38, 16), (21, 6), (6, 15), (20, 38), (37, 32), (27, 18), (3, 32), (32, 25), (9, 16), (10, 13), (35, 8), (22, 18), (2, 27), (4, 0), (7, 46), (8, 18), (21, 42), (39, 22), (20, 35), (31, 25), (12, 39), (12, 32), (19, 37), (24, 46), (19, 14), (15, 29), (39, 19), (17, 29), (29, 33), (7, 13), (29, 23), (32, 18), (23, 0), (10, 3), (19, 23), (0, 19), (31, 10), (41, 37), (8, 10), (1, 13), (2, 12), (30, 17), (12, 42), (10, 7), (1, 9), (18, 6), (30, 41), (38, 25), (3, 29), (17, 2), (20, 41), (4, 38), (1, 21), (27, 45), (8, 44), (17, 4), (23, 29), (23, 20), (37, 29), (15, 28), (36, 4), (28, 40), (24, 19), (21, 35), (6, 9), (26, 40), (35, 4), (21, 7), (10, 33), (28, 21), (15, 42), (25, 27), (40, 20), (7, 5), (38, 2), (3, 37), (22, 19), (18, 13), (34, 33), (8, 35), (15, 20), (36, 44), (22, 30), (10, 34), (36, 28), (8, 34), (32, 2), (21, 15), (24, 9), (23, 46), (4, 16), (40, 1), (22, 14), (11, 38), (16, 18), (8, 38), (0, 40), (2, 41), (2, 39), (17, 22), (35, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 18), (3, 20), (17, 4), (35, 39), (29, 14), (36, 45), (12, 8), (0, 2), (22, 10), (30, 23), (17, 19), (9, 35), (37, 33), (12, 38), (37, 38), (7, 19), (14, 4), (3, 25), (14, 0), (26, 19), (4, 33), (14, 37), (31, 41), (39, 15), (11, 30), (3, 7), (11, 17), (14, 10), (21, 32), (44, 33), (36, 35), (7, 28), (19, 0), (23, 37), (1, 4), (18, 16), (1, 34), (44, 0), (18, 44), (8, 37), (26, 23), (29, 42), (18, 14), (33, 8), (2, 38), (1, 11), (36, 28), (29, 22), (37, 1), (23, 35), (4, 12), (7, 32), (12, 39), (20, 42), (28, 35), (5, 22), (2, 13), (23, 2), (25, 25), (1, 35), (6, 22), (16, 34), (32, 17), (34, 20), (42, 17), (15, 15), (11, 8), (22, 41), (32, 20), (18, 39), (9, 30), (44, 8), (21, 38), (39, 8), (2, 30), (18, 8), (44, 32), (18, 24), (2, 35), (11, 11), (8, 0), (9, 41), (43, 13), (18, 23), (25, 45), (42, 40), (17, 40), (33, 35), (1, 12), (25, 6), (22, 43), (0, 27), (4, 39), (8, 5), (21, 41), (32, 43), (16, 6), (7, 22), (2, 27), (37, 5), (42, 43), (46, 13), (22, 1), (10, 20), (14, 9), (28, 19), (16, 29), (0, 32), (16, 2), (8, 4), (35, 30), (22, 44), (12, 33), (2, 12), (30, 1), (5, 1), (44, 19), (36, 26), (44, 3), (25, 15), (7, 1), (9, 24), (7, 42), (32, 42), (5, 6), (37, 16), (7, 39), (40, 6), (9, 36), (7, 3), (24, 2), (36, 9), (38, 32), (29, 41), (16, 15), (20, 26), (8, 13), (24, 29), (27, 13), (46, 10), (15, 33), (41, 27), (35, 34), (28, 30), (44, 26), (20, 17), (8, 16), (23, 30), (41, 30), (34, 3), (38, 3), (20, 29), (5, 15), (15, 28), (45, 15), (46, 15), (13, 33), (32, 31), (26, 18), (0, 16), (14, 24), (41, 42), (14, 29), (43, 42), (7, 13), (36, 32), (41, 5), (4, 23), (22, 31), (21, 35), (27, 23), (14, 27), (5, 8), (16, 5), (27, 28), (16, 44), (2, 9), (21, 30), (11, 25), (38, 4), (8, 28), (42, 13), (20, 31), (14, 14), (39, 22), (44, 5), (43, 3), (27, 31), (12, 23), (2, 5), (44, 11), (22, 19), (20, 2), (27, 35), (6, 19), (23, 23), (2, 1), (15, 25), (20, 0), (23, 4), (40, 43), (6, 3), (35, 26), (4, 35), (36, 43), (37, 0), (8, 33), (45, 3), (36, 19), (45, 25), (5, 44), (25, 36), (12, 35), (1, 39), (4, 44), (18, 22), (45, 38), (21, 5), (6, 0), (28, 16), (33, 7), (34, 40), (38, 20), (14, 41), (39, 17), (32, 0), (33, 27), (46, 31), (6, 21), (39, 24), (18, 10), (15, 0), (29, 19), (8, 10), (40, 13), (34, 42), (42, 2), (41, 35), (7, 4), (27, 21), (19, 22), (29, 0), (8, 45), (8, 6), (36, 8), (26, 34), (33, 38), (8, 1), (24, 45), (3, 33), (17, 27), (6, 14), (31, 15), (15, 41), (38, 45), (28, 14), (27, 41), (30, 42), (23, 3), (30, 40), (13, 30), (13, 32), (6, 1), (36, 10), (21, 6), (45, 16), (39, 2), (45, 10), (21, 26), (39, 31), (20, 36), (7, 45), (17, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 39), (1, 15), (48, 4), (0, 31), (38, 38), (45, 41), (14, 16), (33, 19), (9, 0), (3, 38), (20, 35), (45, 34), (5, 23), (41, 22), (48, 25), (28, 24), (43, 37), (30, 33), (42, 15), (45, 4), (44, 30), (29, 12), (13, 22), (21, 1), (19, 41), (23, 24), (20, 33), (44, 21), (5, 39), (32, 38), (27, 6), (47, 8), (4, 5), (7, 31), (18, 25), (40, 17), (32, 35), (6, 26), (24, 8), (4, 19), (12, 8), (22, 0), (42, 4), (36, 30), (26, 40), (31, 5), (21, 25), (12, 19), (32, 23), (30, 34), (24, 19), (44, 10), (45, 21), (9, 37), (17, 39), (47, 20), (14, 0), (0, 5), (40, 24), (24, 37), (22, 16), (13, 4), (10, 33), (45, 15), (18, 21), (47, 39), (27, 21), (40, 19), (38, 20), (11, 13), (19, 0), (0, 14), (23, 37), (39, 43), (11, 5), (16, 3), (34, 6), (3, 0), (28, 6), (18, 3), (3, 5), (25, 25), (14, 5), (9, 23), (42, 9), (17, 5), (12, 41), (34, 1), (15, 11), (27, 22), (17, 30), (13, 36), (9, 7), (2, 37), (42, 43), (26, 8), (16, 20), (14, 12), (20, 1), (43, 28), (21, 7), (37, 32), (34, 28), (16, 5), (17, 1), (11, 8), (45, 9), (12, 32), (28, 34), (29, 34), (31, 17), (12, 35), (40, 3), (24, 20), (1, 3), (7, 32), (4, 23), (11, 6), (24, 32), (15, 10), (30, 14), (12, 4), (17, 4), (20, 21), (24, 28), (26, 32), (46, 16), (9, 6), (37, 26), (48, 36), (22, 30), (17, 3), (45, 17), (27, 26), (18, 38), (1, 14), (34, 38), (6, 29), (33, 37), (39, 15), (4, 11), (26, 22), (35, 8), (2, 0), (16, 7), (4, 2), (18, 23), (36, 4), (22, 43), (5, 36), (29, 16), (44, 5), (22, 1), (0, 21), (48, 29), (13, 27), (8, 0), (8, 24), (22, 33), (6, 1), (31, 13), (23, 16), (19, 20), (23, 29), (41, 19), (39, 31), (27, 16), (29, 38), (7, 24), (0, 27), (13, 9), (12, 22), (28, 29), (24, 26), (41, 2), (4, 8), (44, 22), (30, 5), (16, 10), (9, 43), (2, 5), (18, 24), (8, 21), (46, 15), (6, 32), (6, 5), (30, 36), (23, 10), (40, 4), (45, 25), (39, 21), (24, 11), (44, 25), (2, 4), (36, 39), (23, 7), (25, 19), (24, 30), (4, 28), (30, 22), (37, 18), (34, 23), (38, 29), (23, 12), (14, 6), (25, 12), (26, 43), (9, 39), (43, 29), (26, 33), (38, 8), (45, 38), (40, 14), (26, 14), (13, 0), (34, 36), (37, 11), (8, 7), (8, 12), (38, 31), (36, 29), (12, 12), (10, 31), (29, 42), (48, 38), (9, 40), (11, 28), (44, 41), (18, 7), (31, 37), (26, 3), (44, 28), (37, 36), (4, 16), (1, 1), (48, 10), (34, 29), (39, 34), (16, 23), (34, 19), (46, 1), (33, 30), (42, 23), (30, 19), (8, 3), (28, 40), (25, 39), (38, 35), (44, 6), (43, 33), (46, 35), (40, 28), (22, 4), (1, 32), (26, 42), (8, 40), (3, 26), (3, 43), (21, 13), (25, 28), (22, 13), (10, 30), (38, 0), (2, 28), (16, 36), (27, 5), (33, 7), (30, 21), (16, 32), (3, 42), (13, 8), (48, 12), (9, 12), (35, 27), (40, 2), (43, 11), (32, 24), (41, 13), (7, 21), (43, 13), (10, 20), (28, 27), (28, 38), (8, 15), (17, 24), (0, 32), (7, 5), (29, 40), (29, 14), (9, 18), (45, 14), (28, 15), (41, 28), (24, 18), (43, 30), (5, 34), (10, 3), (19, 1), (35, 22), (40, 15), (26, 30), (27, 12), (48, 31), (10, 2), (47, 2), (14, 13), (34, 0), (39, 12), (15, 21), (25, 21), (20, 23), (6, 35), (35, 7), (18, 16), (43, 42), (8, 39), (31, 15), (43, 35), (1, 6), (40, 23), (15, 39), (29, 28), (2, 35), (30, 9), (18, 14), (32, 6), (31, 11), (28, 12), (41, 12), (10, 17), (16, 11), (18, 26), (4, 17), (37, 24), (6, 21), (47, 23), (31, 39), (6, 12), (13, 2), (42, 25), (17, 0), (13, 13), (13, 40), (12, 7), (3, 17), (16, 31), (25, 34), (1, 8), (10, 23), (27, 19), (28, 42), (23, 18), (7, 40), (45, 33), (20, 12), (34, 40), (27, 17), (37, 1), (16, 0), (27, 31), (13, 29), (20, 13), (30, 20), (46, 10), (15, 5), (42, 5), (3, 20), (28, 23), (40, 6), (41, 1), (42, 24), (39, 7), (16, 29), (28, 19), (37, 27), (0, 28), (30, 43), (33, 35), (25, 18), (5, 32), (26, 28), (21, 27), (38, 2), (6, 18), (11, 16), (25, 1), (27, 30), (14, 4), (32, 20), (33, 20), (16, 41), (30, 13), (35, 35), (17, 42), (9, 28), (1, 22), (15, 14), (29, 9), (4, 33), (5, 31), (21, 34), (46, 11), (46, 0), (22, 27), (26, 23), (5, 25), (4, 36), (4, 6), (16, 6), (20, 39), (1, 11), (31, 26), (1, 23), (48, 18), (29, 22), (22, 7), (42, 8), (39, 27), (0, 40), (7, 10), (42, 18), (43, 8), (14, 35), (26, 13), (16, 35), (41, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 43), (26, 25), (10, 22), (20, 21), (22, 11), (3, 41), (41, 18), (5, 18), (34, 3), (41, 31), (43, 6), (11, 30), (20, 24), (43, 33), (19, 6), (34, 36), (39, 23), (22, 43), (13, 21), (2, 2), (25, 7), (26, 36), (22, 4), (12, 17), (20, 5), (3, 0), (35, 21), (8, 1), (22, 33), (3, 38), (6, 26), (38, 26), (11, 17), (8, 12), (31, 30), (10, 27), (27, 21), (21, 41), (32, 41), (9, 14), (23, 17), (31, 38), (10, 23), (2, 20), (25, 22), (35, 15), (9, 25), (43, 18), (25, 28), (20, 23), (5, 26), (6, 20), (40, 20), (30, 1), (36, 29), (19, 33), (37, 17), (39, 15), (8, 3), (41, 32), (11, 27), (8, 43), (12, 42), (42, 20), (1, 31), (8, 9), (42, 7), (36, 32), (12, 26), (40, 11), (31, 23), (26, 35), (8, 17), (19, 18), (27, 14), (36, 41), (9, 26), (18, 40), (16, 16), (7, 3), (28, 26), (40, 8), (25, 26), (32, 0), (36, 37), (18, 42), (19, 10), (29, 6), (40, 16), (5, 13), (4, 19), (40, 12), (42, 38), (17, 43), (3, 22), (36, 14), (12, 24), (0, 18), (27, 12), (28, 36), (8, 22), (7, 6), (13, 30), (18, 39), (0, 1), (33, 9), (41, 11), (10, 8), (12, 7), (21, 15), (1, 43), (6, 38), (28, 34), (3, 6), (6, 31), (23, 20), (30, 43), (14, 21), (25, 38), (12, 2), (22, 5), (19, 23), (0, 31), (29, 28), (18, 16), (14, 1), (37, 19), (11, 34), (19, 1), (23, 0), (7, 12), (16, 2), (19, 37), (14, 31), (31, 15), (20, 39), (28, 0), (38, 28), (33, 2), (35, 12), (39, 35), (33, 28), (21, 1), (12, 31), (15, 10), (6, 9), (17, 4), (6, 16), (43, 1), (15, 11), (41, 12), (6, 29), (5, 34), (26, 29), (36, 22), (17, 38), (19, 32), (12, 3), (42, 32), (26, 5), (2, 15), (33, 12), (32, 24), (3, 4), (7, 30), (41, 1), (33, 0), (26, 39), (17, 32), (20, 14), (43, 8), (34, 13), (11, 41), (41, 21), (29, 13), (12, 28), (18, 24), (23, 5), (25, 12), (20, 42), (4, 5), (23, 30), (26, 38), (1, 10), (7, 28), (42, 3), (28, 28), (27, 30), (41, 15), (16, 32), (17, 0), (33, 23), (34, 39), (3, 29), (7, 15), (5, 25), (7, 25), (21, 28), (35, 32), (22, 25), (12, 9), (19, 40), (24, 43), (1, 20), (3, 16), (6, 0), (35, 9), (40, 17), (33, 3), (14, 27), (11, 33), (26, 26), (7, 21), (36, 12), (27, 25), (29, 9), (33, 36), (11, 32), (28, 16), (10, 19), (11, 3), (23, 18), (41, 35), (8, 32), (0, 37), (17, 41), (17, 12), (0, 23), (35, 42), (34, 18), (13, 1), (30, 24), (11, 9), (14, 9), (9, 17), (33, 26), (6, 22), (2, 8), (28, 18), (40, 6), (20, 19), (31, 4), (7, 18), (4, 6), (5, 22), (23, 13), (15, 42), (34, 42), (35, 26), (21, 14), (23, 40), (38, 11), (36, 23), (6, 27), (37, 26), (18, 32), (2, 32), (5, 0), (42, 13), (4, 12), (2, 38), (20, 10), (24, 31), (29, 12), (13, 34), (2, 6), (39, 28), (1, 26), (5, 2), (32, 42), (30, 10), (29, 30), (38, 41), (26, 20), (30, 23), (35, 16), (39, 11), (16, 17), (0, 28), (21, 2), (42, 34), (42, 33), (38, 29), (17, 13), (32, 22), (11, 4), (32, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 26), (16, 7), (41, 9), (8, 19), (27, 13), (4, 18), (28, 36), (28, 11), (14, 15), (3, 5), (13, 30), (26, 23), (24, 4), (15, 7), (34, 21), (18, 38), (37, 22), (2, 24), (1, 42), (18, 1), (15, 17), (1, 38), (6, 38), (36, 19), (1, 3), (6, 3), (28, 42), (18, 18), (31, 25), (1, 39), (4, 6), (39, 31), (9, 29), (19, 34), (32, 44), (1, 27), (40, 39), (38, 14), (23, 0), (3, 19), (12, 30), (30, 15), (39, 0), (37, 9), (21, 40), (41, 15), (34, 18), (21, 35), (34, 5), (21, 25), (7, 30), (24, 35), (6, 5), (40, 44), (40, 16), (4, 38), (16, 0), (37, 24), (27, 2), (39, 8), (16, 13), (25, 24), (23, 35), (40, 40), (37, 17), (1, 23), (27, 17), (9, 43), (3, 14), (35, 6), (39, 16), (33, 4), (10, 44), (0, 41), (36, 0), (11, 36), (36, 37), (32, 32), (26, 1), (32, 41), (35, 7), (18, 5), (38, 30), (40, 33), (2, 38), (25, 20), (12, 13), (10, 18), (17, 10), (18, 26), (34, 34), (32, 26), (16, 30), (11, 14), (22, 23), (12, 35), (19, 25), (38, 25), (3, 15), (26, 14), (18, 28), (20, 8), (15, 1), (25, 38), (28, 25), (36, 27), (37, 1), (34, 39), (31, 20), (35, 38), (29, 20), (21, 1), (20, 22), (37, 13), (39, 23), (1, 9), (28, 12), (11, 10), (6, 6), (5, 14), (38, 38), (5, 3), (18, 33), (22, 17), (26, 33), (26, 9), (12, 11), (1, 22), (8, 30), (25, 15), (35, 29), (28, 22), (7, 34), (27, 44), (4, 36), (3, 29), (31, 30), (33, 33), (12, 39), (38, 41), (17, 22), (17, 42), (0, 36), (37, 37), (30, 1), (38, 10), (12, 42), (15, 22), (31, 33), (9, 20), (23, 20), (11, 23), (3, 10), (6, 20), (37, 36), (9, 37), (36, 12), (28, 26), (29, 1), (39, 9), (7, 19), (40, 14), (30, 3), (14, 2), (35, 31), (23, 43), (31, 42), (30, 19), (37, 20), (8, 22), (0, 32), (17, 19), (29, 37), (12, 6), (36, 15), (3, 23), (25, 39), (3, 20), (27, 40), (9, 26), (1, 44), (26, 17), (16, 29), (29, 39), (9, 5), (30, 39), (40, 5), (0, 16), (6, 13), (26, 29), (23, 23), (13, 40), (30, 27), (30, 28), (13, 13), (24, 9), (8, 3), (8, 10), (9, 44), (38, 15), (13, 41), (28, 34), (27, 31), (30, 14), (35, 32), (27, 6), (2, 37), (13, 7), (29, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 37), (27, 21), (36, 5), (14, 29), (28, 36), (17, 28), (34, 18), (10, 10), (14, 17), (34, 29), (34, 28), (36, 22), (20, 38), (23, 25), (5, 24), (25, 19), (10, 16), (15, 28), (6, 14), (29, 7), (0, 23), (19, 27), (23, 8), (27, 15), (22, 42), (25, 2), (24, 18), (18, 4), (33, 5), (1, 10), (28, 32), (4, 25), (30, 0), (36, 25), (32, 43), (31, 9), (20, 42), (11, 4), (5, 36), (41, 8), (41, 37), (13, 8), (36, 18), (22, 23), (16, 36), (6, 44), (2, 10), (9, 16), (25, 12), (11, 5), (13, 16), (2, 17), (9, 0), (27, 30), (8, 36), (23, 46), (19, 34), (31, 14), (25, 40), (8, 6), (16, 46), (33, 1), (24, 6), (5, 44), (26, 22), (0, 20), (32, 17), (26, 8), (4, 39), (23, 31), (8, 25), (2, 40), (26, 25), (15, 2), (21, 15), (31, 12), (21, 33), (33, 4), (32, 25), (10, 2), (34, 42), (17, 4), (21, 34), (6, 35), (16, 38), (39, 26), (12, 15), (1, 12), (11, 43), (1, 0), (23, 24), (41, 27), (32, 29), (12, 27), (4, 45), (9, 9), (10, 37), (23, 19), (23, 33), (13, 36), (25, 30), (6, 39), (19, 14), (12, 12), (26, 21), (2, 23), (10, 12), (25, 32), (20, 43), (39, 23), (32, 35), (0, 36), (14, 5), (35, 0), (13, 4), (33, 33), (30, 26), (10, 22), (35, 16), (14, 9), (4, 28), (37, 10), (13, 9), (37, 13), (2, 30), (26, 37), (34, 40), (29, 19), (40, 41), (1, 34), (4, 0), (3, 42), (31, 23), (1, 35), (38, 21), (24, 24), (38, 30), (38, 7), (24, 28), (33, 8), (10, 5), (32, 26), (3, 7), (9, 36), (0, 45), (31, 24), (38, 45), (35, 10), (21, 11), (38, 46), (1, 25), (21, 22), (22, 6), (39, 31), (4, 4), (19, 10), (14, 25), (27, 39), (3, 9), (22, 41), (26, 13), (5, 12), (14, 28), (31, 7), (29, 26), (22, 3), (29, 39), (35, 17), (39, 20), (39, 42), (40, 31), (18, 11), (37, 18), (19, 16), (8, 40), (29, 2), (33, 7), (38, 37), (39, 16), (16, 2), (1, 45), (19, 5), (23, 4), (16, 27), (39, 12), (22, 34), (23, 9), (2, 7), (18, 34), (36, 14), (14, 42), (32, 2), (3, 6), (14, 46), (9, 41), (26, 3), (19, 38), (22, 38), (15, 34), (0, 15), (1, 3), (16, 19), (27, 8), (3, 20), (30, 2), (30, 3), (8, 32), (31, 34), (32, 31), (9, 38), (34, 14), (38, 36), (29, 11), (30, 46), (32, 12), (9, 39), (5, 20), (36, 39), (14, 32), (8, 2), (15, 30), (27, 14), (34, 2), (40, 35), (34, 26), (7, 36), (21, 2), (12, 44), (34, 8), (29, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 8), (12, 27), (29, 11), (34, 34), (1, 6), (22, 18), (1, 0), (9, 15), (28, 11), (17, 40), (36, 0), (24, 10), (42, 3), (14, 9), (34, 2), (40, 19), (20, 11), (30, 3), (30, 14), (43, 8), (10, 22), (4, 34), (17, 30), (40, 1), (12, 2), (13, 2), (23, 20), (23, 36), (16, 15), (41, 1), (5, 32), (27, 1), (41, 32), (28, 35), (25, 36), (0, 16), (28, 6), (22, 20), (18, 6), (32, 8), (35, 5), (41, 28), (1, 24), (13, 24), (31, 37), (42, 35), (34, 23), (19, 22), (37, 35), (16, 33), (13, 32), (9, 1), (20, 40), (39, 26), (10, 37), (2, 32), (0, 9), (11, 17), (43, 7), (10, 25), (29, 32), (29, 26), (43, 22), (16, 39), (13, 29), (10, 15), (29, 23), (40, 26), (34, 15), (19, 34), (42, 33), (27, 30), (16, 28), (24, 2), (18, 16), (0, 12), (11, 3), (13, 18), (9, 14), (27, 29), (4, 32), (21, 24), (23, 12), (27, 4), (27, 25), (8, 25), (8, 32), (1, 18), (21, 3), (33, 3), (34, 28), (18, 7), (33, 12), (23, 30), (39, 3), (38, 27), (23, 13), (28, 21), (10, 0), (27, 37), (21, 18), (15, 39), (33, 28), (38, 7), (39, 14), (18, 37), (15, 15), (43, 1), (32, 1), (40, 16), (7, 13), (22, 40), (37, 22), (42, 8), (42, 21), (1, 37), (22, 25), (18, 19), (16, 6), (33, 32), (14, 37), (43, 31), (16, 34), (0, 32), (19, 13), (13, 5), (30, 31), (11, 24), (10, 2), (33, 29), (28, 27), (35, 27), (2, 7), (29, 6), (6, 5), (7, 40), (7, 18), (22, 27), (17, 25), (38, 10), (3, 37), (42, 36), (23, 18), (26, 40), (1, 14), (18, 27), (13, 12), (6, 2), (43, 17), (23, 35), (28, 15), (3, 2), (20, 9), (37, 30), (4, 35), (18, 10), (31, 5), (8, 19), (3, 8), (13, 17), (17, 29), (33, 25), (20, 12), (31, 13), (37, 4), (12, 12), (29, 19), (7, 3), (9, 8), (21, 33), (21, 2), (16, 38), (17, 15), (4, 2), (41, 39), (38, 40), (42, 39), (17, 21), (37, 3), (39, 38), (22, 22), (27, 21), (20, 23), (38, 30), (22, 15), (40, 32), (37, 2), (6, 23), (27, 2), (17, 8), (5, 15), (18, 12), (37, 24), (1, 7), (7, 22), (34, 5), (12, 5), (23, 4), (5, 39), (28, 4), (11, 12), (21, 36), (27, 12), (41, 25), (41, 35), (10, 4), (31, 6), (25, 12), (34, 39), (2, 6), (12, 15), (16, 18), (42, 17), (35, 2), (15, 28), (35, 26), (42, 6), (37, 17), (43, 38), (12, 29), (14, 39), (9, 16), (11, 7), (40, 4), (26, 9), (38, 37), (7, 7), (5, 35), (7, 29), (29, 40), (35, 23), (18, 15), (17, 2), (7, 5), (26, 29), (10, 19), (2, 14), (40, 20), (32, 35), (26, 1), (30, 1), (32, 0), (21, 9), (23, 38), (13, 36), (35, 24), (39, 4), (16, 7), (23, 19), (40, 11), (38, 35), (25, 24), (14, 40), (15, 37), (12, 19), (36, 25), (16, 16), (30, 38), (11, 23), (20, 8), (33, 27), (22, 28), (36, 15), (3, 29), (12, 33), (25, 0), (27, 17), (15, 18), (10, 1), (11, 27), (23, 6), (21, 35), (33, 33), (14, 6), (21, 19), (11, 16), (27, 15), (25, 22), (7, 37), (30, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 27), (32, 28), (43, 41), (22, 14), (9, 22), (4, 35), (7, 22), (39, 36), (9, 28), (13, 44), (41, 33), (43, 19), (37, 0), (13, 43), (21, 17), (23, 41), (20, 2), (40, 18), (18, 39), (32, 42), (13, 8), (13, 35), (4, 31), (34, 26), (35, 3), (40, 13), (6, 9), (26, 30), (36, 42), (28, 5), (46, 39), (42, 12), (9, 6), (37, 34), (31, 11), (32, 15), (13, 33), (40, 32), (30, 47), (26, 11), (14, 41), (31, 24), (40, 22), (3, 27), (32, 7), (44, 33), (13, 39), (41, 34), (0, 41), (45, 19), (35, 12), (9, 26), (13, 47), (40, 20), (29, 14), (38, 5), (5, 6), (17, 27), (5, 44), (2, 37), (42, 7), (9, 48), (28, 23), (47, 40), (21, 4), (11, 19), (31, 47), (31, 25), (12, 32), (35, 21), (10, 46), (34, 44), (39, 47), (22, 11), (8, 40), (7, 45), (30, 21), (26, 27), (33, 27), (4, 32), (18, 20), (26, 7), (32, 29), (42, 15), (27, 33), (47, 22), (13, 9), (17, 14), (15, 18), (1, 32), (22, 40), (34, 6), (46, 44), (45, 3), (46, 27), (15, 35), (8, 8), (25, 3), (23, 26), (46, 8), (30, 1), (36, 48), (16, 44), (32, 26), (26, 6), (28, 46), (1, 5), (21, 23), (41, 43), (29, 15), (4, 0), (22, 37), (32, 46), (8, 3), (44, 18), (20, 4), (0, 43), (25, 27), (0, 29), (25, 19), (25, 4), (14, 17), (39, 38), (1, 10), (10, 26), (34, 15), (22, 16), (36, 20), (26, 12), (28, 9), (36, 18), (45, 32), (8, 23), (15, 12), (16, 3), (32, 6), (40, 16), (47, 28), (17, 41), (0, 16), (43, 4), (19, 11), (47, 46), (36, 40), (19, 42), (29, 11), (20, 5), (9, 0), (24, 10), (42, 10), (21, 9), (14, 1), (9, 35), (0, 24), (21, 0), (24, 28), (26, 23), (28, 17), (29, 21), (5, 31), (30, 17), (21, 20), (40, 40), (45, 10), (16, 5), (1, 23), (2, 24), (20, 38), (23, 11), (11, 25), (8, 25), (23, 29), (30, 45), (34, 2), (35, 43), (8, 37), (4, 24), (25, 18), (0, 10), (38, 6), (16, 27), (6, 28), (18, 13), (35, 45), (6, 24), (39, 4), (21, 48), (16, 7), (31, 27), (11, 36), (5, 32), (37, 6), (12, 16), (26, 32), (36, 11), (12, 24), (26, 3), (21, 32), (46, 33), (20, 33), (29, 26), (4, 4), (41, 36), (21, 1), (27, 20), (0, 5), (31, 2), (38, 12), (10, 19), (14, 12), (43, 18), (23, 6), (16, 20), (20, 14), (7, 10), (33, 28), (25, 45), (40, 33), (9, 2), (34, 21), (21, 21), (44, 15), (15, 24), (2, 45), (3, 45), (35, 34), (27, 7), (37, 28), (31, 34), (18, 22), (36, 30), (24, 34), (37, 24), (27, 21), (12, 31), (16, 32), (41, 13), (5, 35), (32, 0), (36, 46), (17, 33), (32, 4), (12, 25), (31, 42), (30, 43), (28, 38), (4, 34), (8, 21), (30, 11), (43, 37), (6, 37), (41, 32), (47, 20), (18, 15), (10, 15), (20, 39), (18, 28), (30, 35), (44, 38), (10, 30), (23, 14), (15, 4), (11, 23), (33, 45), (14, 0), (44, 37), (23, 37), (22, 3), (31, 36), (22, 35), (37, 12), (5, 34), (27, 35), (45, 2), (34, 7), (25, 35), (16, 31), (21, 29), (46, 15), (23, 15), (44, 26), (9, 30), (36, 45), (46, 42), (22, 41), (32, 13), (23, 18), (11, 46), (35, 32), (40, 15), (25, 22), (21, 19), (27, 28), (9, 39), (21, 24), (34, 20), (0, 44), (29, 35), (33, 20), (24, 36), (11, 8), (30, 2), (35, 35), (9, 4), (24, 48), (8, 12), (5, 22), (34, 48), (13, 23), (34, 27), (29, 18), (34, 9), (43, 33), (29, 39), (19, 32), (32, 17), (6, 2), (24, 29), (34, 29), (7, 37), (23, 2), (47, 21), (19, 22), (16, 10), (0, 27), (42, 6), (35, 17), (1, 6), (41, 15), (2, 23), (10, 38), (24, 37), (12, 11), (47, 23), (45, 9), (15, 30), (28, 0), (10, 36), (36, 0), (47, 15), (19, 17), (39, 0), (17, 11), (38, 41), (1, 36), (36, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 18), (29, 23), (47, 32), (38, 29), (24, 18), (41, 9), (45, 17), (40, 17), (12, 1), (4, 6), (7, 3), (34, 22), (13, 29), (26, 30), (31, 21), (43, 30), (23, 13), (26, 16), (11, 13), (27, 5), (7, 30), (23, 17), (38, 4), (6, 10), (21, 3), (0, 5), (38, 34), (19, 25), (22, 39), (13, 13), (34, 34), (36, 0), (42, 35), (1, 31), (0, 21), (30, 2), (46, 31), (24, 6), (26, 22), (44, 38), (18, 36), (29, 4), (17, 2), (14, 39), (0, 17), (34, 23), (6, 38), (44, 15), (42, 14), (7, 23), (46, 35), (1, 16), (10, 16), (16, 32), (5, 37), (39, 39), (18, 21), (2, 30), (14, 21), (27, 13), (37, 1), (22, 3), (4, 9), (18, 15), (33, 30), (11, 8), (39, 33), (12, 37), (4, 33), (41, 15), (38, 24), (37, 17), (35, 10), (47, 7), (31, 13), (14, 34), (5, 4), (42, 19), (47, 28), (12, 12), (27, 21), (7, 26), (18, 8), (36, 19), (3, 19), (29, 27), (43, 25), (34, 6), (44, 0), (34, 9), (32, 31), (28, 19), (13, 8), (25, 8), (3, 5), (17, 28), (9, 23), (36, 26), (25, 15), (17, 6), (45, 16), (4, 18), (34, 31), (11, 39), (25, 3), (15, 7), (43, 31), (13, 39), (1, 12), (4, 11), (9, 2), (26, 17), (20, 27), (42, 6), (25, 11), (40, 4), (23, 16), (36, 27), (32, 27), (22, 14), (8, 19), (10, 25), (30, 39), (41, 17), (40, 8), (27, 11), (30, 35), (26, 0), (30, 26), (28, 30), (19, 30), (22, 27), (17, 18), (11, 10), (1, 34), (14, 33), (2, 16), (27, 16), (32, 39), (4, 29), (41, 20), (3, 28), (9, 15), (1, 17), (21, 18), (19, 36), (25, 38), (32, 18), (27, 8), (9, 31), (34, 8), (4, 14), (0, 29), (27, 33), (19, 14), (47, 36), (47, 13), (3, 32), (14, 12), (18, 34), (31, 0), (27, 25), (39, 8), (0, 13), (30, 10), (2, 38), (21, 38), (44, 37), (45, 4), (11, 1), (5, 19), (22, 8), (8, 32), (30, 36), (1, 27), (5, 17), (27, 34), (43, 8), (3, 37), (10, 28), (10, 15), (9, 13), (32, 21), (33, 13), (11, 18), (20, 25), (15, 6), (7, 29), (0, 35), (45, 12), (34, 15), (22, 4), (12, 33), (2, 13), (10, 9), (45, 38), (9, 17), (46, 2), (44, 27), (18, 28), (22, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 47), (1, 40), (34, 40), (4, 27), (25, 26), (43, 1), (26, 19), (23, 47), (13, 41), (23, 13), (27, 45), (16, 17), (25, 29), (9, 4), (16, 47), (21, 46), (10, 8), (24, 40), (12, 31), (32, 25), (29, 28), (5, 34), (44, 22), (17, 26), (26, 40), (1, 2), (22, 47), (28, 35), (5, 4), (10, 0), (32, 19), (24, 35), (16, 12), (15, 34), (7, 24), (43, 21), (6, 22), (13, 16), (3, 40), (36, 1), (24, 39), (7, 12), (30, 13), (2, 4), (3, 34), (2, 37), (34, 46), (35, 15), (9, 37), (7, 46), (13, 17), (29, 21), (28, 30), (38, 43), (13, 35), (28, 15), (38, 44), (25, 47), (13, 8), (2, 18), (46, 28), (24, 43), (11, 6), (38, 28), (10, 6), (12, 15), (17, 43), (3, 30), (30, 40), (5, 24), (46, 16), (29, 30), (5, 26), (8, 29), (31, 24), (37, 42), (7, 3), (19, 3), (9, 24), (24, 1), (34, 12), (12, 37), (17, 0), (31, 15), (44, 13), (20, 2), (15, 43), (20, 8), (1, 14), (37, 5), (26, 22), (15, 14), (25, 7), (12, 40), (27, 41), (4, 25), (18, 31), (21, 31), (27, 23), (36, 46), (12, 29), (6, 46), (9, 28), (45, 7), (7, 47), (28, 10), (38, 37), (16, 9), (15, 35), (2, 29), (1, 16), (28, 29), (43, 31), (0, 4), (25, 46), (26, 39), (33, 9), (29, 11), (30, 44), (7, 36), (2, 1), (33, 18), (22, 45), (13, 22), (12, 20), (28, 45), (4, 9), (19, 35), (33, 39), (6, 47), (29, 26), (22, 20), (37, 8), (4, 13), (33, 0), (16, 29), (38, 5), (19, 11), (2, 46), (2, 15), (14, 19), (11, 19), (17, 12), (31, 6), (1, 29), (14, 35), (45, 17), (17, 1), (37, 39), (3, 8), (34, 20), (39, 41), (33, 44), (21, 25), (30, 20), (46, 18), (3, 19), (5, 36), (6, 29), (13, 47), (38, 38), (28, 2), (15, 15), (6, 43), (46, 13), (1, 17), (6, 24), (40, 37), (23, 11), (20, 14), (43, 15), (31, 46), (36, 25), (31, 31), (20, 44), (12, 30), (9, 40), (44, 47), (26, 12), (8, 27), (26, 33), (16, 15), (25, 23), (27, 15), (7, 29), (2, 20), (0, 10), (10, 43), (25, 34), (16, 34), (10, 24), (25, 25), (5, 11), (6, 8), (37, 3), (21, 9), (18, 36), (17, 10), (22, 9), (40, 3), (46, 15), (42, 43), (3, 1), (45, 6), (27, 1), (24, 31), (40, 19), (8, 10), (9, 47), (0, 27), (40, 33), (1, 37), (29, 15), (15, 4), (9, 42), (6, 34), (34, 4), (11, 29), (3, 7), (39, 13), (14, 22), (41, 23), (13, 36), (39, 21), (2, 30), (42, 5), (25, 16), (36, 20), (30, 32), (12, 23), (11, 45), (9, 10), (12, 44), (0, 25), (16, 26), (0, 44), (29, 22), (4, 4), (14, 10), (19, 47), (14, 28), (40, 16), (42, 20), (7, 39), (22, 3), (16, 27), (0, 39), (36, 31), (44, 18), (45, 31), (21, 39), (14, 11), (37, 40), (19, 31), (44, 39), (30, 7), (30, 29), (4, 24), (22, 23), (19, 21), (17, 17), (22, 40), (36, 9), (14, 6), (34, 8), (16, 19), (21, 3), (17, 15), (10, 36), (10, 9), (33, 31), (46, 9), (37, 18), (34, 13), (21, 42), (16, 2), (46, 6), (40, 45), (23, 1), (20, 47), (31, 17), (21, 18), (22, 17), (30, 19), (32, 41), (27, 2), (35, 10), (43, 33), (27, 17), (5, 23), (34, 11), (33, 35), (8, 8), (33, 29), (19, 12), (23, 46), (29, 40), (19, 7), (23, 28), (29, 19), (16, 39), (9, 0), (13, 15), (17, 22), (20, 41), (4, 34), (24, 2), (4, 31), (4, 26), (12, 46), (7, 0), (2, 24), (32, 44), (38, 22), (15, 16), (3, 25), (34, 14), (4, 3), (36, 42), (34, 17), (44, 44), (34, 28), (29, 2), (29, 39), (31, 29), (8, 11), (23, 18), (17, 36), (20, 21), (34, 7), (2, 34), (0, 6), (23, 8), (38, 25), (1, 6), (39, 15), (27, 14), (35, 40), (1, 30), (18, 46), (45, 13), (10, 11), (36, 14), (33, 23), (30, 24), (45, 40), (38, 13), (37, 30), (18, 4), (33, 10), (39, 17), (21, 17), (23, 14), (30, 23), (5, 13), (28, 7), (30, 22), (38, 33), (26, 18), (32, 32), (18, 37), (9, 6), (22, 10), (25, 20), (8, 28), (7, 45), (33, 11), (11, 9), (17, 40), (19, 38), (10, 18), (2, 28), (17, 5), (8, 3), (4, 8), (11, 21), (42, 44), (20, 46), (41, 42), (16, 4), (3, 42), (37, 9), (3, 2), (17, 33), (24, 11), (4, 19), (46, 20), (25, 39), (15, 38), (9, 38), (23, 39), (4, 35), (4, 18), (17, 38), (12, 6), (23, 21), (14, 25), (4, 37), (25, 10), (35, 27), (33, 43), (8, 9), (42, 26), (45, 25), (44, 26), (0, 36), (32, 30), (26, 14), (37, 23), (25, 21), (28, 36), (38, 32), (2, 11), (42, 39), (16, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 26), (1, 0), (1, 3), (13, 26), (8, 19), (33, 8), (15, 1), (14, 27), (2, 35), (10, 3), (13, 8), (20, 24), (10, 44), (35, 28), (4, 20), (15, 42), (6, 17), (24, 5), (40, 13), (13, 21), (21, 26), (11, 2), (0, 16), (34, 22), (5, 45), (34, 34), (33, 16), (28, 42), (33, 45), (14, 21), (25, 34), (27, 2), (27, 9), (7, 3), (25, 33), (21, 1), (17, 13), (26, 12), (5, 31), (30, 44), (30, 15), (3, 33), (23, 33), (26, 40), (22, 38), (28, 35), (4, 33), (36, 38), (3, 15), (31, 13), (2, 25), (34, 44), (14, 2), (22, 24), (0, 11), (23, 0), (32, 8), (3, 4), (14, 34), (0, 3), (25, 32), (16, 4), (1, 33), (33, 20), (32, 25), (13, 30), (26, 32), (35, 43), (28, 28), (32, 10), (5, 12), (3, 10), (23, 1), (31, 33), (24, 38), (28, 1), (4, 37), (13, 32), (15, 44), (25, 28), (26, 14), (13, 29), (32, 3), (5, 39), (11, 22), (8, 1), (33, 41), (24, 8), (3, 41), (32, 21), (19, 27), (0, 24), (4, 4), (18, 1), (32, 5), (12, 34), (31, 23), (0, 12), (8, 9), (19, 15), (7, 7), (3, 43), (22, 33), (4, 6), (5, 7), (26, 23), (6, 19), (40, 7), (26, 15), (16, 24), (1, 36), (40, 28), (23, 11), (13, 25), (21, 19), (25, 17), (39, 15), (8, 37), (4, 44), (29, 18), (35, 39), (12, 7), (6, 27), (20, 42), (26, 26), (16, 16), (39, 5), (20, 25), (8, 18), (21, 9), (14, 33), (2, 26), (9, 32), (13, 17), (17, 8), (21, 45), (29, 27), (33, 38), (38, 15), (20, 2), (22, 42), (23, 5), (37, 12), (25, 16), (20, 11), (9, 43), (11, 20), (39, 44), (34, 4), (40, 32), (30, 13), (5, 18), (9, 45), (35, 13), (15, 39), (9, 40), (3, 30), (4, 42), (6, 3), (17, 24), (0, 27), (39, 6), (20, 7), (37, 20), (0, 43), (4, 7), (2, 9), (16, 36), (26, 42), (13, 42), (28, 7), (27, 18), (21, 24), (34, 38), (31, 11), (12, 10), (31, 8), (29, 40), (5, 1), (22, 2), (35, 2), (22, 13), (37, 38), (24, 10), (34, 39), (16, 43), (21, 38), (38, 17), (10, 18), (31, 29), (28, 9), (5, 35), (37, 32), (19, 34), (26, 4), (30, 35), (29, 10), (34, 45), (18, 24), (33, 10), (27, 21), (12, 15), (25, 20), (12, 28), (32, 29), (10, 2), (14, 26), (32, 28), (16, 34), (3, 18), (0, 38), (10, 11), (30, 20), (6, 28), (13, 40), (33, 14), (3, 0), (2, 20), (25, 29), (30, 4), (17, 12), (1, 24), (10, 43), (37, 8), (30, 40), (12, 30), (19, 31), (29, 42), (33, 2), (10, 36), (12, 5), (37, 19), (9, 16), (7, 5), (4, 29), (17, 45), (3, 14), (21, 5), (39, 22), (40, 4), (8, 3), (16, 21), (24, 19), (40, 1), (4, 22), (17, 28), (39, 31), (7, 41), (32, 32), (33, 3), (39, 30), (40, 19), (4, 36), (26, 5), (25, 5), (16, 15), (35, 10), (13, 45), (10, 26), (40, 16), (7, 30), (33, 39), (26, 39), (33, 34), (1, 8), (30, 18), (16, 44), (23, 4), (10, 27), (29, 1), (0, 5), (24, 44), (7, 39), (5, 16), (15, 21), (21, 16), (5, 13), (7, 14), (15, 5), (3, 22), (38, 41), (24, 43), (15, 6), (20, 19), (9, 18), (21, 4), (18, 9), (9, 5), (38, 38), (7, 24), (40, 5), (24, 39), (7, 4), (37, 42), (33, 31), (7, 13), (29, 17), (27, 27), (11, 40), (17, 5), (33, 17), (28, 22), (25, 41), (16, 38), (1, 41), (30, 6), (11, 26), (29, 30), (11, 11), (20, 16), (13, 9), (38, 30), (37, 45), (23, 10), (17, 7), (0, 41), (36, 35), (14, 38), (5, 19), (12, 40), (0, 2), (6, 36), (23, 8), (17, 14), (10, 39), (12, 14), (38, 40), (27, 4), (2, 44), (8, 12), (7, 31), (31, 24), (0, 21), (35, 32), (11, 3), (4, 41), (6, 20), (3, 8), (5, 32), (14, 18), (23, 43), (14, 4), (34, 37), (33, 44), (11, 13), (14, 40), (27, 22), (12, 27), (40, 39), (32, 34), (1, 28), (30, 31), (11, 35), (33, 19), (31, 34), (19, 29), (16, 9), (10, 24), (3, 27), (29, 9), (13, 7), (3, 42), (33, 1), (36, 15), (30, 26), (40, 40), (14, 3), (39, 11), (4, 19), (34, 33), (33, 25), (0, 20), (30, 37), (21, 14), (31, 25), (12, 12), (36, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 9), (4, 9), (3, 13), (7, 28), (7, 22), (3, 7), (28, 10), (15, 4), (31, 20), (12, 3), (13, 18), (19, 23), (6, 32), (10, 37), (30, 26), (9, 9), (16, 36), (4, 10), (18, 24), (1, 22), (1, 6), (20, 39), (40, 25), (8, 40), (11, 14), (31, 23), (4, 13), (0, 38), (37, 14), (28, 9), (12, 37), (38, 20), (20, 35), (33, 7), (11, 6), (25, 37), (11, 42), (39, 7), (36, 31), (2, 29), (41, 0), (19, 13), (31, 34), (7, 41), (19, 16), (17, 22), (27, 5), (31, 25), (23, 16), (15, 12), (34, 5), (17, 21), (13, 38), (3, 5), (25, 9), (27, 0), (23, 19), (39, 33), (13, 1), (9, 13), (8, 30), (40, 20), (25, 32), (0, 22), (8, 7), (33, 34), (10, 30), (17, 13), (20, 27), (40, 42), (5, 41), (26, 34), (23, 7), (10, 12), (15, 19), (22, 40), (29, 31), (34, 11), (34, 10), (13, 4), (27, 14), (26, 6), (17, 39), (39, 29), (32, 30), (25, 13), (26, 3), (40, 10), (40, 13), (17, 0), (23, 23), (22, 21), (27, 10), (30, 16), (31, 6), (29, 37), (19, 21), (8, 32), (12, 1), (32, 24), (8, 34), (5, 7), (42, 7), (15, 41), (30, 9), (19, 3), (38, 31), (30, 38), (4, 34), (4, 37), (17, 16), (11, 27), (21, 5), (3, 1), (35, 29), (38, 7), (23, 38), (41, 24), (40, 36), (13, 39), (3, 2), (4, 38), (10, 18), (37, 0), (3, 10), (7, 27), (2, 19), (30, 22), (16, 26), (9, 38), (40, 31), (9, 4), (43, 41), (5, 28), (18, 3), (17, 19), (5, 6), (16, 40), (16, 16), (17, 3), (26, 39), (12, 41), (5, 34), (28, 13), (19, 2), (20, 16), (30, 33), (21, 14), (28, 7), (34, 0), (2, 4), (6, 29), (32, 4), (17, 32), (13, 10), (35, 14), (43, 35), (12, 4), (43, 9), (0, 39), (22, 16), (42, 35), (43, 10), (43, 23), (13, 36), (19, 7), (23, 18), (9, 19), (29, 0), (19, 40), (34, 20), (26, 20), (19, 14), (17, 2), (3, 15), (7, 10), (2, 30), (37, 11), (33, 32), (1, 40), (33, 33), (26, 30), (31, 35), (31, 2), (6, 40), (41, 33), (12, 5), (13, 12), (38, 33), (17, 31), (6, 34), (17, 38), (10, 3), (29, 10), (43, 39), (23, 6), (32, 12), (42, 21), (34, 32), (8, 8), (2, 5), (22, 41), (25, 0), (38, 19), (6, 27), (18, 29), (13, 35), (7, 30), (23, 27), (15, 18), (36, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 15), (10, 42), (4, 17), (37, 24), (4, 24), (14, 29), (15, 14), (24, 21), (8, 25), (14, 21), (23, 16), (34, 16), (1, 5), (36, 26), (16, 29), (28, 7), (8, 35), (33, 19), (31, 31), (26, 7), (13, 37), (29, 17), (24, 1), (11, 30), (14, 24), (24, 27), (34, 18), (20, 23), (16, 9), (14, 40), (39, 10), (14, 32), (42, 40), (40, 36), (29, 37), (34, 29), (15, 12), (40, 39), (11, 46), (7, 23), (9, 23), (2, 46), (7, 9), (2, 19), (3, 3), (18, 44), (33, 31), (11, 6), (32, 29), (38, 21), (3, 41), (19, 26), (3, 44), (1, 7), (21, 43), (25, 21), (40, 10), (5, 22), (7, 6), (9, 3), (31, 37), (25, 26), (35, 3), (36, 43), (30, 6), (45, 17), (20, 44), (29, 4), (46, 15), (3, 18), (30, 9), (46, 3), (26, 22), (27, 3), (8, 18), (0, 35), (46, 36), (17, 15), (22, 34), (6, 33), (2, 22), (7, 37), (40, 34), (8, 43), (12, 42), (6, 24), (7, 43), (4, 16), (4, 25), (30, 16), (7, 26), (9, 36), (8, 42), (23, 13), (6, 28), (38, 12), (21, 8), (6, 22), (15, 32), (1, 32), (10, 0), (21, 13), (0, 13), (8, 9), (25, 16), (11, 1), (25, 31), (16, 31), (2, 31), (21, 3), (32, 34), (41, 16), (15, 35), (24, 5), (8, 10), (23, 33), (26, 6), (0, 37), (22, 41), (33, 17), (42, 28), (3, 12), (39, 3), (23, 0), (6, 17), (7, 30), (32, 15), (31, 46), (3, 38), (46, 1), (45, 23), (22, 24), (19, 25), (14, 30), (5, 4), (12, 14), (44, 46), (15, 0), (14, 31), (39, 28), (4, 7), (33, 27), (36, 15), (7, 0), (1, 2), (28, 32), (19, 36), (29, 45), (45, 43), (37, 0), (3, 30), (9, 45), (19, 38), (30, 28), (25, 10), (6, 23), (28, 26), (23, 6), (28, 31), (34, 41), (25, 0), (40, 20), (46, 5), (28, 44), (9, 12), (13, 22), (10, 30), (31, 15), (5, 34), (27, 15), (43, 32), (3, 22), (2, 16), (31, 7), (37, 36), (24, 2), (6, 41), (16, 38), (5, 8), (18, 25), (13, 7), (16, 36), (14, 19), (44, 24), (36, 39), (4, 11), (9, 46), (11, 37), (5, 9), (15, 17), (36, 0), (41, 37), (37, 15), (36, 46), (5, 21), (38, 31), (42, 26), (16, 0), (27, 25), (39, 27), (14, 39), (26, 39), (1, 46), (15, 11), (12, 3), (7, 41), (12, 33), (4, 46), (25, 5), (42, 38), (13, 3), (45, 5), (41, 6), (24, 29), (26, 46), (3, 25), (28, 24), (5, 16), (38, 38), (11, 16), (34, 19), (25, 3), (1, 1), (23, 8), (5, 2), (7, 25), (30, 21), (20, 22), (21, 15), (22, 39), (21, 44), (16, 4), (41, 2), (38, 35), (26, 25), (20, 8), (39, 23), (40, 0), (9, 1), (29, 40), (30, 46), (35, 30), (24, 18), (2, 41), (33, 8), (21, 31), (17, 28), (5, 30), (7, 28), (43, 2), (14, 20), (7, 18), (22, 12), (35, 23), (33, 2), (2, 24), (20, 45), (24, 14), (41, 44), (40, 3), (17, 0), (31, 20), (5, 39), (41, 46), (2, 25), (9, 39), (25, 44), (0, 27), (33, 12), (41, 28), (44, 17), (40, 9), (14, 42), (44, 33), (1, 0), (15, 20), (28, 17), (34, 11), (32, 12), (7, 15), (18, 41), (20, 11), (27, 40), (22, 27), (36, 42), (18, 29), (23, 36), (35, 34), (12, 41), (27, 18), (2, 23), (32, 2), (43, 5), (42, 13), (15, 40), (23, 30), (21, 20), (1, 10), (40, 7), (2, 21), (5, 42), (15, 45), (20, 7), (46, 41), (36, 23), (44, 35), (6, 7), (43, 25), (41, 31), (46, 7), (2, 1), (12, 45), (31, 33), (0, 7), (23, 41), (2, 33), (33, 15), (26, 20), (1, 18), (43, 35), (29, 26), (30, 25), (35, 8), (40, 26), (44, 44), (38, 25), (35, 10), (30, 22), (33, 39), (19, 24), (25, 1), (32, 39), (20, 46), (15, 6), (13, 8), (4, 37), (37, 17), (45, 40), (15, 23), (43, 36), (26, 12), (17, 4), (12, 12), (33, 33), (45, 26), (0, 25), (35, 13), (33, 30), (39, 22), (46, 44), (12, 46), (42, 21), (18, 2), (13, 45), (40, 5), (35, 20), (8, 45), (9, 14), (39, 26), (36, 35), (22, 31), (38, 44), (45, 6), (18, 42), (27, 33), (41, 17), (6, 38), (18, 3), (28, 30), (29, 39), (22, 2), (19, 18), (1, 11), (5, 5), (2, 12), (4, 1), (42, 25), (45, 29), (22, 45), (43, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 27), (25, 37), (9, 17), (4, 23), (35, 17), (43, 31), (2, 14), (10, 29), (40, 29), (0, 26), (29, 6), (1, 13), (9, 24), (9, 29), (16, 41), (15, 20), (31, 3), (16, 38), (22, 0), (16, 28), (26, 38), (40, 10), (25, 3), (3, 2), (1, 3), (20, 2), (24, 32), (12, 24), (8, 40), (41, 18), (34, 31), (0, 15), (7, 34), (40, 38), (31, 39), (38, 11), (3, 12), (10, 18), (6, 9), (13, 13), (39, 5), (11, 16), (10, 28), (37, 13), (12, 30), (11, 2), (7, 1), (14, 5), (39, 30), (35, 11), (30, 6), (15, 12), (29, 34), (34, 5), (12, 18), (12, 25), (20, 4), (9, 19), (33, 44), (19, 38), (24, 13), (20, 13), (34, 36), (18, 33), (17, 31), (21, 23), (12, 9), (28, 30), (39, 26), (0, 38), (2, 20), (13, 34), (33, 16), (4, 9), (31, 19), (14, 11), (4, 16), (0, 1), (17, 39), (36, 11), (34, 1), (27, 37), (18, 44), (6, 32), (30, 20), (34, 9), (8, 26), (17, 3), (4, 17), (38, 20), (37, 34), (4, 18), (36, 32), (0, 6), (39, 34), (13, 0), (21, 0), (1, 5), (9, 41), (42, 6), (34, 4), (15, 37), (12, 2), (11, 13), (8, 10), (32, 0), (43, 3), (2, 36), (41, 3), (19, 16), (3, 27), (21, 13), (11, 30), (31, 4), (26, 10), (20, 19), (42, 35), (37, 15), (38, 6), (15, 44), (30, 24), (16, 31), (3, 1), (29, 0), (6, 2), (43, 22), (14, 32), (37, 27), (16, 18), (0, 43), (25, 40), (23, 7), (4, 43), (7, 13), (5, 11), (41, 8), (28, 34), (34, 3), (41, 31), (11, 5), (19, 17), (34, 6), (35, 12), (5, 12), (36, 10), (5, 38), (26, 2), (6, 22), (30, 19), (35, 43), (21, 5), (3, 28), (6, 15), (17, 12), (28, 21), (12, 27), (22, 12), (5, 18), (31, 7), (17, 7), (24, 6), (38, 22), (16, 3), (12, 15), (16, 6), (31, 22), (22, 21), (23, 19), (20, 8), (20, 21), (17, 35), (26, 20), (23, 40), (28, 42), (8, 17), (18, 9), (7, 12), (27, 11), (39, 38), (24, 4), (33, 34), (42, 27), (37, 20), (1, 42), (9, 44), (26, 35), (20, 40), (25, 23), (41, 33), (43, 15), (18, 23), (30, 9), (38, 14), (41, 38), (17, 26), (28, 13), (17, 44), (14, 20), (39, 25), (34, 26), (17, 6), (10, 6), (27, 32), (41, 7), (6, 11), (8, 14), (43, 11), (7, 17), (27, 8), (29, 23), (39, 32), (20, 26), (24, 38), (2, 25), (37, 9), (14, 12), (25, 7), (31, 28), (42, 29), (42, 1), (40, 22), (35, 21), (16, 32), (30, 36), (5, 41), (1, 19), (19, 32), (8, 24), (39, 27), (14, 13), (31, 0), (28, 20), (41, 42), (9, 27), (26, 27), (8, 0), (20, 6), (19, 39), (13, 3), (14, 8), (37, 28), (15, 36), (16, 43), (36, 15), (41, 4), (39, 43), (1, 2), (13, 37), (36, 16), (22, 34), (13, 27), (34, 27), (19, 14), (43, 34), (6, 3), (41, 27), (42, 16), (19, 25), (19, 29), (30, 39), (5, 34), (23, 16), (29, 8), (20, 30), (17, 34), (0, 32), (43, 27), (33, 38), (37, 10), (17, 28), (35, 39), (38, 7), (20, 0), (43, 30), (4, 36), (37, 42), (35, 28), (23, 20), (0, 3), (27, 26), (2, 34), (1, 16), (24, 26), (31, 29), (33, 22), (3, 17), (17, 13), (31, 32), (13, 30), (43, 33), (5, 40), (40, 9), (29, 32), (32, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 7), (36, 23), (28, 37), (24, 7), (27, 0), (8, 32), (32, 16), (40, 18), (40, 39), (35, 25), (31, 33), (37, 2), (12, 8), (33, 30), (24, 37), (3, 1), (4, 16), (8, 20), (33, 21), (7, 6), (16, 4), (30, 4), (0, 30), (29, 21), (35, 32), (40, 30), (36, 16), (30, 33), (31, 28), (19, 16), (38, 14), (36, 15), (33, 26), (38, 18), (23, 6), (7, 28), (1, 33), (10, 27), (20, 33), (26, 28), (25, 2), (18, 5), (33, 23), (7, 32), (9, 9), (9, 23), (35, 26), (30, 10), (5, 15), (28, 40), (2, 3), (9, 12), (31, 30), (4, 2), (33, 11), (18, 11), (29, 8), (35, 5), (12, 29), (17, 19), (13, 6), (9, 26), (3, 13), (8, 40), (22, 2), (7, 12), (23, 38), (40, 34), (4, 20), (40, 23), (11, 31), (17, 0), (23, 22), (32, 7), (25, 15), (15, 10), (17, 12), (15, 16), (22, 20), (35, 42), (24, 0), (4, 36), (15, 34), (24, 11), (40, 0), (8, 18), (15, 7), (13, 23), (26, 10), (21, 33), (20, 26), (1, 31), (22, 13), (38, 6), (38, 5), (24, 33), (28, 26), (13, 18), (4, 42), (13, 21), (25, 26), (5, 17), (31, 22), (0, 25), (12, 1), (0, 20), (32, 14), (11, 26), (36, 20), (29, 0), (28, 20), (0, 16), (3, 27), (40, 12), (22, 16), (25, 21), (40, 31), (34, 25), (20, 22), (12, 25), (20, 17), (4, 35), (17, 1), (11, 11), (1, 27), (9, 14), (8, 5), (7, 11), (18, 32), (12, 12), (16, 32), (23, 41), (34, 31), (35, 20), (10, 40), (18, 3), (38, 19), (39, 7), (27, 6), (8, 22), (34, 8), (1, 20), (14, 24), (14, 39), (1, 4), (16, 38), (25, 10), (17, 22), (21, 5), (31, 10), (13, 28), (37, 18), (4, 28), (26, 7), (13, 39), (1, 23), (4, 1), (27, 25), (22, 27), (15, 6), (28, 38), (33, 39), (11, 19), (34, 7), (28, 18), (10, 11), (18, 39), (9, 41), (38, 37), (2, 26), (39, 10), (15, 14), (32, 1), (37, 24), (14, 8), (22, 24), (15, 29), (38, 11), (33, 17), (25, 39), (1, 11), (27, 28), (16, 20), (40, 17), (18, 15), (33, 35), (3, 18), (19, 8), (0, 14), (16, 30), (18, 31), (24, 13), (15, 12), (28, 0), (36, 27), (34, 3), (6, 8), (24, 14), (3, 31), (6, 29), (28, 41), (8, 26), (40, 6), (34, 24), (25, 35), (15, 30), (8, 0), (39, 2), (4, 29), (13, 35), (16, 13), (9, 32), (6, 2), (16, 14), (38, 2), (35, 17), (1, 9), (7, 39), (15, 19), (38, 28), (25, 37), (23, 12), (34, 39), (35, 39), (24, 23), (29, 23), (28, 33), (13, 37), (21, 2), (18, 28), (8, 2), (12, 4), (2, 23), (17, 34), (37, 17), (14, 38), (7, 18), (39, 9), (9, 42), (10, 22), (3, 14), (26, 4), (14, 0), (20, 4), (35, 13), (4, 26), (20, 35), (21, 20), (7, 35), (14, 13), (36, 2), (30, 16), (10, 14), (2, 27), (21, 11), (17, 15), (5, 0), (6, 13), (33, 33), (3, 34), (1, 40), (29, 27), (0, 39), (11, 16), (37, 34), (25, 27), (17, 18), (5, 35), (10, 31), (5, 33), (38, 42), (27, 3), (37, 19), (11, 42), (27, 39), (32, 30), (36, 30), (39, 21), (8, 8), (37, 35), (24, 30), (40, 41), (5, 1), (6, 19), (39, 23), (19, 36), (38, 12), (9, 13), (22, 31), (18, 26), (36, 29), (29, 37), (38, 25), (26, 27), (20, 12), (0, 13), (4, 23), (12, 5), (26, 3), (35, 37), (3, 37), (22, 8), (32, 42), (16, 39), (24, 25), (21, 24), (26, 15), (37, 27), (33, 10), (37, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 10), (13, 44), (2, 32), (2, 13), (29, 32), (34, 4), (2, 37), (23, 25), (16, 24), (8, 41), (9, 13), (34, 46), (14, 34), (7, 29), (33, 33), (37, 6), (30, 8), (18, 23), (21, 24), (38, 33), (5, 27), (1, 8), (6, 39), (14, 6), (10, 38), (31, 9), (20, 32), (27, 44), (20, 17), (8, 22), (30, 5), (0, 25), (2, 46), (3, 5), (19, 16), (20, 8), (25, 43), (10, 37), (24, 24), (13, 46), (24, 25), (4, 23), (31, 33), (3, 29), (8, 8), (36, 17), (32, 28), (33, 17), (26, 11), (5, 21), (31, 44), (27, 3), (4, 42), (4, 15), (31, 30), (3, 20), (38, 30), (37, 21), (27, 20), (36, 38), (28, 14), (31, 1), (20, 5), (29, 0), (32, 8), (28, 1), (21, 36), (26, 18), (12, 1), (34, 2), (18, 16), (38, 2), (32, 7), (17, 10), (6, 33), (27, 28), (15, 42), (24, 28), (26, 17), (18, 6), (13, 7), (37, 8), (0, 38), (17, 45), (37, 25), (38, 19), (20, 34), (10, 0), (35, 31), (38, 40), (38, 23), (39, 37), (28, 22), (36, 7), (28, 37), (27, 33), (31, 37), (0, 18), (16, 8), (27, 34), (5, 15), (16, 15), (38, 11), (12, 39), (19, 11), (12, 33), (2, 12), (32, 21), (13, 32), (10, 10), (25, 32), (39, 33), (3, 14), (0, 27), (4, 9), (21, 19), (21, 6), (39, 8), (5, 46), (25, 7), (26, 37), (36, 28), (19, 3), (16, 6), (19, 1), (17, 39), (5, 6), (11, 31), (34, 17), (26, 36), (8, 2), (19, 2), (1, 19), (13, 9), (39, 3), (15, 20), (30, 18), (9, 10), (24, 12), (27, 8), (32, 12), (31, 12), (11, 44), (18, 26), (15, 36), (26, 10), (10, 26), (5, 28), (1, 27), (23, 29), (35, 43), (0, 45), (37, 9), (39, 20), (37, 45), (31, 40), (16, 20), (29, 13), (18, 7), (7, 10), (13, 16), (13, 25), (21, 22), (35, 5), (38, 39), (3, 8), (38, 24), (1, 36), (12, 22), (30, 21), (22, 36), (20, 39), (9, 34), (2, 33), (14, 8), (37, 35), (3, 46), (14, 39), (0, 10), (28, 18), (34, 21), (22, 43), (23, 15), (39, 28), (27, 17), (23, 17), (7, 13), (17, 21), (36, 37), (1, 30), (0, 9), (31, 4), (32, 3), (35, 6), (39, 0), (37, 27), (1, 43), (14, 32), (8, 36), (9, 25), (38, 27), (33, 43), (11, 38), (22, 26), (11, 2), (9, 7), (32, 18), (25, 44), (22, 41), (24, 41), (19, 23), (2, 6), (34, 27), (34, 12), (34, 38), (16, 10), (12, 40), (32, 24), (26, 16), (15, 35), (6, 0), (1, 3), (28, 9), (29, 8), (17, 12), (18, 33), (25, 13), (0, 37), (37, 2), (38, 13), (2, 31), (10, 3), (34, 44), (8, 19), (29, 9), (9, 4), (29, 21), (32, 42), (17, 8), (36, 39), (5, 24), (26, 45), (29, 19), (9, 44), (3, 2), (19, 28), (29, 12), (32, 30), (8, 6), (34, 26), (37, 10), (34, 14), (26, 25), (31, 23), (30, 19), (17, 2), (36, 46), (31, 35), (3, 0), (6, 45), (26, 4), (31, 6), (16, 31), (4, 22), (3, 18), (31, 19), (26, 5), (21, 25), (0, 41), (19, 26), (14, 2), (19, 14), (39, 29), (39, 11), (32, 0), (6, 9), (12, 18), (38, 46), (4, 6), (34, 3), (24, 15), (12, 5), (28, 11), (4, 7), (13, 40), (22, 40), (4, 35), (27, 18), (24, 43), (26, 40), (16, 16), (15, 46), (24, 45), (5, 42), (1, 14), (32, 11), (21, 9), (5, 39), (12, 28), (11, 17), (19, 24), (33, 5), (16, 21), (30, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 9), (11, 14), (15, 38), (9, 27), (24, 5), (14, 5), (7, 17), (7, 22), (25, 43), (29, 35), (16, 13), (39, 6), (30, 40), (16, 35), (16, 21), (37, 33), (39, 26), (15, 42), (22, 20), (19, 14), (35, 43), (7, 25), (32, 37), (24, 23), (2, 17), (8, 22), (24, 41), (31, 42), (31, 28), (35, 31), (35, 26), (22, 5), (26, 6), (33, 44), (27, 4), (13, 15), (1, 24), (25, 5), (37, 39), (17, 20), (21, 9), (26, 36), (16, 3), (32, 34), (2, 8), (22, 9), (3, 39), (26, 39), (22, 34), (17, 18), (15, 32), (8, 39), (5, 19), (32, 31), (19, 31), (30, 31), (12, 38), (21, 10), (0, 4), (32, 11), (10, 40), (16, 10), (25, 10), (11, 39), (10, 39), (38, 19), (34, 14), (37, 37), (18, 22), (33, 0), (22, 24), (5, 0), (15, 13), (14, 1), (9, 1), (5, 39), (14, 20), (24, 3), (38, 38), (10, 15), (33, 40), (9, 44), (2, 33), (39, 24), (21, 14), (39, 42), (38, 25), (39, 12), (36, 19), (14, 17), (34, 4), (4, 30), (1, 4), (2, 18), (11, 23), (9, 41), (22, 13), (25, 6), (29, 44), (31, 38), (32, 41), (30, 3), (8, 42), (31, 0), (33, 33), (36, 27), (4, 33), (26, 34), (6, 20), (23, 20), (30, 29), (4, 15), (0, 29), (33, 3), (34, 10), (6, 7), (31, 9), (18, 36), (22, 17), (5, 11), (36, 4), (6, 3), (3, 17), (0, 31), (1, 0), (32, 6), (13, 13), (31, 33), (19, 29), (0, 30), (5, 43), (2, 25), (37, 0), (16, 26), (14, 36), (23, 28), (33, 13), (21, 17), (22, 0), (25, 21), (28, 22), (5, 10), (39, 35), (29, 11), (27, 28), (37, 43), (36, 15), (38, 3), (27, 43), (5, 13), (33, 2), (6, 11), (39, 40), (32, 35), (13, 10), (27, 22), (20, 17), (36, 34), (14, 0), (26, 27), (22, 35), (28, 31), (29, 24), (14, 31), (15, 40), (27, 40), (4, 16), (12, 26), (7, 19), (17, 35), (22, 16), (35, 20), (36, 43), (30, 33), (3, 5), (14, 12), (25, 39), (6, 21), (4, 10), (23, 39), (34, 37), (8, 8), (35, 34), (7, 0), (17, 17), (16, 32), (1, 40), (10, 43), (35, 9), (36, 7), (15, 39), (10, 25), (27, 34), (12, 32), (18, 11), (25, 28), (9, 32), (37, 15), (27, 5), (17, 37), (13, 16), (37, 7), (37, 6), (32, 38), (26, 8), (37, 2), (16, 37), (2, 28), (28, 14), (0, 39), (21, 32), (1, 39), (19, 36), (14, 3), (19, 44), (16, 44), (21, 34), (29, 26), (16, 14), (39, 30), (0, 18), (37, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 18), (33, 45), (39, 43), (43, 27), (27, 36), (25, 13), (39, 47), (22, 35), (3, 48), (39, 42), (27, 39), (11, 25), (7, 9), (5, 2), (18, 46), (31, 46), (37, 19), (19, 5), (38, 37), (8, 38), (19, 23), (23, 31), (23, 45), (8, 0), (43, 42), (40, 36), (25, 18), (43, 34), (18, 23), (26, 42), (28, 41), (29, 7), (13, 24), (28, 2), (7, 45), (43, 35), (14, 6), (4, 19), (7, 47), (13, 16), (33, 22), (34, 31), (41, 19), (26, 41), (43, 30), (15, 0), (16, 32), (33, 8), (18, 11), (42, 36), (26, 48), (16, 38), (30, 32), (34, 32), (41, 12), (14, 28), (12, 3), (1, 21), (38, 1), (41, 21), (43, 8), (0, 28), (34, 42), (26, 23), (33, 32), (43, 31), (29, 21), (8, 44), (27, 2), (36, 33), (1, 0), (32, 10), (13, 38), (11, 8), (37, 11), (16, 26), (20, 43), (29, 12), (43, 29), (15, 23), (12, 28), (24, 27), (24, 45), (0, 40), (18, 19), (10, 2), (31, 22), (9, 38), (12, 39), (32, 36), (7, 8), (9, 19), (13, 0), (31, 2), (31, 31), (41, 26), (37, 24), (35, 36), (38, 38), (22, 33), (27, 17), (38, 30), (6, 10), (10, 42), (38, 5), (2, 9), (26, 11), (35, 35), (21, 13), (23, 20), (40, 0), (2, 26), (34, 35), (43, 13), (39, 22), (27, 22), (34, 29), (24, 26), (8, 13), (5, 34), (40, 43), (40, 29), (8, 24), (35, 37), (24, 24), (1, 23), (3, 6), (4, 18), (10, 3), (10, 37), (42, 5), (21, 27), (19, 16), (24, 18), (13, 28), (2, 3), (7, 25), (18, 36), (30, 2), (12, 44), (38, 6), (9, 11), (25, 4), (40, 10), (18, 16), (31, 7), (8, 32), (23, 16), (17, 20), (34, 40), (1, 30), (38, 15), (30, 27), (42, 14), (43, 7), (28, 18), (23, 2), (15, 45), (13, 46), (36, 31), (21, 45), (19, 42), (19, 31), (32, 28), (41, 44), (40, 8), (1, 6), (41, 31), (4, 33), (15, 9), (34, 44), (13, 15), (29, 37), (20, 42), (34, 46), (40, 23), (17, 42), (17, 16), (16, 1), (30, 48), (0, 31), (11, 23), (31, 23), (10, 34), (15, 22), (14, 39), (22, 37), (30, 10), (3, 42), (27, 30), (0, 39), (27, 1), (9, 26), (11, 15), (39, 44), (4, 9), (4, 10), (20, 23), (17, 7), (17, 3), (24, 15), (15, 17), (1, 5), (39, 29), (32, 46), (0, 18), (6, 38), (25, 23), (33, 16), (30, 4), (6, 8), (3, 39), (16, 16), (3, 24), (28, 31), (19, 48), (21, 5), (41, 22), (23, 44), (24, 6), (32, 9), (18, 7), (2, 22), (42, 25), (43, 45), (32, 35), (23, 36), (4, 5), (37, 38), (43, 15), (21, 14), (19, 1), (37, 36), (40, 7), (15, 46), (12, 6), (37, 41), (7, 43), (42, 38), (15, 27), (16, 4), (35, 34), (22, 40), (26, 16), (18, 38), (41, 1), (30, 22), (6, 48), (30, 8), (37, 18), (23, 23), (34, 22), (21, 48), (34, 48), (9, 43), (32, 4), (8, 41), (10, 23), (31, 43), (7, 19), (35, 21), (9, 10), (40, 4), (4, 17), (28, 9), (26, 21), (0, 8), (20, 16), (37, 2), (23, 41), (2, 2), (9, 14), (32, 29), (6, 20), (6, 41), (34, 30), (7, 31), (24, 47), (36, 6), (15, 32), (35, 26), (25, 8), (18, 45), (36, 11), (14, 40), (22, 19), (42, 9), (33, 1), (7, 39), (11, 40), (9, 9), (36, 14), (28, 45), (4, 27), (34, 5), (11, 42), (33, 30), (2, 43), (2, 25), (23, 1), (21, 37), (8, 19), (25, 3), (12, 19), (26, 7), (26, 45), (19, 15), (31, 33), (30, 7), (21, 30), (5, 5), (18, 42), (22, 11), (1, 13), (29, 39), (2, 17), (26, 36), (42, 28), (23, 38), (10, 9), (0, 29), (12, 47), (37, 31), (9, 32), (12, 20), (35, 0), (28, 21), (13, 47), (26, 12), (29, 20), (32, 42), (19, 25), (11, 18), (5, 45), (14, 37), (5, 33), (20, 4), (26, 10), (3, 47), (14, 0), (12, 5), (34, 11), (1, 40), (38, 40), (11, 9), (38, 36), (37, 39), (37, 42), (7, 15), (43, 47), (10, 6), (5, 46), (4, 25), (8, 40), (11, 22), (5, 1), (3, 22), (7, 0), (5, 6), (38, 45), (2, 12), (31, 17), (27, 14), (36, 18), (20, 24), (31, 30), (33, 27), (17, 33), (8, 2), (39, 34), (19, 8), (41, 10), (18, 3), (28, 6), (4, 20), (7, 26), (14, 26), (25, 27), (24, 11), (1, 38), (13, 40), (38, 4), (28, 0), (13, 4), (39, 2), (14, 29), (25, 14), (30, 36), (31, 40), (22, 23), (4, 7), (11, 6), (39, 13), (10, 40), (11, 34), (26, 31), (4, 2), (33, 20), (5, 14), (15, 15), (33, 34), (41, 41), (33, 2), (26, 32), (27, 40), (13, 10), (42, 21), (40, 11), (22, 3), (33, 24), (31, 19), (38, 21), (18, 40), (24, 7), (40, 14), (41, 11), (28, 29), (39, 19), (35, 44), (43, 40), (26, 20), (39, 6), (15, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (46, 25), (46, 13), (13, 28), (21, 9), (41, 3), (0, 22), (26, 24), (27, 13), (7, 18), (16, 0), (12, 13), (34, 31), (41, 13), (22, 33), (9, 23), (19, 9), (31, 22), (14, 6), (37, 9), (41, 24), (38, 3), (31, 10), (8, 19), (25, 34), (38, 15), (8, 23), (24, 20), (26, 45), (46, 33), (25, 6), (27, 30), (11, 21), (46, 35), (43, 46), (29, 28), (43, 25), (25, 16), (31, 12), (32, 46), (14, 2), (24, 13), (6, 28), (16, 7), (0, 26), (18, 29), (9, 13), (31, 46), (4, 27), (31, 31), (3, 44), (17, 15), (33, 15), (15, 40), (3, 13), (5, 10), (4, 4), (37, 3), (27, 12), (0, 44), (17, 24), (9, 1), (10, 0), (20, 45), (11, 0), (46, 44), (3, 5), (35, 20), (40, 36), (19, 26), (46, 40), (2, 14), (19, 6), (22, 43), (17, 4), (24, 39), (36, 35), (2, 26), (24, 28), (6, 10), (33, 32), (28, 29), (34, 14), (33, 16), (7, 46), (28, 10), (22, 3), (5, 16), (42, 30), (26, 16), (15, 39), (46, 8), (28, 31), (35, 6), (45, 14), (31, 43), (37, 45), (39, 6), (45, 28), (38, 12), (36, 6), (14, 34), (21, 24), (9, 11), (28, 14), (3, 26), (40, 8), (20, 42), (22, 5), (45, 17), (37, 27), (5, 18), (9, 33), (38, 30), (29, 15), (33, 9), (25, 27), (21, 0), (41, 47), (6, 37), (28, 28), (36, 21), (40, 43), (11, 1), (2, 37), (46, 4), (44, 37), (20, 18), (9, 19), (45, 12), (32, 3), (22, 27), (1, 27), (34, 28), (34, 29), (29, 31), (44, 15), (44, 10), (32, 47), (14, 5), (9, 29), (12, 17), (5, 21), (44, 33), (23, 42), (35, 5), (18, 26), (9, 36), (18, 16), (16, 14), (5, 45), (36, 39), (30, 11), (4, 41), (1, 37), (33, 25), (18, 15), (44, 25), (3, 9), (35, 27), (8, 37), (3, 4), (0, 11), (35, 8), (18, 41), (8, 45), (24, 35), (44, 29), (6, 8), (38, 1), (35, 44), (38, 2), (4, 19), (11, 35), (1, 39), (1, 22), (27, 8), (40, 2), (21, 15), (20, 21), (15, 22), (13, 45), (35, 39), (33, 8), (8, 4), (4, 12), (3, 11), (12, 1), (22, 46), (34, 4), (43, 39), (40, 34), (4, 6), (37, 4), (34, 35), (1, 25), (46, 42), (38, 31), (31, 19), (30, 4), (16, 42), (42, 4), (5, 40), (19, 7), (39, 33), (12, 4), (21, 8), (28, 12), (20, 19), (11, 18), (40, 13), (37, 15), (4, 7), (40, 26), (6, 39), (41, 35), (17, 21), (21, 35), (39, 19), (28, 15), (18, 19), (3, 40), (8, 11), (8, 12), (11, 19), (14, 23), (8, 32), (21, 29), (11, 22), (18, 44), (10, 17), (38, 6), (38, 41), (40, 17), (28, 19), (37, 40), (30, 7), (14, 11), (7, 40), (37, 35), (44, 12), (40, 39), (35, 34), (7, 24), (26, 4), (31, 8), (44, 41), (35, 42), (10, 3), (5, 39), (37, 14), (32, 36), (17, 19), (28, 30), (0, 14), (38, 10), (4, 3), (20, 36), (8, 34), (22, 0), (34, 26), (39, 10), (30, 36), (21, 39), (31, 28), (35, 33), (29, 47), (37, 26), (16, 47), (46, 30), (10, 14), (42, 45), (37, 1), (34, 21), (26, 23), (39, 7), (1, 31), (33, 37), (14, 35), (0, 15), (23, 28), (14, 17), (15, 44), (33, 20), (8, 31), (14, 42), (7, 10), (18, 13), (12, 36), (2, 25), (26, 36), (21, 45), (16, 28), (15, 32), (7, 3), (39, 43), (18, 2), (9, 42), (10, 34), (11, 44), (27, 14), (43, 6), (41, 27), (5, 17), (14, 31), (12, 18), (3, 37), (17, 37), (43, 34), (33, 26), (22, 16), (46, 3), (37, 38), (41, 4), (31, 21), (39, 36), (27, 0), (42, 22), (20, 31), (35, 1), (21, 4), (0, 28), (15, 8), (39, 16), (33, 39), (22, 12), (29, 40), (33, 47), (13, 27), (23, 7), (5, 44), (33, 42), (7, 35), (24, 32), (33, 41), (32, 6), (28, 45), (8, 8), (2, 27), (8, 0), (43, 3), (8, 3), (29, 14), (29, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 38), (11, 25), (36, 40), (13, 38), (35, 44), (7, 36), (23, 7), (13, 10), (19, 42), (24, 2), (27, 16), (21, 34), (37, 37), (6, 13), (0, 32), (38, 31), (29, 23), (21, 13), (23, 42), (33, 33), (33, 31), (4, 22), (1, 31), (32, 3), (34, 23), (9, 4), (15, 42), (19, 22), (25, 16), (35, 26), (35, 1), (15, 40), (4, 17), (16, 41), (36, 39), (8, 32), (26, 12), (3, 39), (14, 4), (3, 29), (16, 8), (24, 13), (14, 18), (30, 44), (11, 35), (23, 3), (39, 15), (2, 25), (36, 5), (41, 21), (37, 6), (39, 12), (39, 13), (36, 22), (21, 7), (33, 44), (16, 33), (1, 7), (2, 27), (37, 27), (25, 9), (33, 29), (32, 10), (13, 7), (40, 14), (36, 16), (37, 13), (7, 44), (38, 8), (10, 33), (34, 18), (12, 11), (14, 1), (26, 26), (16, 39), (10, 0), (22, 0), (31, 28), (14, 38), (11, 23), (11, 9), (4, 40), (26, 7), (29, 46), (38, 10), (15, 45), (4, 14), (37, 26), (9, 1), (32, 8), (3, 32), (24, 12), (33, 13), (18, 22), (24, 30), (4, 25), (35, 9), (34, 28), (41, 45), (25, 17), (29, 34), (33, 0), (32, 35), (30, 32), (23, 12), (36, 34), (36, 46), (16, 28), (38, 43), (26, 40), (20, 23), (35, 36), (39, 5), (6, 9), (18, 37), (28, 44), (26, 30), (32, 7), (30, 37), (37, 18), (9, 28), (9, 22), (27, 27), (34, 43), (0, 39), (19, 20), (4, 5), (29, 3), (18, 38), (37, 21), (22, 34), (23, 23), (27, 5), (15, 37), (17, 1), (17, 22), (16, 11), (27, 8), (34, 19), (12, 15), (9, 34), (24, 31), (13, 19), (15, 0), (39, 2), (17, 17), (22, 21), (37, 3), (34, 36), (3, 8), (23, 9), (3, 27), (5, 8), (10, 30), (15, 14), (16, 0), (30, 14), (23, 4), (41, 26), (3, 43), (28, 30), (25, 41), (34, 35), (23, 25), (1, 35), (13, 1), (27, 44), (15, 18), (8, 24), (13, 36), (3, 34), (19, 33), (40, 1), (9, 16), (17, 40), (36, 35), (1, 26), (34, 15), (24, 43), (11, 7), (14, 10), (15, 10), (9, 7), (36, 18), (13, 4), (38, 33), (40, 42), (6, 21), (25, 27), (15, 39), (24, 4), (27, 31), (32, 36), (35, 10), (31, 39), (28, 7), (35, 5), (26, 42), (7, 13), (5, 38), (5, 30), (2, 15), (6, 23), (7, 0), (31, 8), (37, 0), (32, 37), (41, 17), (37, 25), (35, 33), (40, 10), (3, 14), (2, 22), (1, 6), (7, 43), (32, 16), (32, 14), (0, 15), (3, 5), (12, 46), (35, 21), (36, 45), (32, 41), (12, 44), (20, 4), (21, 26), (13, 14), (11, 4), (40, 36), (41, 40), (11, 19), (20, 36), (0, 19), (27, 9), (3, 37), (1, 39), (10, 7), (16, 20), (25, 45), (13, 3), (7, 2), (28, 11), (5, 2), (11, 30), (29, 7), (4, 31), (40, 45), (1, 27), (22, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 38), (40, 6), (26, 35), (37, 10), (37, 31), (35, 3), (11, 15), (46, 15), (32, 7), (18, 36), (1, 8), (22, 7), (18, 37), (4, 36), (20, 42), (43, 1), (28, 1), (8, 15), (0, 15), (45, 14), (8, 27), (41, 40), (45, 27), (25, 0), (28, 21), (0, 26), (41, 33), (29, 13), (15, 31), (42, 23), (10, 25), (42, 33), (1, 33), (33, 18), (40, 8), (38, 14), (18, 27), (7, 30), (32, 39), (43, 28), (24, 10), (20, 29), (24, 5), (40, 41), (7, 23), (30, 20), (39, 27), (15, 0), (39, 28), (16, 22), (44, 16), (21, 24), (44, 29), (12, 27), (42, 12), (32, 0), (35, 15), (13, 36), (33, 17), (35, 0), (34, 13), (8, 22), (42, 1), (37, 16), (21, 38), (17, 33), (9, 12), (25, 20), (19, 37), (39, 26), (14, 30), (39, 1), (13, 14), (38, 15), (26, 15), (19, 18), (21, 42), (23, 34), (5, 34), (38, 1), (1, 26), (14, 23), (7, 7), (32, 20), (43, 21), (15, 5), (45, 26), (7, 36), (29, 16), (15, 9), (18, 35), (0, 36), (30, 16), (45, 38), (43, 16), (12, 13), (36, 37), (10, 32), (34, 32), (25, 36), (27, 7), (12, 16), (45, 32), (43, 30), (32, 16), (4, 9), (46, 17), (12, 26), (4, 4), (3, 29), (4, 2), (42, 35), (37, 34), (20, 12), (7, 16), (2, 12), (22, 0), (37, 3), (40, 9), (39, 19), (33, 4), (31, 19), (42, 13), (28, 35), (27, 17), (13, 9), (41, 39), (30, 17), (6, 31), (4, 34), (0, 17), (21, 30), (2, 40), (31, 29), (42, 25), (25, 33), (14, 6), (30, 14), (19, 8), (2, 36), (40, 2), (32, 17), (11, 38), (32, 34), (35, 6), (31, 15), (32, 5), (44, 11), (2, 14), (31, 40), (23, 19), (46, 27), (31, 26), (9, 41), (8, 39), (12, 15), (35, 40), (6, 17), (19, 12), (15, 38), (36, 4), (32, 11), (23, 9), (21, 39), (32, 27), (30, 42), (15, 28), (21, 23), (8, 36), (18, 33), (1, 1), (46, 41), (0, 21), (32, 4), (12, 4), (3, 40), (7, 29), (18, 16), (27, 24), (0, 10), (41, 8), (3, 33), (45, 8), (20, 34), (43, 5), (39, 34), (14, 2), (29, 42), (42, 18), (39, 32), (8, 21), (30, 8), (24, 30), (42, 10), (13, 32), (34, 42), (0, 34), (10, 35), (2, 4), (13, 23), (41, 24), (16, 25), (17, 11), (37, 23), (0, 11), (10, 26), (7, 14), (0, 7), (23, 5), (37, 27), (38, 32), (8, 32), (21, 5), (40, 21), (15, 4), (13, 39), (5, 10), (26, 8), (18, 3), (27, 1), (21, 15), (28, 20), (30, 36), (23, 14), (3, 3), (11, 13), (31, 17), (40, 22), (41, 25), (6, 27), (45, 39), (36, 41), (15, 17), (42, 28), (38, 36), (47, 40), (39, 9), (24, 7), (23, 35), (40, 1), (0, 2), (41, 26), (29, 37), (23, 8), (11, 30), (30, 25), (46, 39), (45, 11), (41, 14), (22, 17), (14, 20), (21, 28), (40, 40), (38, 8), (31, 0), (27, 22), (37, 8), (3, 21), (43, 14), (40, 23), (34, 38), (33, 11), (22, 25), (0, 4), (16, 18), (30, 1), (14, 32), (47, 25), (43, 38), (11, 33), (21, 3), (31, 27), (25, 29), (28, 15), (15, 12), (28, 37), (34, 33), (34, 11), (34, 20), (39, 35), (18, 25), (1, 30), (9, 26), (44, 4), (1, 25), (32, 36), (39, 30), (17, 25), (33, 1), (36, 38), (21, 29), (11, 39), (9, 38), (44, 40), (14, 34), (33, 7), (19, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 28), (24, 17), (34, 39), (26, 10), (40, 39), (12, 18), (1, 1), (34, 26), (36, 26), (38, 46), (18, 8), (38, 38), (35, 23), (3, 20), (15, 37), (18, 40), (13, 37), (7, 33), (15, 45), (27, 8), (36, 6), (1, 12), (7, 6), (20, 30), (23, 16), (25, 9), (20, 45), (19, 27), (37, 10), (1, 9), (35, 41), (38, 0), (43, 40), (30, 44), (3, 9), (7, 22), (22, 0), (37, 44), (25, 46), (19, 5), (19, 8), (7, 9), (38, 11), (31, 13), (15, 19), (23, 6), (31, 38), (7, 3), (29, 5), (24, 27), (31, 30), (3, 28), (21, 7), (26, 25), (17, 31), (30, 29), (20, 26), (3, 3), (40, 11), (2, 34), (32, 4), (24, 33), (19, 14), (41, 28), (2, 38), (29, 43), (2, 13), (40, 2), (0, 19), (31, 23), (4, 1), (3, 25), (2, 18), (26, 30), (34, 19), (9, 47), (31, 40), (16, 30), (10, 47), (13, 26), (34, 46), (21, 36), (28, 16), (37, 23), (20, 16), (7, 30), (5, 14), (15, 3), (42, 21), (40, 27), (21, 20), (24, 35), (35, 22), (5, 26), (6, 34), (0, 38), (19, 0), (0, 40), (43, 9), (14, 25), (5, 24), (21, 23), (30, 15), (32, 24), (24, 18), (24, 16), (14, 13), (34, 13), (27, 39), (10, 13), (44, 36), (7, 27), (9, 33), (28, 42), (29, 39), (11, 35), (34, 43), (34, 45), (22, 20), (28, 6), (35, 25), (22, 17), (8, 19), (34, 34), (43, 36), (40, 6), (14, 11), (0, 16), (20, 22), (16, 10), (19, 36), (1, 37), (12, 15), (5, 29), (17, 11), (13, 16), (21, 45), (34, 22), (33, 45), (11, 47), (44, 40), (2, 35), (16, 26), (10, 44), (16, 19), (39, 30), (3, 23), (29, 18), (32, 25), (27, 27), (40, 35), (44, 26), (35, 4), (11, 11), (21, 30), (2, 20), (0, 37), (6, 38), (22, 7), (7, 24), (32, 38), (30, 25), (1, 44), (42, 28), (33, 14), (15, 33), (12, 30), (1, 41), (30, 27), (34, 2), (32, 13), (32, 11), (29, 32), (39, 33), (0, 47), (41, 6), (17, 22), (30, 14), (38, 43), (33, 31), (42, 2), (29, 17), (8, 0), (8, 31), (41, 0), (35, 15), (27, 41), (37, 21), (19, 25), (4, 35), (1, 47), (9, 24), (26, 36), (16, 16), (21, 35), (37, 29), (8, 32), (0, 33), (2, 44), (27, 33), (2, 36), (2, 43), (12, 23), (13, 30), (43, 17), (16, 9), (14, 38), (28, 1), (7, 21), (24, 24), (44, 28), (15, 27), (37, 17), (33, 30), (8, 2), (16, 43), (36, 9), (8, 42), (14, 32), (39, 27), (33, 22), (42, 22), (16, 14), (23, 4), (0, 20), (29, 14), (35, 39), (3, 46), (40, 0), (19, 6), (33, 15), (21, 2), (6, 41), (16, 47), (1, 33), (5, 10), (30, 30), (28, 30), (44, 30), (35, 5), (42, 5), (32, 47), (0, 29), (16, 0), (38, 25), (11, 24), (34, 27), (20, 43), (42, 25), (25, 15), (22, 40), (15, 12), (10, 17), (35, 20), (43, 44), (3, 41), (13, 27), (6, 11), (2, 31), (37, 37), (34, 28), (1, 13), (0, 5), (43, 37), (31, 21), (8, 3), (35, 37), (32, 32), (26, 0), (2, 2), (6, 22), (6, 40), (28, 25), (22, 35), (11, 28), (3, 31), (35, 24), (23, 27), (9, 35), (31, 19), (19, 20), (10, 42), (23, 20), (14, 18), (25, 30), (6, 18), (35, 36), (2, 46), (19, 16), (34, 11), (25, 22), (18, 33), (1, 15), (20, 39), (23, 34), (41, 33), (10, 37), (23, 47), (26, 17), (27, 5), (18, 25), (25, 7), (25, 6), (21, 42), (6, 14), (23, 19), (21, 38), (5, 4), (22, 38), (26, 28), (3, 36), (37, 41), (35, 27), (21, 40), (25, 19), (25, 32), (41, 13), (26, 6), (10, 31), (30, 34), (4, 22), (35, 18), (43, 8), (21, 41), (16, 23), (1, 43), (4, 11), (15, 11), (35, 21), (16, 39), (6, 4), (31, 35), (7, 20), (2, 0), (36, 21), (36, 32), (8, 44), (9, 6), (36, 36), (36, 13), (16, 20), (0, 39), (40, 45), (22, 23), (17, 40), (11, 21), (6, 46), (8, 9), (31, 36), (39, 39), (18, 15), (31, 15), (14, 10), (20, 37), (12, 19), (5, 25), (41, 46), (28, 17), (21, 1), (25, 29), (5, 21), (38, 37), (44, 44), (21, 3), (10, 3), (0, 4), (18, 11), (31, 33), (3, 27), (1, 7), (34, 31), (32, 10), (40, 37), (26, 9), (32, 37), (43, 46), (40, 10), (5, 6), (6, 32), (11, 37), (11, 38), (22, 5), (38, 28), (22, 36), (32, 2), (37, 30), (6, 16), (25, 35), (35, 13), (20, 27), (27, 47), (5, 11), (26, 1), (35, 47), (16, 35), (29, 9), (34, 35), (25, 40), (22, 4), (28, 41), (8, 39), (10, 21), (32, 3), (3, 37), (19, 17), (12, 21), (34, 47), (4, 44), (9, 39), (25, 36), (28, 36), (9, 43), (17, 15), (11, 4), (43, 2), (37, 34), (3, 12), (39, 12), (40, 33), (12, 12), (7, 40), (2, 1), (19, 37), (16, 31), (15, 43), (14, 6), (28, 46), (9, 41), (23, 44), (36, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 21), (2, 19), (1, 14), (27, 41), (23, 35), (47, 38), (37, 15), (23, 3), (6, 9), (18, 25), (8, 7), (30, 29), (25, 42), (7, 16), (43, 19), (16, 1), (42, 3), (21, 17), (2, 16), (15, 24), (30, 30), (2, 14), (14, 35), (43, 44), (30, 39), (19, 25), (30, 42), (28, 23), (27, 1), (8, 0), (19, 29), (31, 18), (23, 23), (18, 2), (22, 40), (14, 36), (8, 17), (46, 45), (40, 43), (33, 12), (27, 44), (16, 20), (11, 6), (42, 29), (30, 44), (34, 35), (27, 8), (0, 39), (45, 5), (1, 41), (8, 40), (24, 1), (43, 0), (26, 34), (4, 16), (22, 11), (3, 41), (4, 37), (34, 44), (31, 22), (35, 24), (10, 44), (26, 46), (39, 20), (41, 34), (21, 32), (43, 30), (1, 23), (22, 39), (15, 20), (11, 23), (14, 42), (33, 40), (40, 23), (43, 8), (45, 46), (12, 33), (33, 38), (15, 8), (15, 18), (31, 34), (41, 9), (2, 35), (43, 36), (16, 38), (22, 25), (9, 5), (3, 44), (25, 43), (30, 7), (27, 6), (3, 13), (44, 18), (0, 38), (4, 31), (2, 30), (34, 30), (17, 2), (33, 4), (14, 9), (0, 6), (39, 46), (38, 29), (46, 20), (12, 14), (39, 2), (11, 35), (16, 36), (8, 12), (38, 10), (36, 2), (34, 37), (24, 19), (35, 46), (29, 44), (42, 30), (36, 43), (0, 24), (2, 23), (39, 38), (39, 5), (26, 42), (1, 28), (20, 1), (37, 21), (21, 22), (8, 41), (5, 2), (37, 41), (29, 18), (17, 26), (28, 18), (35, 6), (23, 44), (2, 33), (10, 22), (32, 3), (2, 25), (46, 18), (20, 10), (40, 19), (22, 14), (35, 5), (38, 23), (42, 36), (36, 5), (42, 5), (32, 5), (44, 17), (8, 23), (7, 40), (10, 7), (45, 21), (4, 30), (17, 44), (44, 39), (36, 34), (22, 4), (33, 37), (16, 41), (32, 25), (1, 42), (30, 32), (30, 19), (7, 32), (12, 8), (5, 4), (38, 33), (15, 14), (31, 35), (13, 36), (18, 24), (13, 32), (28, 16), (9, 10), (20, 2), (26, 29), (4, 45), (18, 28), (38, 21), (25, 7), (13, 29), (6, 8), (45, 23), (21, 43), (24, 32), (33, 10), (41, 27), (6, 28), (29, 2), (13, 14), (13, 23), (32, 38), (21, 30), (11, 43), (1, 17), (29, 22), (35, 9), (28, 44), (18, 17), (9, 28), (29, 26), (38, 6), (14, 6), (46, 13), (30, 3), (38, 44), (39, 21), (22, 27), (20, 34), (12, 21), (18, 7), (34, 24), (45, 44), (46, 21), (5, 40), (47, 33), (23, 22), (42, 14), (42, 46), (8, 45), (36, 42), (22, 45), (25, 33), (40, 27), (41, 32), (29, 7), (40, 8), (13, 19), (15, 13), (22, 5), (7, 21), (3, 10), (36, 40), (33, 7), (19, 2), (13, 35), (1, 21), (20, 25), (0, 8), (39, 33), (36, 17), (35, 4), (44, 24), (0, 2), (38, 1), (14, 18), (31, 36), (21, 1), (21, 21), (29, 19), (8, 1), (17, 34), (47, 2), (45, 24), (47, 10), (20, 29), (38, 4), (40, 38), (42, 17), (35, 22), (41, 24), (38, 16), (41, 14), (17, 8), (41, 45), (17, 37), (16, 18), (17, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 5), (42, 9), (21, 4), (10, 33), (16, 35), (22, 1), (15, 7), (21, 30), (27, 29), (17, 31), (17, 27), (3, 0), (17, 21), (42, 45), (4, 42), (0, 29), (25, 21), (22, 38), (11, 38), (7, 26), (3, 44), (29, 2), (10, 37), (6, 16), (9, 41), (13, 35), (38, 41), (18, 33), (18, 38), (4, 25), (6, 7), (9, 36), (14, 8), (39, 27), (16, 45), (11, 7), (35, 23), (25, 26), (3, 35), (11, 15), (21, 44), (4, 21), (31, 30), (1, 26), (12, 4), (39, 26), (6, 8), (26, 35), (29, 6), (32, 16), (12, 9), (4, 0), (33, 21), (12, 2), (36, 4), (29, 38), (43, 35), (10, 44), (15, 21), (31, 43), (38, 4), (22, 31), (40, 18), (44, 15), (4, 12), (5, 40), (21, 20), (35, 13), (42, 33), (10, 30), (37, 22), (37, 20), (38, 27), (42, 24), (14, 31), (9, 22), (15, 41), (19, 21), (4, 33), (37, 36), (13, 2), (4, 36), (30, 25), (8, 7), (33, 6), (3, 31), (20, 28), (21, 40), (24, 21), (2, 32), (42, 16), (41, 24), (10, 26), (29, 18), (26, 44), (8, 31), (34, 24), (2, 22), (24, 30), (12, 27), (32, 36), (30, 45), (13, 24), (16, 20), (32, 11), (41, 13), (26, 14), (41, 14), (3, 16), (26, 2), (6, 38), (19, 3), (0, 20), (0, 40), (17, 0), (28, 5), (40, 8), (7, 0), (44, 26), (0, 25), (14, 1), (44, 18), (11, 31), (0, 32), (28, 34), (21, 24), (28, 38), (24, 24), (17, 5), (9, 2), (4, 41), (5, 17), (37, 10), (40, 0), (11, 27), (26, 19), (20, 12), (33, 18), (35, 33), (37, 24), (30, 18), (34, 31), (8, 34), (18, 22), (34, 0), (14, 45), (3, 19), (0, 8), (38, 32), (19, 22), (10, 27), (6, 19), (23, 25), (37, 25), (38, 30), (20, 14), (19, 37), (16, 38), (16, 32), (22, 24), (24, 10), (37, 42), (30, 43), (35, 0), (20, 36), (24, 0), (1, 19), (7, 41), (21, 3), (28, 15), (12, 38), (43, 33), (28, 9), (9, 42), (40, 26), (28, 39), (40, 45), (22, 42), (36, 19), (38, 38), (18, 29), (43, 14), (13, 26), (28, 4), (41, 36), (31, 27), (7, 8), (2, 39), (32, 39), (38, 20), (36, 13), (23, 32), (10, 21), (33, 25), (30, 7), (14, 16), (21, 13), (9, 1), (34, 40), (43, 37), (29, 3), (24, 16), (40, 24), (40, 39), (43, 21), (14, 17), (9, 14), (6, 15), (3, 17), (23, 30), (25, 17), (37, 13), (19, 20), (39, 15), (22, 14), (13, 10), (14, 14), (4, 40), (39, 5), (28, 12), (6, 3), (39, 33), (8, 6), (40, 43), (39, 29), (2, 25), (4, 22), (12, 44), (27, 4), (10, 31), (20, 25), (5, 22), (19, 28), (44, 36), (40, 41), (10, 6), (42, 22), (39, 39), (34, 5), (17, 32), (22, 44), (37, 41), (22, 6), (23, 38), (30, 42), (23, 36), (9, 33), (0, 19), (10, 23), (39, 25), (19, 26), (25, 42), (20, 4), (24, 4), (12, 30), (16, 29), (4, 45), (42, 3), (12, 25), (16, 13), (44, 21), (2, 6), (41, 30), (31, 45), (22, 28), (27, 25), (19, 35), (16, 36), (31, 23), (39, 16), (15, 36), (10, 16), (29, 42), (34, 17), (30, 41), (21, 31), (0, 42), (42, 28), (21, 5), (37, 16), (23, 8), (12, 10), (42, 6), (31, 31), (3, 5), (23, 4), (40, 32), (11, 29), (6, 30), (19, 12), (29, 17), (16, 2), (22, 26), (2, 0), (40, 20), (2, 13), (24, 40), (1, 6), (8, 36), (34, 11), (4, 32), (15, 10), (11, 36), (30, 3), (27, 10), (35, 16), (9, 21), (9, 3), (7, 3), (27, 16), (31, 41), (3, 38), (5, 18), (28, 44), (16, 34), (9, 13), (28, 6), (16, 21), (32, 44), (6, 21), (26, 9), (19, 2), (19, 39), (26, 18), (11, 23), (19, 7), (21, 37), (25, 35), (40, 35), (10, 2), (5, 34), (41, 15), (2, 21), (25, 29), (43, 10), (12, 41), (36, 24), (16, 19), (33, 32), (20, 11), (18, 6), (22, 21), (10, 5), (6, 11), (16, 30), (14, 43), (32, 2), (31, 3), (39, 30), (37, 6), (25, 33), (9, 38), (27, 2), (34, 12), (10, 19), (38, 36), (3, 14), (41, 0), (1, 15), (35, 3), (1, 4), (38, 22), (2, 42), (24, 22), (43, 45), (39, 21), (25, 12), (19, 40), (8, 3), (22, 5), (43, 29), (19, 17), (3, 4), (42, 20), (4, 23), (28, 11), (14, 30), (40, 36), (28, 23), (4, 29), (26, 27), (31, 11), (26, 24), (33, 1), (8, 33), (7, 39), (42, 2), (5, 12), (26, 45), (16, 7), (28, 24), (3, 30), (28, 1), (34, 44), (15, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 31), (1, 30), (19, 32), (16, 46), (15, 43), (21, 42), (6, 41), (2, 46), (1, 35), (29, 29), (34, 32), (30, 36), (39, 40), (27, 26), (35, 19), (29, 41), (24, 27), (6, 13), (13, 9), (19, 40), (35, 26), (4, 9), (13, 41), (26, 38), (2, 13), (3, 48), (15, 7), (18, 20), (21, 28), (3, 7), (34, 28), (15, 38), (8, 26), (38, 9), (23, 47), (19, 35), (36, 7), (30, 24), (37, 30), (2, 4), (38, 8), (5, 32), (22, 2), (14, 15), (35, 10), (17, 29), (7, 8), (1, 36), (17, 32), (17, 37), (40, 34), (10, 43), (37, 47), (39, 38), (7, 26), (0, 9), (36, 12), (38, 43), (31, 10), (28, 2), (32, 34), (23, 18), (4, 41), (12, 22), (32, 32), (6, 5), (12, 42), (21, 30), (19, 11), (7, 44), (40, 33), (33, 41), (6, 28), (5, 5), (6, 26), (28, 4), (28, 25), (7, 27), (18, 15), (20, 43), (20, 29), (4, 17), (18, 39), (39, 48), (25, 20), (39, 17), (37, 42), (26, 22), (10, 5), (37, 40), (24, 29), (5, 37), (7, 7), (25, 40), (21, 36), (15, 1), (12, 48), (2, 17), (7, 23), (8, 35), (15, 23), (3, 19), (29, 3), (10, 27), (18, 11), (35, 9), (0, 12), (21, 8), (2, 44), (4, 36), (21, 41), (11, 25), (32, 21), (38, 35), (7, 13), (25, 45), (10, 41), (20, 23), (5, 13), (8, 39), (25, 0), (32, 30), (5, 2), (14, 44), (30, 33), (27, 47), (15, 19), (40, 21), (2, 48), (7, 28), (23, 34), (10, 26), (2, 33), (9, 26), (19, 24), (6, 38), (2, 36), (3, 45), (36, 37), (32, 43), (9, 30), (33, 42), (16, 41), (26, 39), (23, 29), (27, 40), (31, 26), (39, 5), (27, 25), (29, 43), (15, 31), (18, 29), (37, 46), (7, 24), (10, 23), (33, 43), (39, 1), (27, 39), (21, 14), (37, 37), (0, 32), (8, 15), (32, 41), (13, 20), (25, 38), (37, 5), (21, 19), (3, 41), (15, 15), (14, 37), (2, 14), (25, 33), (19, 34), (31, 23), (13, 15), (0, 47), (18, 9), (28, 16), (8, 19), (29, 24), (7, 2), (8, 42), (20, 38), (0, 40), (18, 37), (4, 42), (24, 12), (19, 4), (34, 42), (6, 43), (15, 4), (28, 43), (28, 33), (26, 0), (3, 3), (29, 2), (3, 5), (24, 0), (26, 32), (1, 28), (11, 17), (13, 21), (23, 14), (37, 34), (9, 17), (21, 9), (18, 47), (3, 16), (39, 31), (39, 12), (2, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 15), (4, 19), (37, 41), (18, 4), (14, 2), (42, 28), (12, 16), (27, 34), (24, 31), (8, 14), (33, 32), (28, 3), (15, 16), (6, 3), (31, 37), (2, 15), (23, 2), (16, 1), (13, 32), (22, 24), (12, 7), (34, 28), (45, 32), (28, 47), (35, 26), (9, 16), (15, 26), (30, 1), (36, 45), (15, 35), (24, 46), (35, 46), (42, 31), (45, 9), (23, 18), (2, 30), (15, 23), (22, 35), (10, 46), (23, 42), (18, 37), (43, 30), (45, 10), (19, 12), (9, 47), (6, 46), (28, 27), (45, 40), (30, 6), (23, 0), (4, 37), (23, 38), (41, 47), (37, 20), (7, 44), (25, 37), (22, 40), (17, 8), (6, 21), (48, 15), (30, 19), (13, 28), (30, 25), (37, 26), (3, 38), (21, 44), (37, 29), (47, 22), (3, 29), (6, 8), (2, 42), (29, 17), (21, 16), (11, 26), (20, 2), (3, 48), (14, 19), (15, 4), (8, 10), (17, 29), (45, 4), (39, 45), (12, 34), (21, 18), (2, 36), (14, 40), (26, 3), (1, 35), (31, 26), (16, 45), (17, 19), (29, 31), (14, 28), (1, 17), (29, 34), (12, 0), (11, 29), (48, 26), (30, 44), (8, 34), (35, 0), (3, 41), (18, 30), (16, 46), (41, 11), (24, 23), (46, 20), (41, 18), (15, 22), (2, 34), (4, 1), (10, 13), (37, 4), (45, 23), (12, 48), (7, 29), (19, 7), (43, 38), (6, 37), (44, 12), (35, 36), (19, 10), (8, 1), (3, 20), (6, 10), (7, 5), (33, 34), (1, 41), (27, 27), (1, 18), (11, 39), (2, 21), (8, 9), (9, 45), (35, 15), (38, 0), (8, 15), (37, 23), (5, 48), (18, 9), (43, 15), (3, 19), (31, 17), (0, 10), (37, 45), (17, 37), (1, 23), (48, 25), (38, 34), (45, 41), (35, 5), (17, 45), (22, 25), (10, 43), (24, 40), (9, 2), (25, 44), (13, 11), (2, 4), (38, 2), (24, 28), (4, 39), (40, 4), (19, 19), (30, 48), (31, 47), (21, 17), (19, 13), (0, 17), (0, 28), (23, 7), (41, 27), (10, 15), (1, 2), (25, 34), (48, 24), (38, 43), (32, 33), (40, 30), (14, 13), (13, 17), (8, 12), (14, 26), (42, 11), (27, 22), (28, 2), (25, 17), (43, 41), (35, 1), (20, 16), (38, 37), (0, 33), (5, 35), (39, 15), (0, 12), (36, 1), (9, 17), (0, 25), (8, 33), (42, 20), (30, 45), (11, 6), (1, 6), (43, 34), (20, 22), (4, 29), (22, 31), (9, 21), (21, 3), (47, 14), (36, 22), (36, 24), (9, 24), (8, 37), (38, 30), (37, 35), (31, 15), (12, 35), (7, 39), (21, 20), (23, 12), (19, 22), (16, 18), (15, 12), (13, 36), (2, 25), (44, 36), (32, 27), (42, 47), (35, 47), (4, 30), (24, 22), (16, 27), (4, 27), (11, 13), (35, 14), (37, 13), (31, 34), (48, 14), (1, 29), (3, 37), (44, 31), (38, 39), (9, 8), (20, 15), (18, 39), (3, 2), (13, 23), (39, 11), (42, 21), (30, 26), (45, 16), (16, 26), (40, 11), (39, 33), (32, 46), (10, 0), (0, 24), (36, 19), (26, 38), (5, 19), (11, 30), (48, 36), (16, 9), (5, 43), (0, 35), (33, 4), (18, 35), (39, 36), (47, 21), (32, 47), (18, 17), (31, 22), (47, 30), (38, 1), (42, 9), (5, 17), (18, 36), (15, 3), (34, 34), (27, 12), (4, 23), (19, 29), (37, 38), (40, 5), (36, 18), (30, 18), (37, 2), (5, 29), (8, 46), (32, 38), (0, 38), (26, 1), (36, 42), (2, 37), (39, 6), (3, 32), (28, 28), (8, 40), (45, 1), (17, 21), (1, 3), (29, 27), (7, 34), (2, 19), (31, 18), (35, 40), (20, 46)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 2), (20, 45), (10, 14), (41, 12), (27, 23), (35, 20), (11, 7), (37, 4), (35, 10), (36, 16), (15, 19), (36, 3), (5, 9), (11, 14), (31, 37), (5, 4), (37, 37), (42, 21), (20, 39), (41, 11), (21, 1), (19, 8), (15, 23), (35, 14), (30, 41), (7, 13), (32, 13), (19, 34), (13, 39), (27, 0), (12, 9), (23, 36), (17, 22), (29, 3), (3, 23), (12, 13), (42, 12), (0, 22), (6, 41), (34, 6), (13, 1), (12, 37), (7, 19), (15, 42), (37, 45), (25, 20), (36, 29), (27, 12), (23, 13), (40, 32), (40, 17), (6, 42), (37, 42), (24, 19), (12, 21), (40, 27), (25, 30), (3, 29), (28, 0), (26, 4), (38, 39), (41, 10), (27, 6), (24, 26), (25, 43), (19, 7), (36, 11), (22, 26), (8, 16), (30, 23), (31, 18), (33, 11), (16, 14), (29, 44), (25, 2), (10, 27), (18, 7), (2, 44), (16, 5), (13, 24), (30, 45), (23, 1), (18, 31), (14, 12), (22, 9), (9, 4), (31, 7), (12, 10), (21, 19), (18, 38), (23, 22), (17, 13), (24, 42), (23, 6), (10, 4), (39, 40), (31, 3), (21, 7), (31, 36), (42, 5), (31, 40), (39, 14), (31, 21), (20, 5), (14, 37), (1, 14), (36, 43), (20, 15), (14, 23), (20, 8), (40, 40), (35, 44), (11, 4), (8, 3), (23, 41), (2, 20), (28, 31), (4, 30), (27, 38), (25, 17), (28, 21), (23, 9), (5, 25), (21, 10), (10, 23), (22, 8), (2, 35), (4, 43), (8, 41), (15, 28), (28, 30), (2, 22), (10, 19), (12, 26), (5, 42), (1, 29), (30, 3), (40, 21), (27, 22), (11, 44), (3, 35), (17, 7), (41, 9), (42, 20), (19, 3), (14, 29), (20, 16), (0, 27), (20, 9), (8, 35), (27, 10), (24, 27), (35, 19), (12, 17), (9, 34), (1, 39), (38, 20), (27, 3), (11, 35), (42, 9), (33, 26), (15, 25), (33, 25), (33, 21), (21, 37), (26, 8), (33, 44), (41, 5), (24, 39), (0, 38), (10, 36), (34, 19), (18, 4), (12, 31), (36, 10), (7, 4), (9, 0), (23, 0), (18, 32), (9, 40), (22, 16), (42, 16), (1, 7), (20, 30), (4, 36), (1, 37), (0, 18), (1, 25), (20, 44), (15, 22), (36, 40), (2, 38), (34, 0), (27, 1), (37, 16), (31, 30), (15, 14), (4, 17), (33, 36), (10, 42), (36, 41), (3, 33), (25, 36), (42, 11), (0, 2), (28, 39), (40, 10), (6, 2), (32, 14), (5, 14), (25, 23), (3, 38), (7, 3), (25, 9), (5, 2), (18, 0), (22, 30), (10, 7), (33, 9), (34, 18), (18, 14), (30, 39), (7, 17), (34, 1), (34, 38), (3, 44), (17, 3), (4, 39), (34, 23), (40, 6), (6, 15), (4, 44), (10, 6), (18, 5), (2, 15), (20, 34), (37, 36), (38, 22), (18, 25), (6, 12), (24, 11), (38, 4), (32, 15), (19, 27), (32, 27), (12, 0), (22, 5), (41, 38), (37, 14), (26, 25), (39, 25), (26, 31), (23, 25), (42, 14), (13, 31), (37, 40), (39, 36), (24, 20), (18, 37), (25, 8), (5, 8), (28, 17), (23, 21), (33, 16), (15, 31), (32, 43), (20, 20), (14, 14), (3, 41), (4, 28), (35, 18), (4, 32), (10, 9), (36, 37), (40, 38), (3, 18), (15, 21), (29, 35), (3, 12), (35, 40), (32, 1), (24, 15), (13, 33), (42, 31), (11, 24), (3, 36), (21, 30), (34, 8), (16, 42), (39, 16), (9, 13), (20, 10), (38, 18), (1, 42), (24, 16), (12, 34), (37, 12), (19, 15), (7, 30), (5, 28), (17, 18), (12, 11), (39, 44), (19, 9), (20, 42), (29, 21), (8, 6), (24, 40), (26, 29), (3, 3), (28, 38), (17, 9), (27, 27), (15, 17), (34, 20), (41, 20), (2, 1), (18, 13), (0, 6), (7, 42), (31, 27), (40, 31), (32, 5), (7, 41), (33, 2), (27, 2), (6, 7), (35, 41), (17, 30), (8, 21), (2, 39), (35, 0), (22, 14), (37, 44), (12, 29), (11, 33), (7, 8), (38, 28), (12, 44), (15, 3), (27, 40), (38, 26), (37, 3), (7, 26), (5, 44), (30, 14), (18, 39), (42, 42), (30, 25), (33, 30), (32, 7), (17, 25), (34, 13), (11, 30), (0, 32), (40, 43), (38, 23), (30, 1), (30, 26), (12, 40), (15, 13), (22, 6), (18, 11), (13, 28), (6, 45), (7, 23), (21, 0), (39, 24), (11, 38), (41, 36), (28, 22), (26, 3), (2, 3), (19, 45), (28, 18), (24, 23), (9, 24), (25, 13), (37, 0), (14, 45), (33, 40), (28, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 27), (31, 33), (1, 16), (27, 14), (37, 32), (5, 28), (23, 27), (44, 28), (28, 15), (36, 18), (39, 11), (25, 26), (40, 36), (9, 20), (26, 22), (0, 25), (15, 26), (33, 13), (12, 10), (1, 23), (27, 34), (42, 31), (1, 17), (13, 37), (22, 34), (37, 24), (34, 30), (16, 24), (16, 3), (37, 11), (32, 35), (13, 4), (10, 29), (28, 30), (33, 7), (9, 31), (14, 33), (6, 7), (44, 24), (37, 14), (29, 32), (14, 1), (18, 13), (41, 12), (31, 9), (19, 22), (10, 20), (37, 18), (30, 31), (27, 38), (13, 24), (24, 33), (5, 5), (13, 21), (28, 12), (17, 39), (25, 36), (44, 11), (10, 5), (27, 41), (8, 17), (34, 38), (14, 32), (2, 16), (28, 1), (36, 42), (12, 2), (16, 36), (11, 4), (32, 11), (34, 1), (21, 13), (16, 16), (42, 21), (23, 23), (23, 16), (18, 17), (9, 10), (44, 17), (5, 40), (7, 30), (3, 1), (21, 42), (30, 27), (21, 32), (33, 29), (7, 0), (43, 7), (22, 3), (14, 20), (41, 14), (0, 12), (33, 17), (21, 37), (33, 33), (33, 1), (2, 35), (40, 28), (13, 1), (27, 3), (36, 33), (29, 28), (25, 13), (18, 31), (20, 12), (3, 7), (36, 20), (20, 41), (38, 40), (21, 31), (24, 24), (5, 34), (26, 20), (30, 40), (12, 18), (6, 13), (11, 23), (37, 3), (35, 18), (9, 38), (8, 29), (40, 16), (7, 7), (40, 41), (31, 35), (1, 15), (34, 35), (6, 38), (27, 22), (35, 14), (11, 20), (38, 16), (36, 14), (41, 39), (42, 22), (29, 16), (12, 40), (31, 24), (26, 23), (44, 39), (42, 42), (42, 18), (10, 3), (39, 20), (31, 1), (41, 3), (24, 12), (30, 26), (7, 40), (30, 28), (35, 19), (40, 4), (17, 12), (6, 40), (27, 20), (4, 25), (32, 27), (28, 25), (32, 29), (34, 4), (21, 9), (5, 22), (0, 17), (15, 36), (10, 11), (18, 12), (15, 38), (37, 13), (3, 2), (43, 33), (10, 1), (12, 30), (7, 27), (5, 21), (27, 2), (12, 35), (42, 17), (17, 28), (5, 1), (30, 4), (7, 33), (22, 20), (32, 24), (19, 1), (1, 40), (27, 37), (15, 28), (2, 4), (32, 42), (20, 31), (22, 31), (13, 11), (42, 26), (27, 23), (12, 9), (31, 40), (32, 30), (11, 35), (5, 32), (35, 22), (32, 0), (29, 37), (40, 23), (31, 18), (12, 1), (8, 3), (15, 18), (33, 20), (25, 42), (10, 40), (39, 29), (32, 38), (38, 34), (43, 24), (19, 26), (9, 6), (44, 21), (41, 20), (0, 33), (43, 27), (30, 37), (5, 37), (6, 18), (7, 38), (22, 13), (15, 37), (33, 26), (16, 22), (24, 18), (44, 7), (42, 23), (40, 35), (28, 18), (36, 21), (41, 6), (5, 30), (36, 11), (35, 8), (26, 24), (28, 41), (38, 13), (2, 24), (12, 34), (22, 32), (38, 21), (23, 19), (9, 4), (6, 22), (33, 5), (19, 28), (11, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 37), (29, 41), (10, 1), (41, 19), (37, 1), (45, 3), (18, 47), (8, 29), (10, 21), (33, 23), (7, 44), (38, 43), (2, 44), (43, 38), (41, 38), (12, 42), (20, 3), (21, 29), (47, 2), (5, 9), (6, 23), (39, 3), (24, 46), (46, 23), (20, 9), (7, 5), (30, 19), (26, 11), (34, 40), (24, 34), (23, 39), (12, 25), (14, 18), (14, 31), (35, 7), (20, 41), (40, 18), (21, 44), (27, 35), (24, 7), (27, 46), (33, 25), (21, 12), (11, 39), (16, 30), (12, 2), (2, 35), (43, 3), (7, 13), (17, 27), (24, 42), (26, 7), (37, 40), (3, 34), (33, 21), (8, 4), (17, 10), (42, 47), (46, 9), (40, 7), (42, 28), (25, 2), (16, 8), (16, 33), (1, 8), (19, 30), (23, 46), (24, 23), (21, 10), (48, 24), (47, 35), (11, 23), (42, 7), (4, 0), (12, 37), (3, 5), (26, 25), (27, 39), (48, 47), (6, 32), (21, 16), (28, 33), (44, 22), (19, 21), (0, 7), (31, 39), (30, 12), (31, 35), (5, 31), (1, 28), (10, 34), (37, 18), (23, 27), (38, 36), (14, 45), (16, 6), (35, 45), (35, 42), (37, 13), (36, 10), (29, 13), (17, 21), (17, 6), (28, 36), (7, 8), (13, 4), (47, 25), (29, 9), (9, 44), (38, 40), (31, 36), (20, 23), (4, 44), (0, 11), (1, 43), (16, 46), (7, 27), (12, 8), (9, 16), (8, 21), (13, 32), (14, 4), (40, 0), (27, 31), (11, 8), (4, 45), (4, 28), (30, 15), (13, 18), (43, 29), (38, 19), (32, 23), (33, 43), (16, 37), (36, 27), (45, 7), (31, 14), (5, 21), (10, 33), (4, 43), (30, 9), (42, 15), (6, 44), (43, 23), (8, 42), (33, 48), (1, 42), (24, 26), (27, 3), (7, 35), (8, 10), (4, 33), (0, 43), (20, 0), (19, 20), (6, 4), (41, 11), (1, 4), (43, 17), (33, 35), (9, 18), (28, 27), (26, 37), (12, 35), (5, 34), (44, 13), (30, 5), (40, 9), (10, 31), (47, 39), (16, 9), (1, 16), (4, 25), (0, 18), (27, 36), (26, 8), (38, 42), (0, 21), (43, 24), (22, 5), (30, 27), (32, 29), (5, 16), (15, 28), (23, 20), (14, 13), (9, 21), (29, 22), (22, 13), (19, 16), (47, 47), (2, 47), (2, 26), (11, 21), (9, 26), (30, 34), (7, 31), (17, 5), (37, 31), (8, 19), (33, 1), (22, 44), (12, 21), (26, 30), (37, 27), (43, 15), (24, 37), (14, 27), (7, 12), (37, 23), (3, 8), (15, 13), (43, 7), (2, 37), (2, 33), (27, 41), (25, 16), (44, 45), (45, 19), (44, 15), (12, 29), (4, 46), (23, 1), (3, 14), (11, 17), (9, 38), (33, 41), (34, 46), (12, 48), (37, 24), (6, 3), (34, 6), (33, 14), (0, 46), (5, 14), (22, 43), (8, 8), (41, 21), (17, 23), (3, 44), (33, 9), (44, 7), (4, 19), (33, 39), (4, 47), (9, 28), (32, 33), (14, 41), (29, 5), (38, 27), (37, 45), (28, 29), (12, 9), (20, 14), (33, 47), (37, 30), (10, 8), (34, 22), (6, 34), (19, 39), (7, 23), (24, 16), (35, 37), (23, 5), (2, 46), (24, 21), (26, 31), (42, 14), (34, 30), (33, 27), (33, 5), (16, 2), (32, 8), (45, 6), (46, 8), (42, 44), (36, 37), (14, 19), (0, 32), (33, 34), (47, 14), (5, 25), (45, 28), (27, 7), (34, 47), (43, 36), (25, 20), (42, 46), (11, 15), (16, 20), (27, 14), (34, 42), (19, 26), (10, 6), (22, 40), (44, 37), (39, 32), (1, 44), (6, 0), (18, 28), (6, 33), (34, 9), (33, 4), (27, 20), (28, 37), (14, 29), (31, 11), (10, 46), (29, 10), (11, 28), (25, 6), (40, 40), (44, 28), (22, 24), (29, 12), (36, 45), (29, 44), (39, 47), (48, 9), (13, 19), (33, 19), (1, 38), (37, 29), (45, 48), (47, 34), (30, 14), (19, 33), (8, 28), (29, 2), (36, 43), (11, 47), (34, 12), (19, 32), (22, 21), (1, 27), (11, 43), (16, 15), (38, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 18), (43, 12), (13, 20), (4, 22), (14, 22), (20, 18), (34, 27), (0, 19), (25, 4), (36, 34), (7, 20), (33, 19), (23, 35), (23, 17), (39, 10), (4, 2), (41, 3), (22, 3), (19, 3), (15, 0), (2, 37), (24, 11), (30, 2), (17, 10), (22, 13), (40, 14), (18, 31), (16, 20), (12, 3), (6, 6), (3, 22), (0, 30), (1, 24), (35, 15), (20, 39), (1, 13), (0, 23), (9, 25), (23, 18), (19, 19), (37, 22), (40, 20), (31, 29), (5, 16), (22, 11), (24, 35), (43, 32), (2, 11), (8, 21), (10, 4), (27, 37), (3, 39), (24, 9), (42, 6), (4, 36), (42, 30), (43, 16), (31, 14), (0, 10), (5, 25), (5, 27), (33, 33), (20, 5), (9, 20), (34, 26), (12, 30), (9, 2), (9, 9), (31, 11), (6, 36), (11, 25), (5, 28), (11, 37), (23, 12), (6, 32), (28, 20), (25, 22), (2, 8), (1, 11), (9, 23), (20, 30), (0, 3), (17, 30), (26, 9), (31, 2), (5, 39), (1, 21), (13, 32), (21, 23), (2, 13), (21, 16), (22, 1), (16, 39), (36, 39), (30, 28), (27, 29), (43, 7), (35, 25), (39, 9), (11, 7), (8, 31), (18, 9), (21, 34), (31, 38), (16, 22), (20, 13), (29, 29), (35, 14), (15, 8), (1, 8), (29, 15), (12, 31), (3, 28), (36, 13), (30, 21), (22, 8), (26, 32), (1, 40), (22, 5), (27, 0), (31, 8), (21, 22), (43, 26), (1, 29), (30, 27), (14, 25), (40, 17), (1, 35), (21, 18), (16, 14), (39, 40), (39, 11), (14, 3), (15, 21), (31, 39), (9, 27), (6, 30), (34, 25), (30, 20), (15, 10), (25, 19), (35, 9), (11, 22), (34, 24), (33, 2), (34, 36), (8, 3), (18, 3), (27, 14), (14, 19), (22, 35), (36, 31), (18, 0), (17, 39), (4, 14), (14, 28), (6, 0), (34, 13), (24, 37), (33, 24), (16, 31), (5, 19), (13, 21), (43, 27), (14, 18), (37, 3), (20, 36), (19, 20), (33, 16), (5, 0), (0, 35), (33, 20), (21, 19), (9, 36), (42, 12), (37, 20), (40, 31), (33, 15), (14, 26), (10, 17), (38, 13), (42, 40), (1, 25), (40, 23), (6, 21), (10, 40), (26, 39), (39, 36), (24, 16), (15, 25), (19, 24), (9, 10), (31, 20), (0, 40), (0, 15), (10, 24), (42, 23), (30, 37), (30, 22), (32, 4), (13, 17), (2, 30), (27, 9), (2, 22), (10, 21), (7, 25), (19, 39), (21, 25), (41, 40), (19, 17), (32, 31), (21, 12), (20, 29), (33, 35), (41, 15), (14, 13), (38, 23), (1, 18), (19, 7), (41, 25), (36, 10), (20, 14), (40, 18), (7, 38), (34, 10), (39, 4), (42, 18), (4, 12), (1, 1), (0, 1), (12, 34), (30, 23), (22, 12), (12, 20), (5, 22), (2, 6), (30, 18), (33, 3), (23, 38), (42, 29), (23, 6), (4, 1), (5, 20), (26, 29), (11, 10), (25, 32), (12, 36), (26, 14), (1, 7), (1, 27), (0, 28), (27, 8), (30, 10), (28, 30), (33, 26), (3, 2), (28, 5), (22, 9), (14, 16), (11, 4), (20, 22), (28, 12), (16, 25), (26, 22), (17, 13), (21, 31), (32, 3), (14, 30), (32, 32), (2, 36), (26, 6), (28, 6), (17, 34), (7, 34), (38, 33), (4, 39), (10, 0), (33, 13), (38, 40), (24, 36), (2, 19), (11, 9), (29, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 0), (35, 26), (14, 14), (32, 41), (14, 28), (5, 1), (18, 35), (34, 20), (38, 25), (36, 41), (20, 2), (8, 14), (13, 24), (27, 30), (4, 17), (23, 17), (13, 21), (40, 22), (39, 43), (15, 5), (6, 21), (24, 11), (35, 1), (40, 20), (7, 35), (17, 43), (4, 31), (6, 40), (35, 11), (12, 41), (13, 23), (35, 14), (39, 3), (40, 31), (33, 25), (10, 10), (12, 6), (31, 13), (2, 7), (11, 7), (27, 18), (5, 20), (28, 1), (34, 39), (13, 37), (18, 21), (40, 34), (11, 30), (22, 14), (14, 9), (35, 18), (21, 17), (25, 17), (15, 25), (41, 25), (5, 19), (9, 10), (13, 8), (12, 17), (30, 25), (17, 40), (20, 4), (15, 1), (20, 3), (7, 31), (3, 11), (36, 29), (21, 13), (19, 3), (2, 25), (1, 42), (17, 23), (33, 26), (11, 16), (20, 10), (20, 28), (1, 15), (30, 23), (21, 29), (43, 21), (24, 3), (21, 26), (12, 15), (8, 12), (4, 1), (41, 5), (11, 37), (24, 23), (2, 13), (22, 20), (8, 13), (27, 41), (20, 7), (27, 32), (8, 16), (9, 38), (36, 24), (22, 21), (8, 11), (39, 11), (33, 4), (32, 38), (43, 6), (35, 30), (34, 22), (26, 22), (35, 24), (13, 28), (22, 28), (39, 33), (22, 4), (17, 27), (2, 8), (25, 40), (37, 19), (24, 21), (7, 7), (40, 3), (36, 35), (34, 16), (10, 24), (37, 43), (38, 6), (14, 36), (19, 37), (22, 25), (24, 19), (43, 34), (27, 39), (31, 22), (41, 12), (37, 1), (21, 36), (21, 19), (26, 27), (37, 35), (24, 27), (28, 40), (20, 9), (5, 42), (42, 37), (4, 38), (21, 42), (2, 40), (30, 32), (40, 41), (8, 7), (25, 38), (22, 6), (31, 18), (3, 32), (26, 34), (18, 14), (16, 3), (32, 31), (34, 27), (23, 35), (35, 7), (22, 42), (38, 34), (39, 27), (2, 36), (43, 23), (29, 21), (22, 9), (22, 26), (28, 41), (41, 40), (40, 16), (20, 13), (40, 15), (13, 10), (13, 40), (29, 11), (13, 6), (38, 27), (13, 32), (14, 7), (37, 10), (35, 16), (17, 6), (27, 22), (1, 4), (35, 8), (35, 12), (32, 2), (40, 36), (16, 28), (24, 16), (7, 23), (17, 5), (13, 27), (23, 27), (42, 7), (25, 28), (10, 5), (41, 1), (8, 42), (4, 13), (10, 4), (0, 8), (28, 5), (42, 6), (14, 19), (29, 14), (3, 8), (29, 15), (32, 10), (28, 32), (0, 25), (3, 20), (22, 17), (14, 41), (16, 19), (17, 21), (21, 14), (0, 15), (5, 13), (8, 34), (4, 5), (3, 42), (38, 0), (4, 22), (11, 22), (43, 11), (4, 6), (38, 30), (25, 25), (34, 8), (31, 10), (28, 21), (32, 22), (40, 38), (11, 9), (25, 29), (27, 37), (15, 31), (24, 13), (39, 0), (29, 16), (29, 23), (36, 2), (21, 33), (15, 22), (3, 3), (39, 39), (18, 33), (30, 10), (30, 36), (39, 4), (41, 23), (6, 33), (15, 29), (43, 27), (23, 5), (12, 25), (26, 12), (39, 6), (39, 19), (2, 2), (13, 29), (29, 19), (5, 28), (19, 8), (15, 28), (30, 12), (1, 10), (21, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 39), (19, 24), (37, 29), (44, 31), (41, 39), (0, 35), (31, 38), (34, 13), (41, 31), (46, 11), (28, 24), (36, 5), (18, 7), (40, 33), (34, 27), (21, 26), (45, 33), (32, 23), (27, 28), (26, 28), (10, 20), (37, 7), (43, 1), (33, 20), (17, 3), (40, 14), (22, 22), (16, 35), (4, 36), (33, 32), (17, 4), (6, 10), (43, 35), (5, 29), (15, 9), (28, 37), (2, 11), (38, 4), (7, 0), (29, 15), (41, 28), (0, 10), (11, 33), (20, 2), (33, 21), (10, 6), (0, 30), (7, 29), (18, 5), (39, 0), (2, 4), (27, 30), (24, 6), (37, 10), (3, 14), (25, 39), (15, 22), (12, 13), (3, 9), (38, 32), (4, 34), (28, 19), (4, 30), (23, 13), (44, 38), (23, 36), (36, 21), (18, 21), (26, 11), (32, 32), (34, 37), (17, 8), (11, 31), (20, 12), (46, 27), (23, 8), (10, 30), (6, 4), (7, 24), (0, 37), (41, 11), (38, 3), (14, 33), (28, 11), (34, 6), (38, 14), (8, 15), (6, 38), (32, 11), (33, 29), (33, 12), (8, 12), (15, 36), (1, 35), (24, 16), (44, 1), (6, 37), (19, 9), (5, 34), (43, 28), (32, 39), (9, 9), (15, 18), (36, 40), (17, 39), (27, 3), (20, 34), (34, 9), (41, 5), (44, 23), (26, 17), (7, 14), (22, 12), (28, 3), (7, 25), (8, 29), (18, 13), (26, 16), (24, 1), (14, 8), (12, 7), (11, 17), (18, 39), (19, 30), (21, 27), (21, 35), (3, 34), (20, 4), (27, 2), (37, 2), (7, 16), (9, 15), (34, 0), (32, 25), (24, 22), (2, 33), (12, 38), (41, 35), (30, 24), (5, 27), (30, 5), (10, 27), (36, 7), (9, 17), (22, 28), (10, 3), (42, 19), (30, 3), (12, 14), (5, 33), (26, 9), (22, 29), (34, 35), (28, 5), (9, 24), (34, 30), (9, 37), (20, 5), (43, 2), (32, 9), (13, 20), (46, 25), (27, 12), (44, 8), (23, 31), (18, 2), (2, 7), (3, 22), (45, 22), (2, 38), (46, 3), (9, 26), (44, 21), (32, 20), (40, 40), (45, 27), (29, 17), (38, 37), (12, 0), (23, 24), (27, 37), (10, 21), (3, 21), (39, 27), (16, 33), (1, 13), (17, 7), (15, 17), (42, 12), (5, 10), (10, 10), (1, 34), (32, 5), (46, 5), (17, 9), (45, 0), (5, 6), (19, 28), (2, 25), (7, 6), (15, 7), (36, 30), (43, 34), (0, 40), (19, 27), (4, 3), (23, 11), (28, 33), (7, 5), (11, 21), (37, 22), (32, 10), (27, 10), (12, 32), (11, 5), (32, 27), (30, 4), (45, 11), (37, 13), (23, 16), (24, 19), (46, 34), (22, 40), (32, 12), (3, 31), (3, 17), (32, 34), (45, 40), (8, 16), (24, 0), (12, 40), (25, 33), (1, 26), (8, 31), (47, 17), (38, 35), (23, 3), (39, 24), (23, 19), (1, 18), (46, 33), (8, 18), (11, 28), (27, 40), (33, 1), (27, 6), (18, 4), (41, 14), (30, 8), (40, 22), (40, 29), (44, 20), (35, 3), (25, 22), (38, 10), (25, 9), (47, 20), (12, 18), (11, 36), (39, 8), (12, 19), (16, 28), (18, 30), (37, 30), (38, 8), (43, 18), (7, 2), (20, 40), (12, 12), (9, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 29), (2, 13), (35, 17), (26, 6), (28, 23), (41, 26), (36, 27), (10, 15), (27, 21), (21, 15), (19, 27), (45, 45), (33, 27), (18, 38), (32, 32), (23, 26), (29, 4), (13, 19), (3, 48), (30, 16), (36, 34), (46, 7), (9, 33), (4, 27), (35, 40), (41, 42), (24, 43), (1, 42), (26, 35), (20, 46), (4, 26), (1, 1), (21, 19), (25, 8), (38, 14), (46, 20), (45, 1), (45, 16), (44, 10), (27, 17), (43, 30), (26, 10), (45, 15), (42, 1), (10, 12), (35, 44), (39, 4), (7, 27), (36, 5), (6, 21), (36, 6), (9, 41), (29, 45), (36, 32), (46, 33), (17, 29), (21, 44), (2, 2), (16, 12), (33, 16), (46, 14), (25, 45), (20, 5), (10, 27), (33, 36), (19, 21), (16, 5), (7, 35), (1, 27), (14, 6), (29, 18), (11, 33), (34, 29), (9, 20), (14, 18), (22, 21), (8, 42), (35, 29), (37, 43), (15, 40), (22, 31), (20, 43), (6, 32), (1, 23), (7, 9), (33, 10), (28, 4), (0, 29), (44, 0), (0, 39), (19, 23), (36, 35), (5, 2), (28, 15), (21, 46), (22, 32), (31, 19), (4, 40), (12, 9), (40, 33), (2, 11), (42, 20), (33, 46), (24, 38), (36, 39), (26, 47), (17, 8), (22, 41), (24, 35), (42, 36), (25, 36), (24, 24), (15, 21), (0, 43), (9, 30), (7, 6), (34, 24), (9, 46), (1, 34), (5, 43), (45, 20), (1, 44), (32, 12), (25, 4), (6, 7), (5, 4), (13, 46), (15, 42), (6, 34), (29, 48), (32, 13), (40, 5), (44, 43), (22, 6), (17, 46), (44, 46), (46, 19), (11, 36), (38, 32), (22, 42), (33, 37), (6, 28), (15, 46), (21, 25), (14, 7), (20, 3), (27, 48), (24, 3), (41, 16), (34, 34), (46, 13), (12, 27), (10, 21), (23, 4), (24, 5), (11, 5), (7, 41), (13, 2), (40, 16), (43, 24), (4, 18), (16, 2), (1, 17), (35, 22), (6, 12), (38, 23), (35, 15), (4, 4), (24, 31), (17, 40), (31, 46), (23, 20), (16, 28), (46, 1), (15, 19), (13, 11), (9, 0), (42, 33), (14, 39), (8, 44), (21, 10), (13, 9), (14, 1), (43, 25), (45, 47), (28, 9), (43, 12), (14, 19), (31, 45), (32, 10), (22, 13), (28, 3), (29, 41), (37, 9), (43, 17), (8, 11), (23, 3), (31, 22), (32, 37), (43, 35), (11, 22), (15, 27), (30, 45), (38, 26), (0, 18), (28, 21), (43, 18), (0, 9), (1, 29), (0, 13), (15, 9), (25, 27), (30, 19), (7, 20), (9, 44), (42, 24), (16, 10), (12, 19), (26, 2), (36, 10), (28, 5), (1, 48), (2, 26), (19, 28), (25, 21), (3, 4), (20, 8), (2, 34), (1, 5), (20, 23), (12, 4), (1, 7), (21, 28), (34, 38), (39, 3), (19, 48), (2, 9), (25, 47), (25, 0), (35, 24), (12, 29), (28, 27), (23, 22), (3, 3), (29, 44), (6, 23), (34, 14), (22, 29), (45, 3), (46, 11), (2, 18), (15, 6), (39, 47), (2, 36), (26, 45), (4, 10), (18, 33), (19, 15), (42, 10), (31, 35), (16, 35), (39, 42), (31, 25), (19, 3), (13, 25), (31, 44), (31, 1), (20, 47), (2, 5), (8, 23), (9, 25), (30, 39), (42, 34), (7, 12), (42, 43), (12, 36), (5, 37), (32, 48), (21, 20), (45, 30), (29, 34), (26, 5), (38, 19), (25, 9), (4, 8), (35, 26), (37, 8), (28, 16), (18, 10), (11, 21), (33, 17), (1, 14), (0, 33), (45, 37), (43, 8), (39, 40), (39, 22), (30, 37), (3, 20), (28, 32), (8, 7), (20, 37), (29, 47), (35, 23), (42, 17), (10, 37), (46, 34), (40, 44), (8, 19), (20, 15), (22, 7), (28, 48), (31, 10), (6, 46), (31, 32), (9, 24), (34, 9), (19, 17), (28, 17), (27, 39), (45, 41), (18, 9), (6, 25), (25, 12), (9, 22), (10, 35), (21, 17), (46, 23), (2, 10), (15, 10), (20, 9), (4, 30), (31, 26), (28, 37), (36, 20), (5, 1), (37, 27), (45, 12), (7, 40), (14, 15), (40, 26), (24, 36), (27, 26), (16, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 38), (6, 22), (34, 38), (12, 25), (29, 7), (7, 7), (24, 25), (37, 5), (25, 11), (8, 33), (25, 34), (20, 32), (10, 32), (37, 21), (16, 13), (43, 28), (14, 37), (43, 29), (18, 11), (35, 15), (5, 10), (32, 1), (21, 12), (31, 47), (26, 11), (16, 22), (16, 47), (37, 24), (10, 10), (2, 44), (9, 0), (24, 23), (27, 1), (36, 34), (22, 6), (26, 14), (30, 26), (45, 39), (37, 14), (20, 34), (42, 19), (37, 19), (31, 7), (36, 4), (46, 25), (38, 14), (18, 8), (1, 37), (0, 10), (13, 2), (17, 16), (38, 12), (17, 35), (36, 39), (7, 28), (36, 32), (21, 44), (16, 1), (39, 14), (26, 33), (46, 33), (21, 17), (11, 23), (21, 18), (12, 17), (3, 12), (38, 18), (2, 21), (40, 47), (41, 45), (26, 38), (45, 17), (11, 8), (21, 33), (33, 22), (27, 14), (40, 33), (18, 10), (24, 17), (23, 7), (12, 5), (1, 4), (22, 30), (28, 46), (46, 12), (27, 20), (9, 26), (6, 44), (22, 38), (29, 25), (42, 46), (24, 34), (6, 45), (23, 41), (7, 20), (17, 44), (0, 20), (41, 23), (41, 22), (45, 43), (13, 25), (14, 19), (2, 7), (25, 24), (21, 11), (4, 35), (0, 15), (28, 30), (37, 23), (43, 13), (43, 0), (22, 7), (33, 41), (12, 44), (46, 16), (21, 39), (32, 4), (27, 37), (8, 25), (11, 14), (16, 32), (5, 45), (42, 26), (16, 43), (35, 28), (2, 23), (4, 45), (26, 3), (34, 19), (29, 1), (26, 24), (24, 45), (12, 26), (0, 19), (24, 22), (3, 38), (31, 29), (41, 20), (6, 5), (11, 20), (8, 17), (11, 32), (35, 41), (7, 16), (17, 38), (8, 24), (21, 0), (4, 27), (27, 18), (13, 41), (36, 17), (40, 34), (18, 30), (25, 4), (37, 39), (15, 8), (2, 10), (1, 35), (21, 10), (19, 26), (42, 32), (25, 17), (43, 1), (34, 5), (11, 44), (5, 5), (26, 35), (41, 6), (13, 28), (24, 46), (41, 42), (39, 43), (45, 28), (15, 26), (6, 30), (7, 29), (10, 31), (43, 30), (37, 1), (30, 18), (30, 40), (13, 10), (26, 6), (6, 47), (21, 23), (3, 25), (27, 10), (10, 47), (37, 37), (16, 35), (11, 22), (21, 41), (16, 40), (5, 43), (16, 19), (35, 4), (6, 35), (16, 33), (14, 43), (30, 28), (41, 38), (46, 17), (5, 3), (38, 1), (36, 43), (42, 23), (12, 0), (18, 3), (45, 44), (44, 2), (10, 0), (2, 24), (3, 39), (37, 6), (43, 43), (8, 20), (28, 15), (16, 9), (37, 31), (45, 14), (36, 16), (39, 12), (28, 39), (23, 0), (24, 41), (34, 45), (3, 45), (2, 32), (13, 22), (6, 23), (18, 15), (46, 21), (42, 8), (16, 28), (10, 39), (34, 44), (36, 45), (42, 4), (0, 42), (36, 9), (30, 2), (9, 33), (14, 13), (32, 7), (25, 5), (9, 25), (46, 42), (1, 3), (38, 35), (32, 47), (1, 16), (6, 31), (9, 22), (5, 8), (4, 25), (24, 20), (2, 42), (10, 26), (3, 46), (23, 11), (1, 0), (33, 18), (22, 20), (20, 8), (39, 22), (29, 32), (44, 46), (5, 17), (19, 23), (16, 26), (8, 23), (41, 37), (18, 44), (38, 19), (4, 16), (20, 24), (2, 17), (22, 22), (7, 2), (38, 47), (35, 24), (17, 37), (17, 42), (19, 33), (1, 31), (42, 11), (0, 14), (42, 35), (41, 26), (14, 31), (31, 36), (12, 13), (34, 41), (41, 8), (0, 22), (3, 24), (28, 3), (6, 7), (42, 25), (40, 3), (1, 27), (30, 3), (32, 36), (23, 12), (29, 47), (1, 22), (0, 38), (44, 41), (42, 45), (20, 15), (46, 14), (36, 38), (13, 30), (34, 4), (35, 44), (4, 46), (11, 24), (25, 36), (21, 1), (20, 14), (30, 43), (26, 8), (23, 33), (22, 43), (12, 31), (5, 21), (35, 6), (34, 8), (35, 17), (6, 46), (34, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 18), (9, 40), (12, 8), (23, 7), (1, 46), (9, 14), (20, 37), (6, 20), (9, 38), (26, 0), (28, 28), (38, 32), (6, 29), (15, 44), (18, 23), (33, 11), (5, 35), (16, 17), (40, 22), (32, 10), (11, 10), (22, 45), (19, 44), (13, 25), (36, 33), (37, 6), (8, 39), (42, 38), (2, 14), (31, 21), (6, 37), (13, 38), (31, 41), (11, 45), (13, 28), (22, 42), (25, 7), (29, 33), (22, 10), (23, 44), (35, 3), (18, 12), (16, 43), (41, 45), (10, 39), (18, 40), (1, 0), (16, 15), (32, 40), (36, 30), (14, 33), (6, 25), (30, 31), (26, 15), (16, 24), (34, 23), (38, 20), (33, 6), (6, 17), (13, 43), (35, 6), (9, 37), (19, 36), (8, 36), (36, 22), (11, 41), (38, 17), (8, 11), (16, 3), (34, 37), (21, 0), (30, 11), (1, 33), (5, 12), (31, 25), (11, 3), (7, 23), (23, 42), (8, 2), (30, 4), (9, 25), (10, 38), (11, 13), (5, 41), (1, 9), (36, 17), (6, 38), (2, 11), (0, 13), (5, 18), (1, 1), (2, 40), (3, 47), (11, 39), (29, 29), (20, 20), (34, 46), (18, 30), (7, 30), (15, 23), (0, 10), (42, 37), (7, 16), (40, 6), (10, 24), (33, 47), (12, 5), (20, 32), (4, 37), (0, 7), (21, 47), (1, 36), (19, 8), (32, 11), (17, 33), (0, 8), (41, 15), (20, 4), (21, 45), (43, 45), (30, 20), (0, 34), (27, 35), (23, 14), (37, 18), (37, 34), (29, 37), (22, 35), (8, 1), (15, 18), (13, 6), (34, 0), (15, 34), (6, 8), (26, 3), (14, 18), (34, 5), (33, 1), (27, 32), (19, 15), (28, 14), (0, 33), (27, 12), (6, 23), (20, 24), (5, 1), (32, 19), (37, 21), (5, 15), (24, 7), (29, 25), (26, 27), (12, 35), (28, 43), (26, 47), (41, 5), (14, 31), (34, 18), (33, 25), (25, 41), (10, 17), (36, 35), (21, 4), (25, 10), (35, 43), (19, 34), (41, 19), (43, 14), (40, 30), (26, 17), (38, 36), (16, 33), (8, 27), (23, 31), (30, 46), (30, 6), (21, 23), (18, 20), (34, 6), (8, 5), (16, 7), (27, 24), (29, 24), (13, 26), (31, 9), (1, 3), (30, 39), (0, 19), (28, 30), (6, 14), (19, 10), (1, 29), (31, 12), (14, 23), (6, 46), (31, 30), (34, 11), (4, 25), (3, 12), (32, 3), (35, 46), (30, 9), (12, 10), (35, 42), (17, 7), (10, 46), (1, 35), (32, 24), (29, 0), (28, 19), (23, 47), (1, 27), (25, 20), (42, 15), (30, 41), (42, 28), (5, 8), (25, 43), (38, 46), (7, 37), (39, 38), (37, 28), (31, 8), (2, 12), (1, 11), (3, 19), (41, 20), (20, 41), (32, 4), (2, 41), (29, 15), (26, 43), (32, 33), (0, 39), (8, 19), (6, 6), (31, 45)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 32), (31, 21), (14, 4), (6, 39), (31, 39), (8, 34), (1, 24), (10, 15), (23, 1), (15, 22), (8, 40), (24, 42), (41, 30), (26, 30), (32, 24), (36, 11), (7, 37), (6, 20), (10, 35), (2, 8), (18, 19), (1, 36), (22, 37), (6, 6), (11, 4), (34, 20), (26, 28), (38, 3), (1, 23), (11, 10), (28, 31), (16, 14), (34, 36), (31, 12), (9, 29), (30, 0), (14, 25), (7, 11), (26, 11), (23, 0), (20, 33), (18, 21), (9, 10), (22, 19), (24, 28), (25, 4), (27, 40), (43, 38), (38, 21), (16, 20), (3, 38), (5, 7), (24, 9), (9, 18), (20, 10), (43, 5), (34, 15), (18, 40), (22, 29), (35, 33), (35, 20), (21, 8), (13, 20), (11, 0), (9, 4), (32, 14), (17, 33), (36, 40), (6, 42), (28, 23), (5, 38), (38, 35), (34, 6), (19, 6), (16, 37), (3, 23), (41, 26), (30, 39), (38, 32), (0, 5), (26, 34), (25, 35), (39, 41), (28, 2), (0, 18), (15, 34), (17, 9), (4, 24), (13, 21), (22, 20), (14, 38), (27, 23), (11, 30), (12, 14), (6, 30), (18, 11), (25, 30), (0, 35), (43, 37), (17, 42), (24, 38), (4, 39), (13, 9), (34, 28), (30, 9), (8, 16), (21, 4), (40, 3), (14, 0), (6, 41), (6, 33), (11, 7), (2, 29), (10, 9), (16, 24), (33, 7), (14, 21), (9, 7), (6, 29), (41, 39), (14, 16), (31, 25), (41, 27), (7, 19), (3, 35), (3, 33), (41, 12), (21, 36), (26, 5), (1, 30), (36, 17), (18, 31), (2, 22), (20, 37), (26, 35), (40, 28), (41, 29), (1, 29), (39, 38), (1, 4), (15, 19), (37, 23), (32, 37), (12, 28), (43, 26), (13, 19), (19, 11), (16, 15), (36, 12), (36, 27), (23, 23), (43, 0), (28, 5), (24, 35), (39, 20), (7, 22), (9, 5), (29, 41), (27, 0), (4, 25), (17, 39), (16, 34), (0, 25), (43, 10), (42, 37), (18, 18), (0, 19), (2, 31), (15, 27), (27, 13), (2, 4), (32, 31), (8, 25), (2, 20), (36, 3), (7, 13), (11, 16), (3, 2), (35, 1), (11, 11), (29, 0), (13, 39), (40, 40), (9, 24), (0, 21), (34, 9), (31, 23), (39, 23), (0, 14), (43, 6), (14, 3), (5, 22), (31, 29), (4, 6), (41, 31), (22, 13), (42, 16), (36, 38), (4, 34), (15, 2), (1, 14), (10, 3), (14, 39), (21, 16), (12, 33), (26, 8), (15, 16), (29, 10), (5, 16), (9, 12), (41, 32), (15, 36), (34, 11), (41, 18), (42, 25), (9, 13), (32, 39), (13, 3), (42, 15), (6, 28), (39, 24), (8, 5), (39, 25), (43, 14), (38, 14), (19, 30), (14, 36), (26, 33), (16, 33), (29, 38), (20, 7), (14, 18), (6, 13), (25, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 17), (2, 7), (27, 8), (35, 14), (37, 9), (36, 24), (22, 31), (38, 3), (0, 11), (35, 24), (29, 12), (16, 13), (14, 5), (8, 23), (29, 16), (35, 9), (20, 22), (25, 34), (6, 28), (35, 37), (6, 3), (7, 32), (25, 0), (12, 6), (28, 39), (40, 27), (10, 27), (11, 36), (19, 2), (22, 30), (11, 12), (37, 15), (34, 23), (24, 34), (29, 17), (21, 38), (21, 22), (15, 20), (1, 27), (21, 31), (5, 7), (10, 18), (20, 13), (29, 34), (2, 19), (7, 8), (40, 8), (35, 38), (29, 26), (13, 17), (11, 5), (13, 31), (39, 37), (30, 18), (29, 30), (10, 33), (14, 22), (10, 0), (7, 35), (11, 3), (1, 38), (29, 39), (11, 34), (33, 1), (13, 15), (11, 30), (29, 29), (19, 36), (39, 6), (35, 23), (18, 26), (34, 29), (21, 8), (8, 0), (30, 35), (17, 5), (39, 20), (5, 33), (32, 26), (19, 5), (20, 21), (3, 13), (8, 35), (29, 36), (18, 2), (35, 11), (38, 2), (15, 17), (26, 16), (0, 4), (22, 8), (6, 5), (11, 11), (0, 7), (27, 9), (24, 4), (17, 20), (22, 1), (7, 25), (30, 5), (8, 3), (30, 9), (40, 9), (12, 20), (39, 10), (7, 29), (30, 21), (17, 8), (1, 36), (19, 26), (10, 30), (9, 31), (9, 27), (25, 15), (7, 36), (38, 9), (12, 4), (25, 17), (39, 32), (8, 10), (37, 2), (14, 30), (22, 36), (21, 34), (35, 20), (37, 38), (3, 36), (13, 28), (35, 33), (17, 19), (24, 9), (32, 15), (20, 9), (36, 3), (33, 27), (10, 39), (9, 2), (6, 29), (15, 7), (9, 21), (7, 33), (36, 16), (35, 36), (19, 13), (7, 19), (33, 35), (38, 29), (28, 6), (15, 16), (20, 10), (4, 29), (40, 38), (29, 2), (27, 30), (3, 34), (7, 23), (26, 38), (6, 6), (1, 30), (39, 7), (19, 18), (23, 17), (28, 15), (16, 16), (17, 14), (1, 8), (15, 30), (8, 18), (29, 1), (11, 37), (35, 7), (15, 4), (0, 16), (5, 11), (31, 34), (28, 25), (11, 35), (17, 38), (11, 15), (37, 34), (19, 37), (3, 33), (25, 1), (18, 23), (22, 32), (2, 15), (1, 25), (27, 4), (23, 39), (24, 12), (31, 5), (36, 35), (36, 27), (33, 36), (11, 38), (29, 25), (19, 3), (21, 13), (10, 14), (28, 17), (23, 19), (0, 29), (38, 24), (34, 34), (12, 34), (3, 15), (30, 31), (37, 1), (13, 13), (30, 38), (36, 10), (5, 20), (39, 5), (21, 0), (15, 37), (6, 23), (27, 3), (40, 30), (2, 1), (6, 13), (37, 11), (3, 38), (27, 26), (13, 8), (31, 12), (18, 8), (31, 7), (10, 11), (17, 29), (14, 0), (23, 2), (1, 4), (2, 37), (20, 33), (33, 12), (24, 2), (25, 22), (15, 9), (27, 1), (28, 22), (13, 1), (3, 7), (8, 37), (38, 31), (37, 7), (32, 27), (15, 33), (39, 19), (2, 26), (9, 28), (31, 14), (14, 32), (4, 13), (2, 10), (37, 22), (36, 31), (12, 37), (39, 33), (18, 29), (7, 20), (26, 29), (32, 6), (1, 26), (33, 39), (25, 10), (28, 35), (20, 24), (13, 7), (36, 7), (22, 37), (1, 28), (15, 15), (8, 17), (32, 36), (38, 11), (15, 11), (19, 17), (13, 10), (16, 6), (25, 14), (21, 17), (19, 6), (7, 31), (1, 35), (35, 4), (36, 2), (7, 15), (32, 0), (3, 29), (39, 29), (15, 13), (12, 39), (17, 0), (27, 11), (6, 20), (9, 4), (7, 27), (25, 30), (40, 19), (5, 16), (33, 24), (10, 31), (5, 30), (5, 23), (23, 8), (38, 6), (17, 3), (4, 37), (37, 12), (2, 17), (15, 21), (0, 9), (34, 38), (26, 1), (28, 27), (6, 19), (20, 14), (3, 4), (37, 18), (29, 38), (5, 28), (15, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 41x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 22), (28, 0), (3, 4), (13, 26), (35, 25), (10, 20), (3, 21), (35, 4), (4, 22), (23, 1), (20, 41), (16, 20), (34, 34), (34, 11), (26, 14), (32, 39), (38, 4), (10, 11), (4, 7), (17, 7), (34, 45), (32, 11), (40, 36), (22, 41), (30, 33), (16, 27), (8, 25), (11, 29), (19, 43), (18, 28), (21, 11), (13, 35), (37, 39), (10, 28), (36, 19), (36, 11), (34, 7), (39, 29), (38, 15), (11, 45), (6, 45), (18, 12), (1, 29), (39, 28), (29, 0), (29, 20), (40, 23), (29, 43), (15, 32), (31, 20), (14, 9), (15, 19), (40, 32), (34, 17), (39, 30), (26, 27), (0, 43), (3, 30), (35, 11), (13, 12), (17, 14), (15, 25), (24, 6), (6, 19), (30, 44), (40, 22), (2, 42), (24, 4), (9, 29), (8, 45), (13, 33), (9, 32), (0, 29), (1, 16), (30, 41), (3, 18), (33, 45), (12, 1), (3, 7), (9, 18), (6, 1), (24, 0), (24, 17), (27, 0), (16, 5), (19, 25), (20, 1), (20, 18), (22, 43), (0, 19), (20, 30), (2, 7), (32, 38), (22, 17), (10, 31), (3, 0), (37, 40), (19, 9), (40, 34), (1, 40), (24, 45), (39, 31), (38, 38), (36, 27), (2, 43), (29, 37), (12, 19), (37, 10), (1, 10), (20, 45), (15, 38), (10, 7), (19, 32), (11, 34), (0, 44), (7, 40), (37, 19), (35, 42), (2, 0), (14, 24), (28, 12), (21, 16), (34, 30), (2, 8), (2, 28), (28, 11), (8, 20), (22, 26), (35, 21), (26, 12), (37, 7), (10, 3), (24, 43), (7, 7), (22, 7), (8, 35), (39, 7), (10, 8), (18, 42), (35, 24), (22, 15), (6, 15), (12, 35), (11, 32), (8, 31), (39, 0), (28, 31), (38, 42), (10, 26), (20, 3), (31, 1), (25, 25), (25, 16), (21, 4), (9, 0), (26, 33), (35, 0), (24, 38), (19, 10), (23, 5), (38, 37), (15, 29), (7, 8), (20, 36), (16, 35), (7, 16), (7, 28), (38, 29), (15, 2), (26, 23), (22, 16), (40, 35), (25, 18), (32, 1), (16, 4), (9, 23), (29, 3), (37, 9), (4, 38), (40, 13), (20, 11), (21, 0), (7, 19), (28, 45), (1, 26), (13, 27), (31, 34), (20, 34), (39, 22), (5, 27), (3, 19), (10, 23), (35, 16), (24, 3), (0, 2), (18, 21), (32, 13), (29, 16), (34, 43), (33, 21), (34, 25), (26, 34), (17, 44), (2, 5), (37, 8), (26, 7), (5, 22), (34, 41), (1, 43), (14, 43), (23, 9), (10, 17), (31, 38), (30, 15), (12, 40), (25, 37), (22, 25), (39, 14), (6, 25), (38, 20), (38, 11), (13, 34), (13, 18), (33, 24), (22, 14), (19, 4), (12, 10), (22, 35), (27, 30), (24, 27), (2, 40), (8, 42), (27, 31), (20, 29), (38, 10), (7, 31), (36, 16), (22, 31), (4, 18), (15, 23), (23, 25), (31, 35), (27, 2), (23, 11), (10, 37), (23, 36), (28, 17), (25, 0), (12, 30), (32, 29), (12, 13), (10, 45), (10, 21), (5, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 17), (3, 23), (30, 14), (26, 13), (3, 20), (23, 5), (18, 35), (3, 12), (37, 6), (42, 40), (3, 16), (28, 19), (14, 10), (1, 7), (6, 6), (0, 8), (25, 9), (15, 6), (32, 36), (42, 13), (0, 34), (19, 4), (10, 1), (29, 21), (5, 20), (35, 19), (6, 17), (18, 31), (17, 1), (15, 31), (12, 17), (12, 37), (46, 39), (42, 3), (36, 11), (40, 31), (35, 33), (25, 29), (42, 27), (29, 18), (13, 2), (14, 27), (22, 7), (33, 38), (32, 35), (31, 19), (39, 2), (22, 4), (36, 16), (46, 3), (0, 9), (42, 11), (0, 32), (25, 31), (13, 38), (29, 16), (5, 17), (19, 17), (24, 7), (38, 12), (6, 2), (28, 24), (14, 33), (23, 1), (8, 17), (2, 40), (41, 6), (24, 15), (1, 0), (34, 36), (16, 13), (25, 22), (35, 12), (4, 40), (43, 14), (5, 22), (23, 24), (16, 6), (30, 3), (29, 30), (4, 13), (2, 0), (43, 9), (22, 3), (35, 20), (32, 38), (10, 12), (37, 24), (23, 18), (44, 26), (26, 32), (13, 8), (30, 37), (35, 25), (16, 34), (31, 3), (11, 37), (39, 26), (18, 17), (14, 23), (3, 25), (5, 31), (18, 13), (16, 22), (17, 0), (29, 23), (37, 31), (2, 20), (19, 25), (33, 17), (10, 10), (10, 39), (1, 27), (42, 5), (28, 30), (13, 21), (32, 2), (35, 26), (2, 6), (21, 10), (9, 30), (14, 34), (43, 12), (6, 39), (4, 4), (24, 27), (9, 11), (19, 34), (36, 18), (12, 32), (29, 1), (11, 21), (41, 13), (5, 8), (33, 25), (33, 27), (6, 25), (32, 3), (20, 6), (23, 38), (16, 23), (44, 0), (41, 4), (25, 7), (12, 18), (16, 19), (13, 6), (42, 25), (40, 10), (45, 38), (15, 22), (43, 5), (30, 6), (44, 11), (17, 18), (11, 30), (27, 29), (22, 13), (16, 32), (14, 22), (1, 39), (11, 17), (6, 24), (29, 5), (29, 40), (37, 32), (25, 10), (17, 15), (28, 12), (3, 21), (12, 6), (43, 40), (44, 33), (27, 35), (46, 19), (18, 32), (9, 27), (12, 20), (45, 10), (44, 24), (15, 2), (19, 35), (29, 27), (4, 39), (29, 10), (25, 37), (30, 18), (44, 21), (6, 22), (23, 34), (43, 4), (10, 29), (27, 18), (20, 14), (44, 22), (12, 4), (40, 38), (43, 25), (7, 36), (17, 26), (7, 35), (18, 40), (7, 17), (33, 24), (2, 28), (17, 2), (26, 40), (41, 1), (6, 16), (25, 4), (26, 26), (21, 21), (20, 18), (25, 30), (27, 27), (38, 29), (10, 23), (43, 15), (22, 28), (38, 13), (24, 35), (43, 7), (18, 2), (27, 21), (22, 29), (37, 8), (42, 37), (14, 15), (39, 37), (46, 29), (18, 34), (11, 35), (42, 35), (39, 7), (26, 4), (18, 16), (15, 23), (33, 18), (44, 35), (36, 37), (3, 17), (18, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 14), (31, 12), (12, 14), (12, 15), (33, 25), (27, 1), (22, 18), (22, 3), (14, 31), (34, 11), (3, 0), (0, 30), (17, 11), (12, 31), (40, 35), (34, 30), (38, 48), (11, 33), (33, 6), (4, 10), (28, 27), (10, 12), (31, 6), (31, 45), (30, 33), (36, 29), (18, 3), (25, 20), (14, 46), (0, 48), (8, 35), (31, 11), (34, 35), (18, 48), (1, 3), (36, 25), (0, 37), (25, 10), (14, 43), (4, 27), (39, 13), (24, 44), (28, 0), (33, 28), (10, 31), (1, 22), (37, 44), (11, 27), (40, 37), (24, 36), (11, 23), (9, 11), (40, 42), (19, 5), (6, 37), (1, 30), (40, 31), (8, 33), (25, 41), (7, 48), (23, 19), (2, 29), (16, 0), (19, 25), (10, 40), (11, 9), (23, 20), (7, 17), (14, 48), (25, 34), (7, 10), (17, 1), (23, 29), (7, 35), (6, 27), (0, 41), (10, 39), (29, 19), (13, 18), (41, 28), (0, 19), (34, 2), (19, 9), (33, 5), (3, 31), (11, 44), (17, 12), (13, 34), (21, 29), (8, 19), (27, 39), (8, 43), (21, 14), (23, 11), (37, 13), (8, 34), (26, 12), (37, 16), (39, 43), (30, 29), (15, 44), (23, 2), (11, 42), (5, 35), (14, 47), (40, 45), (34, 37), (40, 44), (0, 15), (2, 22), (6, 41), (8, 3), (15, 7), (39, 3), (30, 31), (41, 2), (23, 8), (34, 24), (35, 6), (19, 31), (25, 44), (14, 40), (1, 6), (4, 38), (37, 45), (40, 10), (11, 8), (18, 35), (20, 47), (13, 15), (38, 5), (3, 25), (17, 6), (21, 13), (32, 13), (34, 40), (6, 43), (19, 27), (11, 48), (2, 9), (31, 46), (26, 14), (24, 6), (3, 11), (35, 9), (24, 43), (9, 31), (5, 38), (30, 18), (14, 17), (7, 14), (41, 9), (18, 32), (38, 46), (23, 37), (22, 48), (39, 23), (24, 19), (8, 20), (13, 4), (22, 4), (16, 1), (27, 35), (13, 2), (10, 14), (13, 17), (39, 36), (8, 11), (34, 4), (12, 6), (18, 26), (13, 41), (26, 23), (4, 40), (34, 31), (7, 43), (29, 13), (0, 32), (28, 5), (36, 6), (22, 27), (27, 16), (37, 27), (10, 24), (25, 21), (35, 29), (40, 30), (26, 6), (14, 25), (16, 22), (2, 40), (23, 25), (31, 27), (24, 13), (7, 19), (16, 17), (11, 38), (39, 28), (6, 1), (30, 25), (21, 32), (37, 30), (25, 3), (23, 46), (5, 3), (30, 27), (1, 38), (30, 8), (21, 2), (5, 26), (13, 40), (4, 5), (33, 23), (40, 24), (40, 41), (3, 29), (16, 13), (9, 25), (9, 15), (2, 30), (34, 15), (25, 42), (20, 18), (28, 35), (23, 15), (11, 1), (30, 39), (41, 4), (35, 23), (0, 33), (29, 17), (14, 15), (15, 25), (20, 38), (3, 7), (23, 42), (7, 46), (19, 3), (37, 26), (18, 20), (19, 47), (40, 40), (41, 13), (13, 6), (36, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 21), (12, 15), (24, 22), (3, 8), (34, 4), (20, 29), (5, 32), (18, 39), (2, 5), (21, 21), (40, 31), (30, 11), (27, 15), (19, 23), (12, 25), (4, 32), (13, 36), (16, 6), (40, 16), (27, 20), (34, 24), (14, 39), (17, 6), (19, 24), (10, 21), (30, 32), (10, 1), (18, 26), (3, 29), (24, 4), (36, 4), (13, 17), (18, 10), (19, 9), (32, 16), (36, 36), (23, 7), (16, 20), (10, 33), (21, 37), (35, 7), (26, 10), (2, 34), (32, 7), (38, 10), (1, 13), (33, 19), (31, 13), (42, 26), (8, 21), (29, 14), (5, 35), (20, 30), (19, 20), (19, 14), (24, 11), (11, 2), (34, 6), (31, 5), (29, 30), (11, 17), (21, 17), (33, 40), (20, 25), (8, 24), (12, 16), (42, 25), (27, 13), (31, 30), (35, 39), (18, 0), (37, 5), (29, 6), (22, 37), (7, 12), (32, 28), (41, 35), (20, 34), (31, 31), (14, 5), (25, 40), (1, 25), (41, 32), (0, 26), (16, 18), (28, 28), (21, 29), (6, 4), (10, 8), (27, 25), (31, 28), (27, 18), (13, 24), (26, 2), (24, 0), (8, 34), (4, 9), (12, 30), (25, 5), (26, 1), (23, 8), (18, 32), (22, 27), (42, 39), (30, 17), (20, 16), (9, 0), (26, 36), (32, 23), (13, 20), (32, 36), (22, 25), (0, 12), (32, 35), (32, 39), (24, 12), (6, 24), (28, 34), (39, 9), (28, 13), (31, 21), (21, 9), (23, 12), (42, 1), (40, 39), (21, 16), (32, 19), (26, 20), (9, 1), (29, 17), (10, 12), (1, 19), (36, 25), (0, 8), (25, 10), (21, 25), (35, 30), (38, 25), (16, 1), (37, 23), (19, 28), (29, 27), (39, 23), (19, 4), (12, 5), (17, 29), (34, 32), (24, 32), (13, 25), (20, 9), (36, 16), (18, 36), (13, 22), (18, 14), (17, 22), (37, 13), (40, 6), (39, 19), (31, 14), (33, 8), (9, 34), (37, 35), (28, 12), (12, 24), (15, 31), (6, 38), (9, 28), (21, 33), (37, 3), (3, 19), (40, 23), (3, 13), (31, 1), (15, 2), (7, 17), (16, 0), (21, 39), (29, 38), (1, 11), (16, 24), (9, 14), (25, 8), (14, 38), (15, 5), (30, 19), (36, 2), (42, 8), (29, 7), (31, 40), (13, 15), (14, 30), (23, 17), (19, 32), (36, 32), (17, 14), (38, 33), (6, 33), (30, 3), (5, 39), (31, 22), (18, 29), (4, 40), (10, 16), (30, 29), (2, 36), (16, 5), (42, 13), (33, 11), (35, 24), (40, 7), (20, 38), (41, 28), (0, 38), (33, 36), (34, 2), (22, 36), (15, 7), (37, 19), (35, 33), (35, 18), (42, 28), (12, 39), (12, 37), (9, 24), (3, 4), (11, 6), (5, 15), (2, 22), (19, 2), (3, 12), (37, 10), (31, 16), (14, 20), (5, 14), (32, 8), (23, 35), (28, 22), (30, 1), (2, 4), (31, 29), (18, 7), (4, 15), (36, 20), (13, 19), (33, 12), (14, 35), (1, 17), (17, 34), (1, 33), (31, 19), (32, 33), (34, 27), (7, 0), (7, 5), (21, 28), (24, 9), (24, 16), (19, 35), (19, 15), (6, 39), (25, 23), (35, 12), (11, 32), (0, 13), (4, 12), (12, 14), (15, 20), (9, 29), (19, 26), (10, 25), (5, 22), (37, 40), (3, 36), (11, 21), (39, 33), (30, 16), (15, 29), (26, 35), (27, 21), (39, 40), (18, 19), (0, 37), (23, 10), (3, 3), (40, 37), (3, 20), (38, 26), (17, 40), (36, 13), (1, 31), (5, 2), (2, 39), (1, 6), (13, 39), (2, 30), (30, 5), (37, 37), (36, 11), (24, 26), (42, 17), (38, 11), (21, 1), (1, 36), (15, 40), (31, 3), (1, 2), (39, 34), (10, 31), (0, 20), (21, 20), (10, 18), (28, 9), (41, 27), (16, 11), (36, 10), (41, 6), (19, 8), (5, 13), (7, 23), (40, 24), (28, 36), (28, 11), (2, 38), (31, 27), (5, 16), (32, 1), (21, 34), (34, 16), (27, 2), (42, 19), (17, 16), (8, 3), (4, 18), (9, 16), (27, 27), (3, 26), (38, 0), (30, 24), (8, 40), (10, 24), (27, 38), (14, 14), (4, 5), (11, 14), (6, 31), (6, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 30), (45, 20), (6, 38), (44, 9), (19, 18), (23, 2), (37, 6), (43, 25), (1, 13), (15, 25), (38, 6), (39, 42), (15, 31), (29, 13), (32, 34), (42, 28), (4, 42), (5, 29), (12, 16), (12, 20), (31, 14), (14, 17), (12, 25), (8, 34), (32, 13), (25, 34), (20, 33), (24, 5), (5, 23), (41, 5), (13, 39), (25, 15), (5, 31), (24, 0), (1, 30), (26, 4), (33, 34), (4, 13), (16, 7), (28, 30), (43, 18), (15, 6), (18, 3), (6, 0), (35, 9), (7, 18), (9, 7), (27, 24), (23, 19), (24, 38), (14, 24), (32, 28), (29, 33), (14, 31), (39, 27), (27, 39), (22, 27), (23, 26), (4, 40), (0, 39), (0, 31), (14, 4), (14, 41), (20, 27), (20, 32), (38, 24), (40, 28), (29, 21), (37, 35), (19, 21), (37, 34), (26, 20), (26, 7), (45, 23), (39, 31), (0, 34), (13, 10), (12, 17), (0, 28), (8, 14), (30, 40), (32, 40), (9, 21), (41, 11), (44, 29), (5, 0), (33, 1), (41, 40), (0, 11), (4, 20), (19, 23), (3, 11), (44, 19), (34, 25), (23, 23), (13, 22), (5, 41), (21, 17), (12, 22), (45, 7), (29, 39), (6, 23), (38, 2), (42, 9), (24, 34), (1, 23), (8, 9), (30, 20), (4, 30), (32, 23), (29, 4), (0, 42), (11, 42), (39, 11), (40, 8), (19, 25), (6, 30), (22, 3), (3, 8), (34, 4), (28, 23), (36, 12), (17, 35), (2, 10), (8, 37), (3, 30), (42, 24), (27, 2), (26, 32), (35, 16), (40, 12), (27, 41), (23, 38), (0, 32), (42, 0), (34, 7), (39, 2), (10, 39), (23, 22), (45, 32), (4, 2), (18, 28), (14, 40), (37, 14), (40, 30), (6, 25), (35, 38), (30, 28), (15, 38), (16, 15), (44, 42), (20, 20), (43, 36), (27, 42), (28, 0), (10, 0), (33, 23), (34, 11), (23, 17), (16, 35), (20, 1), (20, 7), (19, 26), (24, 18), (37, 27), (18, 26), (9, 10), (38, 22), (9, 30), (22, 25), (5, 1), (5, 14), (41, 10), (12, 29), (14, 25), (17, 6), (34, 30), (15, 19), (28, 41), (5, 42), (37, 40), (19, 36), (0, 17), (37, 3), (41, 30), (1, 35), (9, 17), (20, 18), (21, 18), (44, 22), (15, 33), (35, 36), (35, 15), (39, 28), (45, 25), (30, 25), (24, 26), (4, 35), (2, 9), (27, 16), (7, 20), (45, 11), (25, 16), (6, 37), (39, 36), (13, 17), (11, 5), (38, 17), (37, 33), (3, 42), (32, 29), (41, 7), (18, 40), (19, 22), (26, 34), (2, 25), (34, 41), (16, 34), (25, 14), (44, 0), (1, 8), (33, 31), (44, 21), (28, 15), (16, 29), (40, 13), (8, 39), (30, 42), (39, 6), (0, 15), (19, 41), (22, 29), (29, 16), (10, 17), (4, 15), (20, 39), (1, 37), (1, 21), (14, 38), (16, 3), (3, 6), (3, 32), (9, 32), (11, 13), (13, 36), (8, 38), (43, 13), (5, 16), (15, 29), (28, 26), (37, 25), (44, 26), (20, 31), (35, 23), (40, 10), (1, 32), (36, 30), (15, 4), (25, 29), (11, 34), (21, 22), (5, 27), (20, 10), (0, 16), (36, 7), (35, 20), (35, 11), (2, 3), (21, 5), (2, 36), (40, 29), (13, 41), (11, 15), (40, 2), (11, 21), (20, 4), (24, 35), (25, 38), (44, 10), (39, 22), (31, 7), (34, 1), (10, 21), (40, 9), (13, 19), (8, 5), (7, 31), (37, 28), (16, 4), (45, 38), (18, 20), (6, 29), (43, 14), (45, 3), (21, 32), (29, 27), (7, 28), (43, 34), (38, 14), (28, 4), (21, 31), (22, 18), (6, 15), (27, 17), (11, 35), (33, 19), (36, 23), (3, 16), (43, 8), (11, 31), (14, 26), (0, 2), (22, 9), (5, 39), (41, 8), (33, 26), (8, 28), (34, 8), (32, 3), (36, 42), (24, 7), (25, 19), (19, 30), (20, 22), (43, 37), (2, 32), (35, 25), (14, 33), (20, 42), (30, 27), (43, 2), (39, 12), (31, 10), (33, 20), (45, 2), (40, 3), (25, 1), (6, 18), (14, 20), (31, 28), (22, 2), (22, 0), (11, 30), (15, 21), (39, 0), (3, 26), (10, 42), (45, 16), (16, 0), (28, 6), (2, 20), (6, 32), (32, 8), (2, 31), (24, 8), (24, 37), (15, 0), (15, 10), (9, 20), (28, 27), (30, 29), (30, 24), (36, 16), (5, 12), (8, 23), (26, 2), (24, 30), (38, 35), (33, 14), (36, 19), (28, 25), (11, 32), (8, 6), (19, 17), (33, 21), (26, 1), (16, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (15, 11), (23, 11), (28, 38), (20, 39), (17, 37), (31, 7), (4, 39), (21, 30), (16, 15), (21, 27), (18, 31), (32, 6), (25, 6), (4, 11), (15, 1), (22, 25), (38, 25), (29, 14), (1, 32), (14, 38), (7, 16), (5, 9), (29, 39), (14, 15), (1, 8), (19, 39), (24, 23), (18, 19), (37, 34), (32, 15), (21, 9), (40, 31), (15, 17), (34, 17), (45, 29), (42, 33), (23, 15), (45, 19), (23, 36), (24, 39), (17, 20), (15, 3), (12, 14), (25, 33), (46, 15), (20, 12), (8, 33), (10, 10), (16, 24), (0, 2), (4, 31), (10, 29), (42, 35), (1, 35), (21, 17), (22, 17), (2, 19), (44, 38), (8, 29), (39, 1), (31, 1), (28, 22), (30, 32), (37, 3), (17, 40), (42, 31), (40, 9), (41, 15), (26, 30), (22, 0), (10, 6), (36, 1), (27, 20), (34, 0), (24, 14), (0, 22), (3, 16), (14, 28), (18, 38), (7, 33), (21, 12), (23, 14), (28, 11), (21, 6), (3, 5), (30, 20), (27, 37), (40, 29), (22, 32), (38, 37), (10, 3), (10, 5), (41, 19), (11, 27), (7, 0), (26, 0), (6, 12), (32, 40), (39, 22), (20, 0), (18, 22), (31, 26), (15, 34), (2, 28), (41, 25), (18, 13), (23, 2), (21, 2), (45, 5), (2, 1), (32, 4), (31, 28), (32, 3), (23, 33), (16, 3), (23, 37), (44, 31), (15, 23), (2, 39), (9, 24), (13, 24), (36, 0), (3, 11), (5, 3), (9, 33), (29, 27), (26, 5), (17, 30), (23, 27), (7, 12), (2, 13), (46, 22), (36, 31), (13, 16), (36, 15), (38, 34), (17, 18), (23, 28), (28, 5), (12, 11), (13, 12), (5, 23), (33, 6), (17, 1), (19, 23), (38, 31), (38, 22), (23, 20), (30, 22), (12, 40), (8, 10), (19, 26), (44, 1), (45, 40), (38, 26), (14, 25), (28, 2), (15, 30), (26, 1), (34, 20), (17, 7), (4, 27), (26, 2), (42, 5), (35, 7), (38, 30), (28, 32), (38, 36), (16, 17), (40, 32), (21, 16), (15, 4), (44, 6), (20, 27), (5, 26), (22, 2), (19, 22), (1, 36), (22, 36), (6, 37), (37, 2), (45, 11), (43, 10), (43, 32), (30, 19), (18, 11), (39, 4), (6, 8), (6, 26), (25, 9), (5, 4), (30, 28), (1, 13), (20, 17), (39, 20), (45, 9), (37, 18), (33, 16), (29, 19), (33, 19), (29, 8), (37, 39), (37, 4), (34, 21), (10, 12), (6, 35), (7, 25), (29, 22), (39, 17), (23, 4), (42, 36), (30, 24), (28, 23), (10, 11), (29, 4), (20, 7), (25, 12), (18, 15), (2, 35), (18, 21), (37, 29), (35, 14), (4, 32), (18, 32), (34, 5), (28, 34), (35, 24), (5, 33), (41, 8), (15, 16), (27, 11), (27, 31), (45, 22), (3, 28), (12, 33), (12, 17), (46, 17), (11, 39), (7, 24), (17, 8), (7, 22), (39, 39), (39, 18), (8, 35), (21, 5), (16, 40), (28, 30), (15, 32), (28, 31), (9, 6), (35, 2), (15, 31), (27, 14), (2, 25), (17, 0), (37, 17), (11, 11), (6, 0), (3, 4), (42, 22), (10, 33), (4, 36), (25, 15), (24, 35), (7, 8), (9, 39), (1, 14), (12, 1), (26, 3), (6, 2), (35, 23), (27, 24), (14, 39), (20, 3), (44, 22), (7, 23), (26, 20), (45, 27), (39, 11), (44, 10), (4, 34), (21, 29), (28, 26), (10, 24), (11, 21), (43, 5), (2, 4), (8, 7), (17, 13), (19, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (48, 6), (23, 43), (14, 35), (45, 39), (15, 14), (2, 32), (36, 17), (0, 39), (33, 24), (37, 10), (6, 41), (41, 29), (31, 40), (43, 22), (43, 27), (27, 31), (9, 39), (41, 38), (43, 21), (8, 43), (27, 34), (23, 37), (46, 19), (27, 32), (3, 35), (13, 24), (23, 17), (4, 36), (1, 30), (48, 0), (31, 37), (40, 36), (33, 35), (14, 27), (41, 47), (25, 9), (11, 39), (17, 19), (18, 16), (40, 21), (38, 46), (23, 6), (38, 3), (10, 19), (8, 14), (36, 19), (42, 23), (9, 36), (39, 9), (48, 10), (23, 29), (43, 5), (10, 41), (41, 12), (26, 29), (41, 15), (42, 44), (21, 42), (38, 44), (9, 26), (25, 1), (12, 40), (40, 28), (26, 33), (24, 16), (27, 37), (0, 32), (47, 6), (3, 23), (47, 40), (47, 21), (2, 4), (20, 36), (35, 14), (31, 47), (4, 41), (7, 19), (0, 33), (27, 7), (35, 9), (5, 18), (22, 30), (34, 47), (0, 37), (43, 6), (10, 11), (6, 30), (11, 40), (17, 35), (35, 23), (4, 18), (5, 46), (16, 1), (1, 47), (0, 21), (15, 24), (48, 24), (22, 6), (31, 30), (5, 37), (47, 10), (21, 35), (42, 45), (38, 30), (41, 28), (18, 4), (11, 22), (1, 29), (4, 25), (43, 32), (27, 24), (35, 36), (12, 7), (29, 0), (15, 2), (18, 7), (48, 3), (11, 44), (8, 21), (0, 22), (47, 20), (21, 33), (19, 23), (47, 32), (31, 10), (14, 24), (12, 3), (38, 26), (41, 32), (44, 36), (41, 0), (35, 4), (13, 3), (40, 24), (9, 15), (6, 38), (42, 38), (48, 46), (12, 36), (36, 27), (32, 9), (5, 43), (20, 42), (18, 14), (42, 31), (13, 38), (22, 46), (3, 2), (32, 6), (24, 28), (33, 34), (47, 3), (25, 24), (10, 24), (28, 21), (1, 43), (24, 1), (23, 41), (4, 4), (2, 28), (7, 14), (45, 41), (30, 23), (8, 15), (18, 12), (41, 34), (13, 7), (10, 45), (25, 13), (47, 14), (27, 1), (36, 44), (3, 12), (40, 26), (34, 6), (19, 0), (36, 35), (0, 28), (45, 4), (32, 8), (37, 6), (37, 7), (34, 34), (0, 42), (45, 21), (23, 40), (36, 10), (47, 16), (12, 21), (14, 18), (18, 0), (4, 2), (32, 40), (17, 37), (24, 25), (4, 47), (27, 30), (24, 15), (40, 17), (4, 10), (44, 28), (28, 7), (12, 41), (25, 11), (11, 9), (41, 7), (18, 8), (14, 12), (29, 35), (44, 39), (48, 31), (5, 26), (10, 26), (48, 8), (33, 14), (38, 36), (25, 17), (19, 14), (22, 2), (45, 10), (16, 12), (14, 46), (16, 18), (13, 26), (22, 33), (5, 11), (18, 1), (0, 36), (45, 3), (22, 38), (46, 31), (0, 14), (46, 36), (38, 31), (39, 4), (16, 15), (10, 25), (5, 7), (11, 36), (7, 18), (4, 20), (32, 27), (16, 11), (21, 28), (7, 45), (23, 30), (34, 13), (10, 14), (34, 31), (17, 0), (34, 21), (2, 7), (4, 9), (17, 25), (13, 0), (46, 38), (5, 33), (33, 13), (17, 32), (11, 14), (32, 30), (48, 11), (33, 44), (37, 24), (12, 1), (5, 19), (7, 41), (2, 26), (8, 40), (18, 13), (34, 30), (6, 4), (38, 33), (29, 11), (48, 27), (24, 27), (3, 10), (31, 29), (36, 20), (26, 26), (18, 10), (0, 44), (44, 40), (39, 7), (35, 12), (48, 4), (31, 18), (13, 27), (21, 16), (38, 4), (4, 11), (46, 2), (18, 44), (48, 35), (36, 41), (31, 8), (37, 19), (38, 22), (13, 45), (14, 0), (45, 20), (17, 38), (10, 22), (31, 6), (24, 21), (46, 29), (23, 42), (38, 15), (27, 11), (41, 36), (16, 38), (6, 44), (42, 13), (46, 45), (42, 24), (27, 8), (3, 37), (17, 14), (14, 19), (42, 29), (0, 40), (9, 32), (35, 22), (27, 43), (31, 43), (22, 13), (29, 31), (10, 5), (43, 1), (18, 45), (41, 2), (24, 30), (25, 30), (15, 32), (37, 27), (22, 10), (16, 23), (26, 30), (6, 18), (26, 17), (33, 20), (15, 22), (37, 30), (23, 33), (15, 41), (48, 7), (23, 46), (8, 18), (5, 1), (4, 43), (7, 0), (23, 14), (28, 3), (30, 40), (0, 17), (48, 2), (28, 35), (21, 47), (5, 47), (13, 42), (24, 22), (35, 16), (5, 36), (10, 23), (7, 15), (35, 15), (14, 41), (7, 46), (26, 38), (34, 38), (22, 7), (41, 14), (45, 26), (10, 12), (42, 28), (20, 14), (28, 40), (46, 10), (1, 2), (5, 21), (26, 44), (48, 26), (48, 14), (1, 37), (21, 23), (36, 40), (28, 32), (44, 38), (19, 13), (27, 46), (41, 45), (20, 45), (1, 17), (48, 16), (1, 4), (33, 40), (38, 23), (17, 26), (45, 18), (36, 8), (38, 1), (10, 3), (1, 24), (34, 25), (18, 40), (37, 3), (25, 38), (41, 17), (11, 23), (36, 42), (26, 46), (12, 33), (42, 11), (6, 37), (30, 46), (29, 39), (11, 8), (26, 31), (21, 15), (40, 38), (10, 18), (30, 14), (39, 12), (24, 29), (37, 9), (33, 26), (46, 24), (34, 41), (26, 37), (14, 14), (44, 21), (4, 37), (4, 39), (4, 44), (17, 4), (9, 35), (41, 27), (40, 41), (7, 1), (20, 25), (28, 23), (33, 29), (2, 15), (45, 35), (42, 32), (32, 35), (30, 7), (34, 29), (28, 1), (1, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 38), (33, 24), (14, 22), (30, 13), (39, 37), (44, 12), (42, 15), (15, 16), (6, 9), (44, 38), (42, 10), (4, 18), (9, 33), (12, 33), (16, 12), (36, 35), (43, 46), (22, 16), (16, 17), (10, 40), (0, 45), (36, 46), (44, 47), (9, 3), (42, 44), (5, 4), (43, 20), (6, 43), (15, 18), (28, 21), (24, 13), (41, 27), (32, 24), (11, 2), (13, 8), (26, 46), (11, 36), (32, 15), (3, 7), (44, 45), (0, 16), (7, 43), (11, 40), (36, 36), (25, 36), (33, 25), (27, 3), (15, 29), (34, 30), (9, 16), (29, 19), (2, 28), (23, 1), (19, 43), (0, 8), (11, 3), (6, 35), (27, 45), (3, 30), (39, 0), (34, 26), (15, 3), (33, 2), (35, 18), (22, 37), (20, 39), (36, 24), (22, 17), (28, 9), (24, 25), (40, 9), (42, 22), (4, 23), (34, 21), (8, 41), (23, 25), (44, 1), (7, 3), (16, 14), (29, 18), (23, 5), (25, 28), (8, 18), (4, 36), (23, 19), (5, 36), (16, 43), (9, 17), (45, 17), (22, 38), (36, 12), (20, 10), (10, 2), (37, 36), (14, 39), (40, 11), (16, 20), (36, 8), (22, 36), (26, 19), (3, 16), (34, 13), (40, 13), (18, 8), (47, 24), (38, 42), (17, 47), (4, 47), (30, 30), (16, 25), (45, 28), (44, 42), (28, 19), (6, 34), (9, 5), (8, 10), (14, 31), (32, 20), (27, 37), (44, 15), (35, 34), (19, 2), (26, 41), (27, 19), (24, 11), (19, 44), (31, 25), (33, 3), (44, 19), (35, 25), (15, 22), (37, 39), (38, 17), (16, 23), (14, 15), (43, 42), (47, 9), (30, 35), (34, 22), (46, 38), (43, 35), (19, 28), (18, 30), (46, 13), (4, 12), (44, 9), (8, 42), (23, 12), (5, 12), (27, 38), (5, 22), (20, 31), (37, 3), (47, 44), (15, 43), (8, 7), (23, 43), (41, 47), (8, 31), (7, 31), (30, 8), (0, 41), (32, 10), (41, 17), (42, 1), (28, 35), (23, 34), (42, 4), (23, 28), (40, 19), (17, 1), (33, 17), (0, 13), (35, 17), (24, 31), (20, 23), (46, 25), (33, 6), (45, 24), (21, 25), (31, 37), (28, 12), (22, 15), (45, 19), (21, 27), (11, 44), (32, 18), (18, 21), (45, 36), (24, 33), (39, 46), (27, 7), (32, 9), (1, 6), (39, 6), (30, 39), (3, 8), (7, 10), (16, 15), (13, 3), (26, 7), (33, 30), (31, 14), (29, 14), (38, 35), (16, 36), (10, 33), (44, 18), (38, 3), (46, 8), (26, 31), (37, 40), (44, 36), (2, 36), (19, 46), (30, 44), (24, 8), (14, 13), (20, 36), (6, 28), (37, 9), (31, 10), (16, 3), (6, 16), (14, 24), (26, 12), (36, 39), (25, 34), (10, 23), (1, 14), (4, 20), (10, 30), (25, 44), (22, 40), (43, 23), (18, 45), (11, 23), (32, 31), (37, 18), (47, 22), (16, 37), (32, 6), (29, 6), (27, 18), (13, 14), (5, 21), (7, 45), (28, 30), (8, 33), (14, 44), (7, 14), (14, 30), (47, 6), (8, 17), (0, 30), (19, 4), (34, 37), (13, 41), (39, 43), (0, 3), (9, 10), (41, 32), (1, 7), (43, 37), (22, 35), (3, 40), (43, 3), (24, 47), (37, 38), (36, 3), (18, 13), (26, 16), (16, 22), (1, 22), (3, 23), (21, 16), (2, 33), (27, 43), (28, 6), (5, 5), (27, 46), (0, 39), (41, 36), (39, 23), (29, 33), (22, 19), (20, 13), (32, 29), (24, 17), (21, 9), (20, 47), (37, 32), (17, 28), (17, 24), (37, 6), (47, 31), (28, 38), (20, 27), (21, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 28), (31, 20), (3, 14), (14, 11), (10, 34), (32, 10), (12, 12), (42, 33), (18, 36), (22, 6), (25, 38), (40, 7), (29, 11), (8, 4), (32, 37), (41, 9), (44, 1), (20, 17), (16, 36), (16, 38), (14, 31), (24, 34), (23, 28), (41, 35), (43, 29), (5, 16), (24, 36), (14, 2), (6, 1), (3, 19), (43, 25), (24, 21), (22, 12), (18, 18), (12, 34), (8, 11), (26, 32), (39, 32), (14, 26), (13, 25), (16, 19), (3, 5), (19, 10), (2, 33), (21, 2), (27, 27), (37, 8), (30, 33), (28, 6), (3, 0), (35, 0), (22, 20), (19, 23), (14, 0), (30, 4), (40, 9), (32, 34), (8, 29), (9, 29), (16, 1), (30, 8), (27, 32), (45, 29), (18, 31), (29, 36), (43, 23), (27, 36), (19, 16), (24, 0), (44, 5), (3, 37), (9, 26), (38, 18), (17, 21), (20, 39), (5, 13), (40, 34), (39, 36), (12, 14), (15, 28), (4, 17), (7, 12), (18, 8), (27, 14), (28, 9), (6, 14), (9, 34), (13, 17), (15, 4), (28, 27), (7, 9), (26, 24), (33, 5), (14, 4), (1, 3), (25, 28), (16, 33), (38, 16), (32, 33), (8, 30), (20, 27), (12, 3), (31, 14), (2, 12), (5, 37), (38, 33), (23, 10), (30, 32), (38, 39), (21, 7), (25, 26), (24, 25), (29, 39), (34, 12), (16, 20), (17, 39), (19, 0), (4, 37), (14, 20), (20, 15), (23, 19), (39, 4), (39, 20), (33, 17), (21, 36), (44, 35), (3, 35), (10, 22), (12, 37), (25, 39), (5, 36), (29, 26), (31, 35), (36, 15), (31, 28), (5, 15), (21, 18), (34, 16), (17, 2), (42, 15), (4, 7), (6, 19), (6, 7), (29, 18), (23, 30), (5, 1), (7, 29), (25, 18), (26, 22), (16, 14), (0, 1), (38, 3), (6, 11), (7, 7), (36, 28), (22, 16), (17, 15), (29, 22), (38, 36), (1, 24), (43, 3), (25, 35), (13, 11), (21, 19), (39, 37), (10, 39), (29, 34), (39, 1), (9, 19), (17, 16), (4, 34), (20, 4), (1, 39), (0, 16), (45, 18), (7, 36), (13, 10), (34, 7), (31, 34), (16, 35), (39, 21), (3, 36), (42, 4), (25, 0), (37, 21), (24, 35), (38, 32), (1, 13), (2, 32), (45, 25), (40, 0), (8, 17), (35, 36), (5, 38), (6, 25), (43, 18), (11, 33), (43, 32), (12, 21), (8, 24), (22, 34), (14, 38), (10, 4), (27, 20), (20, 30), (42, 10), (21, 23), (16, 32), (6, 16), (0, 29), (16, 17), (45, 6), (32, 14), (22, 7), (37, 35), (15, 34), (2, 22), (8, 19), (6, 9), (30, 10), (30, 31), (35, 1), (5, 9), (3, 27), (25, 11), (38, 29), (22, 27), (37, 3), (21, 20), (2, 30), (13, 31), (2, 25), (11, 22), (6, 24), (1, 27), (39, 16), (32, 13), (27, 25), (4, 31), (43, 39), (29, 7), (43, 5), (10, 0), (9, 3), (34, 20), (17, 23), (45, 36), (23, 17), (33, 18), (17, 35), (18, 29), (5, 29), (9, 35), (18, 17), (16, 39), (43, 19), (13, 38), (9, 18), (39, 2), (30, 22), (16, 2), (11, 0), (38, 31), (24, 9), (25, 24), (4, 10), (1, 15), (17, 24), (19, 30), (33, 21), (42, 1), (38, 38), (7, 21), (7, 24), (10, 23), (42, 25), (15, 7), (6, 23), (24, 12), (9, 33), (43, 28), (40, 25), (33, 36), (41, 8), (31, 22), (14, 7), (0, 4), (11, 31), (22, 9), (14, 27), (43, 0), (27, 21), (42, 35), (34, 13), (13, 2), (22, 37), (25, 10), (11, 37), (7, 28), (18, 9), (43, 38), (24, 13), (37, 22), (15, 35), (1, 10), (41, 37), (29, 8), (20, 33), (30, 7), (4, 1), (13, 4), (39, 33), (19, 37), (13, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 36), (34, 15), (35, 6), (45, 21), (25, 24), (39, 39), (22, 4), (7, 29), (44, 38), (3, 2), (10, 29), (24, 21), (2, 24), (8, 39), (19, 37), (28, 11), (42, 6), (17, 16), (24, 4), (0, 25), (3, 18), (42, 28), (7, 34), (35, 27), (38, 39), (23, 28), (32, 8), (13, 39), (4, 12), (31, 24), (10, 42), (44, 24), (14, 11), (43, 1), (9, 9), (22, 21), (21, 17), (42, 38), (0, 12), (25, 30), (24, 27), (13, 31), (17, 19), (7, 17), (26, 37), (12, 27), (43, 28), (26, 5), (13, 8), (21, 3), (7, 32), (36, 33), (17, 21), (12, 10), (14, 39), (6, 35), (29, 8), (27, 0), (22, 11), (27, 30), (31, 7), (36, 16), (18, 9), (29, 12), (1, 34), (4, 1), (22, 40), (31, 9), (16, 38), (14, 5), (4, 8), (17, 22), (22, 35), (39, 13), (32, 10), (7, 15), (43, 14), (32, 28), (45, 5), (38, 0), (33, 10), (0, 38), (22, 33), (17, 20), (30, 7), (16, 12), (26, 31), (40, 3), (17, 23), (13, 37), (37, 35), (33, 4), (4, 13), (0, 32), (35, 30), (32, 5), (6, 6), (3, 41), (24, 5), (11, 39), (25, 2), (0, 8), (2, 25), (4, 25), (19, 26), (2, 32), (12, 8), (42, 16), (29, 6), (29, 16), (30, 32), (9, 22), (39, 33), (31, 11), (18, 31), (42, 11), (9, 27), (36, 28), (16, 41), (9, 5), (38, 10), (22, 0), (38, 13), (13, 0), (16, 23), (19, 11), (14, 29), (36, 3), (32, 2), (35, 8), (8, 36), (26, 7), (37, 22), (20, 14), (14, 22), (15, 27), (13, 15), (34, 1), (28, 14), (25, 40), (16, 14), (36, 23), (18, 6), (39, 42), (20, 35), (8, 24), (19, 27), (2, 41), (45, 33), (8, 7), (16, 13), (3, 3), (4, 29), (12, 13), (4, 28), (38, 14), (0, 18), (10, 3), (25, 29), (36, 10), (30, 5), (16, 29), (9, 20), (20, 22), (25, 21), (5, 38), (37, 24), (12, 7), (25, 27), (6, 41), (40, 1), (11, 31), (1, 21), (3, 7), (4, 35), (6, 39), (42, 5), (9, 21), (45, 40), (30, 4), (6, 9), (19, 31), (15, 42), (44, 8), (16, 15), (4, 19), (21, 16), (12, 37), (4, 18), (5, 18), (45, 13), (25, 37), (32, 17), (19, 5), (40, 37), (39, 9), (44, 31), (37, 13), (16, 8), (16, 35), (10, 1), (8, 21), (6, 13), (38, 24), (41, 5), (39, 8), (5, 28), (16, 6), (14, 15), (40, 7), (34, 12), (22, 34), (24, 22), (3, 36), (40, 19), (18, 4), (29, 3), (42, 40), (18, 19), (19, 1), (13, 26), (1, 11), (9, 17), (7, 13), (30, 24), (29, 35), (21, 37), (42, 13), (14, 33), (28, 2), (14, 35), (18, 3), (29, 32), (5, 36), (33, 35), (43, 32), (24, 39), (19, 29), (40, 17), (26, 8), (45, 37), (1, 22), (9, 3), (31, 40), (36, 19), (32, 20), (14, 27), (19, 2), (7, 3), (2, 23), (3, 8), (17, 1), (19, 22), (40, 22), (28, 12), (11, 21), (15, 12), (19, 10), (24, 16), (39, 14), (9, 38), (5, 34), (15, 31), (29, 36), (2, 11), (22, 42), (8, 32), (37, 19), (26, 10), (17, 41), (9, 40), (33, 28), (0, 34), (7, 41), (11, 32), (20, 32), (25, 9), (14, 9), (1, 13), (19, 23), (12, 3), (38, 26), (16, 24), (29, 1), (35, 42), (6, 40), (27, 29), (16, 21), (6, 29), (36, 26), (21, 7), (26, 2), (4, 21), (8, 17), (22, 12), (25, 16), (17, 37), (0, 17), (0, 23), (0, 33), (27, 12), (15, 20), (15, 16), (44, 42), (40, 15), (2, 18), (27, 4), (26, 14), (39, 26), (3, 12), (34, 23), (27, 13), (32, 22), (22, 8), (7, 38), (42, 8), (44, 28), (24, 18), (16, 3), (3, 6), (6, 8), (43, 9), (40, 27), (8, 1), (25, 19), (11, 16), (24, 12), (40, 4), (43, 40), (14, 8), (15, 10), (16, 27), (19, 13), (32, 16), (44, 6), (18, 7), (5, 0), (39, 25), (13, 41), (21, 33), (1, 42), (38, 40), (16, 7), (5, 15), (35, 2), (1, 35), (17, 3), (35, 20), (11, 37), (18, 5), (0, 42), (8, 0), (8, 18), (2, 4), (33, 15), (2, 29), (33, 41), (5, 31), (4, 38), (16, 39), (1, 4), (35, 41), (43, 23), (1, 2), (9, 14), (12, 32), (39, 35), (20, 6), (30, 8), (29, 42), (16, 32), (16, 1), (34, 35), (18, 13), (8, 28), (23, 26), (37, 28), (23, 15), (11, 11), (13, 3), (2, 10), (24, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 45), (12, 38), (27, 32), (25, 30), (19, 26), (21, 28), (9, 29), (29, 47), (37, 47), (15, 22), (18, 5), (32, 9), (26, 46), (42, 12), (1, 16), (15, 38), (6, 0), (41, 35), (38, 27), (41, 28), (1, 9), (6, 44), (6, 34), (11, 38), (42, 44), (25, 8), (13, 24), (18, 6), (22, 16), (21, 6), (38, 18), (25, 35), (2, 30), (35, 18), (28, 9), (19, 0), (11, 37), (29, 44), (14, 39), (25, 41), (6, 5), (2, 13), (31, 22), (9, 21), (6, 3), (17, 19), (33, 44), (10, 5), (13, 30), (2, 14), (23, 42), (5, 0), (21, 13), (11, 14), (10, 4), (11, 25), (37, 40), (21, 27), (41, 43), (42, 21), (23, 43), (12, 11), (30, 43), (28, 3), (15, 30), (41, 1), (14, 16), (5, 28), (7, 27), (12, 10), (18, 16), (34, 22), (1, 3), (21, 17), (11, 2), (7, 24), (16, 27), (11, 23), (18, 12), (40, 20), (28, 31), (35, 1), (42, 34), (26, 21), (23, 22), (38, 23), (3, 19), (11, 29), (41, 3), (39, 43), (16, 1), (3, 14), (9, 3), (37, 16), (22, 47), (5, 45), (17, 13), (14, 17), (38, 44), (1, 32), (26, 25), (11, 40), (1, 30), (4, 26), (22, 45), (3, 36), (13, 48), (10, 42), (34, 42), (39, 13), (39, 34), (27, 2), (41, 11), (3, 9), (19, 44), (4, 19), (11, 6), (18, 11), (5, 11), (20, 7), (38, 24), (27, 1), (37, 20), (38, 26), (29, 27), (37, 24), (10, 48), (32, 1), (42, 16), (17, 36), (8, 20), (2, 5), (22, 3), (19, 41), (17, 48), (42, 35), (8, 23), (11, 39), (12, 42), (22, 14), (2, 37), (21, 15), (41, 10), (3, 18), (34, 44), (30, 45), (35, 35), (11, 34), (4, 5), (24, 19), (41, 27), (23, 45), (2, 2), (5, 6), (42, 47), (41, 22), (1, 20), (34, 16), (15, 11), (12, 17), (30, 46), (17, 33), (19, 37), (13, 33), (2, 26), (26, 45), (20, 14), (24, 21), (22, 44), (2, 1), (21, 46), (5, 42), (18, 32), (37, 38), (2, 32), (0, 15), (32, 25), (26, 35), (11, 41), (21, 23), (2, 23), (34, 25), (10, 9), (38, 22), (7, 16), (24, 13), (39, 32), (38, 30), (31, 26), (33, 23), (31, 30), (12, 47), (34, 46), (13, 47), (41, 20), (12, 3), (38, 17), (31, 21), (16, 7), (20, 48), (33, 18), (42, 5), (19, 8), (8, 47), (36, 33), (32, 6), (16, 31), (18, 29), (17, 47), (19, 14), (9, 34), (4, 20), (21, 41), (12, 15), (2, 29), (29, 28), (42, 7), (39, 0), (10, 35), (30, 5), (29, 11), (2, 31), (2, 9), (35, 13), (4, 35), (29, 12), (5, 44), (18, 38), (42, 24), (5, 4), (7, 1), (36, 8), (2, 0), (38, 48), (18, 20), (11, 5), (30, 30), (18, 45), (33, 31), (9, 24), (16, 41), (26, 43), (12, 30), (16, 16), (10, 8), (33, 6), (15, 36), (41, 40), (38, 15), (10, 30), (32, 28), (28, 16), (29, 39), (35, 25), (15, 37), (23, 28), (33, 8), (27, 18), (4, 27), (31, 28), (32, 44), (26, 48), (22, 20), (12, 37), (3, 44), (19, 17), (20, 35), (37, 9), (42, 13), (28, 43), (24, 35), (19, 27), (23, 37), (42, 25), (35, 7), (29, 45), (34, 36), (13, 2), (2, 16), (27, 3), (37, 11), (8, 26), (41, 41), (42, 31), (41, 46), (15, 1), (32, 3), (25, 23), (19, 48)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 18), (17, 33), (40, 30), (38, 35), (21, 17), (37, 27), (15, 30), (20, 29), (39, 29), (15, 26), (11, 38), (29, 41), (40, 9), (5, 5), (38, 20), (25, 3), (30, 19), (28, 21), (3, 31), (16, 32), (23, 40), (18, 21), (0, 15), (33, 7), (32, 4), (1, 27), (20, 27), (28, 2), (18, 34), (32, 6), (6, 16), (4, 37), (39, 27), (2, 2), (6, 34), (1, 10), (10, 15), (5, 24), (32, 5), (37, 5), (9, 39), (13, 8), (3, 37), (35, 18), (3, 14), (34, 32), (10, 31), (4, 42), (18, 28), (8, 22), (38, 15), (20, 23), (14, 15), (27, 10), (13, 41), (25, 16), (18, 16), (24, 1), (16, 25), (28, 42), (14, 22), (40, 32), (39, 18), (35, 25), (33, 13), (31, 4), (13, 5), (30, 16), (21, 4), (33, 38), (39, 39), (17, 35), (28, 17), (24, 40), (33, 20), (40, 33), (1, 25), (20, 35), (21, 14), (23, 0), (26, 27), (2, 23), (19, 7), (4, 28), (14, 7), (30, 12), (16, 29), (9, 20), (40, 21), (14, 6), (4, 38), (26, 17), (30, 40), (36, 30), (14, 41), (31, 0), (28, 37), (32, 27), (4, 9), (30, 9), (35, 11), (32, 35), (33, 33), (8, 5), (27, 13), (40, 16), (23, 15), (2, 32), (30, 24), (27, 1), (19, 38), (4, 33), (14, 17), (9, 33), (24, 39), (27, 37), (12, 27), (30, 21), (20, 12), (31, 32), (26, 29), (40, 12), (36, 2), (13, 1), (14, 31), (17, 4), (19, 35), (4, 7), (35, 42), (9, 36), (1, 29), (21, 15), (30, 35), (2, 21), (14, 24), (23, 10), (8, 30), (9, 4), (38, 32), (24, 7), (38, 10), (25, 25), (35, 41), (25, 29), (0, 29), (9, 40), (1, 40), (11, 20), (9, 8), (14, 28), (33, 32), (20, 7), (30, 25), (0, 38), (17, 26), (15, 28), (21, 25), (2, 11), (24, 26), (22, 31), (3, 27), (24, 11), (17, 6), (16, 4), (34, 22), (34, 26), (13, 28), (34, 11), (20, 4), (15, 24), (26, 7), (9, 26), (6, 11), (14, 39), (3, 21), (8, 26), (32, 36), (24, 21), (6, 9), (14, 13), (31, 40), (0, 3), (21, 9), (8, 7), (40, 29), (37, 35), (36, 10), (18, 10), (22, 27), (4, 39), (7, 33), (7, 8), (40, 22), (2, 29), (5, 23), (0, 1), (39, 34), (28, 13), (18, 29), (37, 39), (3, 10), (32, 39), (28, 16), (31, 31), (29, 28), (40, 4), (30, 36), (36, 18), (26, 18), (11, 5), (22, 21), (19, 30), (32, 9), (13, 36), (8, 40), (2, 7), (9, 9), (0, 6), (11, 3), (27, 34), (15, 39), (13, 9), (18, 24), (36, 17), (29, 15), (16, 22), (11, 36), (20, 5), (3, 39), (28, 23), (35, 31), (27, 27), (6, 31), (9, 41), (6, 30), (27, 18), (12, 17), (30, 31), (13, 24), (13, 14), (18, 32), (30, 18), (31, 42), (4, 6), (36, 31), (21, 22), (10, 40), (2, 4), (33, 17), (36, 15), (27, 19), (23, 35), (11, 37), (6, 32), (38, 37), (14, 0), (6, 39), (15, 6), (8, 13), (33, 21), (34, 5), (1, 42), (3, 13), (23, 23), (0, 14), (11, 4), (7, 2), (18, 20), (32, 28), (33, 22), (2, 15), (22, 36), (32, 33), (13, 4), (4, 3), (7, 35), (28, 15), (17, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 6), (15, 8), (4, 5), (3, 23), (38, 30), (21, 22), (41, 27), (35, 26), (25, 4), (15, 10), (11, 22), (34, 39), (22, 36), (28, 28), (23, 24), (41, 30), (29, 9), (30, 40), (4, 23), (24, 21), (32, 12), (37, 25), (0, 39), (14, 15), (4, 7), (0, 10), (2, 13), (9, 34), (18, 5), (28, 3), (4, 40), (9, 33), (17, 13), (28, 8), (1, 7), (8, 19), (38, 4), (17, 6), (31, 13), (32, 11), (6, 38), (27, 31), (2, 35), (33, 26), (1, 24), (21, 15), (23, 33), (38, 32), (30, 32), (23, 34), (31, 10), (39, 15), (4, 21), (28, 27), (40, 25), (11, 41), (23, 36), (2, 1), (18, 35), (18, 21), (27, 8), (42, 9), (38, 25), (3, 40), (33, 38), (28, 5), (27, 40), (18, 14), (23, 8), (27, 3), (21, 10), (42, 18), (30, 25), (9, 38), (4, 22), (5, 10), (0, 1), (27, 9), (10, 16), (17, 31), (37, 35), (12, 16), (32, 20), (23, 17), (21, 6), (12, 20), (29, 22), (7, 11), (28, 17), (15, 1), (35, 3), (0, 18), (26, 4), (31, 0), (31, 24), (40, 29), (13, 18), (17, 37), (2, 9), (0, 17), (7, 32), (15, 29), (2, 41), (21, 21), (38, 28), (38, 24), (9, 32), (16, 38), (22, 39), (26, 34), (26, 10), (6, 39), (21, 35), (37, 4), (7, 33), (9, 36), (17, 24), (38, 41), (21, 1), (3, 31), (9, 23), (5, 30), (35, 1), (11, 12), (28, 39), (0, 33), (35, 15), (28, 37), (12, 15), (7, 7), (22, 25), (0, 22), (22, 26), (16, 35), (38, 34), (13, 3), (24, 10), (36, 35), (39, 9), (29, 29), (24, 9), (3, 34), (15, 21), (36, 34), (34, 10), (37, 17), (35, 34), (12, 21), (5, 17), (29, 20), (7, 31), (8, 13), (41, 14), (18, 28), (26, 35), (9, 17), (19, 41), (40, 32), (41, 39), (18, 8), (10, 6), (11, 29), (16, 28), (2, 32), (12, 27), (29, 17), (35, 11), (42, 37), (42, 21), (16, 18), (9, 3), (10, 23), (7, 30), (0, 7), (16, 7), (35, 5), (39, 20), (4, 2), (25, 41), (36, 9), (32, 7), (14, 38), (29, 6), (38, 7), (14, 22), (37, 24), (13, 16), (9, 37), (32, 33), (27, 36), (31, 14), (24, 30), (30, 27), (40, 0), (27, 13), (40, 7), (38, 3), (35, 39), (19, 9), (40, 30), (13, 9), (1, 5), (28, 1), (1, 15), (34, 16), (5, 15), (2, 36), (17, 28), (16, 32), (12, 2), (8, 6), (39, 29), (15, 0), (0, 19), (1, 31), (6, 8), (41, 16), (32, 28), (30, 9), (20, 16), (33, 40), (3, 22), (14, 16), (16, 17), (16, 34), (7, 4), (10, 35), (25, 26), (21, 34), (15, 16), (27, 1), (6, 25), (11, 38), (8, 33), (23, 30), (27, 14), (16, 11), (35, 14), (34, 26), (4, 16), (36, 13), (4, 9), (1, 35), (33, 4), (39, 21), (13, 31), (17, 29), (13, 36), (15, 17), (29, 10), (33, 19), (17, 7), (40, 26), (0, 23), (41, 31), (13, 21), (2, 40), (37, 19), (3, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 28), (5, 26), (20, 30), (42, 27), (20, 25), (42, 16), (2, 38), (13, 4), (0, 2), (37, 3), (5, 45), (27, 33), (31, 24), (25, 30), (41, 8), (3, 11), (14, 12), (38, 0), (8, 11), (4, 20), (27, 6), (15, 19), (37, 35), (16, 1), (43, 6), (9, 36), (32, 2), (27, 22), (40, 25), (29, 5), (1, 18), (19, 5), (6, 42), (4, 42), (0, 17), (41, 42), (30, 11), (24, 19), (9, 32), (20, 31), (39, 20), (13, 31), (17, 41), (28, 35), (17, 14), (29, 8), (41, 2), (14, 41), (11, 16), (4, 40), (25, 41), (5, 0), (1, 37), (16, 18), (1, 26), (35, 33), (42, 2), (26, 2), (36, 27), (38, 14), (39, 43), (13, 8), (35, 24), (15, 10), (36, 13), (15, 40), (41, 45), (6, 12), (43, 41), (33, 22), (14, 37), (14, 11), (10, 9), (10, 19), (37, 44), (25, 18), (31, 1), (42, 30), (31, 6), (35, 15), (11, 44), (24, 30), (7, 15), (24, 14), (12, 8), (5, 41), (8, 33), (33, 8), (12, 31), (16, 2), (12, 2), (25, 29), (34, 17), (14, 18), (42, 42), (30, 20), (3, 21), (34, 6), (32, 33), (27, 18), (6, 16), (33, 42), (29, 18), (5, 6), (41, 17), (6, 36), (8, 0), (22, 38), (43, 21), (19, 42), (20, 32), (9, 29), (15, 2), (19, 1), (3, 18), (16, 21), (14, 20), (33, 11), (17, 2), (26, 20), (22, 25), (15, 8), (15, 23), (10, 39), (18, 11), (19, 19), (43, 12), (10, 30), (37, 10), (4, 24), (43, 28), (32, 22), (35, 30), (11, 33), (35, 27), (36, 1), (12, 20), (3, 6), (18, 14), (2, 12), (22, 37), (7, 5), (13, 44), (17, 28), (27, 40), (28, 23), (24, 12), (3, 42), (27, 43), (2, 8), (24, 41), (29, 24), (37, 32), (37, 34), (9, 5), (21, 36), (40, 5), (20, 24), (38, 11), (38, 28), (2, 34), (21, 32), (1, 17), (42, 4), (21, 37), (10, 44), (23, 38), (9, 21), (10, 12), (3, 32), (17, 39), (20, 21), (13, 0), (2, 5), (36, 19), (43, 20), (29, 16), (11, 6), (0, 19), (2, 42), (43, 36), (8, 41), (25, 28), (17, 44), (14, 36), (34, 16), (40, 39), (29, 44), (40, 21), (23, 12), (24, 7), (21, 41), (5, 40), (16, 20), (13, 22), (6, 24), (26, 37), (12, 22), (43, 23), (38, 22), (16, 24), (22, 1), (19, 4), (3, 3), (10, 36), (10, 11), (13, 19), (36, 21), (28, 30), (40, 3), (13, 35), (0, 10), (3, 20), (41, 16), (21, 0), (40, 26), (19, 36), (8, 42), (11, 7), (27, 14), (2, 39), (40, 20), (0, 21), (3, 2), (39, 3), (25, 23), (1, 28), (18, 40), (31, 10), (38, 42), (40, 36), (0, 28), (38, 33), (14, 44), (13, 14), (19, 8), (18, 2), (17, 7), (19, 13), (2, 26), (37, 4), (31, 31), (28, 15), (37, 18), (12, 29), (37, 45), (14, 27), (15, 43), (39, 7), (40, 13), (35, 22), (39, 12), (41, 44), (21, 45), (20, 12), (35, 25), (9, 9), (6, 29), (8, 16), (11, 36), (18, 41), (21, 4), (18, 36), (34, 43), (4, 23), (19, 10), (18, 12), (20, 19), (33, 6), (2, 14), (3, 7), (21, 35), (32, 19), (10, 2), (9, 30), (10, 27), (20, 35), (17, 34), (31, 41), (23, 3), (2, 24), (17, 35), (21, 33), (31, 26), (26, 11), (41, 26), (41, 20), (4, 35), (23, 4), (42, 28), (21, 20), (7, 38), (3, 16), (36, 26), (36, 42), (31, 18), (1, 44), (5, 42), (42, 31), (34, 28), (13, 11), (25, 36), (15, 30), (40, 9), (35, 0), (34, 20), (5, 18), (23, 1), (38, 10), (37, 14), (43, 4), (23, 30), (13, 30), (42, 21), (31, 38), (9, 39), (13, 41), (17, 8), (33, 18), (7, 37), (42, 38), (39, 19), (25, 35), (12, 26), (23, 10), (16, 25), (14, 2), (20, 5), (17, 33), (29, 0), (25, 17), (29, 10), (37, 31), (9, 28), (16, 38), (11, 15), (8, 28), (34, 14), (43, 39), (0, 36), (18, 6), (8, 44), (30, 21), (20, 27), (13, 20), (20, 4), (36, 33), (36, 39), (26, 32), (19, 9), (28, 0), (20, 3), (6, 44), (30, 43), (30, 29), (5, 38), (6, 17), (8, 7), (22, 32), (1, 23), (5, 34), (28, 33), (34, 7), (14, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 18), (11, 20), (38, 7), (15, 19), (28, 2), (31, 8), (3, 21), (26, 16), (34, 16), (4, 4), (30, 25), (26, 1), (1, 3), (20, 10), (7, 6), (8, 25), (2, 32), (27, 1), (25, 23), (27, 39), (34, 37), (16, 8), (30, 2), (34, 11), (15, 35), (39, 4), (21, 14), (20, 34), (3, 25), (15, 24), (41, 4), (17, 3), (28, 31), (41, 37), (18, 36), (8, 6), (6, 38), (10, 18), (8, 4), (20, 14), (2, 31), (20, 39), (27, 26), (26, 5), (21, 33), (10, 30), (30, 6), (24, 25), (18, 40), (24, 42), (6, 3), (5, 6), (4, 8), (3, 39), (19, 15), (20, 3), (41, 29), (10, 8), (23, 1), (10, 19), (40, 13), (2, 20), (36, 38), (22, 13), (3, 7), (18, 37), (32, 5), (13, 10), (9, 21), (4, 41), (32, 34), (39, 38), (22, 11), (1, 34), (22, 36), (22, 4), (31, 15), (31, 23), (9, 18), (36, 22), (42, 17), (0, 9), (39, 17), (7, 19), (1, 22), (1, 42), (17, 9), (39, 10), (4, 18), (4, 16), (41, 23), (27, 30), (18, 10), (14, 24), (13, 4), (25, 13), (24, 6), (3, 33), (9, 29), (31, 34), (34, 36), (21, 3), (12, 20), (28, 38), (25, 8), (5, 42), (8, 19), (27, 33), (28, 10), (18, 15), (42, 29), (24, 21), (21, 24), (40, 19), (18, 35), (3, 31), (42, 0), (8, 30), (41, 39), (23, 20), (3, 1), (33, 16), (0, 20), (20, 32), (40, 26), (23, 29), (38, 29), (12, 37), (37, 25), (27, 7), (34, 33), (27, 8), (19, 16), (16, 38), (42, 28), (3, 24), (15, 6), (8, 2), (34, 1), (13, 36), (27, 40), (34, 30), (3, 17), (22, 22), (30, 22), (35, 0), (42, 11), (3, 29), (34, 6), (18, 24), (28, 7), (30, 26), (7, 10), (0, 7), (29, 9), (37, 10), (3, 37), (38, 21), (16, 23), (41, 5), (40, 37), (20, 5), (28, 3), (7, 33), (31, 28), (3, 41), (41, 32), (0, 12), (19, 13), (37, 19), (15, 10), (13, 26), (36, 24), (9, 19), (16, 17), (33, 6), (32, 20), (35, 27), (25, 35), (22, 5), (40, 24), (39, 34), (13, 13), (23, 42), (29, 10), (33, 36), (36, 10), (39, 23), (20, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 6), (17, 6), (22, 9), (11, 33), (36, 19), (10, 10), (10, 35), (4, 35), (38, 33), (6, 34), (8, 38), (8, 26), (8, 9), (31, 35), (33, 34), (21, 24), (25, 28), (32, 35), (26, 7), (12, 24), (9, 15), (25, 26), (6, 25), (24, 18), (37, 25), (10, 4), (11, 38), (17, 10), (21, 2), (34, 9), (2, 0), (39, 17), (7, 4), (33, 33), (19, 3), (14, 26), (7, 6), (18, 3), (25, 20), (20, 9), (38, 41), (6, 23), (29, 16), (29, 10), (22, 15), (5, 13), (34, 19), (11, 8), (3, 25), (38, 36), (17, 40), (39, 4), (20, 41), (30, 35), (10, 11), (4, 24), (32, 1), (17, 32), (17, 20), (28, 14), (13, 27), (23, 4), (19, 36), (36, 26), (13, 31), (22, 37), (14, 29), (3, 15), (21, 34), (12, 14), (33, 13), (37, 0), (17, 21), (32, 39), (14, 39), (5, 35), (10, 27), (15, 24), (10, 36), (11, 20), (13, 33), (17, 35), (29, 38), (20, 10), (34, 31), (1, 12), (1, 19), (28, 13), (28, 11), (33, 31), (34, 20), (28, 35), (40, 0), (5, 7), (32, 38), (21, 40), (24, 12), (1, 22), (38, 38), (26, 24), (15, 25), (22, 3), (5, 39), (32, 28), (3, 16), (15, 32), (25, 36), (35, 12), (34, 41), (28, 10), (23, 6), (12, 1), (17, 16), (36, 15), (18, 25), (28, 5), (38, 9), (37, 16), (9, 3), (26, 23), (40, 15), (2, 20), (4, 19), (36, 24), (3, 41), (29, 21), (8, 24), (34, 38), (32, 15), (11, 22), (40, 35), (2, 39), (29, 2), (31, 15), (25, 29), (4, 10), (1, 3), (0, 1), (27, 40), (4, 34), (5, 17), (11, 2), (28, 27), (35, 1), (24, 6), (29, 12), (33, 7), (33, 41), (21, 37), (8, 12), (40, 24), (1, 15), (2, 2), (28, 21), (2, 3), (14, 12), (15, 11), (21, 21), (8, 20), (23, 19), (10, 5), (6, 2), (28, 37), (27, 0), (6, 33), (33, 35), (37, 4), (27, 35), (31, 13), (35, 13), (13, 17), (18, 36), (13, 14), (0, 24), (8, 21), (26, 26), (30, 31), (38, 24), (6, 37), (1, 40), (15, 5), (36, 18), (28, 22), (1, 2), (33, 38), (23, 3), (11, 25), (22, 26), (12, 7), (11, 15), (23, 14), (33, 32), (30, 18), (15, 3), (33, 2), (28, 19), (10, 31), (2, 26), (20, 20), (33, 37), (4, 30), (8, 3), (32, 3), (2, 5), (7, 30), (39, 40), (24, 34), (1, 33), (32, 19), (18, 5), (18, 40), (31, 40), (36, 35), (1, 18), (21, 25), (17, 27), (18, 33), (40, 12), (31, 24), (11, 27), (31, 14), (18, 28), (33, 5), (15, 6), (34, 21), (35, 29), (29, 25), (32, 6), (34, 7), (27, 8), (6, 29), (31, 1), (9, 19), (24, 38), (33, 20), (32, 5), (39, 20), (10, 9), (37, 19), (15, 28), (28, 2), (33, 24), (30, 5), (37, 32), (14, 18), (11, 10), (25, 27), (35, 34), (28, 25), (16, 10), (39, 15), (37, 1), (29, 22), (14, 11), (33, 26), (7, 40), (17, 23), (27, 24), (19, 1), (38, 20), (21, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 21), (33, 11), (38, 1), (29, 25), (14, 31), (16, 37), (12, 34), (8, 9), (29, 9), (11, 2), (22, 27), (8, 10), (1, 40), (22, 4), (26, 41), (3, 17), (40, 20), (12, 35), (15, 17), (35, 13), (34, 8), (10, 18), (36, 26), (38, 16), (25, 34), (11, 12), (1, 37), (38, 37), (14, 26), (26, 30), (33, 18), (38, 13), (31, 25), (22, 16), (9, 26), (18, 23), (7, 41), (9, 14), (9, 8), (37, 14), (37, 6), (5, 14), (29, 28), (3, 32), (36, 16), (34, 24), (39, 20), (30, 21), (14, 24), (16, 7), (7, 11), (18, 27), (10, 2), (27, 23), (12, 40), (11, 40), (28, 14), (11, 10), (36, 11), (20, 38), (42, 34), (35, 25), (1, 8), (33, 39), (11, 21), (28, 22), (8, 38), (18, 9), (21, 34), (34, 31), (37, 28), (35, 23), (7, 34), (13, 3), (3, 34), (29, 37), (26, 29), (17, 24), (4, 8), (41, 40), (13, 8), (5, 35), (16, 21), (36, 9), (6, 13), (17, 7), (20, 34), (35, 3), (38, 17), (30, 41), (35, 40), (25, 2), (5, 16), (28, 15), (1, 2), (25, 18), (18, 25), (19, 12), (15, 26), (29, 6), (13, 19), (3, 13), (21, 41), (1, 15), (3, 14), (21, 8), (41, 27), (1, 0), (1, 21), (16, 27), (14, 28), (36, 3), (37, 41), (30, 3), (5, 8), (29, 35), (3, 4), (17, 23), (6, 31), (11, 16), (7, 24), (13, 13), (28, 29), (34, 41), (10, 24), (17, 27), (8, 11), (25, 7), (3, 25), (8, 26), (10, 13), (18, 6), (11, 6), (35, 9), (23, 13), (10, 32), (2, 7), (31, 27), (29, 17), (32, 2), (33, 4), (0, 23), (36, 40), (32, 11), (20, 33), (35, 34), (4, 3), (32, 24), (5, 18), (38, 26), (34, 28), (25, 33), (31, 10), (39, 0), (17, 6), (8, 37), (32, 19), (37, 20), (0, 14), (42, 26), (12, 13), (23, 18), (37, 29), (17, 1), (13, 5), (21, 13), (32, 26), (18, 39), (12, 29), (35, 30), (23, 36), (6, 30), (27, 19), (3, 27), (21, 32), (6, 14), (37, 35), (10, 23), (16, 3), (3, 11), (6, 39), (15, 4), (15, 33), (41, 17), (15, 30), (27, 35), (40, 9), (33, 31), (6, 16), (31, 11), (42, 17), (4, 0), (39, 30), (3, 37), (9, 22), (10, 17), (9, 41), (42, 22), (2, 3), (34, 13), (9, 21), (29, 11), (26, 13), (22, 26), (36, 10), (27, 2), (42, 35), (40, 40), (9, 4), (6, 40), (32, 39), (23, 39), (19, 41), (23, 5), (9, 7), (6, 38), (35, 19), (18, 37), (19, 28), (11, 27), (16, 15), (35, 6), (0, 7), (30, 5), (36, 39), (2, 23), (15, 14), (25, 37), (26, 33), (12, 2), (10, 11), (40, 23), (24, 14), (25, 36), (6, 7), (33, 16), (3, 19), (36, 34), (37, 32), (17, 26), (23, 15), (33, 21), (3, 9), (6, 23), (0, 11), (34, 23), (19, 4), (30, 33), (5, 24), (8, 39), (34, 11), (36, 18), (21, 0), (6, 18), (32, 35), (21, 27), (27, 8), (0, 20), (23, 29), (20, 3), (42, 27), (41, 14), (30, 17), (23, 7), (22, 29), (30, 36), (36, 21), (29, 31), (13, 29), (42, 9), (8, 36), (24, 28), (27, 32), (37, 30), (19, 16), (20, 41), (24, 13), (6, 6), (7, 5), (8, 22), (29, 2), (15, 31), (10, 29), (40, 1), (33, 41), (38, 38), (12, 30), (10, 0), (32, 9), (10, 26), (40, 13), (30, 7), (15, 5), (39, 27), (11, 18), (2, 32), (8, 4), (32, 23), (25, 11), (10, 10), (14, 35), (28, 27), (17, 33), (21, 24), (33, 24), (11, 30), (42, 31), (6, 34), (14, 40), (20, 20), (16, 38), (39, 4), (29, 21), (26, 27), (39, 37), (38, 2), (3, 22), (19, 19), (14, 32), (2, 33), (20, 14), (4, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 34), (30, 10), (48, 12), (4, 45), (24, 25), (42, 14), (28, 40), (27, 1), (35, 11), (12, 16), (26, 2), (9, 39), (34, 4), (31, 9), (26, 24), (38, 30), (11, 15), (27, 19), (26, 45), (5, 18), (34, 7), (43, 11), (45, 32), (27, 42), (26, 16), (44, 25), (38, 16), (47, 19), (5, 26), (23, 10), (31, 17), (40, 40), (21, 33), (28, 29), (35, 36), (36, 36), (30, 36), (4, 23), (35, 18), (7, 22), (35, 25), (21, 32), (30, 11), (4, 43), (35, 30), (43, 38), (47, 4), (42, 32), (19, 36), (18, 9), (18, 5), (33, 3), (20, 44), (14, 45), (11, 26), (40, 30), (5, 3), (41, 30), (11, 28), (33, 18), (20, 7), (29, 4), (9, 36), (37, 17), (44, 26), (11, 13), (27, 36), (33, 15), (29, 37), (27, 38), (19, 31), (17, 21), (21, 15), (24, 11), (5, 12), (25, 12), (30, 13), (8, 21), (34, 30), (21, 23), (43, 9), (13, 14), (31, 11), (38, 15), (13, 24), (24, 10), (48, 27), (22, 31), (12, 38), (12, 14), (16, 33), (47, 15), (41, 12), (0, 41), (4, 41), (15, 18), (8, 40), (1, 31), (2, 30), (43, 44), (14, 22), (36, 42), (1, 44), (43, 25), (4, 37), (15, 30), (40, 33), (40, 19), (36, 30), (37, 34), (31, 45), (9, 23), (2, 18), (48, 17), (22, 39), (47, 12), (31, 36), (20, 15), (12, 33), (32, 27), (19, 1), (22, 10), (9, 42), (45, 23), (37, 44), (18, 27), (40, 12), (44, 43), (17, 7), (5, 21), (48, 18), (32, 7), (14, 4), (43, 32), (35, 10), (29, 30), (38, 34), (25, 5), (44, 11), (8, 18), (7, 12), (35, 4), (21, 12), (24, 12), (8, 1), (42, 27), (10, 27), (18, 2), (5, 31), (42, 20), (43, 43), (7, 15), (47, 8), (2, 11), (6, 9), (36, 21), (24, 28), (37, 25), (7, 28), (5, 34), (20, 13), (28, 9), (37, 8), (7, 13), (33, 20), (28, 1), (3, 16), (18, 18), (35, 28), (34, 25), (42, 37), (15, 41), (42, 21), (30, 40), (33, 42), (9, 10), (45, 20), (34, 18), (18, 12), (40, 27), (45, 7), (26, 36), (35, 27), (32, 30), (24, 31), (43, 35), (2, 28), (18, 0), (18, 41), (32, 34), (34, 34), (7, 5), (33, 22), (22, 4), (37, 40), (26, 43), (35, 20), (38, 21), (46, 40), (47, 25), (43, 33), (44, 15), (46, 12), (16, 37), (7, 43), (38, 33), (30, 23), (19, 41), (48, 10), (36, 11), (11, 43), (28, 23), (34, 16), (14, 1), (5, 24), (13, 7), (34, 28), (11, 42), (47, 42), (15, 42), (10, 11), (47, 41), (5, 40), (8, 14), (34, 3), (47, 22), (34, 43), (23, 14), (33, 29), (17, 6), (15, 7), (46, 43), (17, 12), (24, 19), (19, 15), (13, 17), (35, 13), (19, 44), (26, 38), (0, 1), (6, 22), (2, 3), (10, 44), (11, 35), (10, 28), (39, 1), (1, 5), (19, 16), (45, 3), (42, 43), (23, 21), (12, 20), (30, 30), (23, 7), (44, 45), (39, 28), (4, 35), (7, 39), (42, 15), (34, 22), (17, 8), (11, 39), (38, 44), (34, 40), (0, 14), (48, 19), (25, 36), (25, 9), (48, 28), (43, 14), (11, 44), (13, 23), (3, 39), (39, 45), (17, 34), (28, 3), (47, 32), (16, 34), (17, 19), (45, 30), (32, 41), (6, 13), (29, 34), (15, 19), (4, 30), (34, 1), (44, 9), (28, 5), (45, 16), (36, 2), (7, 9), (21, 39), (9, 38), (34, 33), (46, 8), (15, 39), (24, 33), (36, 19), (44, 35), (16, 14), (7, 17), (45, 10), (26, 5), (42, 10), (28, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 38), (5, 22), (17, 42), (39, 36), (6, 0), (14, 45), (41, 4), (12, 24), (37, 31), (26, 12), (30, 4), (40, 40), (26, 38), (35, 35), (2, 31), (40, 1), (43, 22), (31, 13), (22, 23), (36, 33), (4, 8), (42, 27), (19, 42), (13, 19), (35, 18), (12, 31), (1, 27), (3, 17), (27, 21), (26, 20), (24, 27), (30, 14), (31, 25), (0, 16), (35, 43), (19, 32), (17, 25), (7, 45), (1, 14), (17, 9), (38, 0), (14, 5), (20, 19), (10, 13), (5, 41), (11, 15), (22, 17), (43, 10), (9, 23), (35, 36), (24, 22), (11, 16), (34, 24), (7, 5), (39, 34), (29, 46), (33, 27), (25, 30), (9, 0), (12, 36), (15, 19), (23, 22), (25, 14), (23, 11), (19, 10), (13, 6), (41, 25), (33, 44), (24, 2), (4, 9), (42, 10), (25, 5), (40, 7), (41, 24), (1, 24), (42, 12), (14, 17), (34, 38), (12, 27), (23, 0), (33, 12), (8, 20), (25, 37), (32, 42), (31, 43), (22, 37), (15, 0), (6, 39), (15, 31), (21, 36), (4, 29), (7, 20), (8, 40), (11, 4), (15, 4), (23, 35), (17, 2), (12, 29), (38, 40), (13, 10), (16, 9), (12, 4), (39, 18), (34, 5), (25, 43), (42, 28), (40, 3), (19, 45), (29, 3), (5, 24), (34, 32), (42, 20), (4, 34), (34, 28), (40, 0), (0, 41), (32, 31), (10, 19), (40, 26), (5, 29), (25, 42), (6, 25), (30, 41), (27, 34), (17, 8), (19, 46), (30, 42), (39, 39), (40, 23), (38, 20), (28, 3), (11, 45), (21, 28), (12, 19), (34, 34), (36, 23), (27, 46), (13, 37), (32, 5), (29, 32), (4, 6), (27, 22), (25, 9), (35, 46), (30, 2), (16, 46), (3, 5), (31, 31), (11, 8), (12, 1), (27, 33), (20, 16), (20, 11), (15, 8), (8, 34), (0, 21), (3, 0), (42, 46), (25, 3), (28, 7), (38, 23), (29, 30), (42, 17), (40, 39), (29, 28), (28, 23), (39, 9), (36, 45), (41, 38), (24, 42), (31, 21), (3, 38), (9, 17), (6, 27), (8, 29), (0, 8), (31, 46), (38, 7), (11, 11), (7, 9), (40, 13), (36, 20), (7, 41), (6, 5), (26, 15), (42, 15), (28, 33), (1, 26), (22, 24), (29, 18), (24, 3), (6, 17), (2, 45), (9, 37), (23, 15), (33, 32), (12, 2), (42, 22), (35, 11), (5, 31), (27, 13), (37, 21), (0, 42), (41, 19), (37, 43), (7, 44), (7, 30), (1, 40), (15, 6), (13, 26), (18, 41), (37, 10), (27, 25), (12, 18), (8, 22), (16, 7), (4, 25), (8, 30), (7, 29), (22, 0), (42, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 24), (18, 8), (17, 27), (11, 13), (41, 21), (33, 30), (45, 13), (13, 26), (9, 30), (36, 33), (22, 40), (36, 26), (8, 31), (35, 6), (14, 36), (33, 17), (29, 37), (41, 31), (6, 15), (0, 25), (37, 34), (3, 8), (30, 41), (34, 21), (38, 14), (41, 29), (15, 7), (33, 40), (28, 6), (34, 22), (25, 15), (34, 8), (13, 18), (25, 30), (12, 4), (17, 41), (3, 3), (12, 0), (8, 17), (7, 22), (38, 27), (17, 26), (31, 14), (19, 6), (14, 19), (33, 6), (14, 17), (19, 38), (33, 24), (45, 21), (39, 9), (22, 12), (32, 26), (23, 33), (18, 41), (25, 16), (25, 26), (6, 17), (36, 39), (36, 41), (40, 36), (38, 21), (37, 17), (32, 8), (21, 30), (16, 12), (20, 37), (28, 14), (22, 25), (39, 11), (19, 28), (38, 38), (4, 39), (26, 38), (40, 8), (22, 0), (36, 3), (18, 40), (9, 0), (1, 1), (10, 31), (3, 28), (16, 19), (23, 7), (41, 33), (8, 38), (20, 8), (7, 3), (21, 20), (23, 23), (15, 33), (1, 5), (26, 12), (44, 33), (1, 36), (22, 33), (33, 18), (9, 16), (19, 7), (33, 41), (35, 1), (31, 41), (12, 14), (38, 26), (17, 10), (17, 19), (32, 6), (31, 21), (8, 26), (15, 18), (3, 26), (11, 22), (42, 28), (18, 0), (32, 20), (23, 6), (10, 4), (5, 41), (9, 41), (34, 6), (33, 23), (17, 29), (11, 7), (31, 9), (29, 41), (42, 14), (20, 30), (0, 3), (29, 9), (19, 40), (24, 40), (3, 10), (5, 11), (13, 11), (41, 18), (28, 29), (42, 21), (4, 10), (4, 23), (6, 16), (23, 15), (13, 6), (3, 29), (40, 26), (6, 21), (0, 41), (19, 34), (45, 31), (34, 16), (14, 11), (19, 31), (8, 36), (17, 13), (21, 17), (5, 26), (31, 28), (42, 2), (7, 5), (45, 15), (15, 30), (41, 34), (21, 33), (32, 1), (38, 20), (33, 11), (22, 16), (19, 9), (9, 3), (30, 7), (10, 0), (4, 41), (9, 7), (13, 14), (31, 25), (41, 10), (18, 16), (11, 10), (29, 23), (40, 40), (19, 18), (6, 41), (10, 7), (26, 39), (40, 6), (4, 34), (9, 22), (20, 36), (37, 23), (19, 14), (14, 15), (15, 26), (12, 12), (8, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 7), (36, 1), (30, 25), (7, 30), (2, 21), (8, 34), (32, 26), (15, 31), (30, 31), (19, 32), (31, 10), (28, 39), (31, 11), (8, 2), (25, 28), (34, 1), (5, 7), (32, 15), (1, 5), (37, 29), (24, 11), (1, 35), (19, 22), (17, 40), (19, 23), (34, 10), (31, 32), (29, 34), (37, 38), (0, 15), (21, 6), (35, 29), (1, 11), (12, 14), (20, 3), (32, 34), (41, 34), (6, 40), (40, 21), (7, 21), (15, 12), (1, 18), (31, 30), (16, 4), (0, 22), (24, 10), (18, 18), (37, 7), (32, 31), (9, 10), (13, 22), (11, 6), (12, 35), (24, 20), (34, 34), (11, 1), (39, 11), (5, 13), (8, 31), (2, 6), (1, 16), (29, 0), (12, 2), (39, 27), (22, 20), (34, 6), (33, 34), (18, 20), (20, 29), (40, 32), (23, 10), (31, 21), (20, 6), (15, 34), (1, 8), (3, 5), (25, 27), (24, 17), (18, 12), (17, 37), (37, 24), (30, 2), (18, 25), (18, 6), (23, 22), (31, 17), (27, 24), (15, 2), (1, 29), (6, 13), (38, 8), (16, 23), (24, 14), (25, 31), (12, 3), (40, 8), (4, 36), (11, 0), (30, 8), (38, 5), (36, 32), (8, 37), (18, 36), (25, 25), (2, 40), (31, 22), (34, 27), (27, 4), (32, 33), (7, 33), (21, 21), (1, 27), (34, 26), (20, 21), (38, 18), (36, 41), (16, 27), (19, 34), (28, 14), (29, 5), (1, 30), (10, 19), (34, 8), (17, 25), (16, 12), (20, 37), (40, 38), (34, 33), (9, 16), (38, 20), (28, 16), (13, 16), (22, 4), (13, 4), (21, 9), (1, 33), (19, 13), (16, 19), (25, 22), (25, 20), (34, 13), (8, 7), (1, 28), (15, 32), (38, 19), (40, 26), (4, 19), (27, 18), (8, 24), (37, 2), (13, 11), (33, 2), (38, 40), (29, 2), (34, 41), (30, 16), (12, 11), (26, 17), (28, 8), (27, 35), (37, 4), (24, 15), (24, 19), (37, 5), (8, 8), (8, 19), (10, 30), (37, 36), (28, 19), (25, 18), (28, 9), (22, 22), (5, 24), (15, 29), (23, 30), (39, 26), (20, 19), (15, 40), (11, 23), (13, 7), (26, 27), (30, 1), (17, 8), (35, 41), (10, 23), (3, 21), (26, 33), (11, 32), (29, 6), (1, 39), (20, 35), (32, 41), (36, 23), (1, 10), (28, 36), (34, 14), (4, 22), (33, 0), (30, 29), (33, 15), (19, 4), (11, 18), (23, 34), (13, 29), (29, 20), (3, 22), (5, 16), (41, 24), (24, 24), (13, 38), (15, 36), (6, 24), (12, 6), (40, 12), (4, 13), (35, 10), (13, 5), (39, 36), (19, 25), (0, 19), (10, 9), (14, 8), (3, 20), (19, 30), (41, 38), (30, 6), (0, 39), (40, 37), (11, 24), (10, 6), (32, 27), (23, 15), (2, 38), (34, 0), (7, 1), (20, 20), (25, 10), (25, 29), (38, 11), (6, 36), (5, 0), (7, 27), (3, 24), (13, 8), (11, 38), (35, 34), (7, 26), (36, 16), (14, 14), (37, 33), (10, 26), (22, 7), (34, 21), (4, 7), (13, 41), (1, 26), (39, 28), (17, 35), (15, 15), (37, 16), (25, 4), (5, 19), (30, 26), (13, 28), (33, 5), (10, 28), (30, 17), (18, 11), (33, 35), (4, 27), (20, 15), (13, 1), (19, 33), (30, 9), (3, 16), (32, 30), (6, 19), (35, 9), (0, 37), (12, 36), (25, 7), (6, 29), (19, 5), (22, 35), (36, 20), (35, 14), (23, 38), (34, 28), (27, 26), (13, 20), (19, 21), (8, 21), (0, 31), (37, 23), (28, 10), (21, 27), (17, 15), (34, 38), (30, 23), (18, 33), (40, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 16), (22, 26), (37, 20), (13, 40), (43, 24), (35, 32), (21, 15), (14, 17), (34, 0), (8, 27), (14, 8), (44, 9), (11, 34), (28, 39), (0, 11), (14, 31), (43, 36), (15, 24), (34, 2), (25, 37), (27, 33), (20, 13), (6, 33), (4, 45), (22, 43), (23, 22), (22, 27), (29, 1), (23, 1), (23, 24), (23, 7), (39, 30), (5, 23), (39, 1), (16, 46), (19, 35), (33, 27), (6, 13), (29, 13), (25, 35), (41, 42), (15, 36), (0, 12), (12, 31), (47, 15), (39, 37), (35, 26), (20, 21), (21, 35), (39, 5), (45, 20), (6, 43), (19, 3), (23, 45), (27, 41), (6, 7), (15, 9), (9, 13), (36, 28), (26, 12), (42, 2), (46, 46), (25, 2), (26, 37), (30, 33), (42, 22), (31, 20), (35, 43), (34, 18), (40, 42), (31, 29), (35, 2), (29, 27), (1, 43), (39, 16), (35, 34), (10, 36), (2, 14), (10, 12), (0, 25), (41, 14), (41, 5), (18, 21), (32, 33), (13, 8), (3, 1), (4, 1), (12, 38), (11, 20), (29, 7), (3, 26), (8, 29), (7, 29), (24, 37), (9, 27), (38, 1), (23, 16), (2, 17), (28, 11), (35, 28), (6, 25), (18, 22), (44, 17), (23, 23), (27, 17), (27, 22), (36, 39), (38, 46), (23, 40), (24, 17), (16, 8), (31, 38), (20, 44), (8, 18), (22, 11), (15, 29), (13, 41), (34, 17), (46, 1), (19, 16), (32, 40), (47, 25), (28, 18), (27, 8), (1, 26), (36, 2), (18, 38), (30, 26), (42, 46), (26, 33), (33, 14), (26, 35), (40, 23), (31, 25), (42, 13), (36, 23), (18, 24), (32, 26), (32, 15), (20, 20), (26, 38), (46, 15), (39, 20), (19, 17), (0, 40), (47, 6), (23, 17), (14, 41), (46, 32), (15, 30), (13, 35), (34, 27), (24, 12), (3, 22), (40, 9), (25, 44), (17, 21), (36, 40), (4, 11), (19, 41), (39, 7), (40, 5), (32, 0), (33, 26), (42, 23), (42, 9), (25, 34), (3, 9), (7, 35), (31, 7), (42, 11), (8, 9), (1, 15), (45, 11), (38, 37), (21, 37), (17, 16), (5, 15), (16, 33), (17, 20), (6, 26), (43, 9), (22, 14), (18, 18), (11, 30), (4, 4), (32, 16), (2, 37), (39, 40), (11, 5), (37, 17), (1, 7), (44, 43), (27, 4), (0, 3), (29, 38), (18, 42), (11, 9), (34, 22), (35, 1), (17, 23), (42, 20), (25, 30), (2, 39), (41, 46), (21, 42), (45, 21), (32, 10), (44, 7), (35, 38), (8, 42), (25, 23), (25, 22), (44, 24), (43, 38), (1, 42), (18, 9), (39, 3), (14, 35), (36, 14), (47, 5), (38, 24), (26, 24), (9, 26), (47, 21), (14, 43), (33, 43), (5, 45), (3, 39), (42, 14), (27, 40), (37, 33), (3, 17), (25, 46), (1, 19), (38, 16), (40, 7), (28, 45), (14, 37), (20, 30), (29, 5), (11, 17), (1, 4), (13, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 4), (38, 5), (2, 35), (4, 17), (26, 9), (0, 28), (5, 42), (38, 40), (37, 12), (40, 38), (21, 5), (22, 43), (20, 3), (11, 28), (40, 19), (13, 42), (24, 34), (34, 1), (40, 21), (39, 18), (42, 26), (31, 33), (27, 34), (18, 5), (27, 27), (20, 35), (4, 0), (35, 10), (31, 35), (19, 33), (39, 35), (9, 38), (6, 10), (4, 43), (33, 18), (16, 13), (34, 16), (15, 43), (30, 19), (24, 0), (38, 26), (20, 42), (14, 6), (35, 40), (6, 42), (28, 8), (1, 21), (22, 32), (6, 44), (25, 11), (0, 7), (29, 23), (33, 10), (38, 2), (36, 18), (40, 7), (1, 32), (18, 30), (42, 25), (18, 12), (7, 34), (3, 21), (28, 30), (6, 37), (42, 7), (20, 18), (42, 43), (2, 43), (31, 26), (13, 15), (17, 8), (30, 18), (34, 6), (23, 26), (37, 9), (42, 18), (10, 12), (24, 32), (32, 24), (9, 27), (6, 22), (10, 41), (31, 13), (1, 29), (20, 14), (28, 25), (39, 7), (33, 37), (0, 10), (8, 39), (33, 11), (33, 17), (42, 37), (33, 30), (19, 12), (21, 0), (41, 24), (10, 18), (36, 24), (41, 22), (31, 7), (15, 35), (1, 17), (24, 24), (4, 9), (13, 25), (11, 18), (37, 16), (29, 8), (34, 12), (38, 35), (17, 36), (17, 33), (2, 1), (23, 7), (5, 38), (22, 13), (29, 18), (2, 42), (14, 25), (4, 20), (35, 2), (8, 8), (15, 41), (16, 0), (13, 33), (32, 17), (10, 40), (21, 34), (39, 43), (7, 23), (20, 41), (5, 9), (1, 30), (42, 23), (30, 34), (21, 4), (2, 2), (33, 41), (33, 15), (20, 17), (41, 19), (15, 7), (34, 14), (24, 6), (33, 36), (5, 39), (42, 32), (4, 16), (17, 5), (22, 31), (21, 25), (19, 34), (12, 19), (13, 18), (21, 30), (23, 8), (19, 15), (6, 41), (40, 34), (18, 9), (37, 2), (20, 20), (19, 19), (24, 35), (14, 2), (25, 18), (25, 6), (18, 39), (7, 28), (23, 42), (28, 14), (42, 3), (36, 40), (16, 10), (33, 12), (7, 4), (25, 39), (20, 27), (10, 0), (6, 20), (12, 5), (37, 17), (38, 25), (26, 25), (32, 42), (26, 3), (22, 37), (16, 40), (22, 16), (28, 34), (30, 38), (35, 29), (17, 41), (29, 38), (0, 17), (17, 28), (24, 28), (7, 36), (40, 4), (26, 14), (37, 38), (35, 14), (8, 16), (34, 17), (3, 26), (18, 15), (1, 20), (3, 28), (10, 33), (20, 34), (15, 37), (26, 21), (16, 23), (38, 14), (33, 3), (27, 15), (23, 32), (34, 23), (5, 33), (2, 41), (26, 10), (40, 20), (23, 30), (32, 29), (35, 18), (14, 40), (34, 19), (19, 20), (12, 16), (21, 2), (31, 36), (17, 32), (10, 25), (5, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 41), (14, 0), (18, 19), (40, 44), (7, 29), (29, 36), (25, 3), (26, 24), (10, 34), (10, 5), (15, 45), (30, 36), (17, 19), (17, 30), (23, 35), (23, 40), (35, 42), (13, 12), (24, 5), (11, 11), (25, 2), (26, 37), (3, 36), (39, 18), (6, 30), (14, 37), (0, 20), (32, 10), (26, 11), (34, 20), (35, 29), (23, 22), (36, 8), (26, 45), (18, 10), (20, 46), (31, 0), (39, 5), (33, 31), (28, 6), (28, 39), (24, 17), (19, 33), (31, 7), (12, 36), (28, 21), (7, 47), (26, 15), (5, 43), (21, 25), (30, 29), (18, 46), (26, 4), (17, 23), (5, 25), (17, 12), (13, 40), (30, 22), (28, 4), (21, 19), (2, 8), (31, 34), (18, 36), (4, 38), (29, 27), (5, 33), (0, 18), (35, 35), (24, 20), (39, 7), (0, 21), (2, 24), (30, 45), (10, 17), (25, 30), (14, 30), (7, 19), (37, 37), (0, 8), (33, 17), (11, 14), (35, 9), (20, 9), (35, 36), (0, 22), (36, 16), (22, 45), (7, 33), (7, 8), (12, 16), (24, 40), (34, 3), (3, 21), (14, 2), (25, 42), (22, 23), (40, 35), (32, 37), (26, 13), (25, 6), (35, 13), (28, 14), (5, 6), (25, 40), (1, 32), (4, 44), (2, 31), (25, 7), (20, 44), (23, 30), (19, 35), (33, 19), (34, 16), (13, 35), (23, 1), (34, 35), (17, 29), (38, 13), (15, 44), (25, 11), (3, 39), (18, 12), (33, 39), (19, 18), (13, 3), (20, 40), (30, 16), (34, 47), (13, 20), (37, 19), (4, 0), (32, 0), (15, 42), (28, 2), (0, 5), (29, 46), (35, 30), (36, 43), (13, 25), (30, 8), (8, 23), (14, 5), (32, 13), (18, 15), (25, 10), (20, 47), (39, 11), (22, 16), (8, 27), (10, 36), (36, 22), (39, 26), (21, 28), (26, 34), (21, 44), (28, 47), (23, 5), (12, 46), (5, 28), (17, 20), (23, 11), (6, 12), (21, 33), (7, 31), (29, 24), (25, 31), (0, 41), (20, 8), (23, 38), (28, 0), (12, 20), (7, 38), (31, 32), (40, 22), (31, 42), (33, 35), (18, 39), (10, 41), (13, 11), (32, 20), (15, 7), (1, 23), (2, 44), (34, 1), (24, 6), (40, 9), (5, 42), (19, 27), (29, 22), (28, 18), (32, 1), (10, 29), (40, 31), (37, 30), (12, 22), (36, 47), (14, 15), (5, 41), (31, 17), (30, 7), (39, 38), (32, 8), (40, 6), (21, 34), (8, 40), (19, 45), (11, 33), (38, 42), (38, 9), (9, 40), (13, 44), (13, 4), (21, 24), (3, 23), (4, 41), (20, 4), (16, 35), (35, 44), (20, 33), (37, 18), (6, 28), (28, 37), (10, 40), (33, 29), (26, 32), (25, 36), (38, 36), (36, 18), (18, 21), (24, 41), (36, 34), (14, 10), (31, 4), (23, 17), (16, 42), (0, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 8), (14, 8), (48, 0), (34, 3), (35, 25), (25, 26), (27, 26), (13, 24), (41, 33), (29, 20), (8, 33), (42, 15), (16, 19), (12, 21), (40, 17), (39, 12), (18, 12), (12, 30), (42, 27), (12, 24), (43, 13), (25, 16), (47, 27), (15, 24), (14, 9), (40, 13), (38, 23), (39, 14), (26, 36), (11, 12), (45, 38), (5, 19), (44, 20), (20, 29), (30, 23), (30, 26), (21, 38), (34, 24), (39, 31), (38, 12), (23, 40), (21, 3), (41, 19), (35, 35), (33, 35), (37, 28), (34, 19), (3, 4), (22, 13), (11, 11), (23, 24), (17, 8), (37, 13), (22, 2), (8, 0), (3, 38), (31, 40), (37, 26), (43, 23), (36, 22), (20, 27), (8, 30), (10, 14), (13, 25), (43, 10), (4, 25), (35, 5), (37, 11), (12, 34), (0, 37), (27, 0), (10, 16), (18, 33), (14, 21), (23, 16), (20, 38), (14, 36), (31, 33), (46, 0), (0, 1), (40, 3), (13, 28), (12, 25), (3, 8), (28, 7), (14, 33), (12, 39), (13, 29), (24, 20), (16, 40), (0, 32), (33, 3), (18, 10), (6, 18), (35, 22), (25, 17), (29, 8), (33, 12), (44, 0), (46, 13), (1, 23), (19, 8), (37, 0), (20, 20), (19, 19), (8, 39), (10, 10), (5, 35), (42, 22), (17, 28), (21, 31), (42, 11), (32, 37), (16, 36), (44, 5), (47, 3), (17, 15), (16, 31), (43, 40), (19, 12), (6, 4), (5, 9), (6, 26), (41, 28), (6, 36), (3, 5), (39, 5), (21, 1), (8, 35), (31, 38), (41, 38), (48, 7), (44, 2), (48, 33), (31, 21), (42, 12), (4, 8), (13, 13), (25, 32), (33, 21), (42, 0), (32, 15), (36, 36), (22, 12), (7, 5), (5, 3), (26, 15), (12, 29), (17, 11), (19, 22), (16, 33), (24, 12), (1, 14), (43, 3), (47, 14), (4, 20), (44, 23), (29, 36), (22, 19), (3, 33), (32, 27), (28, 23), (39, 39), (4, 28), (33, 32), (29, 12), (11, 28), (41, 34), (27, 9), (20, 39), (32, 21), (6, 34), (43, 31), (35, 37), (39, 38), (34, 10), (47, 36), (23, 21), (11, 21), (15, 27), (28, 25), (9, 39), (12, 10), (18, 25), (35, 36), (21, 13), (4, 41), (20, 8), (33, 27), (26, 18), (1, 21), (30, 30), (43, 33), (43, 15), (48, 22), (32, 24), (42, 26), (3, 18), (12, 12), (21, 2), (8, 28), (9, 26), (42, 38), (22, 14), (43, 9), (14, 1), (48, 8), (6, 24), (24, 39), (10, 37), (16, 10), (4, 11), (10, 4), (16, 28), (1, 38), (6, 19), (13, 6), (24, 18), (21, 39), (13, 11), (29, 11), (38, 2), (19, 1), (46, 3), (7, 2), (44, 35), (33, 0), (36, 0), (3, 28), (20, 11), (16, 25), (7, 25), (40, 39), (40, 31), (44, 18), (32, 25), (31, 17), (13, 9), (25, 21), (6, 17), (4, 1), (34, 38), (31, 34), (8, 7), (6, 28), (25, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 40x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 39), (22, 36), (20, 6), (17, 24), (36, 30), (28, 37), (35, 18), (26, 16), (9, 11), (20, 25), (11, 3), (29, 41), (31, 32), (24, 10), (1, 35), (33, 5), (22, 30), (23, 24), (30, 28), (2, 0), (25, 29), (30, 16), (31, 10), (5, 23), (29, 18), (17, 37), (11, 22), (5, 24), (11, 14), (3, 41), (1, 22), (8, 7), (14, 30), (26, 4), (24, 28), (39, 12), (14, 24), (22, 24), (32, 3), (34, 25), (38, 20), (24, 39), (0, 1), (10, 10), (26, 40), (4, 14), (13, 3), (2, 15), (4, 12), (24, 21), (0, 25), (23, 23), (27, 41), (7, 17), (4, 23), (16, 30), (17, 16), (35, 13), (36, 25), (1, 34), (21, 30), (1, 21), (5, 30), (35, 29), (30, 6), (17, 19), (19, 15), (35, 19), (37, 8), (35, 3), (8, 5), (23, 27), (10, 33), (22, 22), (39, 32), (19, 36), (2, 9), (38, 19), (15, 33), (32, 26), (30, 31), (23, 12), (13, 8), (33, 40), (16, 22), (32, 31), (3, 25), (37, 32), (34, 29), (33, 12), (19, 14), (33, 20), (31, 16), (29, 24), (5, 1), (28, 30), (27, 38), (25, 27), (2, 35), (23, 16), (27, 29), (12, 12), (21, 28), (9, 17), (9, 1), (27, 1), (20, 40), (10, 4), (33, 35), (15, 23), (33, 33), (29, 25), (31, 40), (11, 5), (38, 12), (16, 4), (16, 35), (38, 9), (25, 14), (33, 7), (27, 24), (34, 34), (19, 2), (14, 36), (23, 33), (18, 23), (37, 7), (36, 1), (29, 32), (23, 40), (32, 13), (8, 0), (33, 14), (17, 29), (16, 6), (35, 40), (9, 5), (37, 40), (28, 29), (14, 35), (9, 3), (31, 28), (36, 40), (5, 39), (21, 6), (17, 35), (13, 33), (27, 11), (30, 3), (20, 37), (0, 5), (29, 26), (11, 16), (34, 7), (13, 41), (34, 10), (12, 3), (13, 37), (25, 7), (14, 23), (20, 23), (20, 13), (27, 2), (29, 23), (29, 2), (37, 11), (15, 36), (16, 41), (22, 39), (25, 6), (38, 5), (37, 33), (36, 29), (0, 16), (7, 34), (36, 37), (1, 27), (38, 29), (30, 40), (2, 20), (34, 26), (21, 4), (10, 23), (5, 33), (24, 29), (36, 14), (22, 40), (27, 23), (1, 19), (27, 34), (38, 15), (8, 28), (20, 8), (24, 4), (6, 16), (12, 8), (37, 41), (19, 40), (5, 8), (2, 23), (7, 13), (6, 29), (32, 39), (33, 21), (12, 33), (27, 14), (22, 0), (0, 8), (35, 28), (1, 11), (4, 16), (18, 34), (25, 12), (37, 16), (28, 10), (38, 2), (22, 11), (14, 13), (13, 14), (23, 19), (8, 22), (9, 7), (34, 11), (37, 14), (23, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 8), (31, 43), (8, 11), (20, 5), (37, 18), (13, 15), (42, 18), (19, 38), (28, 39), (0, 11), (32, 36), (40, 31), (36, 4), (26, 20), (1, 33), (29, 10), (9, 15), (13, 4), (18, 35), (29, 43), (12, 5), (1, 3), (24, 17), (32, 20), (25, 10), (18, 19), (14, 5), (28, 34), (28, 8), (18, 39), (4, 30), (19, 29), (33, 3), (33, 35), (5, 24), (0, 18), (15, 39), (12, 14), (10, 32), (43, 5), (37, 4), (43, 30), (37, 38), (4, 39), (31, 37), (39, 42), (21, 6), (35, 23), (22, 29), (19, 36), (13, 34), (19, 16), (6, 29), (15, 26), (34, 5), (33, 21), (19, 15), (35, 6), (20, 31), (6, 43), (43, 42), (18, 32), (19, 41), (42, 14), (21, 8), (23, 30), (5, 4), (7, 43), (16, 5), (41, 12), (40, 39), (17, 28), (10, 30), (1, 38), (18, 7), (2, 27), (4, 31), (28, 13), (6, 10), (42, 9), (19, 17), (11, 43), (16, 39), (5, 21), (0, 30), (6, 25), (35, 40), (1, 17), (37, 12), (33, 2), (24, 38), (39, 25), (23, 6), (33, 1), (5, 41), (28, 31), (14, 11), (42, 39), (8, 34), (22, 24), (11, 35), (10, 42), (17, 17), (6, 11), (27, 9), (42, 26), (12, 18), (31, 41), (19, 0), (1, 32), (14, 27), (34, 4), (39, 40), (10, 24), (5, 3), (2, 34), (30, 12), (6, 27), (34, 20), (11, 21), (28, 32), (3, 26), (13, 21), (7, 19), (11, 26), (2, 41), (27, 38), (35, 22), (6, 3), (5, 1), (11, 12), (6, 35), (38, 42), (9, 28), (21, 27), (36, 28), (1, 27), (41, 9), (22, 8), (33, 34), (4, 17), (11, 4), (30, 18), (0, 26), (35, 38), (17, 36), (12, 32), (3, 35), (26, 15), (23, 19), (16, 12), (22, 28), (1, 4), (2, 19), (43, 26), (19, 2), (24, 7), (23, 39), (43, 15), (15, 35), (2, 14), (26, 28), (16, 38), (14, 28), (26, 41), (34, 39), (29, 9), (13, 30), (21, 7), (41, 40), (10, 34), (8, 38), (9, 24), (11, 38), (13, 38), (10, 40), (13, 18), (40, 13), (15, 42), (32, 6), (25, 34), (14, 37), (40, 22), (17, 29), (41, 41), (32, 28), (26, 17), (6, 24), (2, 20), (7, 35), (18, 3), (37, 40), (11, 25), (14, 39), (30, 38), (1, 14), (16, 1), (22, 41), (8, 41), (17, 8), (12, 8), (40, 14), (39, 20), (31, 2), (41, 43), (12, 1), (22, 16), (38, 33), (15, 8), (7, 16), (36, 3), (27, 11), (25, 16), (3, 17), (20, 30), (42, 15), (7, 38), (20, 24), (12, 13), (4, 32), (35, 11), (19, 12), (33, 22), (20, 17), (27, 17), (4, 43), (42, 34), (30, 20), (9, 29), (1, 39), (35, 1), (29, 29), (27, 41), (36, 5), (6, 5), (11, 31), (3, 32), (8, 10), (4, 23), (0, 6), (38, 34), (10, 13), (20, 16), (28, 12), (5, 40), (21, 0), (17, 0), (16, 21), (7, 36), (43, 9), (28, 30), (5, 28), (7, 40), (38, 20), (13, 36), (27, 26), (33, 18), (10, 19), (6, 13), (42, 28), (21, 33), (9, 3), (40, 26), (27, 10), (19, 8), (10, 2), (24, 13), (12, 23), (41, 15), (24, 4), (26, 10), (39, 6), (7, 31), (20, 19), (36, 40), (22, 26), (36, 35), (31, 21), (27, 14), (17, 16), (9, 40), (16, 37), (29, 4), (22, 36), (32, 11), (6, 30), (25, 7), (9, 23), (20, 36), (3, 20), (6, 26), (24, 11), (6, 36), (42, 27), (23, 3), (36, 41), (19, 23), (27, 20), (41, 32), (24, 30), (22, 1), (42, 23), (35, 21), (11, 22), (18, 24), (0, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 24), (43, 22), (12, 0), (7, 11), (4, 13), (1, 24), (2, 28), (26, 40), (35, 33), (11, 19), (17, 21), (4, 5), (34, 33), (1, 8), (1, 37), (26, 3), (0, 15), (34, 2), (36, 22), (41, 18), (4, 34), (30, 17), (31, 35), (21, 38), (10, 19), (8, 16), (10, 16), (3, 0), (23, 0), (4, 25), (33, 37), (35, 2), (28, 2), (34, 32), (2, 38), (25, 7), (20, 20), (3, 17), (26, 22), (21, 5), (6, 34), (5, 4), (43, 34), (38, 36), (40, 30), (15, 7), (9, 33), (16, 39), (4, 16), (42, 18), (34, 21), (6, 11), (24, 39), (21, 15), (24, 34), (4, 31), (14, 7), (26, 29), (4, 4), (30, 30), (25, 25), (25, 23), (2, 40), (17, 14), (36, 4), (0, 38), (41, 24), (38, 20), (5, 9), (17, 9), (2, 32), (18, 21), (10, 3), (4, 0), (29, 18), (32, 16), (8, 23), (9, 34), (23, 2), (36, 5), (15, 22), (10, 25), (43, 9), (22, 38), (9, 0), (22, 25), (36, 7), (37, 5), (23, 19), (36, 10), (30, 0), (3, 18), (16, 36), (33, 32), (27, 30), (34, 35), (4, 9), (0, 5), (22, 1), (32, 22), (21, 17), (22, 3), (27, 17), (16, 40), (28, 40), (19, 35), (27, 27), (32, 3), (14, 32), (35, 39), (12, 16), (7, 27), (32, 7), (40, 1), (41, 25), (38, 1), (5, 38), (43, 19), (26, 25), (40, 14), (41, 10), (16, 2), (14, 20), (39, 4), (1, 21), (0, 34), (33, 7), (21, 21), (40, 9), (30, 18), (3, 34), (5, 32), (1, 11), (32, 2), (6, 19), (0, 31), (37, 33), (4, 10), (3, 25), (41, 27), (41, 12), (0, 27), (40, 22), (14, 39), (7, 34), (13, 26), (9, 2), (28, 8), (17, 31), (25, 4), (12, 30), (4, 17), (6, 5), (42, 0), (43, 15), (3, 12), (41, 1), (6, 15), (30, 12), (28, 16), (28, 38), (43, 5), (40, 10), (6, 20), (21, 25), (10, 6), (7, 35), (33, 12), (24, 19), (10, 10), (29, 17), (43, 6), (19, 21), (23, 3), (27, 2), (10, 27), (14, 5), (19, 16), (24, 9), (31, 32), (32, 20), (32, 18), (39, 6), (14, 6), (40, 32), (26, 24), (24, 7), (28, 17), (42, 16), (6, 4), (4, 14), (25, 18), (12, 2), (13, 35), (26, 13), (42, 10), (28, 12), (43, 39), (37, 24), (10, 31), (38, 2), (17, 39), (29, 7), (28, 1), (38, 15), (28, 27), (39, 32), (26, 18), (42, 15), (19, 26), (0, 12), (9, 36), (15, 12), (40, 18), (10, 17), (4, 39), (36, 9), (20, 2), (0, 37), (29, 16), (34, 17), (17, 10), (29, 31), (30, 11), (8, 1), (36, 39), (0, 33), (40, 37), (5, 23), (15, 31), (38, 30), (41, 40), (5, 39), (7, 33), (12, 5), (3, 6), (9, 39), (14, 26), (25, 37), (25, 5), (39, 25), (33, 19), (10, 5), (31, 30), (37, 17), (15, 19), (4, 21), (18, 25), (24, 27), (10, 24), (37, 2), (38, 11), (30, 26), (29, 15), (3, 20), (17, 37), (34, 34), (14, 9), (31, 15), (41, 30), (11, 17), (7, 36), (5, 36), (16, 31), (29, 22), (27, 20), (6, 2), (6, 29), (5, 21), (1, 2), (32, 34), (43, 29), (10, 12), (20, 22), (35, 28), (30, 32), (38, 16), (27, 5), (12, 15), (13, 5), (17, 4), (28, 29), (34, 14), (27, 25), (12, 13), (23, 6), (33, 20), (36, 0), (25, 33), (11, 31), (7, 38), (34, 6), (43, 17), (28, 39), (33, 26), (35, 37), (7, 19), (31, 18), (28, 9), (32, 6), (42, 24), (10, 30), (10, 2), (40, 35), (6, 31), (19, 28), (20, 1), (31, 36), (3, 7), (34, 23), (43, 38), (20, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 21), (18, 39), (8, 40), (8, 41), (14, 22), (11, 45), (29, 16), (13, 27), (23, 28), (27, 23), (4, 21), (13, 24), (15, 37), (5, 32), (34, 3), (5, 0), (18, 23), (32, 23), (32, 5), (31, 13), (24, 10), (5, 35), (0, 39), (34, 43), (30, 18), (4, 14), (6, 35), (37, 14), (7, 23), (39, 16), (22, 19), (1, 24), (26, 24), (16, 3), (26, 40), (7, 15), (21, 41), (31, 19), (18, 9), (39, 6), (31, 4), (24, 30), (14, 24), (11, 3), (36, 24), (11, 24), (1, 42), (5, 13), (10, 31), (11, 20), (15, 22), (12, 12), (26, 41), (19, 38), (16, 22), (17, 14), (19, 7), (40, 36), (3, 28), (25, 36), (24, 39), (9, 29), (40, 30), (32, 3), (19, 26), (38, 24), (24, 3), (24, 34), (7, 43), (29, 9), (35, 44), (13, 22), (9, 41), (17, 12), (27, 32), (32, 31), (32, 16), (28, 10), (13, 41), (37, 46), (5, 19), (21, 33), (13, 2), (4, 22), (20, 28), (12, 8), (14, 14), (0, 8), (36, 2), (5, 34), (2, 46), (21, 45), (33, 43), (34, 17), (23, 10), (0, 16), (39, 21), (20, 30), (26, 45), (21, 4), (37, 19), (40, 14), (11, 17), (33, 35), (31, 15), (5, 16), (19, 12), (33, 0), (35, 24), (24, 11), (32, 12), (26, 26), (13, 32), (0, 6), (11, 34), (8, 15), (16, 21), (33, 29), (10, 44), (13, 44), (28, 30), (8, 17), (32, 0), (5, 11), (36, 18), (5, 2), (14, 33), (29, 22), (31, 24), (21, 10), (26, 16), (9, 46), (36, 15), (30, 36), (11, 9), (28, 2), (40, 3), (16, 42), (19, 18), (15, 40), (22, 14), (39, 11), (40, 11), (37, 45), (36, 46), (1, 41), (30, 26), (5, 29), (24, 1), (28, 21), (15, 24), (15, 28), (10, 15), (13, 15), (12, 26), (26, 35), (30, 9), (38, 29), (25, 9), (1, 38), (24, 4), (14, 39), (29, 24), (19, 45), (39, 28), (29, 42), (18, 13), (5, 41), (30, 40), (1, 5), (32, 6), (19, 15), (28, 0), (31, 32), (22, 36), (24, 15), (10, 12), (8, 16), (39, 17), (2, 31), (22, 26), (8, 37), (12, 44), (35, 34), (34, 36), (17, 39), (39, 32), (6, 44), (14, 10), (34, 28), (31, 0), (2, 1), (38, 16), (31, 44), (18, 4), (26, 29), (39, 29), (6, 19), (18, 5), (21, 44), (3, 35), (9, 22), (38, 0), (26, 5), (17, 42), (23, 21), (28, 32), (34, 23), (29, 36), (14, 5), (32, 41), (3, 32), (4, 5), (39, 20), (18, 12), (27, 30), (14, 4), (19, 1), (0, 32), (16, 19), (24, 8), (27, 26), (22, 34), (23, 23), (34, 19), (29, 12), (22, 1), (3, 36), (22, 27), (26, 13), (24, 32), (20, 17), (33, 23), (32, 44), (28, 37), (18, 11), (9, 32), (37, 22), (13, 46), (7, 33), (2, 33), (33, 37), (15, 9), (27, 39), (1, 16), (26, 6), (2, 9), (13, 0), (32, 4), (21, 42), (4, 19), (40, 22), (33, 41), (9, 4), (16, 43), (30, 30), (27, 15), (21, 34), (5, 23), (33, 15), (34, 16), (37, 30), (20, 22), (7, 35), (29, 4), (37, 40), (29, 21), (5, 36), (25, 13), (24, 23), (24, 22), (23, 19), (19, 43), (36, 34), (10, 23), (9, 11), (8, 27), (12, 34), (17, 25), (4, 13), (2, 13), (5, 7), (20, 15), (27, 4), (3, 46), (40, 37), (19, 23), (21, 29), (27, 43), (4, 32), (12, 28), (11, 14), (4, 2), (25, 8), (1, 21), (27, 13), (18, 3), (36, 19), (9, 9), (0, 46), (40, 24), (6, 21), (38, 7), (4, 45), (7, 14), (29, 37), (11, 43), (10, 3), (12, 14), (6, 17), (14, 45), (8, 43), (12, 3), (30, 39), (28, 17), (0, 12), (20, 25), (31, 45), (7, 21), (32, 1), (1, 8), (20, 40), (23, 2), (21, 39), (7, 10), (25, 33), (10, 25), (6, 20), (4, 1), (12, 40), (19, 29), (1, 11), (3, 30), (16, 32), (16, 18), (34, 46), (28, 38), (11, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 15), (46, 12), (25, 1), (10, 45), (38, 24), (43, 42), (36, 42), (44, 35), (38, 22), (9, 20), (37, 29), (38, 26), (26, 43), (29, 10), (29, 31), (35, 6), (18, 46), (10, 29), (22, 42), (42, 21), (39, 20), (3, 27), (5, 8), (10, 24), (44, 3), (4, 3), (8, 2), (14, 42), (26, 29), (0, 24), (31, 25), (42, 14), (13, 9), (4, 40), (10, 26), (44, 34), (24, 14), (6, 23), (29, 32), (21, 40), (14, 45), (40, 46), (44, 28), (9, 44), (26, 17), (6, 12), (8, 13), (32, 47), (14, 27), (5, 19), (46, 46), (31, 34), (22, 22), (26, 21), (21, 4), (15, 23), (6, 1), (0, 33), (6, 44), (25, 10), (33, 2), (46, 8), (3, 3), (34, 30), (35, 0), (31, 18), (24, 22), (32, 39), (0, 19), (19, 32), (18, 24), (35, 24), (26, 10), (2, 4), (29, 15), (30, 39), (1, 21), (15, 4), (40, 27), (40, 22), (10, 44), (43, 5), (45, 33), (44, 18), (39, 2), (20, 4), (14, 6), (35, 47), (17, 9), (8, 45), (43, 21), (36, 13), (21, 17), (32, 27), (46, 1), (9, 36), (32, 30), (25, 4), (16, 42), (34, 36), (41, 15), (46, 11), (9, 26), (30, 24), (12, 23), (33, 6), (14, 18), (20, 23), (11, 33), (13, 4), (35, 30), (35, 5), (26, 41), (18, 6), (16, 45), (1, 32), (22, 47), (8, 7), (33, 15), (41, 32), (36, 15), (14, 28), (37, 34), (6, 28), (24, 39), (15, 36), (25, 29), (28, 11), (0, 45), (25, 16), (28, 21), (39, 19), (34, 35), (38, 0), (37, 27), (40, 5), (21, 23), (27, 14), (11, 27), (24, 44), (25, 12), (10, 38), (46, 9), (40, 19), (8, 43), (6, 41), (16, 22), (2, 17), (38, 15), (13, 45), (14, 41), (18, 37), (3, 7), (40, 34), (17, 0), (23, 47), (23, 17), (19, 14), (38, 6), (45, 0), (36, 46), (41, 37), (40, 26), (28, 12), (32, 38), (39, 23), (10, 28), (17, 30), (45, 21), (14, 36), (19, 4), (46, 38), (46, 28), (15, 25), (21, 34), (32, 29), (16, 35), (30, 22), (30, 2), (15, 5), (13, 24), (18, 23), (16, 16), (15, 7), (17, 36), (16, 36), (4, 20), (7, 36), (17, 44), (38, 14), (36, 7), (46, 30), (7, 40), (22, 13), (21, 5), (23, 39), (9, 7), (3, 11), (36, 10), (25, 13), (32, 7), (9, 23), (6, 11), (2, 30), (35, 44), (45, 20), (29, 36), (34, 5), (41, 40), (8, 44), (44, 6), (8, 11), (9, 21), (35, 20), (12, 47), (13, 7), (20, 28), (34, 17), (1, 29), (43, 35), (0, 25), (26, 16), (32, 16), (39, 10), (31, 3), (11, 20), (36, 8), (12, 44), (45, 46), (28, 20), (27, 8), (10, 8), (26, 23), (29, 34), (40, 42), (44, 31), (22, 32), (32, 42), (11, 36), (42, 27), (12, 36), (16, 4), (29, 38), (42, 36), (41, 1), (7, 46), (28, 31), (43, 41), (7, 44), (43, 1), (3, 18), (12, 14), (46, 14), (12, 34), (19, 38), (24, 5), (3, 13), (41, 20), (17, 26), (42, 26), (17, 22), (29, 43), (12, 46), (22, 5), (38, 16), (18, 15), (35, 37), (26, 4), (22, 31), (32, 8), (35, 2), (30, 37), (31, 45), (36, 26), (25, 37), (32, 2), (12, 17), (30, 23), (41, 27), (33, 14), (5, 22), (32, 3), (18, 18), (41, 39), (43, 25), (4, 45), (22, 19), (42, 2), (8, 23), (29, 26), (14, 37), (44, 40), (36, 11), (3, 39), (43, 6), (1, 9), (13, 27), (9, 31), (19, 27), (31, 16), (16, 41), (33, 16), (41, 44), (36, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 34), (34, 30), (32, 18), (16, 21), (1, 3), (37, 7), (10, 17), (41, 8), (0, 20), (38, 40), (34, 11), (29, 23), (7, 12), (38, 35), (6, 0), (5, 31), (30, 19), (0, 36), (31, 34), (29, 28), (38, 17), (7, 40), (27, 20), (20, 2), (15, 10), (29, 29), (13, 38), (1, 45), (19, 2), (6, 22), (34, 44), (17, 8), (37, 14), (39, 16), (32, 6), (15, 33), (24, 27), (30, 21), (34, 19), (14, 5), (37, 6), (4, 14), (34, 27), (39, 42), (32, 3), (18, 24), (33, 14), (36, 40), (13, 35), (34, 22), (39, 1), (32, 28), (13, 20), (18, 29), (42, 40), (16, 37), (27, 46), (13, 16), (36, 22), (37, 41), (23, 10), (19, 32), (19, 15), (32, 33), (42, 44), (42, 41), (10, 24), (16, 38), (10, 3), (1, 31), (34, 3), (40, 1), (16, 0), (37, 35), (40, 38), (34, 36), (31, 44), (5, 39), (1, 33), (32, 22), (10, 36), (11, 41), (33, 23), (5, 29), (39, 35), (37, 1), (30, 31), (28, 9), (13, 28), (13, 13), (38, 13), (28, 16), (12, 14), (4, 20), (21, 0), (29, 40), (42, 0), (40, 40), (10, 1), (32, 23), (9, 18), (1, 16), (26, 36), (34, 21), (18, 1), (35, 22), (2, 37), (11, 44), (24, 21), (10, 30), (43, 16), (7, 16), (9, 43), (2, 8), (15, 27), (28, 8), (18, 4), (3, 41), (4, 16), (0, 28), (17, 35), (19, 1), (8, 22), (7, 46), (21, 37), (10, 25), (15, 38), (38, 32), (26, 7), (16, 7), (34, 20), (11, 4), (13, 24), (28, 46), (24, 10), (18, 19), (28, 42), (5, 42), (30, 46), (21, 26), (19, 10), (42, 28), (31, 7), (42, 37), (14, 42), (1, 32), (33, 36), (38, 5), (15, 3), (0, 30), (15, 40), (39, 23), (30, 29), (26, 4), (8, 35), (35, 39), (4, 46), (25, 14), (32, 27), (16, 10), (10, 33), (25, 10), (43, 24), (14, 20), (25, 35), (10, 34), (4, 8), (4, 27), (9, 37), (12, 32), (12, 45), (8, 18), (0, 9), (39, 43), (35, 7), (35, 38), (0, 31), (2, 40), (43, 22), (40, 11), (31, 27), (7, 35), (38, 9), (18, 40), (40, 37), (9, 27), (32, 15), (3, 26), (7, 32), (38, 27), (36, 41), (20, 17), (13, 44), (21, 2), (1, 15), (3, 16), (16, 13), (32, 42), (1, 42), (15, 28), (28, 29), (36, 30), (39, 38), (32, 2), (12, 23), (43, 18), (36, 24), (2, 45), (18, 8), (36, 32), (0, 26), (26, 42), (27, 38), (2, 46), (2, 43), (7, 30), (43, 17), (16, 5), (37, 18), (39, 12), (38, 7), (8, 27), (7, 17), (25, 37), (43, 36), (10, 39), (13, 18), (11, 20), (40, 10), (27, 45), (20, 38), (23, 4), (27, 16), (18, 31), (14, 40), (0, 19), (41, 44), (23, 36), (29, 24), (1, 40), (2, 27), (33, 2), (36, 36), (32, 10), (35, 29), (31, 2), (13, 12), (2, 24), (4, 41), (27, 2), (4, 42), (21, 35), (7, 14), (18, 32), (1, 7), (29, 39), (4, 44), (24, 42), (23, 34), (3, 46), (21, 36), (31, 19), (12, 40), (19, 12), (34, 9), (2, 6), (19, 36), (7, 3), (24, 2), (8, 0), (8, 28), (25, 1), (13, 15), (16, 27), (26, 26), (2, 29), (32, 0), (12, 13), (33, 16), (8, 23), (41, 19), (42, 39), (37, 31), (31, 18), (6, 32), (24, 1), (11, 5), (19, 16), (15, 8), (35, 46), (42, 10), (29, 36), (13, 1), (28, 5), (9, 31), (1, 44), (7, 43), (5, 12), (31, 13), (16, 4), (36, 16), (0, 7), (24, 43), (14, 0), (28, 25), (20, 3), (11, 10), (29, 30), (15, 7), (16, 14), (9, 2), (8, 46), (12, 35), (20, 43), (17, 25), (37, 28), (40, 13), (23, 8), (35, 37), (6, 38), (13, 26), (25, 36), (5, 6), (23, 27), (41, 46), (14, 32), (40, 33), (8, 31), (6, 4), (17, 41), (15, 19), (37, 45), (4, 18), (2, 31), (38, 30), (4, 37), (8, 8), (41, 10), (24, 13), (31, 9), (42, 33), (16, 40), (20, 23), (26, 15), (4, 28), (7, 36), (12, 16), (23, 35), (17, 6), (43, 15), (31, 22), (27, 23), (0, 12), (41, 14), (19, 22), (11, 11), (28, 36), (35, 5), (39, 8), (26, 1), (7, 11), (24, 16), (31, 28), (15, 15), (22, 33), (12, 5), (18, 7), (6, 17), (37, 9), (6, 7), (9, 13), (26, 8), (1, 29), (34, 4), (37, 21), (26, 25), (8, 4), (38, 31), (15, 29), (20, 41), (37, 16), (9, 26), (28, 35), (24, 24), (32, 12), (29, 45), (8, 13), (14, 11), (31, 4), (25, 19), (11, 46), (40, 6), (22, 38), (16, 15), (14, 26), (3, 0), (17, 40), (0, 17), (43, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 19), (29, 20), (30, 17), (20, 4), (16, 39), (40, 24), (22, 22), (1, 37), (29, 38), (39, 0), (33, 15), (37, 2), (28, 38), (4, 19), (28, 8), (16, 3), (1, 7), (20, 27), (37, 19), (5, 6), (4, 36), (3, 23), (4, 39), (15, 38), (30, 15), (19, 21), (7, 7), (27, 33), (36, 2), (14, 26), (21, 28), (17, 29), (3, 37), (19, 11), (23, 37), (36, 24), (4, 5), (39, 4), (11, 28), (16, 17), (9, 6), (36, 22), (15, 34), (15, 35), (3, 25), (18, 6), (10, 14), (36, 17), (1, 23), (9, 34), (14, 32), (41, 32), (8, 9), (38, 28), (12, 38), (40, 13), (30, 30), (24, 33), (20, 10), (13, 17), (22, 35), (32, 0), (16, 23), (20, 22), (12, 11), (4, 35), (30, 12), (40, 36), (31, 3), (39, 32), (13, 28), (29, 4), (18, 22), (17, 5), (1, 22), (18, 4), (20, 21), (24, 23), (40, 34), (2, 27), (36, 18), (29, 16), (10, 26), (27, 29), (40, 15), (3, 31), (6, 16), (15, 24), (2, 35), (19, 6), (4, 27), (11, 25), (17, 24), (26, 29), (10, 39), (25, 28), (21, 36), (19, 0), (39, 30), (22, 15), (7, 31), (10, 17), (21, 29), (39, 20), (27, 11), (21, 13), (27, 10), (37, 5), (25, 18), (27, 9), (32, 1), (13, 18), (11, 35), (4, 32), (40, 16), (25, 4), (33, 37), (8, 0), (34, 25), (4, 20), (38, 10), (12, 0), (5, 15), (21, 32), (8, 1), (14, 14), (34, 1), (17, 23), (3, 17), (41, 14), (36, 29), (31, 9), (41, 24), (11, 24), (17, 39), (36, 12), (5, 20), (18, 16), (17, 36), (5, 2), (37, 4), (10, 33), (13, 37), (21, 9), (36, 25), (15, 22), (16, 25), (13, 1), (37, 21), (24, 21), (37, 32), (1, 10), (23, 39), (15, 27), (28, 27), (22, 2), (0, 27), (10, 35), (19, 13), (35, 8), (4, 11), (3, 4), (15, 15), (39, 39), (32, 9), (13, 26), (28, 17), (29, 31), (13, 30), (36, 34), (41, 38), (32, 36), (7, 25), (35, 38), (11, 29), (14, 38), (36, 31), (6, 15), (6, 30), (19, 2), (29, 13), (36, 36), (35, 11), (14, 2), (11, 19), (19, 23), (0, 38), (6, 5), (22, 9), (0, 32), (0, 20), (24, 0), (9, 35), (9, 24), (28, 4), (22, 31), (23, 4), (2, 32), (28, 13), (20, 31), (18, 17), (25, 32), (40, 7), (2, 31), (31, 24), (15, 17), (11, 20), (17, 21), (7, 15), (14, 12), (26, 39), (1, 9), (5, 16), (2, 7), (8, 6), (30, 7), (35, 18), (0, 9), (1, 35), (39, 35), (39, 36), (38, 25), (18, 7), (1, 20), (36, 4), (37, 38), (33, 12), (40, 4), (20, 5), (38, 29), (10, 34), (10, 22), (30, 36), (18, 18), (23, 30), (10, 23), (18, 9), (6, 14), (0, 22), (6, 4), (0, 15), (14, 0), (19, 5), (30, 18), (23, 9), (37, 20), (36, 3), (24, 3), (19, 9), (31, 20), (11, 30), (13, 29), (34, 36), (8, 4), (26, 15), (13, 13), (13, 22), (11, 18), (40, 23), (2, 22), (9, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 12), (38, 8), (18, 24), (4, 11), (20, 14), (20, 12), (42, 38), (2, 24), (19, 11), (7, 28), (0, 10), (3, 2), (21, 27), (20, 13), (10, 4), (26, 0), (24, 20), (6, 28), (14, 0), (2, 28), (26, 40), (8, 7), (12, 2), (9, 1), (16, 23), (2, 6), (18, 18), (29, 38), (40, 18), (20, 22), (31, 24), (38, 32), (37, 10), (12, 18), (20, 18), (33, 16), (5, 5), (19, 35), (3, 34), (15, 28), (25, 13), (28, 15), (3, 31), (6, 4), (24, 8), (13, 4), (39, 29), (21, 21), (36, 1), (35, 0), (17, 38), (16, 15), (1, 14), (26, 30), (30, 32), (39, 17), (5, 12), (18, 15), (41, 17), (35, 37), (34, 22), (36, 24), (0, 27), (33, 9), (11, 7), (37, 33), (29, 32), (31, 15), (34, 10), (32, 6), (7, 32), (38, 28), (20, 31), (13, 19), (32, 7), (10, 1), (3, 22), (44, 11), (43, 3), (25, 18), (19, 1), (21, 25), (20, 33), (41, 5), (8, 23), (16, 35), (26, 23), (2, 17), (44, 0), (9, 33), (20, 10), (10, 27), (29, 6), (32, 29), (41, 39), (34, 15), (2, 1), (9, 21), (22, 6), (41, 18), (37, 4), (38, 2), (24, 35), (20, 24), (19, 37), (29, 31), (43, 22), (6, 19), (9, 29), (22, 31), (22, 32), (33, 31), (18, 11), (28, 24), (40, 6), (22, 2), (35, 32), (28, 12), (25, 8), (25, 20), (15, 24), (4, 19), (17, 1), (18, 28), (22, 12), (20, 7), (8, 13), (13, 11), (41, 20), (7, 26), (12, 13), (22, 17), (27, 1), (13, 37), (0, 12), (42, 29), (4, 26), (26, 2), (41, 9), (18, 1), (13, 10), (25, 40), (5, 3), (41, 25), (27, 5), (2, 30), (29, 40), (27, 6), (32, 22), (7, 39), (25, 27), (44, 3), (5, 16), (4, 5), (7, 27), (31, 16), (18, 36), (41, 33), (19, 9), (35, 1), (43, 16), (9, 20), (3, 8), (13, 24), (37, 34), (29, 0), (6, 6), (11, 16), (26, 29), (10, 21), (13, 35), (27, 4), (4, 21), (37, 9), (28, 38), (31, 14), (39, 8), (39, 14), (21, 5), (30, 16), (26, 18), (8, 28), (24, 17), (6, 11), (12, 12), (34, 28), (42, 2), (30, 34), (0, 38), (13, 33), (0, 16), (31, 37), (5, 30), (6, 9), (31, 25), (17, 3), (37, 24), (14, 27), (23, 24), (26, 19), (16, 21), (24, 3), (43, 12), (34, 20), (21, 13), (43, 36), (11, 34), (33, 32), (36, 36), (14, 11), (39, 38), (2, 31), (43, 0), (20, 27), (40, 16), (25, 29), (8, 22), (43, 14), (44, 28), (38, 38), (31, 38), (14, 10), (1, 0), (41, 22), (35, 34), (36, 37), (43, 30), (39, 37), (13, 22), (4, 17), (7, 15), (8, 9), (18, 5), (0, 20), (5, 38), (6, 16), (13, 16), (37, 20), (29, 10), (7, 31), (19, 20), (40, 2), (3, 7), (37, 2), (31, 40), (41, 21), (23, 37), (43, 5), (12, 15), (0, 11), (15, 32), (0, 2), (31, 7), (22, 26), (29, 23), (2, 11), (8, 34), (10, 37), (19, 26), (22, 9), (36, 4), (30, 22), (38, 11), (25, 37), (12, 8), (44, 12), (12, 17), (26, 3), (37, 6), (26, 27), (5, 20), (0, 28), (43, 39), (7, 3), (39, 6), (1, 40), (8, 10), (36, 9), (2, 20), (17, 7), (37, 5), (39, 16), (32, 39), (29, 25), (13, 31), (41, 35), (12, 9), (31, 10), (17, 22), (16, 26), (22, 0), (5, 22), (32, 16), (0, 32), (18, 25), (8, 25), (34, 0), (41, 32), (19, 40), (41, 31), (38, 34), (10, 35), (4, 36), (22, 36), (40, 12), (23, 16), (22, 38), (35, 38), (8, 17), (35, 31), (28, 11), (19, 38), (42, 40), (24, 5), (25, 32), (36, 25), (30, 12), (38, 21), (9, 28), (36, 3), (32, 8), (13, 9), (27, 40), (20, 9), (42, 24), (26, 16), (9, 0), (12, 38), (4, 33), (38, 31), (26, 35), (3, 9), (31, 30), (27, 3), (18, 40), (26, 13), (24, 9), (44, 29), (25, 5), (30, 40), (6, 39), (4, 13), (33, 0), (15, 1), (10, 9), (43, 25), (7, 24), (5, 6), (20, 16), (36, 34), (19, 32), (30, 30), (34, 27), (3, 25), (27, 25), (39, 1), (19, 0), (28, 5), (16, 40), (23, 25), (12, 33), (16, 39), (22, 37), (22, 24), (10, 14), (11, 18), (27, 12), (42, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 37), (36, 8), (31, 0), (39, 34), (20, 4), (0, 23), (16, 17), (37, 35), (33, 12), (34, 7), (33, 38), (8, 16), (20, 23), (23, 3), (12, 34), (39, 26), (18, 5), (40, 25), (20, 31), (39, 23), (12, 0), (8, 28), (8, 19), (19, 0), (11, 19), (31, 37), (33, 36), (39, 33), (24, 40), (6, 25), (30, 36), (14, 11), (27, 32), (20, 18), (27, 36), (39, 13), (5, 20), (3, 30), (16, 31), (36, 32), (29, 0), (24, 17), (38, 14), (39, 39), (1, 30), (4, 7), (4, 36), (34, 36), (25, 22), (38, 26), (34, 38), (6, 35), (27, 40), (20, 30), (2, 15), (7, 0), (17, 15), (0, 10), (11, 30), (4, 38), (8, 1), (12, 2), (32, 18), (19, 31), (39, 9), (36, 3), (3, 14), (31, 7), (13, 5), (39, 6), (6, 24), (38, 13), (37, 38), (33, 35), (20, 19), (6, 34), (36, 14), (25, 10), (38, 0), (5, 32), (9, 18), (31, 16), (28, 6), (28, 10), (4, 13), (28, 5), (32, 4), (13, 16), (5, 30), (14, 6), (40, 24), (39, 25), (7, 4), (37, 19), (12, 28), (15, 0), (24, 3), (20, 38), (8, 33), (9, 20), (29, 18), (36, 0), (39, 37), (8, 2), (29, 23), (34, 21), (23, 22), (29, 39), (9, 6), (2, 25), (24, 27), (6, 5), (0, 4), (33, 4), (4, 27), (27, 18), (0, 7), (25, 29), (40, 19), (5, 10), (29, 37), (7, 34), (27, 33), (16, 5), (6, 16), (35, 40), (8, 3), (40, 33), (9, 8), (19, 18), (9, 26), (12, 30), (15, 2), (15, 8), (13, 11), (11, 32), (35, 11), (39, 4), (28, 27), (20, 22), (18, 32), (30, 3), (34, 19), (6, 21), (0, 5), (12, 13), (23, 37), (32, 37), (26, 2), (12, 6), (33, 5), (19, 8), (23, 16), (22, 7), (40, 15), (18, 38), (4, 3), (24, 19), (14, 34), (11, 36), (27, 22), (38, 16), (6, 7), (24, 2), (20, 27), (13, 20), (38, 17), (1, 2), (9, 1), (22, 2), (0, 35), (27, 9), (22, 20), (19, 35), (26, 19), (38, 25), (35, 23), (1, 38), (2, 31), (35, 1), (17, 16), (2, 4), (22, 11), (8, 10), (13, 12), (39, 20), (27, 23), (16, 1), (31, 6), (6, 18), (25, 32), (5, 21), (39, 21), (28, 34), (31, 14), (14, 37), (22, 3), (3, 5), (12, 21), (6, 29), (4, 26), (36, 38), (25, 21), (20, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 47), (24, 42), (37, 28), (2, 43), (12, 23), (31, 14), (12, 6), (20, 14), (10, 16), (8, 4), (25, 16), (1, 46), (21, 47), (7, 19), (25, 42), (16, 9), (28, 41), (9, 43), (32, 41), (29, 4), (36, 30), (3, 17), (26, 36), (17, 1), (15, 32), (26, 29), (22, 18), (33, 11), (29, 11), (20, 41), (4, 40), (39, 2), (22, 35), (4, 15), (19, 38), (36, 4), (3, 20), (23, 9), (14, 32), (37, 34), (28, 18), (21, 33), (26, 13), (5, 42), (5, 30), (10, 34), (18, 17), (32, 15), (11, 45), (38, 34), (15, 44), (19, 47), (28, 4), (39, 4), (4, 12), (17, 9), (7, 10), (18, 9), (34, 40), (11, 22), (27, 33), (6, 32), (14, 46), (6, 44), (9, 28), (32, 1), (0, 17), (34, 11), (3, 31), (32, 40), (3, 4), (32, 11), (19, 1), (14, 39), (1, 25), (19, 18), (23, 18), (23, 42), (15, 38), (36, 19), (37, 35), (18, 7), (28, 25), (17, 29), (32, 32), (20, 39), (33, 36), (39, 0), (39, 12), (33, 35), (20, 18), (34, 29), (10, 42), (23, 23), (6, 14), (10, 5), (33, 1), (5, 40), (14, 31), (5, 45), (21, 7), (6, 27), (8, 9), (25, 26), (15, 11), (28, 19), (7, 23), (7, 34), (7, 33), (14, 18), (12, 17), (35, 30), (13, 18), (8, 40), (30, 45), (34, 22), (34, 45), (35, 36), (25, 24), (1, 38), (20, 19), (6, 40), (16, 11), (28, 6), (6, 33), (13, 31), (19, 34), (30, 9), (9, 24), (8, 27), (17, 23), (2, 9), (22, 3), (31, 22), (8, 3), (20, 30), (21, 42), (29, 41), (6, 25), (8, 26), (26, 38), (5, 27), (7, 37), (27, 44), (34, 8), (39, 29), (3, 16), (11, 16), (0, 29), (4, 39), (33, 42), (1, 16), (11, 23), (18, 32), (16, 28), (21, 16), (8, 43), (1, 17), (29, 32), (13, 43), (32, 10), (15, 25), (22, 14), (26, 23), (21, 10), (2, 5), (38, 45), (21, 23), (34, 39), (29, 7), (38, 24), (0, 44), (18, 20), (7, 2), (35, 2), (22, 23), (33, 7), (22, 40), (23, 30), (25, 25), (15, 17), (19, 32), (28, 37), (29, 5), (13, 28), (10, 29), (36, 23), (3, 13), (24, 14), (35, 46), (24, 33), (20, 3), (12, 34), (13, 30), (18, 8), (27, 31), (39, 24), (1, 15), (3, 25), (37, 36), (9, 38), (24, 31), (29, 42), (30, 28), (10, 6), (6, 37), (38, 0), (25, 14), (27, 17), (18, 45), (17, 2), (6, 22), (6, 21), (6, 1), (37, 45), (31, 27), (15, 33), (22, 38), (17, 21), (36, 18), (34, 47), (5, 23), (14, 13), (12, 45), (23, 7), (24, 4), (2, 45), (36, 27), (5, 7), (25, 22), (27, 43), (4, 47), (28, 22), (14, 28), (32, 30), (12, 16), (36, 2), (39, 35), (15, 34), (12, 7), (20, 17), (37, 18), (34, 12), (16, 17), (1, 5), (18, 22), (1, 9), (23, 26), (25, 32), (20, 28), (7, 46), (8, 31), (23, 6), (13, 38), (19, 28), (17, 35), (8, 15), (3, 46), (14, 10), (11, 14), (32, 45)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 38), (0, 21), (17, 13), (19, 32), (22, 22), (28, 38), (32, 9), (3, 20), (6, 39), (24, 6), (13, 32), (9, 33), (13, 5), (23, 13), (22, 18), (2, 19), (22, 15), (34, 32), (38, 23), (24, 32), (4, 4), (6, 13), (13, 2), (2, 37), (18, 38), (17, 7), (22, 37), (13, 25), (20, 23), (28, 29), (38, 26), (37, 35), (12, 26), (33, 0), (7, 22), (35, 14), (9, 32), (25, 21), (28, 26), (32, 7), (23, 6), (7, 33), (10, 30), (6, 28), (21, 20), (5, 3), (13, 9), (18, 15), (4, 3), (34, 11), (29, 14), (26, 28), (22, 17), (16, 33), (29, 36), (37, 0), (35, 29), (35, 24), (38, 31), (34, 16), (20, 18), (6, 11), (12, 4), (3, 33), (39, 22), (17, 19), (35, 22), (22, 0), (9, 8), (22, 20), (18, 18), (4, 32), (35, 16), (22, 25), (37, 8), (13, 11), (29, 21), (15, 27), (11, 16), (12, 9), (2, 16), (1, 4), (38, 15), (23, 15), (14, 20), (25, 33), (7, 26), (27, 14), (5, 21), (4, 6), (31, 5), (25, 24), (36, 22), (27, 10), (36, 32), (25, 4), (2, 20), (5, 24), (20, 25), (28, 0), (18, 21), (27, 17), (35, 17), (37, 13), (6, 25), (18, 27), (19, 22), (13, 30), (19, 40), (3, 8), (13, 0), (34, 2), (21, 29), (34, 5), (14, 36), (20, 8), (13, 29), (4, 5), (29, 32), (5, 10), (9, 2), (3, 16), (0, 33), (15, 10), (2, 12), (17, 32), (39, 7), (28, 4), (33, 37), (9, 25), (3, 30), (17, 24), (29, 17), (22, 21), (7, 1), (7, 19), (23, 24), (30, 18), (37, 22), (26, 4), (7, 20), (9, 23), (18, 19), (29, 7), (20, 5), (24, 19), (9, 27), (4, 14), (12, 20), (24, 25), (39, 9), (34, 22), (0, 30), (34, 25), (10, 14), (22, 29), (21, 25), (23, 0), (13, 4), (24, 5), (4, 31), (29, 30), (32, 14), (36, 38), (6, 27), (33, 30), (15, 33), (38, 9), (20, 12), (39, 39), (11, 5), (3, 23), (17, 26), (18, 23), (3, 39), (2, 25), (35, 3), (17, 33), (26, 21), (29, 27), (24, 2), (20, 32), (3, 0), (24, 0), (35, 23), (32, 13), (27, 38), (38, 14), (28, 1), (20, 34), (15, 12), (34, 1), (29, 6), (10, 37), (1, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 12), (19, 5), (14, 0), (13, 20), (27, 43), (30, 22), (4, 43), (23, 8), (32, 37), (2, 23), (11, 37), (18, 25), (7, 8), (27, 24), (1, 14), (25, 12), (2, 35), (17, 8), (1, 23), (28, 25), (7, 36), (36, 15), (7, 9), (35, 17), (32, 1), (26, 9), (35, 3), (10, 11), (33, 23), (25, 8), (39, 16), (34, 3), (16, 10), (7, 33), (21, 42), (26, 36), (27, 32), (38, 2), (11, 27), (13, 14), (9, 1), (24, 29), (9, 9), (32, 6), (20, 37), (12, 9), (0, 22), (24, 20), (21, 6), (21, 1), (35, 0), (11, 0), (21, 36), (17, 23), (2, 43), (14, 11), (12, 37), (14, 34), (30, 20), (16, 3), (32, 32), (24, 39), (26, 4), (11, 36), (28, 36), (38, 27), (30, 4), (21, 40), (10, 36), (0, 21), (5, 37), (14, 43), (9, 12), (24, 0), (29, 29), (1, 22), (27, 31), (40, 32), (22, 11), (37, 29), (22, 0), (0, 2), (27, 38), (14, 8), (19, 10), (13, 10), (39, 42), (0, 17), (3, 30), (22, 40), (32, 3), (18, 10), (2, 32), (4, 4), (5, 35), (24, 11), (7, 25), (14, 15), (28, 43), (36, 23), (24, 23), (40, 34), (31, 16), (20, 27), (38, 5), (2, 4), (12, 35), (10, 34), (27, 16), (22, 26), (3, 38), (30, 32), (33, 8), (22, 19), (10, 29), (32, 36), (22, 36), (24, 7), (9, 22), (16, 41), (40, 12), (26, 2), (10, 21), (27, 6), (27, 33), (25, 25), (5, 20), (19, 41), (25, 41), (15, 8), (28, 8), (15, 32), (29, 28), (3, 7), (13, 3), (24, 15), (37, 13), (15, 21), (30, 29), (5, 28), (25, 24), (29, 1), (16, 1), (21, 15), (40, 2), (36, 43), (33, 1), (8, 31), (37, 33), (2, 13), (17, 30), (13, 34), (17, 0), (35, 6), (38, 19), (13, 27), (0, 25), (3, 10), (14, 32), (24, 33), (23, 36), (18, 23), (7, 32), (25, 21), (39, 43), (26, 30), (5, 39), (9, 30), (3, 33), (11, 28), (35, 29), (11, 30), (25, 3), (2, 19), (2, 0), (23, 25), (25, 27), (37, 12), (25, 7), (21, 5), (40, 16), (21, 31), (1, 10), (15, 23), (24, 5), (5, 30), (31, 42), (37, 24), (17, 13), (18, 5), (12, 4), (2, 9), (17, 33), (10, 40), (34, 11), (21, 26), (1, 9), (2, 22), (5, 34), (25, 26), (0, 20), (20, 41), (24, 30), (8, 9), (24, 28), (32, 34), (15, 1), (20, 33), (3, 1), (25, 5), (36, 30), (1, 21), (8, 24), (20, 29), (16, 30), (9, 19), (8, 42), (12, 30), (38, 7), (38, 34), (1, 35), (11, 40), (1, 11), (13, 38), (23, 29), (24, 40), (35, 20), (8, 16), (7, 14), (20, 9), (40, 11), (8, 26), (38, 26), (38, 3), (2, 1), (37, 6), (3, 22), (1, 13), (15, 19), (19, 43), (31, 24), (9, 18), (15, 7), (18, 33), (25, 40), (25, 13), (11, 5), (7, 6), (28, 9), (14, 6), (17, 6), (18, 27), (19, 35), (29, 32), (38, 39), (18, 14), (9, 26), (11, 7), (19, 30), (36, 38), (32, 21), (33, 5), (27, 3), (20, 17), (36, 36), (18, 32), (31, 8), (25, 28), (34, 33), (34, 18), (37, 40), (35, 27), (31, 13), (18, 13), (30, 13), (7, 10), (20, 31), (6, 23), (25, 17), (32, 13), (40, 31), (0, 13), (35, 10), (8, 34), (36, 1), (1, 18), (6, 31), (37, 5), (11, 29), (7, 4), (40, 40), (23, 18), (20, 6), (18, 43), (3, 25), (22, 5), (12, 16), (4, 12), (8, 14), (26, 14), (13, 5), (18, 40), (23, 10), (30, 26), (21, 20), (33, 35), (21, 37), (28, 20), (0, 26), (2, 7), (15, 16), (38, 11), (4, 1), (6, 22), (24, 2), (9, 29), (31, 14), (4, 38), (1, 33), (35, 16), (17, 22), (3, 41), (9, 10), (33, 11), (16, 6), (22, 39), (10, 26), (8, 41), (23, 24), (26, 34), (31, 30), (35, 35), (10, 2), (16, 5), (32, 35), (7, 21), (34, 23), (7, 34), (34, 28), (3, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 31), (9, 16), (39, 0), (19, 20), (42, 5), (32, 25), (3, 26), (2, 36), (8, 10), (19, 31), (14, 20), (13, 16), (1, 36), (0, 35), (5, 25), (37, 10), (16, 6), (33, 39), (5, 7), (6, 4), (36, 2), (0, 9), (8, 18), (16, 19), (14, 0), (23, 37), (38, 23), (42, 40), (27, 21), (42, 9), (13, 21), (17, 11), (16, 12), (33, 25), (5, 36), (15, 6), (44, 32), (21, 32), (24, 31), (14, 23), (14, 11), (14, 5), (44, 5), (37, 23), (43, 1), (8, 28), (43, 39), (23, 14), (42, 22), (18, 34), (5, 11), (28, 38), (23, 18), (39, 28), (43, 6), (23, 1), (13, 25), (29, 30), (15, 19), (2, 8), (40, 31), (2, 15), (2, 4), (40, 28), (12, 21), (12, 26), (20, 23), (23, 34), (4, 30), (12, 16), (36, 40), (2, 11), (7, 30), (27, 31), (28, 16), (32, 11), (11, 12), (15, 12), (19, 17), (18, 9), (3, 40), (36, 9), (29, 2), (31, 15), (25, 17), (29, 0), (35, 16), (11, 32), (23, 24), (11, 6), (15, 20), (22, 24), (14, 33), (37, 31), (13, 30), (6, 13), (18, 12), (42, 17), (9, 9), (1, 16), (37, 30), (40, 22), (15, 26), (39, 35), (32, 20), (16, 5), (0, 28), (2, 30), (2, 18), (34, 38), (35, 18), (6, 26), (21, 5), (0, 5), (9, 8), (18, 32), (37, 34), (10, 17), (14, 8), (4, 1), (28, 27), (26, 6), (0, 13), (31, 37), (17, 25), (4, 35), (7, 15), (9, 10), (3, 3), (19, 3), (2, 17), (27, 14), (43, 10), (9, 31), (1, 37), (29, 36), (22, 38), (26, 38), (8, 22), (23, 2), (5, 29), (32, 24), (32, 2), (21, 11), (13, 15), (17, 29), (21, 14), (34, 0), (6, 37), (2, 3), (1, 6), (31, 34), (36, 24), (37, 24), (25, 40), (30, 29), (37, 25), (23, 20), (13, 19), (28, 3), (42, 33), (41, 9), (40, 12), (41, 38), (29, 26), (2, 38), (9, 35), (24, 9), (9, 23), (36, 25), (21, 15), (1, 2), (7, 35), (42, 18), (29, 38), (30, 18), (9, 40), (32, 3), (24, 29), (30, 15), (26, 37), (31, 4), (10, 26), (44, 11), (20, 9), (20, 30), (7, 23), (42, 7), (16, 27), (14, 17), (40, 9), (23, 27), (9, 20), (44, 14), (5, 21), (3, 13), (28, 31), (44, 15), (3, 33), (17, 13), (37, 40), (5, 1), (27, 19), (22, 22), (42, 32), (14, 27), (29, 22), (23, 29), (26, 3), (11, 1), (29, 9), (40, 1), (38, 37), (25, 35), (11, 26), (0, 40), (16, 18), (16, 3), (40, 29), (31, 26), (11, 8), (10, 27), (4, 34), (2, 23), (2, 25), (7, 26), (7, 3), (8, 6), (42, 27), (0, 37), (15, 40), (39, 24), (23, 3), (36, 30), (26, 22), (9, 22), (42, 26), (11, 14), (14, 30), (18, 28), (40, 2), (37, 17), (19, 35), (41, 25), (34, 10), (39, 12), (27, 5), (2, 26), (0, 19), (16, 14), (20, 5), (30, 25), (5, 4), (14, 19), (12, 14), (0, 17), (8, 35), (26, 29), (19, 39), (7, 13), (26, 34), (35, 7), (3, 14), (3, 38), (14, 21), (38, 26), (43, 36), (4, 14), (15, 28), (28, 33), (44, 13), (28, 32), (42, 13), (2, 37), (25, 29), (25, 1), (23, 0), (30, 10), (33, 6), (39, 4), (34, 23), (4, 26), (3, 37), (37, 38), (16, 35), (36, 13), (39, 32), (29, 33), (21, 29), (36, 27), (35, 19), (24, 2), (14, 38), (5, 16), (8, 31), (23, 11), (39, 39), (8, 4), (36, 10), (43, 18), (6, 5), (19, 0), (10, 33), (14, 16), (7, 37), (20, 28), (24, 38), (4, 25), (22, 19), (44, 33), (8, 39), (9, 13), (27, 2), (34, 27), (7, 38), (43, 0), (33, 27), (2, 29), (23, 7), (35, 0), (7, 0), (34, 4), (9, 32), (18, 11), (38, 36), (23, 21), (0, 33), (21, 18), (8, 23), (41, 34), (42, 39), (3, 4), (0, 21), (32, 14), (38, 24), (26, 30), (22, 15), (44, 2), (27, 7), (6, 1), (10, 38), (9, 26), (12, 24), (12, 35), (30, 11), (21, 38), (31, 19), (40, 24), (42, 0), (33, 12), (13, 9), (14, 1), (24, 17), (38, 29), (27, 34), (6, 14), (31, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 7), (30, 2), (4, 25), (34, 3), (39, 20), (20, 14), (10, 3), (16, 23), (12, 23), (11, 5), (23, 36), (41, 34), (6, 7), (39, 25), (18, 37), (20, 16), (27, 2), (30, 9), (2, 2), (2, 20), (34, 38), (10, 26), (4, 27), (32, 14), (26, 10), (40, 11), (30, 35), (25, 0), (5, 38), (16, 6), (10, 14), (6, 18), (38, 22), (39, 10), (26, 30), (37, 4), (1, 14), (4, 35), (25, 12), (3, 36), (23, 12), (23, 32), (21, 39), (40, 23), (1, 29), (35, 21), (42, 2), (4, 22), (8, 0), (43, 13), (12, 11), (35, 16), (26, 16), (30, 13), (41, 12), (31, 13), (42, 24), (41, 28), (35, 13), (4, 6), (18, 18), (8, 10), (38, 10), (20, 19), (5, 32), (13, 19), (39, 11), (11, 4), (18, 30), (4, 13), (12, 1), (29, 31), (6, 34), (35, 36), (37, 34), (19, 39), (33, 10), (33, 8), (11, 36), (2, 28), (8, 34), (20, 37), (7, 19), (38, 33), (2, 21), (29, 16), (10, 15), (24, 32), (25, 4), (21, 38), (10, 33), (40, 36), (33, 35), (13, 20), (7, 37), (29, 0), (3, 20), (30, 37), (15, 7), (21, 9), (38, 17), (33, 20), (0, 30), (1, 16), (8, 27), (9, 9), (6, 0), (20, 9), (41, 18), (14, 32), (5, 19), (2, 5), (40, 0), (32, 29), (33, 18), (34, 23), (30, 25), (35, 32), (33, 1), (19, 4), (18, 25), (33, 4), (25, 28), (32, 10), (15, 13), (10, 17), (22, 30), (33, 28), (33, 15), (12, 28), (14, 19), (36, 22), (27, 21), (11, 14), (34, 27), (32, 37), (30, 19), (12, 5), (22, 7), (11, 6), (15, 30), (40, 35), (21, 12), (29, 15), (1, 7), (26, 4), (25, 34), (7, 8), (18, 9), (13, 0), (29, 25), (3, 30), (4, 29), (8, 33), (28, 17), (40, 8), (31, 11), (1, 8), (6, 28), (5, 14), (30, 5), (3, 18), (42, 1), (34, 30), (30, 12), (8, 35), (1, 11), (43, 19), (6, 20), (17, 1), (13, 1), (20, 34), (31, 33), (30, 27), (27, 9), (22, 4), (14, 33), (32, 24), (23, 0), (36, 15), (3, 37), (35, 1), (15, 19), (20, 27), (41, 32), (3, 29), (37, 2), (25, 2), (27, 6), (34, 12), (42, 8), (32, 20), (30, 18), (13, 28), (40, 34), (20, 5), (42, 19), (41, 26), (29, 1), (23, 5), (1, 1), (33, 6), (26, 14), (3, 13), (25, 23), (5, 11), (29, 23), (15, 39), (24, 11), (30, 16), (13, 16), (34, 0), (20, 32), (0, 27), (4, 17), (15, 38), (33, 32), (4, 0), (37, 8), (26, 11), (21, 34), (21, 35), (17, 7), (2, 4), (5, 9), (35, 18), (1, 21), (8, 38), (1, 4), (14, 14), (34, 35), (43, 9), (22, 19), (24, 23), (36, 16), (4, 34), (22, 31), (16, 29), (17, 15), (40, 13), (23, 15), (11, 20), (20, 33), (6, 2), (13, 5), (17, 34), (4, 2), (3, 31), (19, 29), (0, 26), (21, 0), (32, 12), (9, 30), (8, 1), (22, 25), (35, 10), (14, 25), (12, 24), (39, 24), (25, 6), (4, 9), (12, 21), (37, 25), (18, 31), (42, 7), (30, 1), (23, 2), (28, 2), (43, 4), (6, 21), (10, 39), (2, 17), (14, 15), (38, 8), (16, 28), (34, 37), (27, 35), (38, 27), (13, 37), (5, 16), (1, 35), (9, 17), (3, 26), (36, 28), (19, 20), (39, 35), (26, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 18), (10, 13), (39, 39), (28, 40), (37, 35), (31, 40), (18, 37), (36, 29), (21, 36), (40, 45), (4, 12), (4, 25), (6, 11), (33, 11), (13, 19), (26, 42), (0, 14), (43, 25), (42, 2), (35, 23), (20, 9), (25, 26), (15, 45), (26, 30), (42, 30), (17, 27), (26, 2), (35, 26), (11, 16), (4, 44), (15, 39), (38, 18), (41, 4), (20, 12), (41, 42), (39, 2), (31, 10), (20, 7), (42, 5), (32, 6), (11, 12), (9, 9), (0, 9), (30, 37), (18, 4), (9, 45), (8, 8), (42, 27), (37, 33), (18, 5), (37, 37), (15, 34), (38, 17), (6, 9), (38, 23), (41, 22), (27, 31), (18, 13), (7, 42), (11, 41), (20, 27), (16, 37), (10, 32), (26, 29), (42, 42), (20, 30), (12, 10), (31, 17), (28, 19), (37, 1), (35, 15), (32, 39), (17, 16), (29, 38), (26, 33), (32, 33), (43, 30), (22, 17), (22, 34), (18, 7), (16, 42), (31, 31), (36, 16), (19, 3), (13, 42), (23, 28), (40, 2), (15, 33), (11, 3), (38, 11), (42, 37), (21, 11), (25, 0), (17, 3), (6, 17), (11, 7), (20, 26), (16, 21), (9, 39), (10, 6), (17, 15), (21, 22), (4, 40), (18, 21), (6, 8), (10, 10), (32, 18), (25, 16), (16, 14), (12, 3), (14, 22), (39, 9), (23, 45), (10, 8), (34, 39), (21, 29), (25, 6), (30, 34), (5, 28), (27, 17), (37, 25), (43, 24), (36, 13), (34, 22), (19, 27), (12, 17), (40, 15), (19, 10), (25, 28), (5, 34), (28, 3), (24, 10), (26, 23), (5, 44), (38, 15), (34, 38), (25, 33), (20, 42), (27, 41), (27, 5), (27, 23), (3, 38), (23, 32), (42, 41), (34, 7), (11, 44), (14, 6), (20, 13), (39, 38), (14, 28), (42, 23), (1, 5), (2, 4), (7, 25), (20, 38), (7, 7), (27, 37), (12, 18), (20, 22), (30, 25), (13, 38), (2, 19), (10, 0), (25, 30), (10, 31), (34, 33), (20, 1), (20, 2), (39, 28), (14, 4), (42, 7), (43, 9), (25, 19), (39, 29), (1, 12), (4, 29), (9, 21), (18, 24), (17, 43), (32, 26), (5, 11), (39, 0), (28, 24), (21, 7), (13, 27), (32, 20), (40, 25), (2, 24), (8, 35), (2, 39), (12, 26), (36, 4), (39, 35), (16, 44), (26, 34), (18, 22), (35, 31), (30, 28), (28, 22), (2, 42), (40, 16), (15, 35), (36, 24), (0, 8), (18, 23), (11, 18), (21, 20), (29, 17), (2, 18), (8, 27), (33, 7), (10, 33), (20, 45), (40, 29), (33, 29), (17, 32), (37, 21), (40, 38), (8, 37), (0, 17), (2, 11), (1, 43), (25, 17), (27, 19), (5, 2), (15, 26), (4, 41), (22, 41), (17, 36), (7, 9), (23, 39), (10, 14), (18, 39), (34, 21), (2, 43), (17, 7), (24, 42), (17, 31), (36, 21), (21, 45), (13, 3), (38, 24), (3, 35), (4, 17), (0, 26), (26, 10), (26, 36), (17, 14), (4, 28), (40, 26), (31, 6), (0, 39), (6, 31), (32, 7), (10, 24), (41, 27), (31, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 8), (10, 27), (11, 12), (14, 9), (18, 30), (41, 35), (23, 17), (29, 29), (3, 25), (26, 13), (10, 22), (29, 2), (42, 8), (25, 33), (39, 18), (13, 28), (39, 22), (2, 15), (28, 27), (1, 27), (20, 20), (39, 23), (16, 37), (36, 15), (5, 22), (40, 12), (2, 3), (30, 39), (25, 37), (15, 30), (32, 0), (4, 1), (14, 30), (16, 32), (6, 36), (17, 4), (36, 14), (20, 34), (40, 21), (12, 16), (16, 16), (18, 36), (31, 6), (33, 38), (4, 10), (1, 4), (36, 30), (26, 22), (13, 18), (3, 37), (18, 31), (21, 6), (42, 33), (6, 35), (22, 16), (24, 15), (17, 7), (2, 25), (28, 31), (20, 38), (32, 27), (4, 4), (2, 1), (41, 30), (32, 30), (31, 22), (10, 4), (28, 28), (37, 7), (37, 27), (37, 17), (10, 15), (10, 34), (3, 16), (1, 2), (10, 39), (24, 1), (6, 33), (8, 4), (26, 6), (32, 33), (9, 36), (38, 19), (32, 28), (32, 12), (15, 32), (38, 4), (7, 37), (31, 1), (9, 16), (39, 26), (9, 7), (39, 6), (23, 5), (5, 10), (14, 23), (6, 28), (10, 7), (19, 10), (13, 30), (8, 24), (12, 19), (27, 7), (9, 18), (10, 16), (4, 14), (32, 19), (25, 17), (6, 11), (38, 22), (34, 5), (41, 9), (1, 22), (25, 24), (29, 0), (3, 19), (26, 16), (22, 29), (35, 11), (35, 27), (33, 25), (27, 20), (20, 22), (16, 39), (38, 36), (35, 22), (2, 17), (9, 39), (8, 19), (5, 2), (34, 28), (13, 36), (9, 30), (28, 33), (10, 24), (25, 2), (38, 23), (39, 35), (36, 33), (12, 14), (36, 1), (6, 21), (28, 6), (21, 31), (6, 7), (36, 37), (5, 20), (7, 17), (6, 34), (16, 34), (40, 19), (35, 32), (7, 20), (32, 38), (36, 3), (41, 28), (1, 38), (27, 35), (1, 0), (21, 39), (41, 26), (24, 28), (32, 39), (0, 27), (20, 37), (41, 25), (22, 22), (24, 16), (33, 10), (26, 39), (16, 13), (25, 38), (19, 19), (18, 1), (40, 36), (15, 33), (17, 20), (4, 36), (24, 25), (15, 23), (10, 29), (28, 34), (18, 23), (21, 33), (13, 35), (35, 19), (29, 3), (37, 4), (21, 14), (21, 24), (16, 18), (10, 32), (23, 10), (1, 15), (12, 33), (27, 36), (9, 14), (13, 0), (39, 12), (31, 16), (41, 10), (23, 32), (33, 26), (42, 3), (12, 8), (33, 12), (32, 20), (7, 4), (21, 27), (40, 29), (6, 8), (38, 30), (33, 21), (28, 24), (12, 2), (3, 4), (0, 24), (12, 7), (23, 33), (39, 27), (4, 19), (20, 9), (37, 35), (34, 9), (30, 29), (22, 14), (37, 11), (39, 24), (8, 21), (37, 1), (20, 28), (28, 22), (21, 22), (2, 11), (4, 24), (33, 34), (21, 23), (6, 14), (41, 3), (16, 2), (28, 19), (3, 17), (30, 4), (2, 28), (19, 17), (10, 10), (42, 15), (17, 32), (24, 3), (39, 13), (1, 20), (42, 26), (37, 39), (14, 35), (1, 23), (13, 15), (20, 10), (20, 39), (19, 5), (23, 21), (4, 7), (23, 0), (21, 5), (20, 30), (15, 10), (34, 35), (40, 16), (31, 19), (6, 3), (42, 6), (5, 13), (42, 29), (42, 32), (15, 9), (15, 19), (33, 5), (39, 9), (42, 23), (0, 17), (19, 32), (6, 30), (40, 10), (12, 36), (10, 19), (1, 7), (35, 39), (9, 34), (30, 9), (37, 10), (41, 6), (6, 12), (11, 11), (10, 18), (42, 34), (41, 4), (42, 16), (38, 9), (23, 36), (31, 2), (2, 8), (8, 30), (11, 24), (28, 10), (15, 12), (21, 1), (12, 15), (21, 25), (17, 10), (15, 39), (4, 23), (11, 15), (35, 29), (4, 30), (10, 20), (34, 36), (0, 12), (8, 29), (40, 9), (16, 20), (26, 36), (15, 13), (7, 39), (12, 18), (33, 29), (2, 22), (25, 25), (31, 23), (26, 28), (5, 21), (4, 32), (0, 13), (27, 9), (30, 3), (1, 35), (32, 35), (38, 14), (10, 31), (9, 33), (6, 37), (11, 13), (37, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 4), (35, 11), (2, 17), (9, 0), (22, 10), (31, 3), (24, 29), (6, 4), (14, 28), (32, 8), (31, 37), (6, 21), (27, 11), (31, 31), (10, 24), (47, 22), (10, 40), (46, 24), (26, 27), (33, 23), (25, 22), (18, 31), (46, 41), (27, 40), (43, 11), (44, 3), (30, 24), (4, 11), (11, 38), (11, 11), (10, 15), (25, 18), (27, 44), (5, 7), (28, 28), (17, 14), (3, 0), (24, 9), (4, 45), (8, 38), (17, 10), (41, 10), (11, 13), (26, 38), (15, 41), (45, 16), (32, 3), (24, 28), (20, 21), (18, 42), (44, 37), (27, 36), (36, 9), (22, 6), (36, 36), (26, 16), (10, 5), (12, 4), (2, 10), (15, 42), (27, 3), (8, 37), (2, 2), (33, 39), (46, 33), (7, 11), (18, 28), (11, 40), (20, 48), (16, 29), (30, 44), (28, 45), (36, 30), (18, 9), (6, 1), (4, 12), (38, 7), (28, 22), (17, 5), (32, 36), (6, 27), (5, 48), (15, 39), (45, 21), (6, 6), (29, 21), (21, 7), (5, 11), (8, 8), (1, 48), (23, 6), (29, 16), (22, 18), (13, 36), (14, 41), (24, 46), (37, 30), (42, 12), (39, 44), (0, 37), (1, 5), (1, 1), (26, 48), (2, 39), (6, 45), (18, 47), (39, 26), (0, 20), (14, 45), (16, 21), (13, 1), (7, 17), (27, 6), (11, 20), (20, 43), (41, 2), (14, 18), (18, 29), (17, 7), (19, 21), (10, 44), (18, 3), (41, 12), (36, 32), (32, 28), (39, 19), (1, 34), (19, 30), (32, 29), (29, 15), (17, 13), (20, 16), (42, 42), (30, 23), (38, 48), (18, 32), (26, 32), (45, 9), (33, 14), (10, 16), (33, 16), (10, 12), (9, 24), (19, 1), (32, 37), (6, 38), (22, 43), (10, 48), (35, 28), (34, 42), (33, 38), (45, 7), (26, 41), (43, 46), (33, 31), (1, 41), (28, 38), (18, 21), (30, 0), (37, 25), (37, 26), (22, 32), (0, 11), (32, 18), (22, 13), (3, 34), (30, 35), (36, 2), (17, 23), (3, 37), (7, 41), (14, 2), (24, 6), (36, 29), (16, 15), (6, 33), (32, 16), (8, 47), (13, 12), (35, 7), (25, 28), (12, 14), (46, 13), (23, 9), (45, 28), (21, 38), (24, 42), (9, 36), (17, 22), (26, 44), (29, 43), (19, 23), (6, 0), (41, 5), (12, 16), (45, 15), (32, 5), (47, 47), (39, 34), (13, 26), (34, 19), (28, 11), (30, 30), (0, 40), (34, 9), (24, 25), (10, 32), (31, 10), (15, 27), (7, 22), (15, 34), (30, 33), (32, 48), (6, 13), (11, 18), (21, 5), (32, 44), (43, 17), (41, 15), (40, 48), (41, 42), (24, 14), (4, 1), (7, 12), (39, 48), (4, 13), (2, 41), (15, 11), (16, 44), (3, 41), (9, 39), (38, 8), (43, 38), (26, 18), (0, 38), (13, 35), (1, 0), (35, 30), (6, 35), (46, 38), (5, 25), (24, 3), (26, 28), (38, 37), (12, 46), (15, 16), (46, 39), (28, 23), (38, 5), (7, 1), (43, 1), (45, 41), (23, 10), (11, 21), (12, 47), (34, 37), (25, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 29), (46, 35), (43, 19), (22, 23), (16, 23), (20, 2), (21, 38), (5, 24), (41, 13), (39, 12), (14, 37), (32, 3), (41, 0), (28, 35), (1, 15), (12, 34), (12, 13), (11, 6), (4, 29), (18, 34), (0, 1), (5, 22), (37, 33), (7, 21), (34, 13), (18, 32), (14, 13), (40, 1), (39, 23), (19, 35), (42, 10), (18, 27), (14, 17), (39, 35), (20, 35), (34, 3), (0, 25), (46, 6), (17, 32), (8, 23), (19, 39), (38, 33), (4, 27), (29, 13), (33, 11), (8, 1), (37, 2), (23, 33), (17, 26), (33, 36), (30, 4), (16, 35), (37, 21), (46, 10), (45, 35), (38, 12), (8, 3), (25, 30), (24, 12), (35, 24), (6, 16), (14, 36), (40, 3), (25, 16), (4, 36), (12, 20), (13, 16), (32, 20), (37, 3), (20, 27), (23, 14), (6, 6), (30, 29), (38, 30), (25, 29), (41, 17), (40, 7), (22, 13), (23, 35), (22, 21), (40, 0), (24, 29), (24, 34), (9, 26), (23, 26), (36, 30), (8, 27), (18, 8), (25, 3), (0, 37), (39, 10), (36, 3), (4, 22), (37, 23), (0, 34), (46, 7), (11, 22), (41, 36), (27, 38), (37, 16), (8, 6), (37, 27), (9, 33), (16, 32), (25, 15), (25, 12), (27, 20), (30, 28), (30, 33), (11, 7), (20, 1), (3, 0), (20, 9), (8, 29), (10, 31), (19, 23), (38, 17), (43, 10), (5, 14), (0, 10), (33, 14), (24, 32), (5, 1), (9, 3), (37, 24), (40, 17), (26, 32), (0, 31), (21, 16), (29, 37), (20, 23), (40, 33), (10, 17), (33, 3), (15, 35), (6, 17), (15, 15), (42, 8), (17, 31), (21, 8), (26, 30), (15, 22), (6, 35), (8, 36), (5, 20), (39, 9), (43, 39), (29, 23), (30, 31), (28, 20), (18, 10), (3, 1), (2, 27), (23, 17), (34, 17), (32, 22), (7, 34), (10, 2), (44, 29), (35, 31), (31, 16), (14, 9), (6, 33), (46, 16), (15, 29), (36, 38), (44, 36), (40, 35), (32, 19), (34, 32), (42, 2), (32, 25), (32, 24), (31, 22), (14, 28), (34, 19), (28, 26), (35, 9), (35, 36), (24, 3), (22, 22), (11, 11), (36, 16), (26, 38), (24, 28), (20, 12), (3, 12), (35, 11), (33, 0), (44, 25), (22, 35), (9, 38), (23, 27), (4, 13), (46, 11), (12, 0), (39, 16), (40, 9), (40, 36), (41, 39), (4, 1), (39, 33), (36, 17), (21, 31), (13, 21), (17, 18), (25, 31), (14, 22), (14, 2), (1, 9), (26, 16), (3, 7), (31, 11), (2, 8), (34, 26), (11, 13), (14, 21), (27, 22), (46, 9), (20, 5), (27, 25), (17, 17), (41, 7), (17, 3), (45, 21), (18, 13), (14, 20), (43, 21), (5, 31), (9, 32), (40, 14), (19, 25), (46, 20), (4, 33), (43, 31), (34, 12), (11, 3), (11, 2), (32, 36), (4, 12), (3, 16), (45, 7), (4, 34), (15, 38), (15, 33), (11, 18), (30, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 17), (5, 16), (9, 34), (14, 0), (38, 29), (11, 8), (29, 22), (39, 14), (36, 34), (13, 28), (41, 27), (24, 20), (31, 32), (23, 5), (32, 18), (14, 26), (5, 0), (29, 31), (37, 23), (36, 29), (17, 10), (4, 24), (30, 23), (0, 6), (24, 24), (38, 9), (38, 22), (28, 20), (34, 12), (11, 32), (25, 28), (43, 17), (35, 9), (27, 4), (4, 28), (28, 11), (17, 15), (15, 6), (7, 20), (25, 37), (39, 34), (0, 12), (24, 39), (10, 10), (11, 39), (41, 16), (20, 2), (7, 23), (4, 4), (0, 5), (25, 27), (19, 30), (7, 38), (9, 0), (18, 26), (26, 36), (15, 10), (27, 0), (13, 32), (8, 16), (23, 14), (21, 27), (16, 14), (42, 3), (11, 20), (14, 31), (9, 7), (24, 16), (11, 40), (43, 8), (4, 23), (12, 22), (31, 7), (44, 38), (22, 8), (0, 35), (10, 34), (4, 39), (13, 35), (26, 38), (4, 33), (39, 6), (34, 33), (3, 27), (26, 29), (37, 3), (43, 26), (34, 22), (28, 15), (9, 4), (21, 28), (24, 21), (5, 15), (43, 37), (5, 10), (41, 1), (24, 37), (14, 18), (5, 1), (22, 6), (1, 38), (4, 26), (38, 36), (33, 13), (3, 0), (35, 25), (3, 33), (31, 35), (8, 12), (40, 32), (27, 12), (27, 13), (20, 11), (43, 38), (35, 27), (19, 38), (18, 31), (34, 36), (38, 17), (35, 20), (4, 31), (28, 5), (3, 39), (23, 35), (41, 40), (1, 30), (5, 12), (34, 25), (19, 4), (25, 14), (42, 22), (24, 10), (1, 15), (15, 30), (32, 22), (24, 33), (33, 20), (26, 11), (25, 15), (16, 26), (30, 9), (40, 10), (2, 12), (7, 30), (13, 11), (13, 14), (44, 1), (8, 27), (21, 25), (24, 13), (4, 2), (24, 18), (33, 23), (44, 12), (35, 19), (13, 8), (0, 17), (3, 14), (23, 34), (27, 27), (22, 28), (5, 29), (36, 21), (15, 1), (33, 1), (37, 4), (38, 20), (20, 0), (8, 26), (8, 28), (32, 10), (1, 11), (8, 34), (22, 4), (21, 23), (7, 8), (39, 38), (18, 1), (1, 26), (6, 26), (22, 33), (18, 15), (19, 12), (38, 25), (18, 0), (9, 3), (21, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 2), (13, 7), (29, 22), (26, 16), (43, 37), (23, 30), (5, 5), (33, 1), (19, 18), (2, 4), (36, 39), (22, 32), (14, 47), (16, 9), (38, 9), (40, 11), (11, 25), (43, 3), (14, 14), (14, 23), (42, 14), (40, 45), (32, 30), (20, 24), (8, 48), (3, 22), (42, 34), (41, 29), (14, 26), (28, 44), (7, 44), (11, 16), (33, 32), (16, 23), (13, 6), (42, 21), (29, 23), (36, 21), (44, 13), (33, 37), (15, 1), (3, 10), (9, 33), (18, 0), (36, 16), (44, 7), (43, 18), (12, 4), (42, 4), (43, 40), (29, 41), (10, 25), (8, 26), (9, 14), (12, 0), (28, 16), (38, 43), (40, 48), (0, 38), (14, 39), (28, 20), (5, 27), (43, 48), (38, 35), (17, 26), (5, 2), (32, 47), (23, 1), (22, 3), (31, 2), (24, 38), (28, 1), (16, 29), (16, 32), (30, 36), (11, 38), (33, 4), (7, 15), (31, 33), (38, 47), (11, 32), (4, 21), (20, 5), (45, 5), (32, 33), (7, 48), (30, 10), (24, 14), (22, 13), (7, 0), (44, 36), (32, 40), (30, 7), (35, 21), (43, 28), (15, 21), (18, 32), (34, 42), (6, 8), (7, 28), (25, 47), (24, 3), (17, 35), (34, 30), (29, 21), (26, 13), (43, 14), (45, 19), (3, 5), (18, 15), (45, 42), (27, 28), (2, 22), (36, 47), (36, 41), (17, 6), (31, 6), (3, 41), (6, 36), (7, 5), (4, 6), (6, 25), (15, 44), (18, 38), (17, 43), (30, 48), (12, 2), (25, 12), (20, 44), (40, 38), (21, 16), (28, 32), (22, 0), (39, 36), (10, 26), (25, 24), (14, 7), (44, 32), (22, 40), (16, 19), (30, 46), (3, 11), (18, 19), (18, 12), (16, 1), (26, 46), (42, 10), (12, 14), (24, 45), (45, 37), (37, 45), (20, 48), (12, 45), (39, 33), (11, 34), (13, 29), (39, 35), (31, 20), (4, 0), (19, 41), (14, 34), (37, 32), (22, 10), (22, 11), (32, 29), (25, 42), (42, 45), (37, 11), (39, 43), (34, 28), (33, 17), (17, 27), (16, 33), (13, 24), (20, 8), (7, 8), (24, 4), (34, 21), (37, 29), (13, 38), (22, 48), (35, 48), (1, 8), (35, 4), (4, 37), (27, 18), (26, 23), (19, 22), (37, 44), (37, 5), (11, 37), (45, 7), (2, 3), (43, 11), (39, 8), (9, 18), (24, 37), (38, 29), (13, 14), (43, 35), (44, 19), (4, 5), (36, 31), (40, 7), (8, 4), (1, 48), (37, 42), (0, 44), (41, 22), (23, 36), (43, 41), (35, 20), (14, 42), (10, 28), (13, 47), (35, 0), (43, 21), (24, 36), (31, 3), (3, 19), (37, 33), (14, 9), (37, 1), (6, 20), (25, 1), (1, 11), (10, 38), (21, 11), (17, 36), (24, 40), (23, 32), (35, 32), (20, 12), (23, 16), (3, 13), (16, 35), (18, 43), (0, 39), (9, 45), (13, 8), (6, 9), (20, 26), (34, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 11), (5, 3), (2, 19), (34, 24), (16, 14), (34, 2), (29, 30), (37, 17), (4, 20), (1, 39), (35, 27), (19, 32), (41, 20), (3, 21), (13, 33), (40, 26), (17, 5), (32, 17), (32, 30), (14, 11), (33, 17), (32, 5), (28, 32), (17, 11), (8, 17), (42, 34), (24, 12), (36, 8), (7, 19), (22, 18), (32, 0), (13, 37), (1, 30), (18, 31), (10, 30), (34, 11), (28, 2), (16, 11), (41, 17), (0, 32), (22, 16), (26, 5), (34, 20), (30, 33), (33, 22), (26, 28), (27, 21), (9, 23), (35, 42), (21, 21), (30, 6), (40, 9), (8, 15), (12, 17), (10, 33), (33, 41), (23, 20), (31, 36), (29, 41), (5, 1), (44, 33), (0, 7), (12, 41), (0, 29), (21, 22), (39, 40), (6, 16), (28, 0), (18, 3), (26, 30), (23, 41), (19, 8), (1, 16), (36, 9), (40, 25), (17, 30), (19, 10), (20, 11), (27, 18), (7, 10), (25, 39), (18, 30), (31, 1), (43, 39), (5, 19), (43, 0), (42, 33), (8, 26), (43, 23), (6, 34), (43, 13), (11, 8), (9, 22), (25, 14), (42, 15), (7, 36), (12, 20), (19, 16), (9, 5), (43, 3), (14, 30), (41, 34), (21, 28), (40, 24), (1, 7), (19, 21), (41, 19), (42, 16), (9, 42), (27, 32), (5, 16), (5, 26), (16, 24), (38, 39), (34, 12), (11, 25), (28, 7), (25, 19), (29, 40), (33, 42), (14, 25), (19, 40), (12, 23), (35, 25), (44, 36), (3, 39), (12, 12), (43, 37), (30, 8), (4, 29), (2, 38), (0, 37), (40, 15), (27, 13), (24, 14), (44, 16), (10, 40), (2, 10), (1, 35), (15, 31), (26, 34), (27, 31), (15, 24), (21, 33), (9, 35), (18, 17), (1, 34), (5, 9), (15, 26), (12, 38), (38, 13), (4, 19), (7, 14), (24, 30), (7, 16), (20, 34), (21, 32), (18, 40), (39, 15), (28, 9), (33, 2), (41, 22), (26, 40), (29, 21), (22, 38), (8, 7), (43, 17), (31, 0), (4, 1), (34, 40), (42, 29), (11, 40), (21, 12), (35, 0), (14, 3), (28, 23), (38, 18), (32, 14), (19, 1), (27, 30), (8, 21), (17, 28), (39, 39), (21, 14), (1, 33), (22, 13), (36, 37), (3, 34), (1, 21), (26, 16), (15, 32), (6, 10), (9, 15), (38, 10), (39, 10), (2, 26), (33, 18), (27, 6), (26, 25), (30, 36), (4, 5), (24, 15), (1, 9), (40, 23), (12, 24), (4, 16), (7, 2), (38, 40), (28, 28), (12, 18), (41, 13), (5, 30), (31, 22), (7, 35), (35, 22), (43, 32), (17, 40), (44, 15), (7, 37), (25, 1), (20, 32), (1, 2), (10, 9), (4, 4), (31, 25), (23, 29), (14, 33), (24, 40), (22, 22), (1, 8), (18, 24), (15, 6), (34, 26), (0, 26), (10, 7), (1, 15), (18, 22), (3, 28), (3, 9), (18, 10), (5, 4), (20, 36), (15, 27), (24, 9), (10, 1), (17, 37), (22, 31), (16, 7), (6, 37), (14, 29), (4, 34), (22, 33), (14, 31), (12, 27), (23, 40), (6, 20), (12, 1), (33, 25), (6, 19), (15, 7), (11, 28), (20, 24), (3, 6), (22, 28), (33, 34), (4, 15), (27, 3), (18, 21), (22, 20), (19, 28), (37, 9), (28, 8), (39, 7), (10, 22), (1, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 25), (17, 2), (41, 48), (12, 46), (35, 22), (7, 2), (20, 33), (9, 20), (38, 19), (10, 0), (31, 12), (24, 11), (19, 40), (30, 17), (26, 31), (41, 31), (43, 2), (0, 41), (29, 20), (0, 6), (10, 19), (30, 10), (11, 37), (43, 17), (35, 39), (36, 24), (41, 6), (30, 8), (0, 18), (21, 44), (25, 46), (14, 13), (36, 41), (8, 45), (9, 44), (3, 13), (38, 24), (0, 2), (18, 22), (45, 45), (15, 30), (19, 6), (25, 35), (12, 47), (9, 1), (37, 8), (8, 32), (39, 7), (42, 27), (15, 11), (24, 21), (42, 6), (24, 28), (39, 22), (40, 19), (28, 48), (5, 25), (6, 27), (12, 48), (44, 47), (26, 2), (14, 33), (43, 3), (16, 40), (19, 15), (7, 30), (8, 15), (32, 30), (7, 12), (12, 45), (23, 45), (47, 25), (33, 45), (44, 11), (8, 2), (42, 18), (29, 14), (20, 45), (32, 14), (39, 47), (1, 19), (21, 10), (43, 33), (45, 41), (14, 21), (44, 31), (3, 45), (47, 47), (24, 31), (42, 2), (13, 32), (3, 42), (17, 4), (46, 17), (8, 43), (2, 12), (7, 46), (16, 48), (17, 11), (32, 45), (21, 0), (46, 39), (41, 46), (30, 7), (30, 37), (26, 46), (9, 4), (29, 9), (36, 36), (23, 23), (4, 31), (0, 12), (28, 35), (7, 0), (20, 37), (25, 23), (18, 25), (46, 40), (45, 20), (12, 28), (7, 38), (43, 41), (43, 37), (32, 41), (1, 18), (6, 11), (21, 43), (4, 5), (10, 24), (24, 17), (20, 15), (9, 25), (12, 30), (14, 9), (38, 38), (42, 47), (36, 28), (13, 42), (34, 45), (3, 4), (15, 45), (0, 17), (47, 41), (37, 22), (36, 23), (22, 47), (18, 15), (29, 4), (15, 8), (17, 10), (45, 35), (35, 40), (35, 38), (40, 9), (7, 39), (14, 3), (25, 36), (34, 24), (45, 25), (31, 15), (30, 38), (6, 16), (40, 38), (35, 10), (35, 3), (25, 0), (38, 45), (33, 0), (24, 25), (2, 9), (14, 47), (26, 29), (41, 19), (0, 33), (22, 10), (28, 20), (24, 3), (7, 34), (9, 33), (28, 27), (10, 40), (44, 38), (39, 44), (20, 32), (39, 2), (32, 12), (0, 31), (9, 11), (4, 48), (16, 22), (19, 16), (36, 25), (27, 9), (11, 45), (47, 22), (37, 7), (3, 15), (14, 41), (0, 27), (0, 47), (47, 42), (1, 35), (46, 11), (32, 8), (32, 44), (20, 48), (15, 43), (26, 5), (16, 19), (38, 1), (3, 21), (10, 33), (28, 12), (0, 38), (4, 12), (3, 35), (32, 24), (34, 41), (4, 17), (17, 38), (43, 48), (46, 36), (12, 35), (6, 26), (32, 33), (37, 37), (8, 11), (38, 18), (19, 20), (12, 20), (17, 39), (10, 48), (21, 33), (36, 19), (41, 32), (43, 34), (18, 44), (14, 25), (3, 44), (12, 36), (42, 1), (21, 45), (33, 21), (0, 11), (46, 32), (7, 4), (22, 31), (40, 17), (35, 8), (41, 47), (34, 23), (28, 8), (19, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (11, 1), (37, 35), (37, 23), (6, 29), (41, 9), (16, 14), (39, 11), (8, 14), (11, 4), (7, 4), (37, 33), (2, 20), (29, 22), (12, 33), (5, 7), (25, 25), (5, 34), (4, 34), (13, 36), (11, 34), (28, 25), (0, 38), (21, 15), (33, 40), (38, 25), (14, 28), (26, 31), (17, 24), (9, 34), (8, 32), (41, 35), (20, 23), (22, 27), (0, 36), (29, 23), (39, 36), (24, 0), (34, 22), (41, 2), (38, 16), (8, 29), (41, 4), (22, 8), (9, 31), (42, 32), (16, 33), (33, 6), (30, 24), (30, 27), (40, 27), (15, 7), (27, 38), (26, 13), (26, 21), (2, 38), (40, 30), (31, 17), (8, 7), (19, 22), (38, 24), (26, 9), (13, 35), (18, 21), (6, 21), (0, 29), (8, 2), (13, 26), (20, 21), (13, 38), (3, 33), (35, 6), (30, 36), (7, 40), (11, 7), (25, 31), (15, 18), (30, 28), (22, 7), (25, 21), (1, 28), (28, 7), (25, 34), (29, 7), (1, 32), (23, 38), (38, 13), (20, 29), (14, 8), (14, 36), (26, 11), (41, 17), (22, 13), (7, 12), (11, 6), (35, 21), (8, 21), (5, 26), (38, 14), (4, 33), (42, 31), (34, 28), (33, 1), (26, 0), (0, 21), (4, 32), (4, 18), (9, 9), (28, 37), (15, 33), (32, 11), (41, 19), (41, 25), (30, 9), (20, 20), (4, 35), (32, 33), (13, 1), (29, 6), (36, 18), (19, 36), (27, 37), (12, 20), (2, 36), (31, 34), (4, 13), (19, 37), (39, 31), (22, 3), (8, 12), (33, 28), (11, 32), (3, 11), (35, 31), (23, 4), (34, 33), (10, 18), (39, 35), (25, 8), (12, 23), (22, 38), (25, 22), (37, 3), (38, 34), (0, 23), (20, 0), (33, 39), (8, 27), (5, 17), (24, 18), (15, 13), (19, 5), (37, 29), (19, 27), (25, 32), (15, 9), (31, 7), (6, 14), (6, 4), (19, 25), (39, 21), (40, 8), (33, 21), (11, 19), (23, 40), (2, 0), (29, 24), (30, 17), (14, 6), (24, 13), (37, 11), (36, 14), (8, 31), (31, 6), (30, 34), (22, 24), (29, 17), (0, 2), (5, 11), (17, 0), (37, 5), (17, 15), (36, 32), (33, 23), (16, 12), (32, 39), (42, 26), (34, 27), (16, 28), (39, 12), (35, 9), (29, 3), (30, 40), (42, 21), (26, 2), (12, 37), (0, 33), (37, 19), (36, 23), (18, 27), (13, 5), (25, 0), (29, 33), (11, 22), (30, 33), (27, 8), (1, 25), (20, 13), (33, 13), (37, 7), (3, 34), (10, 5), (27, 29), (21, 13), (26, 10), (16, 34), (14, 14), (9, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 40), (22, 7), (16, 20), (16, 11), (31, 31), (0, 39), (31, 1), (34, 5), (17, 27), (35, 15), (32, 23), (36, 13), (15, 24), (0, 36), (8, 30), (10, 30), (31, 11), (33, 30), (22, 30), (23, 39), (38, 10), (19, 11), (20, 21), (37, 31), (4, 12), (23, 26), (20, 37), (16, 18), (37, 38), (26, 1), (11, 37), (26, 2), (33, 34), (13, 41), (12, 6), (37, 39), (42, 5), (6, 16), (25, 23), (35, 9), (42, 38), (18, 31), (37, 36), (6, 31), (1, 31), (35, 40), (41, 41), (26, 29), (9, 18), (26, 6), (18, 34), (39, 7), (18, 24), (32, 19), (24, 6), (33, 12), (5, 29), (20, 36), (39, 24), (16, 17), (11, 0), (22, 11), (10, 21), (35, 16), (4, 19), (7, 11), (5, 38), (36, 32), (7, 30), (18, 28), (12, 10), (13, 3), (39, 34), (19, 1), (33, 35), (4, 28), (4, 0), (7, 33), (9, 26), (34, 12), (23, 16), (17, 15), (4, 2), (24, 34), (4, 27), (35, 24), (3, 28), (22, 16), (10, 33), (39, 16), (18, 23), (24, 8), (27, 1), (35, 37), (38, 26), (18, 5), (16, 32), (36, 20), (3, 22), (16, 39), (24, 39), (7, 6), (13, 16), (6, 39), (17, 21), (22, 19), (27, 26), (16, 31), (9, 4), (41, 28), (24, 36), (1, 29), (39, 28), (37, 33), (6, 8), (26, 24), (12, 14), (14, 26), (2, 35), (14, 18), (30, 40), (7, 35), (20, 29), (31, 12), (1, 40), (14, 20), (40, 20), (17, 29), (41, 25), (18, 22), (16, 22), (8, 40), (41, 6), (32, 11), (13, 26), (3, 19), (4, 38), (23, 25), (23, 31), (33, 41), (26, 33), (20, 40), (13, 31), (41, 2), (42, 29), (14, 25), (42, 7), (0, 15), (25, 27), (29, 1), (7, 38), (2, 23), (6, 41), (29, 15), (21, 33), (41, 33), (18, 36), (2, 34), (15, 34), (6, 25), (23, 29), (12, 22), (21, 8), (13, 1), (35, 19), (17, 28), (30, 6), (16, 41), (42, 33), (13, 23), (40, 29), (36, 15), (37, 7), (30, 37), (36, 17), (5, 25), (22, 37), (14, 16), (35, 39), (26, 13), (35, 14), (36, 14), (27, 2), (42, 30), (14, 27), (17, 7), (15, 38), (3, 30), (38, 1), (37, 5), (12, 26), (18, 9), (28, 30), (21, 28), (11, 3), (8, 8), (7, 14), (22, 33), (10, 40), (5, 12), (34, 25), (13, 19), (28, 5), (9, 9), (11, 23), (2, 7), (26, 15), (0, 13), (26, 34), (8, 36), (38, 19), (42, 26), (41, 26), (23, 8), (36, 33), (28, 40), (13, 27), (30, 31), (34, 30), (5, 22), (22, 1), (28, 24), (5, 15), (30, 17), (41, 18), (25, 36), (13, 32), (40, 39), (36, 36), (28, 16), (30, 0), (3, 35), (28, 7), (42, 20), (19, 32), (25, 15), (18, 39), (25, 21), (14, 15), (33, 39), (23, 0), (42, 9), (17, 2), (15, 19), (13, 13), (35, 18), (40, 16), (37, 32), (42, 6), (38, 9), (9, 1), (36, 31), (17, 38), (3, 20), (24, 32), (13, 7), (28, 12), (8, 31), (8, 13), (29, 35), (33, 14), (7, 36), (11, 10), (29, 36), (16, 33), (12, 18), (17, 41), (15, 20), (30, 7), (18, 33), (33, 37), (2, 1), (42, 3), (1, 0), (26, 17), (3, 11), (11, 17), (8, 20), (31, 40), (12, 33), (11, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 9), (15, 12), (28, 37), (7, 42), (34, 23), (7, 14), (45, 41), (1, 4), (32, 38), (35, 27), (14, 15), (21, 22), (43, 29), (38, 10), (39, 37), (14, 44), (14, 43), (0, 6), (2, 26), (41, 18), (10, 45), (3, 0), (12, 4), (34, 25), (13, 21), (40, 27), (24, 29), (11, 36), (44, 38), (1, 39), (13, 1), (9, 31), (4, 40), (43, 22), (43, 32), (28, 4), (46, 43), (6, 26), (41, 39), (21, 24), (7, 38), (24, 28), (21, 8), (9, 22), (18, 45), (18, 36), (13, 14), (10, 34), (37, 34), (25, 42), (3, 24), (29, 9), (27, 11), (11, 13), (41, 25), (46, 26), (32, 15), (2, 6), (22, 41), (18, 39), (46, 18), (29, 26), (5, 13), (15, 21), (0, 43), (26, 17), (43, 44), (12, 12), (1, 44), (7, 16), (45, 45), (27, 45), (30, 14), (31, 30), (43, 35), (37, 2), (23, 9), (24, 7), (41, 17), (34, 38), (42, 2), (44, 15), (40, 20), (36, 23), (16, 37), (7, 10), (44, 1), (23, 18), (30, 11), (34, 3), (40, 45), (31, 29), (1, 18), (11, 19), (26, 38), (16, 33), (4, 22), (19, 43), (4, 16), (46, 3), (24, 24), (19, 15), (17, 4), (17, 8), (24, 2), (10, 5), (34, 45), (10, 28), (17, 45), (38, 5), (12, 3), (21, 36), (31, 23), (38, 26), (24, 8), (14, 41), (36, 35), (40, 39), (46, 36), (18, 19), (46, 40), (10, 9), (36, 42), (16, 20), (20, 38), (36, 24), (34, 22), (2, 1), (44, 36), (36, 13), (0, 5), (43, 37), (18, 35), (45, 22), (34, 1), (37, 23), (30, 41), (1, 38), (4, 5), (28, 6), (6, 24), (17, 3), (33, 16), (10, 26), (45, 27), (14, 4), (42, 37), (40, 40), (24, 20), (39, 11), (1, 14), (7, 28), (5, 24), (29, 6), (29, 8), (1, 1), (6, 44), (19, 9), (39, 8), (36, 30), (30, 22), (12, 26), (10, 3), (5, 15), (29, 41), (37, 30), (44, 13), (3, 1), (27, 21), (1, 23), (31, 9), (12, 34), (32, 39), (36, 7), (28, 23), (32, 17), (27, 24), (2, 2), (7, 5), (40, 21), (23, 43), (30, 18), (44, 32), (5, 45), (46, 5), (16, 31), (6, 10), (3, 7), (40, 37), (18, 21), (5, 1), (40, 44), (36, 2), (14, 38), (12, 31), (1, 20), (34, 42), (25, 7), (6, 34), (27, 0), (15, 41), (35, 35), (34, 33), (29, 35), (7, 26), (36, 4), (19, 45), (20, 8), (23, 39), (45, 25), (42, 14), (24, 31), (28, 7), (10, 27), (4, 2), (28, 40), (11, 32), (16, 1), (21, 4), (2, 5), (39, 45), (39, 4), (15, 37), (39, 12), (35, 21), (21, 16), (34, 6), (6, 31), (37, 12), (36, 22), (22, 12), (17, 19), (22, 9), (11, 6), (9, 41), (10, 24), (4, 35), (43, 5), (44, 7), (7, 30), (28, 41), (8, 33), (5, 31), (4, 29), (4, 11), (28, 35), (6, 20), (1, 12), (2, 10), (8, 32), (26, 13), (31, 43), (4, 17), (5, 19), (40, 34), (36, 15), (16, 34), (29, 30), (5, 6), (29, 36), (8, 7), (3, 2), (41, 24), (17, 0), (34, 18), (19, 36), (26, 31), (34, 29), (15, 29), (6, 25), (14, 0), (24, 44), (23, 8), (26, 20), (30, 8), (34, 7), (28, 5), (46, 8), (22, 20), (7, 3), (28, 24), (15, 42), (12, 38), (7, 40), (26, 16), (43, 43), (1, 34), (6, 39), (25, 20), (13, 32), (9, 36), (44, 25), (30, 10), (12, 11), (31, 0), (19, 41), (44, 34), (13, 5), (2, 36), (4, 4), (29, 1), (17, 11), (36, 27), (2, 24), (36, 10), (17, 7), (42, 18), (34, 16), (33, 18), (20, 44), (30, 34), (37, 17), (5, 34), (31, 40), (39, 13), (10, 13), (25, 17), (35, 8), (31, 41), (32, 8), (24, 21), (18, 40), (32, 40), (16, 22), (35, 12), (30, 26), (12, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 39), (42, 12), (25, 44), (33, 30), (25, 3), (10, 30), (5, 40), (25, 0), (9, 41), (19, 21), (26, 30), (2, 23), (25, 19), (43, 5), (1, 16), (40, 6), (42, 20), (21, 32), (6, 32), (30, 47), (6, 9), (23, 17), (3, 0), (40, 17), (19, 15), (39, 36), (35, 5), (26, 27), (2, 18), (31, 45), (37, 27), (17, 2), (9, 27), (42, 3), (32, 23), (18, 4), (6, 20), (27, 31), (14, 39), (26, 40), (8, 17), (6, 6), (38, 12), (38, 45), (37, 16), (13, 39), (28, 36), (36, 32), (4, 2), (24, 20), (7, 27), (19, 36), (27, 15), (38, 32), (8, 26), (36, 10), (1, 30), (32, 40), (24, 28), (6, 42), (41, 41), (35, 16), (26, 19), (30, 19), (14, 26), (38, 19), (33, 47), (26, 12), (42, 15), (41, 21), (9, 17), (1, 4), (20, 45), (21, 10), (1, 32), (26, 35), (1, 23), (27, 42), (25, 1), (23, 5), (36, 25), (1, 8), (17, 38), (5, 11), (41, 35), (15, 30), (27, 24), (40, 27), (35, 30), (30, 43), (9, 42), (19, 47), (0, 29), (4, 35), (32, 12), (13, 28), (38, 43), (43, 21), (42, 23), (5, 13), (39, 1), (13, 11), (0, 14), (40, 38), (43, 13), (20, 39), (3, 7), (28, 20), (5, 32), (27, 18), (15, 35), (42, 2), (23, 9), (10, 3), (21, 0), (36, 23), (3, 18), (39, 3), (2, 16), (1, 1), (6, 38), (32, 15), (27, 12), (36, 44), (40, 42), (7, 14), (31, 27), (19, 2), (14, 0), (30, 39), (29, 7), (34, 15), (2, 46), (33, 4), (11, 46), (31, 28), (24, 12), (8, 31), (1, 38), (12, 30), (1, 29), (40, 47), (14, 24), (15, 16), (16, 40), (10, 0), (22, 20), (29, 30), (36, 1), (37, 41), (4, 17), (30, 24), (41, 5), (31, 0), (4, 29), (39, 8), (3, 36), (16, 32), (40, 36), (35, 13), (1, 5), (13, 21), (16, 38), (22, 15), (13, 35), (4, 47), (41, 23), (43, 23), (41, 27), (10, 17), (28, 19), (5, 8), (36, 8), (27, 28), (36, 12), (38, 29), (13, 38), (25, 40), (10, 20), (24, 40), (27, 9), (37, 40), (2, 45), (26, 38), (6, 7), (17, 23), (0, 45), (21, 19), (19, 5), (27, 23), (29, 33), (4, 44), (28, 39), (18, 35), (25, 16), (1, 40), (16, 36), (27, 41), (3, 19), (43, 10), (29, 19), (20, 42), (41, 30), (35, 17), (12, 10), (11, 32), (2, 30), (2, 7), (41, 18), (4, 31), (8, 30), (25, 5), (41, 44), (33, 28), (29, 41), (27, 10), (5, 31), (34, 8), (43, 37), (42, 27), (6, 13), (39, 11), (11, 43), (38, 28), (7, 36), (1, 28), (24, 37), (12, 31), (11, 41), (15, 37), (6, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 20), (31, 13), (8, 41), (9, 14), (16, 30), (32, 8), (4, 34), (24, 42), (2, 18), (18, 25), (5, 12), (21, 7), (26, 22), (15, 4), (32, 42), (12, 42), (22, 39), (17, 29), (6, 20), (38, 34), (20, 27), (18, 34), (15, 3), (17, 34), (9, 19), (28, 14), (25, 3), (37, 29), (6, 14), (25, 35), (10, 21), (12, 30), (22, 23), (37, 38), (34, 26), (18, 27), (13, 6), (7, 10), (19, 36), (3, 34), (19, 23), (28, 26), (34, 16), (27, 20), (25, 14), (8, 22), (26, 34), (24, 10), (5, 11), (31, 30), (19, 38), (22, 28), (4, 19), (12, 20), (28, 33), (12, 31), (36, 16), (11, 19), (14, 33), (22, 32), (19, 8), (1, 29), (3, 23), (28, 22), (27, 11), (3, 3), (29, 10), (12, 21), (17, 31), (28, 32), (9, 37), (19, 10), (34, 9), (13, 11), (32, 18), (15, 17), (10, 7), (5, 30), (27, 24), (14, 4), (26, 4), (16, 34), (1, 17), (31, 32), (30, 19), (5, 15), (31, 4), (12, 27), (10, 3), (13, 23), (26, 31), (10, 25), (33, 16), (13, 25), (2, 1), (37, 7), (15, 9), (33, 33), (38, 1), (4, 41), (8, 25), (9, 1), (31, 24), (20, 5), (2, 6), (32, 6), (31, 5), (38, 26), (17, 30), (9, 18), (6, 30), (15, 28), (20, 7), (12, 6), (11, 3), (31, 40), (17, 0), (0, 42), (8, 31), (15, 2), (16, 29), (14, 29), (39, 22), (35, 7), (19, 9), (15, 6), (13, 41), (6, 42), (35, 25), (33, 35), (15, 25), (4, 7), (9, 35), (12, 19), (13, 34), (5, 16), (7, 16), (35, 42), (17, 14), (30, 37), (27, 22), (37, 14), (15, 38), (19, 2), (32, 14), (21, 40), (13, 18), (38, 15), (25, 16), (32, 26), (31, 6), (25, 5), (9, 39), (37, 34), (7, 12), (4, 39), (19, 21), (32, 13), (0, 5), (11, 8), (5, 35), (14, 7), (34, 4), (30, 4), (7, 39), (24, 36), (20, 23), (32, 25), (22, 26), (37, 32), (10, 16), (22, 29), (11, 30), (1, 14), (28, 28), (36, 21), (23, 23), (33, 36), (34, 33), (38, 6), (13, 38), (33, 26), (10, 19), (39, 1), (24, 40), (38, 27), (16, 10), (19, 7), (29, 38), (8, 18), (35, 30), (31, 14), (26, 15), (38, 30), (36, 9), (33, 13), (9, 24), (6, 19), (17, 39), (11, 41), (33, 12), (8, 11), (22, 6), (18, 8), (38, 36), (25, 0), (10, 14), (15, 12), (37, 19), (29, 26), (34, 30), (15, 30), (13, 1), (13, 17), (21, 1), (30, 36), (9, 28), (20, 28), (28, 9), (25, 34), (1, 15), (3, 42), (20, 22), (27, 35), (11, 17), (4, 32), (28, 1), (4, 42), (27, 6), (6, 31), (8, 21), (20, 24), (21, 23), (5, 8), (10, 4), (13, 42), (29, 25), (0, 6), (4, 21), (6, 18), (21, 11), (36, 35), (39, 20), (0, 35), (21, 37), (5, 34), (13, 24), (17, 11), (33, 14), (31, 2), (3, 31), (36, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 42), (0, 33), (4, 23), (32, 18), (28, 14), (9, 11), (1, 9), (6, 1), (9, 39), (17, 4), (16, 4), (24, 1), (20, 15), (2, 41), (32, 10), (21, 43), (37, 44), (8, 32), (44, 41), (41, 38), (32, 29), (27, 21), (24, 27), (2, 22), (36, 15), (43, 43), (7, 40), (15, 1), (46, 30), (30, 16), (3, 7), (22, 21), (9, 16), (1, 5), (40, 15), (14, 28), (37, 9), (42, 6), (22, 30), (14, 15), (30, 7), (29, 15), (43, 15), (6, 0), (8, 8), (22, 3), (4, 7), (1, 37), (9, 19), (10, 21), (13, 16), (13, 22), (30, 20), (37, 32), (25, 6), (12, 42), (12, 39), (5, 40), (11, 27), (11, 43), (41, 25), (3, 32), (40, 11), (27, 33), (2, 26), (39, 8), (10, 16), (36, 9), (2, 1), (37, 6), (15, 24), (1, 18), (3, 6), (41, 42), (38, 44), (6, 36), (40, 35), (45, 12), (42, 10), (21, 13), (15, 30), (20, 18), (30, 26), (36, 29), (32, 13), (15, 38), (1, 44), (5, 42), (3, 1), (42, 15), (34, 8), (2, 6), (35, 32), (38, 28), (26, 43), (16, 21), (44, 27), (17, 11), (39, 4), (30, 5), (44, 10), (2, 21), (18, 19), (1, 17), (18, 6), (29, 14), (17, 26), (15, 34), (0, 16), (7, 42), (11, 25), (25, 12), (4, 10), (17, 9), (37, 0), (46, 31), (46, 34), (13, 7), (26, 18), (14, 37), (26, 14), (14, 42), (39, 11), (17, 13), (11, 11), (33, 42), (44, 2), (22, 2), (17, 7), (9, 6), (29, 23), (22, 22), (27, 3), (9, 4), (41, 15), (32, 1), (21, 33), (38, 42), (36, 19), (10, 20), (45, 21), (11, 42), (0, 12), (39, 34), (23, 14), (3, 21), (24, 31), (24, 32), (46, 11), (18, 3), (33, 22), (16, 26), (45, 24), (17, 40), (27, 24), (43, 0), (40, 16), (27, 15), (43, 4), (44, 12), (30, 28), (28, 42), (36, 11), (45, 41), (11, 8), (11, 9), (7, 26), (24, 23), (34, 15), (35, 41), (39, 41), (24, 8), (21, 26), (31, 23), (1, 15), (38, 8), (6, 41), (11, 0), (25, 25), (27, 1), (10, 26), (45, 14), (7, 11), (35, 6), (22, 29), (12, 44), (13, 41), (3, 18), (7, 25), (37, 3), (29, 19), (40, 38), (40, 19), (3, 19), (29, 35), (41, 0), (32, 39), (39, 17), (5, 27), (29, 22), (3, 2), (19, 40), (44, 44), (33, 1), (27, 23), (35, 8), (36, 1), (26, 2), (8, 38), (13, 0), (4, 13), (42, 30), (27, 17), (17, 34), (26, 21), (37, 34), (42, 39), (23, 39), (37, 15), (6, 43), (34, 24), (23, 23), (23, 31), (34, 36), (19, 41), (6, 37), (31, 2), (33, 32), (27, 39), (4, 38), (12, 43), (35, 37), (11, 5), (43, 21), (6, 14), (34, 40), (5, 4), (5, 8), (36, 36), (1, 32), (0, 6), (16, 14), (19, 27), (24, 38), (38, 16), (10, 33), (13, 34), (38, 0), (42, 32), (46, 17), (30, 2), (3, 15), (17, 24), (12, 32), (3, 27), (38, 41), (21, 44), (31, 5), (43, 41), (27, 16), (45, 36), (23, 35), (5, 12), (27, 25), (19, 0), (9, 40), (24, 22), (18, 12), (0, 2), (30, 37), (43, 3), (28, 29), (8, 27), (42, 40), (27, 29), (31, 8), (31, 21), (34, 10), (31, 3), (2, 29), (14, 0), (40, 20), (20, 32), (24, 3), (38, 22), (32, 33), (3, 38), (38, 9), (9, 1), (25, 34), (27, 9), (12, 6), (43, 19), (24, 9), (2, 31), (15, 10), (36, 14), (19, 13), (44, 36), (3, 37), (4, 39), (26, 24), (10, 32), (14, 4), (15, 16), (19, 21), (0, 40), (6, 17), (46, 4), (31, 29), (6, 11), (11, 41), (43, 10), (43, 27), (1, 38), (22, 8), (15, 36), (43, 37), (9, 23), (33, 6), (33, 9), (39, 39), (44, 35), (15, 18), (4, 37), (13, 42), (33, 27), (18, 7), (28, 28), (5, 1), (11, 34), (33, 38), (37, 11), (39, 1), (22, 43), (19, 17), (18, 26), (19, 7), (0, 35), (42, 7), (40, 18), (3, 9), (38, 34), (45, 2), (24, 16), (17, 3), (17, 44), (11, 15), (31, 33), (24, 33), (1, 4), (14, 31), (37, 21), (0, 4), (15, 39), (21, 8), (0, 7), (25, 20), (20, 33), (36, 12), (31, 37), (31, 41), (23, 44), (33, 39), (25, 21), (28, 24), (29, 16), (38, 4), (7, 31), (28, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 2), (9, 14), (7, 18), (34, 24), (19, 42), (21, 25), (1, 5), (8, 24), (29, 5), (38, 16), (0, 24), (8, 23), (8, 0), (23, 31), (18, 15), (24, 45), (17, 13), (38, 19), (22, 3), (38, 44), (21, 24), (4, 45), (32, 23), (14, 17), (36, 10), (31, 12), (41, 11), (16, 44), (16, 26), (31, 16), (5, 17), (13, 23), (9, 22), (3, 29), (32, 29), (1, 8), (41, 18), (12, 4), (24, 22), (9, 29), (23, 18), (9, 21), (17, 5), (39, 28), (35, 25), (40, 38), (39, 39), (29, 7), (36, 15), (42, 31), (1, 34), (24, 11), (2, 24), (17, 15), (36, 24), (11, 9), (3, 25), (10, 8), (3, 19), (37, 32), (41, 36), (42, 25), (22, 23), (26, 36), (29, 2), (8, 38), (29, 24), (1, 32), (24, 10), (11, 18), (32, 33), (11, 29), (25, 18), (22, 5), (0, 41), (12, 5), (17, 6), (19, 44), (34, 28), (12, 31), (7, 44), (34, 27), (4, 31), (37, 8), (30, 27), (32, 41), (16, 29), (28, 27), (16, 8), (10, 14), (39, 22), (41, 10), (18, 6), (2, 32), (0, 34), (36, 28), (8, 2), (16, 6), (41, 2), (34, 45), (19, 12), (19, 35), (5, 42), (18, 1), (17, 45), (15, 20), (36, 5), (10, 28), (11, 25), (0, 40), (11, 38), (35, 44), (21, 26), (5, 45), (4, 22), (6, 35), (40, 1), (20, 34), (9, 38), (9, 5), (39, 8), (35, 3), (10, 17), (26, 20), (2, 20), (40, 25), (10, 4), (35, 11), (19, 2), (31, 6), (12, 24), (25, 10), (6, 24), (19, 7), (3, 3), (17, 16), (20, 19), (37, 38), (29, 18), (10, 27), (32, 22), (30, 12), (20, 10), (41, 1), (24, 42), (3, 11), (16, 30), (0, 44), (6, 30), (22, 7), (9, 42), (19, 39), (1, 42), (11, 7), (11, 0), (42, 22), (21, 37), (15, 3), (15, 23), (20, 20), (6, 17), (18, 45), (7, 8), (14, 16), (11, 21), (21, 14), (23, 28), (38, 9), (5, 30), (38, 23), (7, 43), (33, 25), (1, 37), (18, 36), (3, 38), (14, 21), (32, 37), (26, 1), (4, 41), (13, 39), (4, 30), (20, 6), (12, 28), (42, 3), (16, 31), (0, 2), (6, 7), (25, 35), (8, 4), (15, 38), (8, 13), (0, 33), (21, 28), (2, 44), (29, 9), (3, 14), (11, 45), (9, 35), (3, 33), (33, 45), (40, 32), (22, 15), (29, 16), (29, 45), (17, 39), (1, 31), (37, 40), (30, 13), (4, 40), (39, 38), (21, 18), (12, 27), (12, 34), (13, 22), (21, 0), (40, 13), (34, 38), (28, 11), (29, 20), (24, 17), (10, 38), (12, 21), (30, 38), (22, 25), (39, 5), (25, 33), (25, 44), (28, 35), (42, 19), (17, 8), (28, 1), (35, 32), (32, 30), (17, 26), (2, 22), (27, 18), (2, 30), (26, 4), (18, 29), (2, 21), (40, 7), (2, 29), (34, 35), (37, 28), (15, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 24), (27, 13), (4, 35), (18, 31), (45, 42), (29, 12), (45, 37), (17, 38), (13, 0), (19, 21), (27, 28), (34, 7), (13, 1), (7, 0), (11, 43), (29, 1), (32, 39), (5, 7), (21, 32), (21, 1), (38, 17), (20, 4), (11, 26), (34, 34), (39, 25), (42, 1), (2, 10), (14, 5), (2, 34), (33, 12), (44, 34), (45, 32), (36, 9), (22, 16), (23, 12), (34, 2), (8, 31), (0, 8), (8, 9), (44, 1), (14, 29), (35, 28), (20, 41), (13, 17), (9, 6), (45, 13), (9, 0), (8, 29), (24, 38), (16, 17), (31, 33), (29, 22), (24, 35), (22, 14), (0, 9), (28, 0), (32, 34), (12, 29), (2, 24), (16, 19), (26, 19), (14, 22), (30, 33), (16, 18), (32, 6), (44, 44), (31, 3), (14, 36), (24, 11), (21, 13), (45, 27), (12, 31), (22, 41), (11, 38), (16, 28), (15, 10), (38, 9), (35, 35), (20, 42), (42, 3), (25, 42), (34, 42), (13, 30), (0, 18), (5, 27), (24, 9), (3, 44), (4, 27), (4, 41), (39, 1), (25, 7), (30, 41), (42, 25), (40, 25), (37, 43), (6, 45), (22, 8), (15, 44), (7, 33), (16, 10), (3, 14), (6, 12), (27, 10), (28, 18), (8, 2), (36, 20), (32, 9), (36, 32), (18, 37), (15, 38), (12, 26), (17, 21), (33, 36), (28, 33), (34, 0), (17, 29), (0, 31), (44, 12), (1, 24), (29, 27), (45, 18), (14, 8), (12, 20), (35, 36), (6, 36), (7, 29), (29, 13), (30, 38), (7, 43), (29, 40), (13, 3), (21, 10), (31, 25), (20, 39), (22, 28), (16, 25), (15, 33), (17, 27), (8, 6), (15, 23), (30, 12), (26, 43), (36, 37), (35, 34), (11, 4), (0, 24), (42, 11), (10, 11), (17, 2), (21, 14), (43, 29), (33, 18), (25, 43), (4, 37), (17, 39), (2, 6), (40, 36), (43, 35), (45, 3), (20, 35), (41, 7), (6, 13), (42, 26), (17, 13), (31, 18), (23, 6), (15, 1), (0, 22), (20, 40), (42, 29), (17, 36), (12, 27), (1, 0), (4, 18), (6, 9), (27, 9), (40, 14), (0, 17), (34, 16), (25, 15), (6, 15), (32, 35), (42, 5), (42, 17), (42, 43), (42, 28), (14, 42), (5, 25), (33, 25), (40, 6), (2, 23), (37, 33), (14, 43), (1, 28), (6, 37), (1, 10), (41, 11), (44, 33), (32, 13), (28, 35), (3, 20), (31, 4), (1, 4), (33, 44), (31, 43), (2, 8), (44, 18), (28, 9), (9, 28), (24, 28), (37, 11), (14, 0), (44, 32), (44, 38), (2, 20), (14, 16), (29, 26), (16, 22), (42, 24), (1, 12), (1, 3), (25, 30), (8, 35), (39, 17), (44, 39), (11, 17), (38, 14), (27, 33), (2, 29), (38, 23), (44, 35), (16, 11), (45, 44), (18, 25), (15, 35), (27, 45), (24, 8), (11, 40), (11, 1), (23, 25), (28, 5), (32, 42), (15, 32), (33, 45), (10, 14), (12, 8), (7, 30), (39, 22), (16, 9), (34, 12), (12, 10), (9, 24), (23, 13), (0, 37), (24, 37), (6, 1), (7, 36), (10, 41), (34, 37), (43, 0), (34, 20), (31, 38), (5, 13), (37, 45), (13, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 40x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 22), (25, 11), (1, 7), (11, 10), (2, 42), (28, 1), (17, 6), (1, 9), (17, 13), (22, 21), (22, 39), (11, 32), (3, 17), (4, 9), (3, 8), (13, 39), (1, 36), (32, 24), (6, 34), (24, 37), (34, 21), (22, 34), (20, 15), (19, 6), (28, 42), (35, 36), (24, 9), (32, 41), (20, 32), (22, 15), (3, 25), (38, 16), (9, 31), (30, 27), (16, 3), (7, 28), (13, 9), (21, 0), (29, 31), (23, 15), (36, 11), (0, 37), (24, 32), (2, 15), (10, 5), (24, 18), (34, 29), (20, 21), (37, 37), (7, 41), (36, 24), (29, 24), (4, 39), (24, 11), (24, 26), (3, 13), (35, 27), (22, 27), (17, 29), (14, 22), (31, 3), (10, 24), (2, 8), (3, 37), (15, 3), (35, 39), (34, 38), (21, 26), (4, 31), (12, 38), (0, 17), (26, 17), (37, 42), (32, 35), (38, 0), (31, 26), (17, 20), (13, 36), (35, 10), (3, 35), (34, 39), (11, 0), (12, 9), (21, 27), (30, 41), (7, 32), (2, 21), (25, 25), (18, 2), (32, 32), (34, 25), (7, 20), (24, 30), (5, 27), (28, 40), (6, 3), (15, 38), (25, 30), (26, 3), (2, 12), (9, 15), (7, 21), (28, 37), (5, 17), (11, 41), (36, 39), (19, 27), (37, 40), (26, 13), (22, 13), (27, 4), (39, 17), (9, 26), (7, 15), (26, 40), (11, 7), (32, 25), (17, 12), (23, 2), (17, 26), (29, 28), (34, 31), (39, 29), (1, 28), (27, 34), (30, 31), (15, 27), (0, 21), (31, 18), (38, 42), (24, 25), (25, 29), (28, 0), (38, 9), (6, 35), (34, 11), (39, 25), (3, 33), (38, 41), (26, 42), (5, 7), (36, 8), (28, 2), (7, 8), (16, 41), (12, 23), (16, 5), (29, 7), (38, 36), (34, 42), (33, 16), (32, 28), (0, 39), (17, 15), (10, 40), (13, 20), (4, 1), (8, 19), (15, 39), (2, 1), (34, 27), (9, 5), (3, 11), (7, 6), (18, 35), (34, 12), (1, 21), (17, 11), (14, 30), (9, 3), (21, 30), (28, 23), (36, 3), (31, 33), (3, 19), (30, 7), (10, 22), (26, 28), (19, 10), (16, 33), (15, 37), (24, 23), (8, 10), (26, 9), (31, 2), (33, 24), (28, 20), (3, 24), (27, 40), (38, 11), (34, 1), (11, 25), (9, 29), (12, 14), (16, 31), (21, 25), (4, 35), (13, 22), (35, 13), (35, 38), (15, 20), (7, 23), (37, 8), (36, 23), (15, 34), (19, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 19), (37, 35), (23, 0), (26, 15), (32, 1), (10, 27), (22, 27), (24, 29), (25, 38), (34, 31), (4, 39), (26, 39), (22, 33), (21, 9), (0, 38), (11, 22), (11, 31), (32, 28), (23, 5), (3, 21), (5, 40), (18, 33), (5, 11), (27, 31), (20, 35), (33, 26), (2, 2), (0, 27), (13, 20), (39, 28), (25, 19), (20, 15), (27, 30), (14, 13), (28, 8), (15, 4), (17, 19), (25, 9), (8, 8), (38, 13), (36, 14), (19, 12), (20, 9), (34, 7), (27, 24), (25, 37), (29, 9), (20, 33), (16, 36), (36, 13), (19, 10), (13, 37), (3, 36), (22, 23), (22, 38), (30, 31), (10, 3), (9, 26), (17, 30), (27, 13), (31, 33), (6, 18), (0, 11), (1, 28), (13, 1), (34, 37), (2, 12), (13, 19), (29, 28), (7, 18), (8, 27), (8, 1), (37, 28), (17, 29), (4, 34), (21, 23), (4, 1), (31, 1), (15, 5), (21, 0), (25, 31), (36, 2), (7, 17), (2, 3), (25, 30), (14, 30), (34, 36), (23, 39), (19, 7), (17, 10), (24, 10), (2, 18), (20, 26), (38, 27), (12, 36), (26, 33), (17, 7), (20, 5), (20, 24), (21, 37), (14, 20), (36, 24), (18, 23), (38, 22), (27, 11), (33, 5), (19, 33), (16, 7), (31, 26), (20, 6), (0, 10), (6, 5), (21, 36), (29, 34), (23, 8), (19, 34), (38, 19), (29, 25), (11, 7), (23, 21), (29, 1), (22, 16), (8, 17), (20, 16), (16, 15), (24, 4), (12, 35), (3, 9), (3, 20), (27, 14), (38, 12), (5, 22), (23, 10), (17, 5), (17, 3), (36, 20), (8, 10), (8, 6), (33, 14), (28, 16), (0, 22), (0, 12), (22, 3), (10, 34), (0, 3), (30, 9), (5, 33), (10, 29), (36, 36), (20, 7), (4, 23), (19, 22), (26, 11), (35, 32), (13, 40), (21, 13), (32, 16), (35, 4), (13, 5), (23, 16), (10, 24), (37, 18), (0, 36), (3, 29), (10, 23), (6, 26), (9, 9), (28, 5), (4, 0), (7, 13), (17, 17), (1, 6), (6, 21), (30, 14), (6, 40), (0, 24), (34, 26), (24, 16), (8, 15), (1, 11), (39, 5), (5, 8), (19, 16), (17, 37), (5, 38), (4, 19), (12, 18), (32, 4), (12, 13), (21, 16), (10, 18), (18, 11), (33, 3), (25, 2), (15, 18), (14, 0), (29, 27), (27, 29), (9, 36), (3, 25), (8, 3), (31, 11), (35, 36), (17, 12), (5, 27), (9, 11), (0, 9), (13, 8), (15, 16), (24, 11), (15, 22), (4, 14), (14, 39), (19, 5), (34, 1), (34, 4), (7, 23), (4, 18), (11, 3), (6, 34), (32, 14), (8, 11), (29, 40), (36, 40), (36, 39), (38, 24), (0, 19), (19, 15), (25, 24), (10, 6), (27, 5), (8, 4), (3, 24), (16, 11), (24, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 34), (16, 37), (4, 26), (35, 32), (37, 26), (12, 25), (26, 9), (12, 3), (8, 26), (35, 34), (31, 1), (18, 19), (14, 32), (43, 31), (20, 23), (41, 28), (26, 28), (29, 19), (1, 30), (18, 30), (12, 31), (28, 16), (34, 35), (26, 29), (12, 10), (30, 29), (23, 34), (29, 36), (9, 11), (25, 23), (24, 25), (5, 5), (20, 30), (37, 35), (12, 24), (25, 3), (10, 12), (14, 12), (43, 4), (29, 12), (1, 8), (38, 30), (33, 25), (8, 30), (27, 36), (21, 26), (38, 22), (31, 17), (7, 36), (4, 6), (17, 14), (29, 4), (26, 4), (28, 37), (7, 19), (36, 7), (31, 9), (36, 0), (17, 13), (33, 5), (38, 10), (24, 17), (6, 33), (37, 40), (19, 30), (11, 24), (37, 7), (31, 19), (14, 27), (43, 9), (40, 14), (30, 7), (39, 7), (39, 32), (40, 5), (41, 9), (41, 7), (32, 11), (20, 26), (36, 13), (8, 8), (31, 32), (0, 1), (7, 29), (17, 1), (32, 13), (2, 37), (29, 1), (1, 38), (27, 16), (23, 1), (8, 5), (3, 27), (28, 23), (14, 28), (40, 35), (7, 28), (20, 6), (18, 37), (25, 29), (1, 24), (33, 15), (3, 30), (34, 4), (25, 8), (16, 3), (14, 40), (38, 36), (25, 37), (42, 16), (17, 33), (17, 6), (4, 24), (0, 24), (18, 26), (8, 15), (21, 25), (16, 26), (6, 6), (30, 20), (16, 17), (9, 34), (38, 40), (34, 24), (42, 27), (9, 5), (9, 1), (25, 34), (13, 36), (30, 27), (36, 9), (4, 34), (37, 37), (40, 6), (37, 2), (28, 36), (31, 11), (27, 2), (25, 7), (40, 17), (29, 8), (33, 34), (37, 30), (2, 11), (12, 1), (38, 7), (38, 14), (20, 37), (15, 14), (16, 12), (24, 8), (27, 29), (30, 16), (8, 36), (20, 2), (3, 5), (21, 17), (15, 38), (26, 1), (14, 2), (8, 1), (20, 0), (37, 20), (22, 0), (25, 6), (25, 14), (22, 9), (29, 2), (7, 23), (4, 23), (38, 29), (14, 11), (34, 37), (31, 3), (16, 28), (37, 36), (41, 37), (29, 27), (29, 24), (18, 35), (43, 17), (34, 21), (32, 19), (33, 12), (3, 4), (30, 11), (18, 17), (6, 29), (13, 7), (40, 40), (29, 30), (25, 22), (17, 18), (39, 6), (4, 2), (13, 16), (23, 30), (11, 32), (42, 1), (42, 32), (30, 22), (34, 25), (18, 40), (4, 0), (36, 12), (24, 39), (38, 12), (38, 25), (0, 10), (24, 21), (0, 18), (43, 26), (1, 28), (39, 18), (13, 2), (26, 32), (6, 40), (32, 4), (20, 14), (29, 21), (34, 7), (41, 15), (3, 33), (11, 19), (35, 20), (0, 26), (4, 22), (24, 38), (42, 31), (41, 23), (20, 16), (17, 37), (16, 35), (9, 30), (42, 18), (23, 23), (1, 1), (11, 16), (20, 33), (20, 21), (9, 37), (2, 25), (16, 24), (33, 4), (21, 20), (9, 29), (15, 18), (25, 31), (17, 34), (0, 16), (6, 15), (43, 1), (18, 10), (35, 16), (36, 27), (40, 23), (34, 26), (6, 21), (34, 36), (40, 18), (15, 7), (3, 37), (5, 7), (2, 2), (19, 5), (17, 29), (23, 18), (23, 36), (39, 15), (12, 20), (28, 39), (19, 33), (38, 13), (5, 25), (40, 9), (34, 30), (28, 40), (35, 28), (3, 16), (8, 24), (19, 26), (10, 8), (26, 13), (0, 35), (16, 32), (27, 3), (4, 10), (25, 2), (10, 20), (14, 3), (5, 40), (16, 29), (41, 3), (33, 35), (42, 37), (32, 38), (42, 20), (37, 19), (10, 36), (23, 13), (41, 36), (38, 5), (37, 32), (32, 29), (13, 1), (42, 7), (5, 39), (26, 30), (24, 15), (22, 11), (12, 6), (9, 8), (12, 9), (5, 31), (33, 22), (39, 19), (7, 35), (34, 29), (15, 13), (24, 31), (4, 12), (21, 2), (15, 24), (13, 39), (15, 11), (1, 35), (35, 13), (36, 17), (42, 36), (14, 14), (27, 33), (1, 39), (20, 25), (22, 25), (29, 18), (12, 29), (15, 27), (11, 26), (19, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 36), (37, 39), (37, 7), (2, 5), (22, 14), (0, 47), (28, 48), (27, 42), (9, 1), (32, 17), (42, 4), (36, 26), (43, 37), (46, 4), (43, 22), (43, 32), (3, 41), (0, 8), (20, 29), (18, 40), (18, 31), (43, 25), (3, 46), (42, 9), (39, 17), (26, 17), (44, 17), (31, 2), (21, 40), (17, 31), (22, 7), (14, 40), (23, 33), (10, 40), (4, 38), (7, 36), (29, 20), (17, 46), (4, 37), (0, 18), (23, 37), (7, 44), (32, 10), (32, 37), (37, 31), (40, 44), (40, 34), (15, 11), (12, 5), (41, 7), (1, 6), (2, 30), (33, 8), (35, 33), (5, 10), (15, 19), (12, 37), (1, 38), (18, 12), (6, 41), (13, 34), (4, 6), (38, 48), (29, 14), (25, 12), (18, 1), (23, 43), (31, 41), (13, 39), (9, 19), (39, 46), (45, 17), (27, 41), (22, 18), (3, 6), (38, 25), (26, 3), (7, 45), (39, 0), (21, 31), (20, 9), (11, 32), (16, 46), (7, 29), (0, 33), (20, 45), (17, 29), (46, 11), (41, 2), (33, 39), (28, 44), (26, 20), (24, 31), (15, 26), (32, 38), (41, 39), (33, 45), (26, 37), (29, 24), (2, 48), (9, 43), (27, 0), (27, 44), (10, 44), (43, 31), (33, 13), (34, 3), (29, 38), (14, 46), (36, 10), (13, 37), (37, 45), (17, 33), (13, 1), (18, 48), (33, 23), (11, 24), (15, 40), (24, 16), (20, 3), (2, 31), (7, 25), (45, 46), (21, 3), (25, 10), (28, 46), (45, 39), (0, 9), (38, 42), (14, 41), (36, 41), (32, 26), (37, 6), (34, 48), (43, 4), (9, 22), (31, 38), (25, 11), (18, 43), (39, 8), (4, 14), (19, 17), (5, 5), (19, 40), (3, 5), (21, 14), (28, 36), (3, 4), (46, 24), (44, 40), (4, 34), (24, 20), (46, 45), (22, 3), (44, 29), (12, 40), (38, 2), (17, 23), (38, 24), (4, 46), (27, 48), (0, 1), (17, 36), (9, 28), (31, 15), (32, 32), (11, 3), (2, 35), (26, 32), (46, 38), (12, 14), (15, 41), (2, 19), (5, 23), (37, 35), (0, 7), (30, 14), (19, 19), (7, 0), (34, 25), (34, 20), (23, 15), (20, 14), (36, 33), (32, 0), (8, 6), (46, 15), (26, 39), (40, 21), (9, 40), (45, 23), (21, 10), (21, 12), (2, 20), (22, 16), (4, 44), (10, 29), (38, 14), (10, 5), (33, 17), (43, 38), (36, 29), (13, 47), (7, 7), (25, 8), (39, 27), (37, 22), (40, 7), (17, 9), (32, 15), (41, 46), (34, 34), (35, 10), (8, 3), (2, 32), (14, 22), (36, 8), (16, 31), (20, 32), (5, 18), (6, 38), (33, 22), (45, 2), (12, 15), (6, 14), (30, 40), (19, 35), (20, 5), (4, 15), (20, 44), (11, 48), (45, 47), (14, 47), (43, 15), (39, 32), (11, 28), (38, 19), (3, 22), (36, 21), (26, 28), (6, 15), (34, 46), (46, 36), (31, 37), (16, 28), (27, 45), (7, 11), (26, 29), (2, 46), (46, 28), (13, 24), (21, 21), (10, 6), (10, 47), (27, 17), (16, 34), (16, 14), (30, 36), (3, 30), (43, 14), (17, 17), (45, 27), (33, 21), (11, 29), (35, 26), (20, 42), (21, 37), (29, 39), (12, 1), (41, 40), (45, 8), (40, 14), (37, 2), (28, 34), (24, 42), (46, 31), (18, 22), (37, 18), (25, 30), (22, 25), (26, 42), (9, 36), (8, 25), (25, 44), (6, 35), (29, 8), (3, 20), (19, 25), (29, 31), (34, 5), (1, 10), (17, 12), (41, 12), (31, 10), (17, 7), (46, 19), (29, 26), (17, 0), (45, 36), (23, 29), (34, 31), (17, 8), (30, 47), (11, 16), (27, 38), (33, 34), (30, 0), (19, 11), (35, 34), (36, 14), (28, 21), (16, 30), (20, 8), (24, 18), (26, 34), (34, 4), (12, 28), (30, 34), (42, 0), (40, 39), (12, 19), (4, 39), (28, 38), (25, 17), (17, 11), (36, 5), (10, 37), (10, 7), (42, 37), (28, 37), (44, 47), (36, 45), (9, 29), (10, 26), (24, 2), (41, 5), (25, 36), (11, 36), (39, 6), (4, 13), (41, 4), (30, 37), (16, 16), (34, 14), (19, 4), (10, 27), (8, 12), (40, 9), (28, 6), (9, 26), (30, 7), (35, 36), (20, 17), (23, 14), (4, 32), (33, 14), (11, 4), (0, 14), (34, 22), (37, 17), (40, 2), (16, 45), (22, 23), (34, 13), (40, 31), (21, 2), (18, 17), (38, 45), (1, 11), (14, 20), (25, 34), (15, 2), (14, 30), (41, 26), (5, 31), (32, 45), (12, 29), (22, 10), (14, 8), (2, 47), (8, 26), (4, 27), (37, 15), (12, 45), (0, 24), (34, 32), (16, 18), (44, 18), (35, 22), (27, 1), (9, 39), (29, 47), (42, 1), (2, 29), (36, 39), (14, 32), (40, 17), (35, 17), (8, 15), (1, 32), (4, 2), (23, 27), (6, 10), (24, 46), (12, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 35), (33, 20), (13, 14), (1, 22), (24, 7), (0, 2), (23, 42), (13, 19), (36, 26), (26, 35), (34, 33), (29, 0), (7, 39), (35, 2), (39, 20), (7, 0), (17, 16), (5, 25), (2, 19), (1, 31), (21, 44), (10, 14), (16, 13), (41, 2), (11, 6), (6, 20), (36, 43), (36, 4), (41, 36), (28, 18), (21, 26), (1, 21), (3, 26), (34, 6), (13, 20), (27, 35), (0, 30), (33, 10), (26, 11), (38, 24), (14, 4), (18, 41), (29, 39), (12, 23), (15, 4), (30, 44), (40, 13), (13, 27), (15, 1), (2, 4), (13, 21), (10, 42), (23, 37), (7, 42), (0, 8), (37, 19), (25, 14), (41, 4), (15, 36), (15, 21), (31, 14), (30, 2), (20, 31), (16, 10), (6, 14), (24, 17), (16, 32), (17, 38), (16, 30), (35, 20), (12, 36), (14, 1), (22, 13), (32, 40), (37, 14), (33, 30), (40, 35), (15, 10), (23, 11), (5, 1), (11, 1), (38, 28), (8, 17), (13, 39), (24, 22), (22, 24), (16, 44), (4, 28), (33, 23), (3, 4), (23, 5), (33, 40), (17, 25), (38, 25), (16, 23), (24, 30), (10, 24), (34, 21), (8, 33), (10, 5), (21, 10), (17, 36), (6, 28), (8, 15), (3, 37), (21, 11), (37, 3), (11, 44), (11, 37), (12, 33), (26, 16), (5, 19), (2, 22), (30, 22), (20, 2), (14, 34), (11, 32), (4, 12), (18, 27), (24, 2), (4, 38), (25, 35), (41, 29), (9, 3), (3, 36), (12, 26), (16, 34), (6, 12), (35, 31), (37, 41), (22, 30), (38, 33), (14, 18), (39, 14), (6, 11), (34, 40), (3, 34), (13, 7), (22, 40), (26, 29), (29, 2), (17, 4), (12, 1), (21, 6), (3, 1), (39, 44), (24, 3), (31, 0), (24, 14), (35, 42), (7, 18), (28, 30), (2, 9), (16, 31), (9, 2), (2, 23), (12, 40), (10, 8), (29, 24), (0, 13), (29, 15), (28, 24), (3, 40), (22, 21), (19, 42), (21, 4), (20, 9), (15, 42), (8, 14), (13, 41), (7, 23), (4, 17), (26, 36), (29, 12), (39, 10), (33, 43), (12, 31), (16, 39), (10, 20), (24, 10), (5, 16), (23, 3), (27, 24), (2, 34), (35, 7), (8, 37), (35, 35), (27, 17), (21, 24), (33, 24), (12, 38), (15, 28), (37, 40), (19, 43), (35, 10), (1, 10), (25, 39), (34, 3), (41, 6), (24, 15), (23, 35), (13, 17), (10, 28), (1, 25), (15, 41), (32, 41), (19, 13), (0, 3), (38, 39), (35, 34), (4, 27), (18, 38), (37, 16), (38, 44), (24, 18), (29, 22), (2, 2), (26, 1), (25, 17), (3, 24), (40, 43), (27, 44), (42, 14), (29, 35), (27, 30), (35, 44), (12, 43), (0, 12), (6, 6), (30, 29), (7, 6), (22, 31), (13, 44), (42, 41), (42, 20), (25, 2), (7, 10), (25, 44), (21, 14), (37, 23), (25, 29), (41, 7), (19, 3), (10, 4), (32, 3), (15, 35), (1, 40), (10, 21), (40, 40), (2, 36), (33, 35), (28, 28), (9, 12), (38, 13), (9, 42), (22, 15), (36, 2), (16, 3), (38, 22), (8, 31), (24, 40), (41, 35), (25, 24), (20, 36), (24, 1), (36, 28), (33, 34), (4, 36), (31, 12), (39, 11), (12, 10), (1, 23), (30, 34), (13, 24), (32, 29), (33, 32), (21, 17), (24, 4), (11, 10), (19, 10), (29, 28), (22, 5), (2, 27), (12, 24), (18, 23), (14, 20), (40, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 18), (29, 4), (6, 27), (16, 13), (27, 34), (31, 12), (6, 20), (10, 5), (8, 37), (1, 23), (18, 2), (10, 11), (31, 34), (28, 13), (0, 25), (35, 12), (17, 11), (40, 26), (31, 6), (12, 18), (38, 34), (13, 9), (5, 13), (40, 6), (5, 0), (1, 36), (28, 11), (13, 11), (31, 4), (32, 33), (29, 31), (32, 12), (34, 29), (9, 3), (27, 11), (2, 14), (2, 7), (14, 7), (20, 15), (39, 32), (30, 6), (31, 29), (2, 31), (12, 0), (5, 27), (22, 8), (25, 3), (25, 17), (0, 22), (18, 39), (19, 8), (12, 3), (29, 1), (19, 15), (32, 21), (25, 23), (26, 8), (34, 30), (21, 5), (13, 16), (19, 22), (38, 11), (27, 29), (34, 14), (34, 6), (37, 35), (24, 31), (20, 16), (8, 0), (38, 1), (6, 18), (39, 6), (9, 0), (8, 26), (37, 34), (28, 35), (27, 15), (14, 27), (33, 2), (6, 4), (25, 13), (32, 1), (9, 19), (29, 3), (3, 2), (36, 17), (7, 6), (36, 18), (3, 22), (14, 2), (7, 32), (17, 20), (10, 13), (37, 30), (8, 38), (8, 21), (28, 8), (5, 20), (21, 2), (0, 35), (24, 1), (37, 28), (17, 29), (26, 23), (9, 20), (32, 32), (5, 9), (19, 23), (8, 40), (23, 37), (7, 3), (16, 32), (27, 21), (19, 39), (5, 11), (31, 18), (21, 22), (33, 14), (4, 23), (37, 7), (32, 15), (13, 7), (20, 26), (15, 24), (7, 33), (24, 37), (34, 28), (3, 6), (31, 0), (8, 20), (25, 15), (5, 1), (19, 19), (3, 3), (1, 27), (9, 16), (15, 1), (6, 2), (31, 17), (37, 16), (3, 15), (5, 17), (12, 30), (18, 38), (7, 2), (1, 9), (36, 37), (31, 19), (28, 34), (17, 5), (9, 15), (1, 5), (39, 31), (10, 14), (9, 22), (8, 15), (8, 31), (21, 4), (5, 39), (24, 23), (1, 18), (23, 16), (15, 33), (25, 40), (20, 35), (24, 13), (40, 5), (17, 33), (4, 27), (12, 39), (8, 9), (30, 23), (12, 32), (12, 17), (29, 20), (1, 20), (14, 36), (3, 8), (15, 2), (19, 14), (35, 38), (26, 5), (33, 0), (6, 3), (30, 16), (26, 16), (10, 25), (30, 3), (27, 33), (6, 23), (37, 1), (34, 38), (25, 12), (15, 18), (14, 6), (3, 10), (12, 36), (28, 1), (35, 8), (28, 10), (17, 24), (29, 21), (12, 7), (18, 26), (12, 26), (22, 34), (28, 31), (23, 25), (7, 7), (37, 22), (11, 29), (11, 34), (22, 27), (1, 31), (4, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 33), (38, 43), (6, 1), (44, 4), (23, 36), (7, 22), (43, 26), (1, 23), (24, 11), (19, 38), (2, 46), (23, 11), (13, 2), (14, 28), (26, 46), (5, 5), (45, 30), (24, 35), (43, 14), (37, 46), (8, 19), (26, 33), (35, 43), (2, 33), (31, 46), (36, 7), (3, 25), (36, 32), (37, 43), (32, 38), (35, 30), (24, 4), (2, 0), (3, 8), (40, 13), (20, 38), (15, 21), (46, 7), (27, 24), (33, 17), (17, 2), (14, 34), (24, 43), (21, 35), (27, 11), (2, 20), (1, 3), (10, 43), (30, 9), (12, 7), (4, 14), (18, 18), (23, 5), (16, 28), (6, 0), (15, 39), (33, 11), (29, 27), (6, 45), (3, 34), (45, 15), (19, 1), (3, 10), (22, 29), (16, 48), (9, 21), (34, 40), (35, 8), (26, 38), (43, 43), (4, 4), (12, 17), (16, 13), (36, 19), (24, 0), (36, 47), (41, 40), (8, 30), (37, 39), (7, 32), (16, 35), (29, 35), (0, 22), (8, 43), (10, 36), (32, 32), (33, 12), (34, 21), (22, 24), (17, 45), (1, 32), (18, 23), (17, 8), (3, 0), (4, 34), (38, 15), (12, 21), (7, 40), (21, 13), (18, 33), (31, 4), (3, 48), (32, 44), (29, 44), (29, 30), (37, 24), (27, 16), (38, 31), (38, 39), (34, 29), (6, 18), (28, 44), (13, 36), (25, 18), (34, 39), (44, 34), (7, 28), (35, 41), (4, 16), (26, 19), (40, 32), (16, 33), (45, 17), (28, 24), (22, 33), (19, 30), (37, 18), (14, 36), (43, 20), (9, 0), (39, 17), (27, 34), (34, 11), (18, 1), (21, 44), (3, 44), (37, 25), (24, 30), (35, 12), (40, 48), (9, 17), (28, 0), (38, 2), (14, 8), (39, 34), (10, 9), (25, 40), (11, 26), (2, 7), (29, 26), (21, 33), (18, 26), (0, 40), (36, 27), (33, 48), (9, 3), (2, 16), (46, 35), (19, 16), (15, 44), (8, 28), (34, 30), (6, 5), (41, 22), (0, 43), (22, 18), (42, 0), (17, 3), (4, 24), (45, 8), (23, 34), (34, 4), (36, 28), (37, 35), (21, 46), (30, 33), (46, 11), (1, 19), (3, 45), (36, 20), (34, 38), (14, 29), (6, 38), (30, 21), (28, 17), (10, 8), (13, 23), (39, 28), (12, 41), (43, 40), (39, 38), (4, 6), (32, 29), (14, 19), (26, 26), (31, 17), (43, 3), (42, 6), (38, 8), (1, 8), (1, 2), (5, 46), (11, 23), (41, 1), (39, 15), (39, 24), (24, 3), (30, 24), (6, 35), (20, 42), (1, 12), (23, 2), (18, 42), (39, 35), (15, 9), (25, 31), (38, 10), (29, 16), (39, 19), (29, 10), (40, 36), (3, 36), (37, 26), (6, 8), (15, 30), (38, 29), (15, 34), (35, 32), (43, 34), (36, 12), (34, 14), (17, 10), (16, 38), (17, 26), (26, 37), (42, 7), (21, 1), (12, 5), (37, 6), (36, 45), (5, 6), (19, 35), (2, 38), (18, 28), (20, 21), (39, 32), (37, 8), (23, 0), (6, 43), (27, 4), (19, 43), (42, 4), (26, 16), (37, 37), (15, 17), (18, 5), (24, 9), (29, 48), (45, 19), (19, 28), (3, 26), (4, 45), (42, 42), (8, 20), (15, 38), (2, 11), (28, 18), (32, 3), (19, 37), (9, 22), (12, 0), (27, 2), (41, 23), (29, 38), (43, 16), (1, 31), (19, 12), (11, 9), (23, 21), (34, 47), (0, 10), (26, 47), (36, 31), (26, 34), (11, 19), (37, 2), (32, 0), (33, 22), (37, 29), (23, 30), (15, 19), (35, 40), (18, 31), (12, 6), (35, 36), (44, 28), (45, 26), (33, 25), (39, 27), (42, 31), (3, 20), (42, 47), (9, 31), (18, 3), (21, 40), (36, 26), (21, 15), (9, 20), (2, 26), (37, 14), (40, 43), (27, 17), (29, 18), (26, 11), (21, 6), (16, 24), (44, 13), (2, 32), (37, 44), (21, 27), (1, 36), (46, 34), (43, 32), (5, 28), (21, 21), (4, 46), (40, 21), (26, 0), (20, 27), (2, 37), (22, 25), (33, 6), (37, 7), (32, 20), (39, 47), (18, 38), (0, 35), (5, 10), (5, 41), (6, 3), (24, 29), (28, 10), (4, 23), (0, 5), (38, 47), (15, 48), (13, 29), (7, 41), (31, 30), (33, 15), (24, 16), (8, 33), (30, 32), (0, 31), (15, 28), (18, 22), (32, 31), (22, 32), (17, 36), (20, 33), (42, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 15), (3, 10), (24, 33), (39, 38), (12, 12), (30, 36), (7, 25), (27, 26), (29, 31), (9, 30), (16, 38), (28, 1), (20, 29), (22, 5), (40, 15), (9, 10), (37, 36), (7, 1), (22, 9), (1, 13), (19, 7), (4, 9), (25, 21), (38, 20), (12, 16), (28, 18), (6, 30), (12, 40), (32, 4), (27, 12), (29, 38), (0, 9), (11, 11), (27, 9), (21, 23), (34, 36), (37, 6), (25, 32), (28, 4), (40, 21), (28, 32), (16, 30), (16, 18), (11, 25), (11, 4), (39, 4), (0, 34), (9, 6), (24, 1), (28, 34), (17, 36), (3, 0), (28, 38), (31, 34), (14, 15), (19, 13), (31, 38), (20, 2), (26, 6), (8, 26), (6, 18), (16, 7), (4, 34), (20, 31), (7, 28), (25, 14), (26, 38), (5, 39), (30, 14), (39, 28), (21, 36), (31, 16), (34, 23), (21, 15), (1, 38), (13, 11), (28, 16), (7, 4), (33, 35), (32, 5), (40, 24), (17, 31), (5, 23), (36, 32), (23, 22), (11, 21), (25, 11), (15, 6), (38, 30), (35, 23), (14, 16), (30, 28), (12, 31), (23, 13), (19, 3), (37, 19), (11, 9), (11, 19), (17, 24), (40, 25), (31, 33), (38, 17), (2, 21), (32, 25), (30, 19), (0, 35), (39, 31), (20, 21), (27, 27), (10, 34), (33, 5), (22, 22), (30, 34), (32, 15), (40, 26), (19, 5), (11, 15), (12, 36), (14, 34), (9, 8), (12, 38), (2, 4), (18, 9), (4, 30), (25, 10), (24, 8), (19, 18), (38, 5), (5, 3), (21, 31), (28, 15), (31, 2), (2, 14), (20, 36), (12, 28), (41, 36), (23, 24), (17, 23), (3, 33), (15, 29), (22, 25), (2, 33), (6, 20), (18, 17), (29, 21), (8, 14), (16, 19), (33, 13), (27, 32), (30, 30), (1, 18), (9, 36), (27, 4), (25, 40), (38, 38), (41, 9), (24, 28), (24, 25), (12, 15), (21, 32), (20, 3), (20, 19), (6, 3), (20, 32), (35, 22), (6, 14), (17, 27), (10, 16), (1, 14), (41, 25), (32, 10), (4, 8), (40, 30), (2, 40), (27, 39), (39, 32), (39, 7), (13, 13), (25, 2), (32, 38), (0, 6), (30, 8), (41, 16), (41, 28), (5, 40), (20, 20), (15, 1), (39, 33), (24, 23), (4, 0), (40, 38), (38, 26), (24, 0), (19, 23), (35, 29), (8, 10), (3, 30), (19, 0), (9, 35), (36, 1), (27, 37), (41, 13), (37, 1), (31, 40), (26, 10), (25, 1), (35, 9), (39, 12), (6, 4), (36, 23), (35, 17), (20, 6), (3, 3), (18, 39), (32, 0), (1, 12), (8, 16), (41, 37), (19, 29), (36, 11), (32, 31), (4, 19), (5, 26), (9, 5), (23, 9), (17, 8), (26, 30), (11, 38), (19, 8), (29, 25), (29, 37), (15, 24), (12, 24), (36, 26), (4, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 17), (40, 3), (31, 22), (11, 21), (32, 3), (41, 1), (45, 29), (22, 1), (8, 19), (29, 11), (43, 20), (25, 24), (31, 46), (10, 36), (41, 32), (33, 31), (14, 21), (23, 16), (32, 5), (30, 4), (20, 2), (40, 33), (26, 11), (12, 22), (34, 45), (33, 35), (35, 35), (34, 36), (23, 45), (34, 27), (14, 3), (8, 46), (15, 22), (32, 25), (11, 14), (31, 30), (32, 46), (34, 31), (17, 19), (12, 25), (2, 2), (20, 5), (31, 34), (23, 5), (32, 38), (7, 21), (9, 46), (4, 37), (8, 28), (39, 0), (30, 7), (24, 33), (25, 35), (1, 25), (5, 11), (31, 11), (29, 31), (8, 13), (4, 18), (30, 0), (23, 22), (34, 40), (39, 2), (36, 18), (26, 29), (6, 6), (34, 24), (45, 21), (37, 40), (19, 39), (32, 4), (14, 1), (7, 9), (44, 19), (37, 28), (5, 29), (20, 9), (18, 10), (34, 33), (3, 41), (9, 43), (7, 1), (30, 41), (3, 1), (28, 3), (5, 42), (19, 0), (44, 24), (13, 33), (39, 14), (41, 31), (34, 9), (42, 14), (29, 14), (39, 32), (2, 22), (11, 43), (17, 5), (20, 29), (25, 26), (31, 40), (3, 27), (33, 27), (26, 20), (12, 8), (26, 17), (17, 46), (5, 40), (1, 16), (27, 20), (8, 2), (0, 31), (7, 26), (43, 8), (3, 24), (32, 2), (1, 26), (24, 14), (31, 23), (33, 17), (43, 39), (6, 21), (45, 7), (28, 11), (18, 6), (21, 45), (8, 43), (16, 11), (41, 7), (19, 46), (16, 19), (2, 9), (15, 8), (15, 26), (43, 30), (33, 3), (26, 2), (11, 7), (10, 0), (11, 24), (20, 38), (23, 18), (18, 19), (9, 31), (14, 19), (40, 45), (23, 36), (28, 12), (9, 19), (26, 8), (41, 4), (37, 22), (23, 42), (31, 25), (18, 23), (42, 3), (35, 8), (27, 45), (21, 18), (7, 11), (42, 41), (25, 0), (3, 14), (16, 0), (8, 5), (41, 34), (14, 8), (7, 12), (7, 4), (31, 26), (34, 32), (12, 35), (1, 17), (42, 1), (38, 35), (43, 23), (39, 45), (20, 15), (29, 15), (37, 2), (10, 23), (31, 1), (29, 42), (35, 24), (2, 19), (5, 9), (4, 8), (20, 24), (5, 43), (33, 37), (41, 20), (33, 46), (7, 7), (13, 46), (24, 9), (37, 38), (4, 16), (32, 0), (17, 16), (43, 16), (18, 20), (17, 11), (17, 15), (3, 13), (15, 11), (0, 38), (16, 40), (36, 12), (40, 41), (25, 40), (43, 15), (44, 12), (6, 36), (15, 45), (3, 45), (30, 25), (18, 0), (18, 29), (38, 20), (6, 3), (16, 45), (42, 15), (11, 34), (40, 34), (18, 39), (42, 42), (43, 42), (20, 3), (18, 43), (12, 5), (43, 41), (2, 35), (12, 1), (35, 16), (12, 10), (45, 14), (43, 5), (28, 18), (24, 38), (24, 34), (20, 28), (44, 28), (36, 9), (12, 6), (35, 40), (17, 41), (21, 28), (24, 26), (30, 36), (25, 21), (7, 18), (21, 14), (15, 1), (33, 38), (25, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 40), (24, 10), (3, 4), (19, 30), (1, 25), (4, 7), (10, 0), (21, 21), (7, 34), (37, 18), (17, 23), (14, 3), (22, 15), (4, 19), (11, 32), (30, 4), (24, 13), (5, 13), (8, 10), (27, 9), (0, 30), (29, 4), (35, 12), (0, 23), (32, 29), (34, 3), (19, 12), (25, 11), (26, 30), (34, 27), (39, 38), (13, 2), (43, 7), (14, 38), (12, 18), (31, 34), (41, 27), (33, 14), (46, 37), (15, 29), (31, 29), (19, 38), (29, 12), (34, 1), (1, 13), (31, 16), (30, 34), (27, 11), (38, 36), (46, 38), (23, 40), (37, 2), (20, 14), (40, 0), (41, 14), (27, 13), (18, 17), (1, 26), (19, 37), (20, 15), (33, 28), (39, 37), (43, 37), (41, 26), (7, 5), (18, 33), (38, 40), (18, 20), (24, 23), (33, 40), (40, 27), (23, 20), (4, 9), (8, 36), (2, 24), (19, 15), (6, 40), (15, 25), (0, 31), (20, 37), (0, 16), (5, 24), (24, 6), (11, 26), (42, 6), (41, 37), (1, 2), (3, 17), (28, 11), (15, 22), (15, 19), (20, 31), (46, 23), (36, 28), (28, 25), (26, 38), (25, 29), (43, 18), (26, 31), (33, 8), (28, 40), (13, 10), (22, 33), (26, 16), (24, 2), (8, 5), (20, 32), (26, 36), (11, 7), (12, 34), (40, 32), (23, 13), (40, 36), (16, 31), (45, 25), (15, 31), (4, 17), (2, 36), (45, 33), (8, 0), (15, 1), (24, 0), (36, 19), (5, 5), (35, 28), (26, 35), (45, 37), (31, 2), (29, 5), (18, 2), (35, 2), (28, 22), (7, 18), (26, 13), (16, 0), (29, 27), (23, 0), (17, 6), (36, 38), (25, 0), (17, 11), (33, 11), (17, 19), (28, 10), (17, 12), (7, 15), (16, 5), (15, 9), (25, 33), (1, 36), (5, 14), (27, 30), (22, 1), (15, 12), (38, 21), (39, 40), (28, 13), (37, 3), (18, 36), (27, 8), (8, 19), (40, 3), (9, 34), (0, 21), (6, 32), (43, 3), (24, 31), (39, 36), (9, 27), (42, 10), (39, 8), (23, 33), (10, 16), (38, 26), (33, 34), (35, 40), (14, 4), (46, 9), (40, 39), (29, 24), (24, 17), (20, 5), (17, 34), (35, 5), (38, 20), (19, 6), (29, 39), (13, 21), (22, 31), (36, 22), (8, 1), (9, 19), (1, 16), (15, 26), (45, 35), (28, 14), (14, 19), (10, 38), (42, 28), (13, 32), (27, 18), (2, 20), (29, 29), (0, 19), (22, 11), (9, 6), (11, 39), (28, 17), (44, 8), (23, 25), (25, 16), (9, 31), (19, 39), (39, 6), (12, 40), (1, 1), (3, 9), (30, 27), (31, 21), (2, 0), (17, 4), (23, 34), (36, 12), (35, 27), (12, 28), (18, 0), (14, 28), (33, 25), (29, 13), (11, 19), (22, 2), (11, 37), (10, 32), (13, 29), (6, 12), (37, 15), (39, 5), (12, 1), (33, 33), (26, 18), (41, 0), (36, 23), (34, 11), (23, 11), (31, 32), (12, 6), (34, 24), (11, 30), (30, 24), (39, 16), (41, 28), (42, 9), (1, 12), (4, 15), (36, 24), (13, 39), (30, 28), (42, 5), (10, 37), (44, 15), (12, 5), (3, 25), (14, 36), (41, 10), (4, 3), (29, 6), (21, 16), (33, 39), (6, 36), (24, 15), (6, 5), (1, 22), (39, 23), (25, 36), (20, 25), (24, 38), (19, 26), (21, 38), (17, 36), (6, 14), (5, 20), (43, 34), (19, 8), (16, 28), (26, 11), (19, 36), (20, 20), (34, 37), (7, 27), (20, 19), (2, 29), (39, 14), (2, 32), (16, 9), (35, 30), (9, 35), (41, 23), (19, 27), (17, 35), (23, 5), (33, 37), (14, 25), (41, 18), (39, 7), (30, 15), (5, 17), (44, 31), (13, 28), (25, 30), (2, 28), (21, 10), (0, 32), (23, 4), (13, 35), (43, 27), (14, 10), (27, 38), (16, 21), (7, 17), (10, 9), (40, 40), (42, 21), (27, 2), (14, 26), (32, 4), (35, 13), (9, 5), (8, 4), (42, 23), (35, 35), (6, 0), (41, 2), (36, 9), (11, 31), (18, 12), (46, 20), (7, 14), (20, 36), (32, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 16), (26, 5), (30, 38), (16, 40), (35, 35), (29, 34), (27, 31), (2, 22), (22, 8), (19, 27), (39, 26), (1, 10), (35, 5), (20, 21), (8, 36), (35, 8), (27, 38), (14, 34), (25, 39), (31, 42), (7, 6), (10, 7), (32, 16), (9, 30), (4, 0), (11, 5), (33, 1), (40, 20), (26, 36), (13, 2), (30, 21), (7, 17), (32, 40), (24, 38), (14, 11), (10, 32), (16, 27), (4, 1), (39, 28), (15, 3), (6, 33), (31, 22), (16, 15), (11, 31), (6, 16), (28, 39), (32, 37), (12, 31), (18, 31), (38, 27), (0, 38), (27, 7), (23, 0), (38, 23), (10, 41), (29, 20), (38, 25), (29, 13), (35, 15), (2, 30), (5, 43), (1, 18), (34, 36), (25, 35), (39, 12), (17, 12), (15, 6), (20, 33), (18, 29), (6, 0), (1, 0), (36, 36), (7, 12), (12, 40), (31, 20), (28, 43), (31, 9), (7, 31), (28, 17), (21, 15), (40, 5), (25, 25), (37, 20), (2, 42), (10, 16), (0, 14), (23, 35), (23, 29), (25, 24), (28, 6), (13, 31), (24, 1), (23, 13), (20, 7), (32, 29), (11, 29), (4, 4), (34, 23), (18, 11), (3, 38), (34, 13), (20, 3), (14, 41), (36, 25), (36, 43), (13, 8), (29, 18), (28, 8), (37, 10), (20, 15), (30, 24), (37, 1), (13, 19), (22, 32), (16, 20), (0, 43), (30, 1), (22, 28), (15, 12), (22, 27), (10, 6), (36, 16), (13, 18), (5, 7), (33, 25), (36, 35), (33, 34), (1, 31), (0, 29), (24, 13), (18, 19), (15, 10), (5, 38), (33, 9), (7, 20), (8, 25), (35, 41), (34, 37), (17, 36), (18, 13), (4, 31), (5, 25), (0, 26), (9, 15), (24, 42), (21, 40), (6, 30), (17, 40), (7, 23), (36, 31), (26, 41), (14, 15), (30, 22), (13, 6), (33, 41), (15, 42), (5, 13), (37, 14), (7, 0), (14, 8), (16, 29), (27, 41), (16, 21), (3, 28), (10, 27), (12, 27), (26, 42), (36, 23), (14, 1), (26, 38), (16, 37), (28, 26), (32, 20), (0, 6), (11, 35), (3, 41), (29, 17), (0, 15), (16, 2), (2, 5), (5, 35), (10, 24), (32, 5), (8, 10), (8, 43), (15, 36), (15, 30), (26, 30), (38, 13), (0, 17), (39, 38), (39, 42), (11, 11), (32, 33), (19, 2), (7, 35), (38, 26), (35, 17), (12, 1), (22, 21), (15, 19), (3, 5), (39, 25), (33, 32), (33, 31), (2, 16), (25, 31), (23, 40), (10, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (15, 17), (35, 22), (14, 5), (11, 10), (24, 28), (2, 25), (35, 21), (36, 23), (30, 23), (35, 20), (37, 32), (21, 1), (22, 2), (2, 17), (10, 3), (18, 38), (15, 37), (0, 22), (11, 45), (11, 43), (21, 26), (37, 33), (20, 31), (27, 37), (7, 14), (0, 36), (8, 19), (16, 41), (1, 23), (21, 16), (10, 26), (17, 16), (35, 23), (21, 22), (15, 35), (4, 41), (15, 1), (26, 27), (27, 43), (36, 4), (12, 27), (20, 20), (36, 8), (10, 25), (24, 33), (22, 42), (1, 38), (20, 14), (0, 35), (30, 16), (36, 34), (16, 11), (0, 17), (1, 18), (25, 0), (9, 36), (1, 40), (13, 10), (15, 38), (24, 16), (33, 7), (13, 13), (17, 26), (17, 35), (25, 40), (37, 42), (9, 10), (37, 47), (4, 43), (21, 36), (39, 10), (21, 42), (38, 43), (29, 10), (27, 18), (34, 13), (10, 36), (2, 45), (16, 9), (16, 14), (30, 2), (29, 1), (4, 27), (17, 11), (23, 35), (17, 8), (34, 23), (5, 7), (29, 9), (7, 9), (14, 29), (13, 27), (1, 32), (21, 28), (9, 6), (22, 13), (8, 42), (37, 10), (21, 0), (38, 34), (17, 38), (25, 11), (24, 38), (21, 17), (16, 45), (29, 18), (16, 4), (39, 13), (33, 27), (10, 42), (4, 23), (36, 30), (18, 43), (22, 23), (21, 29), (32, 7), (1, 45), (13, 43), (25, 23), (20, 43), (37, 3), (34, 36), (14, 37), (34, 40), (0, 24), (38, 35), (30, 35), (3, 47), (31, 6), (20, 37), (22, 31), (6, 47), (38, 33), (14, 46), (7, 18), (24, 22), (5, 0), (30, 6), (16, 15), (27, 36), (10, 41), (19, 30), (11, 31), (4, 1), (4, 5), (26, 16), (22, 14), (35, 9), (21, 10), (38, 9), (27, 17), (8, 40), (5, 34), (33, 14), (37, 26), (31, 17), (3, 12), (33, 43), (18, 22), (12, 12), (2, 4), (29, 22), (16, 40), (32, 21), (29, 40), (0, 16), (12, 26), (7, 41), (15, 21), (17, 23), (1, 19), (11, 4), (16, 8), (33, 20), (16, 42), (5, 8), (25, 24), (4, 3), (5, 11), (14, 19), (24, 0), (19, 5), (1, 11), (6, 26), (15, 40), (11, 1), (37, 40), (26, 4), (7, 17), (3, 9), (28, 21), (4, 46), (4, 24), (10, 24), (11, 2), (21, 18), (18, 7), (36, 1), (5, 45), (14, 30), (32, 29), (34, 45), (3, 8), (17, 46), (14, 31), (9, 19), (4, 9), (18, 41), (32, 19), (13, 44), (0, 13), (13, 23), (9, 30), (29, 4), (32, 13), (17, 15), (32, 17), (26, 45), (25, 12), (18, 15), (7, 4), (20, 38), (8, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 1), (39, 18), (0, 25), (2, 13), (25, 21), (34, 4), (9, 2), (28, 32), (33, 2), (30, 22), (5, 29), (23, 2), (38, 10), (34, 35), (14, 6), (38, 29), (14, 4), (1, 37), (10, 20), (12, 31), (30, 0), (6, 26), (40, 16), (18, 17), (32, 18), (33, 22), (41, 20), (24, 8), (35, 0), (25, 10), (14, 40), (22, 20), (28, 34), (29, 25), (7, 39), (10, 29), (24, 10), (16, 36), (1, 1), (20, 30), (13, 9), (5, 36), (17, 10), (41, 28), (27, 4), (5, 32), (37, 26), (14, 20), (41, 6), (42, 0), (1, 23), (5, 16), (31, 4), (35, 3), (26, 20), (23, 36), (19, 13), (0, 26), (34, 11), (30, 20), (19, 30), (13, 40), (16, 11), (20, 28), (34, 16), (37, 41), (10, 7), (2, 8), (22, 5), (5, 5), (36, 39), (0, 37), (31, 20), (27, 10), (26, 39), (39, 34), (6, 16), (14, 38), (23, 40), (41, 31), (2, 26), (26, 21), (40, 14), (10, 6), (13, 27), (24, 9), (26, 41), (33, 36), (21, 29), (3, 40), (39, 36), (21, 24), (20, 3), (13, 23), (2, 41), (18, 33), (23, 4), (5, 3), (39, 11), (17, 28), (9, 0), (35, 34), (28, 28), (21, 10), (30, 10), (22, 31), (28, 38), (35, 16), (40, 20), (15, 19), (40, 13), (6, 19), (8, 35), (27, 34), (7, 30), (40, 4), (40, 9), (3, 3), (41, 39), (34, 33), (41, 16), (30, 17), (34, 30), (34, 6), (6, 22), (42, 21), (20, 31), (13, 22), (26, 40), (32, 24), (9, 15), (1, 34), (18, 32), (21, 39), (31, 41), (0, 6), (22, 3), (8, 21), (17, 38), (10, 4), (42, 10), (8, 4), (39, 12), (19, 0), (0, 27), (11, 40), (36, 15), (6, 4), (13, 39), (38, 22), (16, 34), (37, 13), (15, 14), (24, 28), (5, 31), (13, 34), (17, 25), (35, 33), (1, 39), (37, 21), (10, 34), (8, 18), (12, 14), (37, 36), (42, 32), (9, 14), (5, 41), (23, 8), (3, 17), (30, 8), (10, 9), (35, 37), (4, 25), (27, 6), (1, 5), (33, 11), (13, 17), (26, 0), (11, 21), (23, 23), (19, 33), (34, 3), (33, 33), (35, 23), (3, 12), (8, 34), (30, 18), (6, 14), (5, 13), (15, 15), (28, 36), (40, 28), (31, 38), (42, 17), (34, 15), (35, 26), (19, 34), (22, 37), (35, 27), (11, 31), (16, 19), (0, 10), (34, 40), (15, 26), (36, 29), (17, 18), (6, 18), (41, 35), (7, 20), (3, 16), (2, 4), (40, 17), (9, 13), (23, 24), (32, 20), (39, 3), (4, 38), (9, 4), (23, 1), (9, 26), (4, 28), (22, 40), (40, 10), (7, 5), (20, 16), (14, 3), (19, 20), (32, 17), (25, 28), (17, 6), (21, 2), (12, 0), (42, 29), (16, 39), (14, 34), (23, 18), (15, 39), (36, 21), (1, 40), (19, 7), (35, 15), (4, 35), (8, 26), (8, 32), (37, 10), (32, 41), (34, 22), (25, 7), (4, 1), (42, 23), (7, 2), (16, 38), (28, 40), (18, 0), (4, 12), (8, 3), (10, 33), (39, 6), (4, 17), (34, 37), (19, 8), (26, 16), (30, 29), (20, 7), (18, 2), (15, 28), (38, 25), (1, 38), (18, 11), (10, 27), (38, 5), (15, 27), (27, 1), (25, 38), (13, 31), (1, 15), (25, 23), (31, 31), (7, 16), (3, 0), (25, 3), (41, 24), (20, 25), (38, 40), (2, 11), (40, 19), (41, 12), (40, 0), (17, 9), (32, 16), (37, 18), (13, 28), (21, 5), (5, 4), (29, 22), (24, 23), (27, 24), (11, 41), (36, 22), (17, 24), (19, 15), (9, 32), (39, 5), (36, 19), (28, 2), (27, 28), (5, 9), (13, 5), (42, 1), (15, 40), (8, 15), (6, 24), (40, 26), (17, 29), (23, 5), (12, 24), (31, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 33), (9, 21), (34, 20), (8, 36), (3, 24), (37, 7), (11, 9), (15, 15), (25, 10), (31, 29), (33, 35), (36, 20), (5, 13), (32, 12), (25, 25), (38, 29), (9, 39), (39, 15), (39, 10), (18, 21), (41, 34), (32, 19), (30, 35), (26, 29), (40, 34), (37, 32), (23, 12), (18, 7), (0, 29), (35, 29), (34, 10), (20, 16), (12, 16), (26, 25), (14, 20), (37, 30), (22, 26), (32, 15), (15, 20), (2, 34), (23, 9), (12, 31), (16, 27), (33, 0), (19, 7), (26, 0), (13, 40), (13, 6), (1, 15), (24, 0), (31, 5), (37, 0), (4, 5), (38, 36), (1, 8), (0, 3), (3, 33), (10, 13), (22, 34), (35, 3), (18, 11), (23, 8), (38, 18), (27, 18), (7, 21), (14, 25), (14, 0), (36, 39), (16, 23), (24, 13), (6, 10), (9, 34), (42, 33), (17, 30), (1, 2), (3, 42), (13, 26), (14, 11), (6, 35), (30, 13), (14, 38), (20, 15), (5, 30), (34, 4), (30, 28), (11, 35), (15, 25), (19, 15), (18, 28), (33, 32), (41, 36), (16, 3), (40, 28), (18, 0), (30, 6), (26, 31), (13, 20), (21, 25), (11, 23), (27, 27), (15, 22), (20, 40), (7, 0), (27, 16), (11, 20), (36, 40), (4, 39), (12, 27), (8, 9), (11, 42), (21, 15), (9, 10), (39, 7), (15, 19), (34, 19), (12, 41), (33, 7), (5, 22), (40, 31), (18, 1), (38, 33), (19, 2), (12, 2), (10, 21), (26, 3), (31, 43), (17, 33), (21, 9), (41, 12), (8, 15), (36, 14), (29, 43), (6, 22), (14, 41), (30, 41), (36, 2), (21, 11), (15, 37), (3, 14), (33, 14), (14, 39), (16, 6), (3, 8), (42, 42), (31, 17), (14, 29), (34, 22), (8, 22), (19, 23), (5, 33), (6, 2), (1, 3), (32, 0), (24, 8), (17, 9), (29, 14), (32, 38), (20, 22), (12, 21), (11, 11), (34, 23), (34, 5), (15, 13), (28, 32), (11, 31), (7, 23), (6, 3), (10, 42), (26, 2), (24, 11), (10, 31), (15, 31), (17, 34), (12, 22), (11, 22), (12, 43), (22, 21), (0, 27), (7, 31), (16, 17), (21, 22), (15, 35), (0, 33), (32, 36), (36, 4), (21, 3), (35, 25), (32, 32), (6, 4), (11, 40), (8, 12), (16, 20), (35, 28), (7, 20), (1, 40), (4, 20), (29, 13), (2, 4), (19, 3), (30, 8), (23, 3), (29, 37), (16, 40), (12, 23), (3, 21), (32, 5), (19, 37), (0, 38), (0, 10), (4, 33), (39, 19), (14, 6), (1, 34), (32, 31), (18, 2), (28, 37), (17, 6), (24, 16), (17, 37), (7, 32), (14, 30), (24, 36), (3, 7), (5, 0), (31, 9), (40, 11), (22, 14), (38, 10), (40, 16), (27, 39), (7, 27), (14, 27), (9, 38), (2, 8), (6, 20), (12, 11), (5, 24), (6, 6), (33, 5), (5, 20), (24, 25), (15, 12), (38, 38), (37, 20), (37, 21), (37, 34), (29, 24), (30, 32), (23, 26), (28, 24), (24, 29), (34, 36), (32, 3), (9, 13), (15, 10), (33, 13), (2, 19), (4, 15), (20, 6), (34, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 31), (0, 19), (6, 11), (12, 3), (6, 2), (39, 13), (29, 12), (9, 6), (22, 19), (22, 26), (8, 29), (1, 0), (22, 42), (30, 21), (1, 11), (24, 5), (32, 39), (10, 2), (12, 0), (44, 16), (3, 6), (10, 7), (39, 38), (7, 30), (9, 16), (16, 18), (38, 39), (20, 20), (42, 1), (7, 39), (2, 10), (42, 29), (18, 41), (13, 35), (28, 6), (44, 4), (18, 5), (43, 33), (8, 1), (5, 35), (38, 36), (5, 22), (2, 15), (39, 19), (42, 19), (26, 1), (37, 40), (23, 36), (39, 9), (11, 25), (34, 35), (26, 25), (20, 5), (1, 3), (36, 33), (30, 8), (31, 29), (37, 36), (42, 41), (25, 37), (31, 2), (37, 19), (13, 18), (9, 24), (23, 2), (19, 35), (11, 42), (31, 31), (6, 15), (12, 36), (28, 33), (6, 5), (31, 19), (27, 9), (16, 15), (30, 10), (32, 41), (15, 42), (35, 14), (40, 19), (44, 10), (9, 36), (39, 5), (21, 4), (24, 13), (26, 16), (35, 11), (31, 9), (24, 23), (5, 3), (10, 34), (39, 11), (15, 13), (35, 29), (19, 26), (39, 23), (13, 16), (33, 10), (28, 34), (14, 35), (11, 41), (30, 18), (38, 17), (3, 34), (26, 35), (9, 37), (41, 42), (21, 23), (13, 6), (40, 27), (3, 4), (35, 28), (25, 17), (11, 35), (34, 40), (6, 42), (42, 5), (19, 34), (44, 24), (16, 34), (43, 40), (4, 40), (25, 27), (27, 10), (18, 15), (2, 19), (42, 12), (42, 38), (14, 31), (40, 36), (35, 0), (31, 36), (4, 13), (38, 1), (37, 21), (21, 10), (14, 19), (8, 24), (5, 27), (2, 29), (13, 23), (12, 24), (42, 3), (16, 36), (39, 35), (9, 11), (24, 30), (35, 42), (41, 16), (18, 13), (8, 27), (36, 0), (41, 35), (6, 32), (40, 18), (26, 20), (35, 16), (33, 39), (27, 20), (15, 35), (23, 30), (43, 21), (33, 14), (6, 24), (13, 33), (7, 33), (3, 19), (3, 21), (36, 39), (9, 28), (34, 13), (32, 27), (0, 27), (19, 17), (16, 39), (42, 8), (9, 18), (11, 31), (17, 31), (8, 38), (24, 42), (38, 34), (8, 10), (0, 28), (38, 16), (15, 32), (27, 27), (29, 35), (10, 31), (25, 29), (23, 13), (35, 31), (32, 30), (34, 33), (27, 34), (31, 38), (31, 4), (2, 13), (42, 23), (40, 12), (26, 6), (37, 17), (32, 13), (10, 24), (7, 15), (19, 2), (8, 6), (18, 6), (10, 30), (38, 14), (6, 1), (22, 2), (17, 13), (32, 36), (33, 3), (18, 23), (38, 26), (22, 10), (15, 19), (25, 12), (25, 13), (21, 34), (27, 0), (10, 17), (40, 38), (11, 29), (38, 8), (31, 42), (4, 22), (23, 11), (17, 27), (31, 3), (10, 37), (42, 40), (14, 23), (34, 22), (44, 32), (38, 28), (35, 32), (23, 22), (20, 24), (12, 34), (41, 9), (14, 27), (9, 8), (18, 16), (44, 38), (2, 38), (12, 11), (16, 28), (1, 8), (26, 19), (8, 39), (10, 20), (27, 19), (41, 18), (24, 8), (15, 10), (3, 3), (33, 36), (42, 21), (3, 41), (12, 21), (11, 0), (7, 0), (30, 2), (13, 1), (40, 40), (7, 28), (15, 18), (3, 23), (30, 38), (34, 19), (2, 18), (27, 17), (29, 20), (13, 12), (39, 10), (22, 8), (0, 9), (14, 15), (32, 29), (26, 29), (36, 8), (40, 29), (12, 14), (6, 18), (0, 24), (2, 25), (23, 37), (43, 41), (26, 32), (34, 39), (5, 40), (12, 17), (26, 31), (11, 2), (22, 18), (32, 12), (19, 0), (43, 27), (5, 34), (37, 24), (29, 2), (37, 31), (32, 37), (8, 35), (2, 7), (31, 25), (26, 2), (37, 35), (26, 26), (24, 14), (18, 36), (40, 31), (22, 31), (35, 17), (21, 6), (15, 9), (7, 2), (22, 0), (41, 0), (32, 6), (31, 17), (39, 31), (32, 25), (41, 19), (28, 40), (25, 3), (18, 10), (40, 7), (11, 40), (41, 23), (28, 20), (22, 4), (32, 7), (14, 34), (44, 17), (15, 6), (25, 21), (17, 10), (40, 14), (20, 14), (17, 15), (41, 17), (16, 5), (32, 26), (5, 38), (34, 20), (35, 33), (35, 24), (9, 14), (12, 5), (18, 22), (20, 18), (17, 9), (5, 2), (24, 40), (31, 7), (24, 29), (36, 34), (9, 1), (37, 22), (38, 10), (25, 33), (16, 2), (31, 34), (33, 4), (35, 5), (13, 24), (36, 16), (18, 39), (25, 0), (5, 6), (0, 11), (32, 34), (17, 11), (0, 13), (17, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 25), (33, 27), (34, 5), (7, 17), (14, 13), (11, 24), (4, 29), (41, 19), (14, 22), (3, 9), (20, 37), (4, 6), (37, 10), (34, 41), (22, 18), (34, 24), (19, 44), (4, 22), (12, 11), (15, 7), (34, 23), (40, 4), (17, 34), (35, 29), (4, 34), (13, 9), (33, 21), (41, 43), (8, 18), (39, 5), (20, 27), (34, 43), (5, 42), (12, 34), (35, 38), (3, 34), (15, 33), (3, 43), (38, 20), (31, 2), (26, 3), (31, 0), (25, 22), (30, 2), (25, 11), (31, 30), (37, 19), (33, 6), (13, 6), (37, 18), (38, 6), (11, 26), (25, 16), (25, 6), (11, 45), (36, 10), (20, 39), (24, 43), (33, 4), (0, 33), (28, 36), (25, 42), (29, 30), (18, 23), (0, 3), (21, 27), (21, 9), (11, 6), (1, 30), (31, 46), (11, 9), (15, 26), (30, 10), (27, 26), (19, 11), (17, 37), (9, 23), (31, 34), (32, 31), (28, 1), (13, 21), (19, 14), (38, 45), (6, 35), (27, 12), (7, 26), (33, 9), (6, 45), (27, 30), (12, 3), (29, 0), (10, 8), (23, 28), (39, 31), (20, 40), (32, 24), (29, 13), (17, 30), (20, 44), (32, 25), (37, 8), (9, 28), (24, 45), (19, 19), (34, 7), (28, 29), (5, 3), (33, 33), (35, 11), (41, 27), (37, 43), (38, 32), (2, 34), (18, 2), (15, 20), (0, 34), (10, 28), (28, 39), (13, 16), (30, 3), (4, 32), (0, 31), (22, 6), (15, 19), (4, 11), (10, 4), (30, 7), (26, 17), (1, 4), (9, 29), (35, 34), (35, 40), (32, 15), (41, 45), (37, 23), (40, 34), (12, 16), (12, 44), (23, 22), (40, 35), (25, 2), (9, 6), (35, 32), (7, 24), (1, 27), (28, 46), (15, 2), (21, 30), (28, 0), (6, 36), (33, 46), (32, 14), (7, 3), (19, 15), (24, 46), (39, 43), (14, 19), (35, 30), (7, 37), (0, 38), (26, 28), (8, 24), (26, 1), (39, 33), (39, 30), (13, 41), (31, 12), (36, 23), (3, 13), (31, 16), (4, 8), (1, 35), (16, 24), (19, 7), (6, 40), (20, 20), (30, 29), (20, 10), (40, 28), (30, 8), (21, 14), (11, 17), (22, 41), (2, 10), (1, 32), (31, 21), (17, 26), (27, 10), (37, 28), (41, 44), (23, 7), (15, 45), (20, 45), (5, 22), (29, 12), (9, 32), (1, 22), (33, 44), (21, 23), (5, 20), (5, 2), (19, 43), (33, 36), (28, 42), (12, 21), (1, 36), (6, 8), (17, 42), (27, 16), (17, 31), (12, 40), (0, 41), (20, 14), (19, 21), (16, 40), (1, 7), (23, 30), (20, 5), (31, 31), (17, 38), (37, 35), (14, 8), (15, 39), (32, 3), (26, 9), (29, 37), (41, 41), (9, 1), (39, 17), (13, 3), (5, 36), (39, 27), (21, 29), (12, 39), (32, 40), (13, 35), (14, 10), (19, 5), (6, 37), (5, 30), (13, 30), (10, 0), (18, 34), (28, 43), (38, 31), (13, 4), (30, 46), (30, 16), (41, 2), (8, 10), (18, 27), (10, 25), (17, 8), (35, 0), (24, 17), (16, 41), (13, 27), (3, 2), (16, 31), (22, 42), (21, 5), (19, 3), (39, 26), (11, 43), (10, 34), (30, 4), (34, 46), (6, 10), (20, 35), (21, 40), (39, 29), (20, 43), (39, 6), (9, 46), (29, 21), (30, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 7), (19, 16), (1, 15), (38, 16), (31, 36), (19, 31), (13, 40), (28, 11), (17, 38), (13, 5), (44, 10), (23, 1), (3, 24), (18, 27), (0, 22), (34, 25), (33, 23), (13, 39), (18, 38), (33, 28), (25, 37), (7, 21), (19, 13), (8, 40), (17, 5), (20, 5), (8, 33), (4, 32), (28, 5), (31, 12), (2, 5), (38, 12), (39, 21), (44, 35), (9, 33), (20, 7), (2, 24), (30, 4), (20, 1), (43, 3), (2, 6), (17, 32), (33, 7), (4, 21), (0, 27), (11, 29), (23, 18), (27, 35), (6, 1), (35, 24), (26, 39), (21, 39), (30, 13), (44, 40), (41, 25), (35, 34), (38, 29), (44, 11), (4, 17), (6, 21), (7, 37), (18, 9), (24, 8), (37, 6), (25, 27), (37, 1), (37, 16), (43, 40), (28, 6), (26, 2), (37, 40), (33, 11), (17, 1), (16, 37), (23, 35), (14, 39), (16, 40), (23, 15), (20, 40), (35, 4), (7, 3), (6, 38), (21, 19), (11, 11), (37, 7), (40, 4), (16, 29), (3, 3), (26, 3), (45, 31), (7, 4), (38, 17), (5, 2), (43, 22), (4, 24), (26, 7), (4, 16), (33, 1), (11, 28), (16, 38), (4, 0), (10, 13), (2, 19), (19, 10), (44, 16), (15, 23), (24, 18), (45, 36), (22, 17), (42, 21), (22, 14), (30, 11), (29, 37), (29, 12), (22, 27), (11, 16), (6, 35), (17, 16), (4, 11), (14, 34), (4, 23), (11, 33), (2, 23), (29, 5), (16, 21), (14, 22), (8, 39), (31, 14), (22, 3), (40, 36), (23, 28), (33, 24), (22, 30), (35, 36), (12, 36), (35, 37), (37, 20), (21, 13), (39, 22), (13, 26), (5, 38), (41, 37), (34, 22), (10, 0), (0, 11), (44, 29), (9, 1), (7, 7), (24, 25), (43, 19), (36, 8), (13, 0), (0, 9), (4, 14), (35, 3), (4, 5), (38, 25), (34, 38), (45, 25), (18, 35), (32, 33), (31, 22), (6, 11), (25, 12), (33, 5), (19, 29), (30, 40), (36, 22), (3, 8), (28, 12), (8, 31), (17, 25), (10, 12), (2, 28), (36, 33), (33, 3), (14, 31), (14, 1), (25, 23), (32, 39), (44, 7), (29, 39), (14, 13), (7, 25), (33, 36), (21, 29), (22, 28), (21, 11), (27, 21), (44, 9), (9, 5), (0, 38), (26, 24), (14, 14), (2, 33), (11, 26), (37, 0), (12, 18), (17, 31), (35, 16), (41, 18), (45, 17), (20, 36), (21, 7), (16, 14), (25, 1), (30, 27), (8, 28), (43, 32), (33, 33), (19, 27), (40, 11), (34, 15), (12, 37), (10, 23), (42, 24), (12, 21), (10, 9), (31, 8), (13, 6), (11, 20), (21, 16), (35, 18), (42, 38), (5, 37), (43, 5), (14, 5), (31, 0), (29, 36), (36, 27), (39, 10), (39, 28), (16, 27), (24, 20), (31, 27), (30, 33), (32, 31), (41, 31), (19, 28), (25, 28), (23, 36), (18, 26), (36, 30), (42, 15), (19, 40), (20, 0), (43, 15), (0, 25), (15, 14), (19, 34), (31, 23), (7, 34), (0, 21), (35, 25), (35, 23), (28, 38), (18, 33), (3, 9), (1, 9), (1, 7), (33, 19), (18, 18), (22, 34), (31, 21), (31, 2), (45, 24), (1, 8), (4, 30), (13, 14), (20, 33), (3, 39), (31, 4), (33, 25), (5, 4), (45, 2), (26, 27), (42, 25), (7, 0), (7, 9), (25, 36), (4, 20), (34, 8), (42, 10), (28, 21), (43, 37), (2, 15), (9, 19), (9, 0), (2, 27), (40, 20), (45, 1), (6, 33), (34, 1), (18, 1), (18, 4), (1, 33), (19, 18), (44, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 39), (25, 42), (7, 18), (34, 8), (12, 20), (41, 12), (18, 17), (28, 44), (1, 28), (19, 43), (39, 6), (12, 14), (9, 11), (18, 6), (2, 26), (14, 40), (18, 36), (23, 40), (30, 41), (38, 22), (32, 44), (33, 9), (11, 14), (20, 9), (5, 5), (30, 13), (4, 30), (13, 40), (6, 44), (34, 10), (16, 21), (6, 38), (3, 28), (26, 19), (31, 33), (36, 27), (35, 32), (10, 17), (33, 25), (22, 35), (36, 8), (30, 20), (6, 18), (23, 37), (9, 34), (1, 31), (44, 2), (22, 10), (22, 24), (35, 3), (44, 36), (22, 9), (8, 29), (23, 13), (28, 24), (40, 34), (44, 35), (15, 28), (28, 1), (12, 2), (28, 13), (14, 10), (28, 3), (17, 37), (27, 11), (16, 13), (20, 39), (38, 29), (30, 26), (11, 27), (27, 2), (11, 31), (41, 6), (0, 15), (7, 28), (4, 19), (37, 10), (10, 27), (40, 20), (4, 32), (15, 25), (10, 11), (8, 19), (40, 3), (1, 24), (23, 6), (7, 29), (21, 5), (0, 21), (7, 20), (30, 36), (25, 12), (21, 4), (14, 1), (37, 0), (28, 32), (44, 14), (41, 33), (38, 2), (35, 13), (16, 16), (12, 19), (22, 31), (5, 43), (26, 13), (1, 44), (2, 11), (9, 17), (20, 17), (21, 26), (21, 13), (44, 12), (17, 1), (41, 22), (13, 38), (22, 44), (44, 3), (11, 20), (30, 6), (11, 44), (14, 43), (22, 39), (28, 8), (20, 3), (10, 34), (10, 16), (33, 18), (28, 34), (15, 44), (29, 28), (6, 32), (23, 15), (33, 32), (31, 21), (36, 28), (22, 8), (13, 16), (42, 10), (28, 17), (2, 21), (25, 28), (17, 34), (27, 10), (41, 36), (10, 10), (29, 31), (43, 25), (43, 21), (33, 34), (43, 28), (9, 40), (33, 17), (41, 32), (21, 28), (13, 20), (22, 25), (41, 43), (40, 44), (6, 6), (28, 0), (13, 13), (39, 19), (7, 1), (14, 5), (26, 10), (2, 7), (24, 36), (17, 16), (44, 30), (37, 23), (4, 38), (23, 32), (36, 37), (6, 25), (30, 18), (32, 36), (31, 13), (42, 29), (11, 30), (44, 17), (22, 27), (21, 23), (8, 24), (4, 31), (20, 36), (16, 3), (19, 25), (12, 9), (15, 35), (8, 18), (40, 1), (30, 16), (5, 44), (32, 9), (8, 16), (11, 40), (14, 2), (20, 38), (18, 39), (44, 22), (4, 23), (11, 39), (27, 41), (13, 8), (0, 29), (44, 19), (1, 37), (36, 31), (4, 24), (43, 36), (17, 33), (14, 24), (40, 13), (0, 38), (9, 4), (3, 20), (24, 40), (31, 16), (17, 29), (41, 34), (32, 43), (25, 0), (8, 3), (16, 34), (21, 42), (29, 43), (43, 34), (7, 11), (20, 6), (33, 26), (34, 25), (7, 33), (22, 22), (0, 10), (14, 15), (16, 27), (21, 22), (20, 1), (40, 33), (1, 39), (5, 18), (41, 40), (43, 26), (30, 28), (28, 41), (9, 18), (43, 23), (31, 35), (11, 37), (36, 22), (27, 13), (2, 32), (28, 20), (35, 44), (35, 8), (35, 6), (38, 25), (2, 19), (42, 28), (16, 38), (43, 15), (34, 40), (6, 12), (6, 16), (6, 23), (18, 5), (25, 44), (32, 0), (29, 25), (36, 26), (28, 19), (25, 10), (15, 42), (41, 10), (25, 43), (5, 35), (21, 8), (29, 13), (9, 28), (27, 12), (21, 1), (2, 0), (22, 43), (4, 22), (40, 42), (5, 16), (37, 37), (37, 34), (2, 28), (0, 28), (4, 15), (35, 39), (22, 6), (32, 11), (15, 22), (20, 0), (11, 12), (34, 43), (32, 20), (42, 20), (31, 24), (41, 14), (31, 17), (8, 27), (37, 43), (8, 40), (25, 36), (8, 28), (42, 15), (26, 27), (5, 42), (36, 30), (24, 12), (36, 3), (17, 4), (28, 10), (16, 20), (2, 13), (15, 8), (5, 20), (18, 16), (4, 4), (29, 3), (24, 5), (20, 2), (37, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 7), (0, 3), (3, 19), (33, 14), (9, 1), (20, 10), (26, 22), (3, 41), (16, 43), (2, 0), (13, 44), (32, 21), (21, 1), (5, 9), (28, 42), (32, 40), (20, 36), (38, 34), (0, 11), (27, 26), (26, 20), (5, 4), (38, 1), (34, 9), (28, 43), (26, 23), (29, 39), (27, 33), (32, 9), (14, 20), (6, 11), (10, 35), (16, 5), (21, 35), (4, 13), (10, 34), (37, 24), (9, 17), (21, 6), (8, 41), (3, 2), (20, 16), (34, 38), (37, 5), (29, 41), (18, 18), (14, 23), (9, 30), (2, 7), (35, 20), (37, 39), (11, 25), (32, 41), (36, 27), (6, 44), (2, 27), (32, 8), (12, 23), (19, 38), (2, 2), (3, 40), (36, 22), (35, 1), (23, 34), (39, 12), (20, 37), (35, 12), (8, 37), (8, 3), (12, 11), (13, 38), (30, 11), (5, 19), (12, 36), (35, 37), (0, 24), (22, 21), (24, 6), (5, 25), (2, 39), (31, 5), (2, 3), (24, 2), (35, 28), (30, 3), (0, 4), (24, 23), (3, 0), (33, 4), (2, 8), (14, 18), (29, 8), (7, 38), (5, 28), (37, 7), (33, 34), (38, 12), (17, 6), (10, 0), (2, 33), (13, 22), (17, 13), (38, 31), (10, 28), (39, 26), (17, 36), (18, 3), (15, 11), (24, 30), (16, 32), (12, 9), (27, 12), (6, 20), (18, 40), (8, 35), (6, 32), (25, 23), (4, 27), (24, 19), (17, 5), (9, 44), (35, 35), (26, 29), (4, 40), (37, 36), (1, 21), (1, 7), (8, 10), (25, 16), (2, 12), (18, 23), (39, 20), (22, 4), (33, 20), (30, 44), (25, 17), (14, 13), (24, 40), (2, 44), (20, 26), (11, 4), (18, 37), (39, 22), (0, 1), (17, 19), (7, 13), (29, 31), (18, 17), (39, 2), (30, 25), (37, 20), (21, 26), (16, 35), (12, 8), (36, 42), (15, 10), (6, 30), (14, 30), (7, 22), (7, 6), (7, 35), (22, 36), (17, 20), (17, 14), (17, 1), (6, 33), (8, 33), (20, 32), (17, 29), (38, 9), (11, 35), (19, 28), (38, 41), (5, 32), (2, 30), (27, 39), (12, 28), (24, 16), (37, 11), (27, 32), (9, 40), (38, 38), (25, 39), (32, 6), (8, 23), (28, 12), (7, 31), (12, 38), (32, 11), (15, 34), (7, 30), (8, 24), (11, 7), (24, 18), (3, 18), (19, 20), (30, 7), (31, 2), (8, 16), (14, 39), (35, 27), (4, 33), (16, 11), (31, 25), (23, 16), (24, 15), (29, 38), (38, 28), (37, 9), (16, 24), (18, 29), (1, 17), (14, 34), (10, 27), (32, 26), (0, 42), (39, 11), (33, 1), (33, 6), (15, 26), (4, 14), (22, 6), (28, 5), (30, 16), (12, 37), (7, 33), (0, 33), (2, 32), (15, 37), (23, 20), (16, 23), (9, 39), (7, 23), (13, 5), (8, 22), (28, 26), (9, 22), (28, 44), (11, 36), (23, 15), (14, 19), (1, 38), (15, 7), (15, 18), (6, 0), (30, 37), (23, 29), (12, 6), (34, 11), (31, 32), (29, 28), (37, 22), (33, 36), (31, 16), (15, 16), (13, 29), (30, 24), (20, 14), (30, 23), (6, 3), (5, 38), (31, 12), (20, 11), (8, 11), (13, 1), (4, 3), (7, 26), (11, 17), (13, 3), (19, 32), (35, 31), (15, 3), (27, 31), (15, 6), (16, 7), (0, 16), (25, 8), (38, 43), (8, 39), (28, 9), (39, 1), (21, 27), (1, 22), (23, 31), (21, 44), (24, 13), (21, 28), (12, 32), (0, 5), (20, 23), (13, 25), (17, 35), (9, 12), (16, 6), (15, 14), (25, 3), (9, 13), (38, 42), (0, 21), (8, 27), (32, 28), (22, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 33), (5, 24), (9, 5), (9, 30), (27, 29), (15, 35), (39, 33), (21, 0), (1, 16), (2, 40), (32, 13), (33, 39), (41, 5), (43, 34), (42, 40), (36, 11), (25, 2), (14, 33), (13, 2), (32, 2), (38, 15), (40, 25), (14, 6), (40, 11), (25, 32), (23, 23), (22, 14), (8, 0), (7, 40), (24, 33), (36, 32), (39, 7), (28, 32), (27, 0), (8, 7), (23, 12), (15, 2), (29, 12), (11, 2), (9, 33), (27, 20), (1, 1), (43, 32), (5, 39), (14, 36), (2, 30), (34, 21), (30, 38), (7, 21), (38, 16), (12, 29), (6, 27), (26, 2), (21, 2), (30, 27), (18, 29), (33, 3), (26, 34), (20, 1), (37, 16), (12, 17), (14, 32), (25, 3), (9, 8), (2, 6), (24, 17), (42, 12), (15, 36), (26, 17), (0, 16), (35, 0), (21, 7), (12, 19), (31, 16), (17, 31), (28, 31), (20, 2), (27, 36), (6, 20), (13, 6), (2, 37), (23, 36), (15, 4), (5, 4), (39, 8), (41, 16), (32, 32), (8, 24), (2, 14), (17, 4), (17, 36), (15, 12), (14, 9), (19, 21), (21, 12), (36, 0), (35, 28), (38, 5), (4, 21), (41, 2), (34, 1), (19, 3), (10, 0), (42, 33), (32, 38), (18, 1), (33, 23), (9, 13), (36, 29), (27, 40), (39, 1), (35, 13), (38, 39), (27, 30), (19, 7), (1, 32), (10, 1), (11, 34), (7, 7), (25, 38), (17, 19), (2, 27), (8, 10), (38, 7), (35, 34), (4, 3), (25, 0), (15, 0), (16, 9), (6, 17), (9, 31), (37, 26), (9, 39), (19, 33), (0, 25), (19, 6), (35, 12), (3, 16), (37, 33), (4, 36), (21, 24), (7, 22), (3, 29), (31, 38), (17, 6), (5, 14), (6, 2), (23, 27), (11, 32), (8, 39), (18, 39), (12, 26), (41, 0), (6, 28), (19, 0), (16, 6), (30, 2), (32, 8), (24, 1), (43, 27), (15, 21), (30, 1), (9, 9), (1, 25), (13, 24), (36, 14), (3, 30), (6, 40), (17, 10), (40, 4), (8, 27), (19, 24), (36, 19), (4, 10), (2, 3), (29, 16), (29, 9), (19, 22), (35, 26), (37, 14), (19, 17), (1, 15), (24, 27), (1, 5), (33, 0), (0, 1), (2, 12), (7, 11), (31, 27), (0, 19), (12, 11), (28, 34), (34, 27), (6, 36), (33, 8), (22, 20), (29, 15), (30, 18), (7, 8), (0, 14), (2, 29), (4, 23), (41, 28), (20, 38), (3, 0), (38, 14), (3, 11), (15, 25), (40, 36), (32, 39), (8, 5), (35, 36), (18, 27), (35, 2), (10, 39), (29, 40), (28, 16), (17, 39), (28, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 42), (18, 23), (17, 28), (17, 8), (18, 31), (12, 9), (13, 24), (24, 34), (32, 22), (34, 34), (31, 34), (7, 15), (2, 29), (2, 9), (1, 5), (8, 10), (2, 30), (25, 19), (1, 36), (13, 39), (29, 25), (27, 40), (1, 12), (28, 35), (16, 40), (27, 29), (22, 36), (38, 33), (24, 8), (3, 20), (7, 8), (9, 5), (13, 15), (31, 28), (22, 15), (20, 42), (13, 4), (17, 2), (36, 11), (16, 6), (20, 24), (1, 8), (15, 8), (35, 0), (38, 9), (31, 18), (23, 11), (29, 22), (17, 13), (25, 26), (25, 9), (36, 5), (5, 9), (11, 26), (19, 0), (30, 24), (12, 13), (40, 37), (1, 20), (2, 38), (35, 4), (36, 40), (31, 10), (27, 20), (13, 28), (34, 36), (11, 22), (23, 9), (26, 21), (4, 36), (15, 41), (16, 7), (13, 0), (36, 29), (33, 42), (40, 7), (7, 12), (2, 31), (24, 26), (8, 15), (40, 25), (1, 29), (1, 23), (8, 19), (13, 14), (25, 0), (5, 15), (26, 30), (29, 6), (31, 13), (18, 5), (16, 38), (31, 6), (16, 30), (20, 21), (20, 9), (23, 34), (19, 5), (31, 11), (30, 0), (15, 19), (20, 15), (16, 26), (6, 9), (23, 37), (14, 37), (3, 21), (7, 9), (23, 3), (16, 36), (33, 8), (16, 28), (23, 29), (7, 14), (39, 38), (5, 26), (11, 27), (24, 30), (27, 18), (37, 8), (2, 28), (14, 35), (31, 3), (19, 35), (1, 10), (2, 25), (12, 27), (16, 24), (5, 4), (40, 31), (5, 29), (11, 36), (7, 36), (25, 41), (5, 27), (5, 5), (39, 19), (4, 12), (0, 31), (26, 24), (36, 38), (23, 5), (36, 39), (21, 9), (2, 0), (36, 4), (25, 39), (31, 0), (7, 30), (27, 30), (10, 31), (33, 21), (40, 12), (9, 24), (7, 38), (1, 17), (21, 23), (29, 23), (12, 36), (8, 21), (34, 38), (20, 37), (34, 4), (24, 2), (11, 8), (27, 42), (40, 13), (3, 18), (33, 6), (36, 14), (15, 11), (11, 35), (4, 30), (24, 32), (21, 17), (5, 36), (21, 24), (14, 34), (38, 30), (7, 11), (6, 2), (35, 3), (29, 38), (24, 6), (26, 26), (29, 36), (8, 1), (21, 26), (19, 14), (26, 10), (23, 41), (12, 40), (34, 22), (19, 17), (10, 0), (40, 10), (34, 6), (20, 27), (36, 35), (0, 30), (11, 15), (28, 10), (17, 17), (37, 26), (5, 25), (35, 39), (19, 36), (20, 38), (31, 14), (37, 42), (9, 41), (7, 29), (35, 11), (37, 4), (3, 29), (4, 34), (21, 7), (4, 9), (8, 28), (11, 20), (22, 39), (25, 18), (17, 25), (26, 1), (16, 22), (28, 30), (17, 41), (9, 32), (31, 31), (8, 14), (7, 4), (0, 39), (39, 15), (10, 29), (38, 16), (34, 17), (28, 39), (36, 3), (32, 38), (19, 42), (10, 7), (5, 18), (16, 15), (26, 19), (39, 20), (17, 21), (7, 39), (18, 0), (13, 25), (39, 22), (32, 25), (20, 39), (38, 29), (31, 20), (18, 14), (2, 12), (22, 33), (6, 37), (40, 17), (10, 22), (28, 20), (26, 37), (20, 18), (35, 20), (11, 30), (6, 25), (35, 32), (11, 7), (34, 25), (11, 19), (24, 5), (3, 38), (9, 34), (10, 10), (29, 29), (27, 5), (38, 2), (9, 29), (24, 19), (35, 38), (18, 7), (11, 14), (25, 5), (2, 19), (35, 6), (17, 19), (1, 16), (33, 41), (24, 7), (29, 39), (23, 2), (9, 15), (7, 34), (1, 34), (34, 40), (27, 21), (40, 26), (36, 30), (37, 2), (14, 18), (10, 4), (30, 15), (0, 42), (37, 17), (14, 3), (16, 37), (37, 36), (12, 30), (4, 17), (21, 40), (15, 10), (36, 18), (28, 8), (14, 12), (37, 14), (35, 37), (19, 32), (34, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 31), (35, 30), (33, 14), (9, 37), (9, 18), (29, 13), (13, 33), (11, 25), (30, 33), (13, 27), (27, 30), (38, 12), (9, 19), (28, 25), (34, 23), (9, 24), (9, 9), (16, 1), (23, 37), (11, 16), (19, 35), (5, 27), (36, 31), (10, 29), (22, 33), (38, 34), (36, 26), (9, 40), (35, 13), (26, 39), (25, 30), (35, 20), (26, 38), (3, 25), (9, 13), (29, 36), (7, 21), (29, 19), (21, 35), (1, 9), (15, 43), (12, 39), (16, 6), (32, 34), (40, 36), (31, 21), (22, 27), (42, 16), (19, 17), (1, 2), (40, 25), (29, 38), (27, 24), (40, 26), (20, 20), (12, 42), (42, 6), (0, 35), (2, 42), (0, 1), (9, 1), (2, 36), (13, 38), (23, 17), (16, 35), (41, 34), (14, 34), (16, 30), (25, 43), (13, 7), (21, 32), (32, 33), (30, 2), (19, 26), (0, 10), (35, 11), (31, 0), (3, 11), (25, 36), (33, 3), (34, 13), (4, 22), (10, 38), (29, 40), (41, 3), (33, 35), (38, 21), (38, 30), (28, 20), (19, 22), (17, 12), (14, 19), (17, 2), (31, 24), (36, 22), (34, 6), (24, 36), (42, 17), (24, 25), (1, 26), (35, 1), (33, 31), (17, 0), (26, 16), (27, 0), (14, 8), (31, 18), (28, 33), (21, 22), (2, 41), (27, 26), (28, 43), (22, 13), (23, 31), (38, 17), (22, 15), (33, 2), (35, 34), (1, 11), (34, 32), (26, 43), (39, 35), (11, 4), (18, 28), (2, 28), (7, 0), (17, 42), (28, 6), (29, 23), (27, 39), (31, 7), (39, 21), (31, 34), (34, 8), (14, 31), (10, 6), (24, 13), (19, 28), (11, 0), (9, 3), (22, 9), (2, 29), (19, 9), (13, 43), (35, 14), (6, 30), (26, 34), (3, 12), (31, 14), (29, 2), (16, 14), (25, 24), (9, 6), (9, 17), (14, 23), (0, 6), (36, 15), (30, 16), (20, 18), (6, 26), (8, 18), (3, 10), (2, 32), (28, 39), (34, 43), (0, 15), (24, 41), (17, 17), (18, 0), (28, 0), (20, 2), (24, 0), (6, 42), (35, 29), (21, 40), (13, 20), (21, 26), (41, 5), (11, 23), (33, 38), (5, 0), (4, 31), (13, 3), (6, 34), (0, 5), (24, 4), (5, 4), (25, 42), (41, 12), (6, 37), (20, 3), (36, 9), (14, 14), (17, 5), (4, 24), (36, 40), (40, 4), (22, 36), (25, 22), (6, 31), (9, 34), (39, 16), (41, 4), (16, 18), (6, 13), (37, 28), (21, 1), (38, 16), (40, 5), (34, 26), (10, 3), (39, 33), (21, 17), (22, 37), (40, 12), (30, 41), (20, 23), (24, 19), (16, 9), (42, 15), (26, 32), (8, 6), (40, 31), (35, 42), (42, 19), (42, 34), (23, 0), (37, 42), (1, 27), (4, 33), (41, 9), (4, 37), (20, 31), (28, 23), (26, 14), (37, 36), (0, 22), (5, 43), (11, 22), (26, 29), (2, 23), (23, 7), (11, 27), (26, 4), (24, 33), (32, 9), (4, 29), (2, 13), (36, 1), (41, 8), (4, 17), (31, 12), (21, 34), (32, 31), (10, 14), (0, 12), (30, 7), (36, 30), (21, 42), (41, 29), (32, 18), (12, 4), (8, 17), (38, 13), (14, 6), (20, 21), (16, 29), (39, 15), (16, 20), (39, 42), (2, 18), (9, 4), (9, 42), (37, 15), (34, 39), (38, 23), (19, 3), (40, 42), (9, 12), (23, 32), (42, 11), (15, 29), (40, 20), (31, 35), (21, 30), (10, 17), (37, 32), (38, 5), (26, 17), (16, 39), (13, 22), (30, 1), (12, 29), (42, 13), (3, 17), (24, 37), (3, 7), (10, 19), (16, 12), (14, 25), (23, 42), (0, 19), (7, 19), (2, 16), (19, 24), (14, 39), (13, 17), (41, 18), (12, 14), (37, 39), (38, 3), (12, 23), (13, 0), (4, 25), (29, 1), (18, 24), (33, 36), (11, 39), (30, 10), (12, 43), (3, 19), (30, 8), (12, 8), (41, 32), (17, 26), (0, 39), (24, 5), (24, 12), (4, 23), (23, 3), (40, 7), (1, 39), (8, 1), (9, 14), (1, 34), (6, 38), (37, 34), (41, 6), (5, 30), (39, 22), (9, 2), (11, 6), (27, 8), (0, 27), (20, 12), (32, 25), (41, 19), (41, 43), (11, 5), (21, 28), (30, 15), (5, 42), (25, 16), (23, 30), (24, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 19), (5, 1), (31, 44), (15, 39), (29, 0), (38, 32), (6, 1), (23, 17), (32, 16), (38, 1), (27, 30), (23, 9), (30, 40), (31, 39), (29, 16), (3, 34), (2, 6), (18, 30), (24, 17), (12, 19), (7, 7), (19, 9), (5, 8), (22, 20), (13, 10), (3, 14), (31, 33), (19, 15), (23, 26), (18, 2), (38, 3), (24, 35), (29, 5), (0, 9), (1, 23), (6, 29), (27, 42), (6, 28), (37, 28), (28, 32), (19, 3), (18, 27), (34, 25), (17, 6), (18, 10), (4, 11), (12, 23), (31, 36), (13, 15), (19, 32), (23, 19), (20, 0), (3, 17), (27, 25), (20, 15), (23, 30), (2, 30), (36, 25), (36, 3), (11, 17), (32, 13), (39, 19), (15, 4), (37, 33), (25, 43), (15, 16), (24, 40), (28, 15), (25, 20), (1, 39), (3, 0), (8, 27), (31, 23), (8, 13), (32, 18), (34, 34), (23, 7), (30, 2), (16, 1), (28, 19), (11, 21), (12, 25), (7, 27), (24, 37), (37, 17), (6, 31), (2, 19), (4, 15), (24, 22), (2, 0), (3, 41), (29, 38), (3, 18), (27, 24), (29, 21), (26, 14), (26, 9), (10, 13), (10, 28), (28, 11), (38, 42), (8, 26), (7, 29), (12, 15), (28, 29), (20, 3), (13, 22), (9, 24), (6, 14), (10, 5), (0, 21), (20, 16), (28, 0), (20, 37), (15, 3), (16, 10), (34, 13), (0, 44), (25, 39), (2, 16), (35, 5), (28, 8), (16, 18), (21, 9), (7, 21), (27, 4), (35, 23), (26, 28), (6, 27), (2, 27), (21, 41), (20, 34), (8, 5), (24, 9), (39, 26), (18, 21), (24, 8), (25, 25), (2, 44), (17, 4), (23, 31), (37, 21), (27, 31), (23, 1), (32, 23), (15, 38), (39, 31), (2, 34), (27, 8), (14, 5), (34, 28), (18, 44), (14, 0), (39, 36), (11, 36), (31, 9), (26, 26), (30, 14), (6, 0), (9, 25), (21, 39), (12, 28), (11, 39), (35, 0), (23, 27), (22, 45), (36, 6), (14, 13), (22, 1), (4, 18), (17, 11), (6, 40), (12, 17), (1, 22), (38, 14), (23, 0), (24, 1), (31, 31), (15, 29), (38, 6), (0, 37), (25, 14), (39, 8), (12, 1), (0, 14), (6, 12), (9, 29), (26, 4), (25, 11), (11, 34), (14, 45), (7, 16), (25, 9), (17, 31), (2, 11), (34, 40), (19, 37), (18, 15), (8, 45), (18, 40), (19, 25), (25, 23), (24, 18), (2, 1), (32, 19), (23, 36), (25, 4), (10, 9), (20, 18), (1, 36), (34, 20), (17, 18), (6, 3), (28, 5), (14, 36), (24, 0), (20, 13), (37, 7), (5, 11), (6, 5), (10, 16), (19, 20), (38, 13), (13, 1), (11, 40), (5, 20), (8, 44), (24, 26), (19, 38), (28, 23), (17, 25), (9, 7), (8, 41), (17, 17), (36, 35), (5, 19), (24, 32), (34, 22), (15, 42), (9, 19), (26, 27), (17, 12), (2, 13), (0, 42), (1, 0), (23, 3), (38, 31), (9, 9), (5, 34), (26, 12), (15, 31), (7, 12), (3, 26), (17, 30), (16, 16), (35, 1), (30, 11), (10, 2), (16, 7), (6, 7), (36, 19), (14, 18), (20, 9), (23, 15), (13, 23), (3, 30), (6, 42), (33, 33), (24, 3), (32, 41), (38, 34), (39, 1), (5, 7), (16, 34), (20, 33), (29, 15), (19, 44), (18, 3), (14, 6), (11, 12), (13, 44), (32, 3), (39, 13), (17, 33), (21, 37), (2, 20), (38, 10), (31, 27), (1, 31), (21, 23), (28, 1), (5, 12), (6, 45), (12, 27), (28, 20), (5, 21), (35, 26), (4, 6), (1, 26), (25, 33), (25, 17), (21, 11), (16, 43), (29, 29), (5, 2), (29, 14), (2, 33), (7, 3), (35, 18), (27, 36), (13, 3), (27, 11), (26, 37), (34, 36), (36, 27), (21, 43), (20, 14), (20, 29), (7, 41), (26, 6), (22, 37), (14, 17), (19, 29), (8, 23), (26, 13), (2, 7), (33, 19), (13, 34), (26, 36), (16, 0), (28, 44), (33, 8), (2, 45), (29, 1), (25, 21), (14, 23), (33, 23), (29, 2), (26, 42), (32, 21), (33, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 47), (24, 14), (23, 11), (18, 18), (33, 17), (16, 21), (11, 17), (26, 3), (29, 35), (4, 26), (37, 47), (14, 20), (27, 1), (3, 35), (9, 1), (37, 23), (9, 5), (20, 38), (40, 16), (16, 37), (8, 44), (20, 0), (16, 5), (39, 11), (27, 8), (1, 8), (25, 8), (38, 41), (6, 9), (39, 18), (25, 7), (29, 25), (36, 18), (31, 33), (29, 9), (21, 39), (26, 41), (12, 31), (40, 26), (34, 6), (21, 30), (14, 32), (2, 39), (30, 10), (38, 10), (15, 11), (30, 47), (4, 15), (36, 37), (19, 19), (11, 12), (1, 11), (11, 43), (17, 2), (25, 28), (2, 29), (40, 5), (21, 20), (14, 6), (7, 46), (31, 14), (24, 13), (12, 0), (5, 42), (9, 43), (33, 14), (35, 34), (28, 28), (26, 15), (38, 12), (11, 14), (29, 14), (17, 35), (16, 13), (9, 46), (38, 9), (33, 21), (34, 1), (5, 37), (4, 32), (34, 12), (20, 22), (3, 16), (35, 44), (21, 15), (23, 1), (14, 24), (18, 23), (40, 9), (31, 3), (35, 24), (32, 16), (22, 20), (15, 43), (37, 15), (0, 40), (20, 11), (17, 16), (26, 10), (35, 4), (10, 10), (28, 3), (2, 30), (27, 17), (29, 2), (5, 14), (3, 0), (20, 36), (28, 14), (24, 44), (20, 17), (27, 21), (8, 45), (1, 9), (8, 43), (26, 19), (21, 41), (38, 3), (15, 26), (35, 22), (13, 27), (28, 0), (9, 28), (1, 34), (27, 44), (21, 5), (20, 8), (6, 18), (30, 41), (19, 5), (9, 32), (10, 2), (26, 32), (32, 30), (2, 5), (20, 18), (3, 39), (24, 19), (34, 45), (24, 40), (39, 12), (37, 19), (7, 44), (38, 15), (21, 36), (8, 23), (19, 33), (16, 44), (25, 16), (20, 33), (27, 36), (29, 17), (1, 6), (4, 44), (40, 19), (17, 40), (29, 46), (16, 42), (2, 0), (19, 7), (24, 7), (7, 47), (38, 34), (40, 38), (11, 41), (34, 32), (13, 36), (28, 6), (32, 22), (23, 16), (17, 12), (38, 8), (30, 4), (6, 37), (28, 10), (18, 12), (21, 19), (12, 28), (19, 21), (21, 11), (3, 20), (38, 13), (32, 2), (12, 34), (22, 24), (30, 15), (21, 17), (40, 40), (4, 2), (20, 26), (36, 22), (14, 7), (29, 6), (6, 34), (12, 43), (16, 11), (12, 13), (26, 27), (25, 19), (12, 39), (31, 26), (25, 4), (11, 10), (24, 4), (17, 25), (30, 23), (26, 18), (18, 14), (13, 10), (15, 5), (20, 19), (25, 20), (31, 7), (36, 24), (20, 41), (20, 9), (8, 6), (35, 32), (40, 35), (36, 40), (35, 18), (19, 35), (17, 6), (1, 17), (14, 23), (36, 47), (39, 32), (7, 4), (28, 42), (28, 35), (29, 40), (32, 39), (36, 8), (14, 38), (28, 47), (13, 1), (34, 10), (7, 43), (27, 9), (15, 1), (39, 21), (17, 43), (16, 29), (29, 5), (36, 26), (23, 2), (0, 37), (20, 14), (25, 35), (6, 28), (20, 44), (1, 2), (9, 38), (27, 43), (10, 25), (27, 35), (24, 36), (6, 35), (9, 4), (23, 18), (32, 23), (17, 14), (25, 43), (39, 3), (38, 44), (14, 43), (37, 5), (1, 1), (15, 24), (38, 4), (15, 12), (2, 25), (36, 2), (18, 38), (8, 20), (25, 25), (23, 40), (35, 20), (40, 10), (26, 29), (25, 22), (29, 30), (14, 15), (33, 46), (24, 41), (6, 4), (38, 23), (27, 10), (37, 1), (36, 33), (9, 7), (22, 28), (32, 47), (22, 21), (17, 13), (18, 20), (29, 26), (23, 27), (8, 33), (11, 20), (7, 0), (37, 45), (33, 20), (11, 19), (31, 15), (15, 29), (3, 32), (17, 15), (12, 33), (7, 2), (5, 41), (29, 22), (25, 36), (22, 12), (5, 12), (16, 23), (16, 40), (4, 20), (5, 44), (8, 30), (30, 0), (10, 42), (5, 8), (40, 31), (9, 35), (30, 30), (40, 46), (38, 32), (24, 29), (22, 9), (4, 42), (1, 39), (37, 32), (0, 19), (5, 47)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 36), (35, 40), (36, 5), (32, 12), (20, 33), (23, 22), (25, 26), (6, 41), (44, 28), (21, 24), (15, 3), (22, 6), (10, 19), (26, 43), (19, 2), (20, 4), (36, 13), (8, 23), (23, 12), (34, 4), (13, 44), (1, 37), (36, 38), (2, 22), (19, 30), (34, 46), (16, 31), (1, 13), (7, 37), (12, 24), (30, 22), (45, 22), (0, 4), (31, 38), (1, 40), (24, 37), (11, 15), (31, 21), (29, 1), (9, 26), (8, 7), (43, 7), (7, 11), (34, 13), (31, 17), (4, 38), (24, 42), (7, 13), (13, 40), (26, 18), (15, 27), (5, 22), (22, 8), (39, 24), (42, 8), (39, 15), (1, 21), (22, 30), (28, 14), (32, 4), (44, 25), (12, 35), (6, 17), (20, 37), (25, 15), (7, 21), (22, 21), (19, 14), (0, 17), (26, 38), (46, 13), (38, 11), (19, 27), (31, 13), (24, 28), (20, 29), (23, 4), (35, 1), (24, 27), (7, 18), (43, 4), (2, 12), (4, 7), (31, 8), (5, 44), (32, 15), (27, 36), (5, 19), (15, 2), (8, 15), (43, 25), (22, 28), (20, 17), (9, 45), (36, 4), (26, 33), (45, 25), (31, 16), (30, 39), (0, 24), (0, 8), (17, 45), (36, 16), (30, 31), (14, 46), (0, 15), (43, 17), (14, 28), (18, 42), (34, 6), (45, 29), (22, 17), (19, 23), (22, 43), (28, 22), (13, 16), (28, 19), (11, 29), (9, 24), (2, 39), (10, 46), (32, 16), (41, 42), (3, 20), (45, 46), (39, 34), (24, 8), (41, 8), (9, 1), (36, 14), (21, 14), (8, 46), (36, 42), (31, 20), (18, 26), (20, 6), (8, 34), (46, 38), (2, 5), (3, 1), (27, 20), (12, 33), (44, 32), (2, 37), (37, 29), (4, 2), (18, 14), (13, 24), (31, 6), (24, 43), (1, 24), (25, 43), (16, 38), (17, 33), (16, 40), (26, 11), (14, 6), (21, 33), (33, 44), (34, 10), (33, 12), (21, 5), (42, 4), (24, 24), (41, 45), (40, 15), (42, 23), (9, 21), (43, 31), (13, 0), (12, 28), (36, 46), (11, 11), (43, 12), (33, 45), (31, 12), (3, 18), (24, 25), (0, 12), (30, 17), (25, 32), (34, 27), (43, 44), (38, 39), (46, 28), (45, 9), (12, 38), (4, 6), (1, 41), (41, 33), (31, 34), (1, 2), (24, 26), (15, 14), (24, 41), (16, 18), (20, 25), (10, 43), (23, 35), (28, 42), (2, 29), (33, 21), (7, 0), (8, 38), (22, 25), (13, 13), (9, 18), (46, 44), (6, 28), (15, 38), (43, 32), (38, 1), (44, 42), (20, 34), (21, 38), (29, 45), (23, 23), (42, 46), (32, 25), (43, 9), (34, 8), (30, 41), (44, 15), (3, 3), (36, 18), (46, 7), (8, 10), (17, 38), (5, 0), (44, 35), (34, 45), (43, 38), (46, 43), (24, 36), (4, 42), (2, 27), (16, 25), (46, 35), (35, 22), (14, 9), (35, 6), (29, 37), (13, 32), (39, 39), (33, 1), (25, 13), (43, 33), (6, 1), (32, 6), (24, 7), (22, 16), (25, 28), (27, 44), (15, 28), (4, 36), (35, 2), (19, 28), (7, 29), (27, 33), (46, 30), (14, 33), (25, 35), (40, 33), (28, 12), (44, 8), (20, 10), (1, 31), (11, 28), (30, 19), (38, 3), (25, 6), (20, 27), (22, 2), (13, 15), (28, 36), (15, 15), (23, 41), (17, 40), (10, 16), (26, 20), (18, 10), (11, 34), (33, 16), (41, 29), (4, 39), (45, 5), (38, 17), (1, 8), (38, 37), (11, 10), (14, 35), (6, 46), (37, 14), (29, 38), (28, 1), (13, 4), (19, 20), (35, 19), (42, 41), (27, 34), (3, 35), (26, 28), (23, 3), (25, 42), (7, 32), (34, 37), (32, 45), (14, 40), (1, 20), (1, 29), (20, 3), (36, 33), (15, 12), (5, 45), (24, 4), (1, 1), (2, 35), (17, 3), (35, 18), (42, 30), (23, 17), (25, 3), (45, 16), (0, 14), (18, 16), (27, 6), (41, 28), (31, 43), (26, 4), (12, 9), (2, 28), (21, 46), (32, 1), (25, 37), (28, 15), (38, 13), (28, 30), (13, 6), (12, 6), (19, 45), (12, 46), (39, 19), (23, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 37), (33, 45), (33, 16), (26, 12), (17, 41), (4, 15), (34, 31), (10, 41), (13, 43), (17, 38), (9, 41), (12, 19), (4, 17), (0, 30), (28, 1), (27, 15), (24, 21), (33, 15), (15, 15), (22, 12), (28, 24), (14, 11), (31, 25), (37, 10), (22, 8), (23, 9), (0, 21), (0, 15), (8, 16), (27, 21), (32, 39), (5, 35), (12, 6), (33, 28), (28, 9), (3, 8), (2, 4), (21, 10), (2, 19), (36, 0), (22, 4), (7, 13), (28, 40), (5, 11), (34, 14), (36, 12), (9, 4), (3, 25), (37, 27), (14, 19), (34, 35), (24, 9), (13, 18), (34, 5), (38, 6), (39, 43), (1, 5), (5, 39), (8, 38), (10, 34), (31, 36), (34, 38), (31, 26), (5, 18), (13, 45), (32, 38), (11, 4), (3, 24), (9, 22), (0, 20), (23, 46), (17, 13), (0, 40), (3, 37), (29, 25), (16, 36), (22, 36), (2, 10), (31, 33), (12, 40), (35, 14), (35, 46), (19, 33), (35, 42), (4, 19), (31, 15), (35, 32), (13, 12), (24, 0), (28, 5), (25, 0), (7, 30), (5, 17), (37, 29), (38, 33), (3, 9), (17, 20), (18, 40), (2, 42), (39, 15), (25, 29), (39, 7), (11, 2), (37, 19), (32, 23), (3, 2), (15, 22), (8, 8), (13, 19), (15, 46), (9, 12), (7, 6), (5, 28), (19, 31), (13, 13), (23, 21), (33, 33), (13, 33), (2, 7), (11, 42), (22, 33), (25, 12), (19, 43), (39, 28), (18, 18), (26, 4), (38, 42), (8, 12), (36, 18), (2, 31), (3, 4), (11, 23), (32, 24), (2, 2), (34, 6), (6, 4), (15, 26), (18, 33), (31, 22), (27, 28), (24, 5), (15, 7), (21, 1), (16, 45), (4, 25), (1, 31), (25, 22), (2, 0), (6, 10), (19, 11), (38, 28), (1, 11), (12, 38), (14, 40), (11, 34), (30, 23), (30, 39), (37, 21), (10, 37), (33, 38), (22, 0), (28, 23), (9, 18), (39, 36), (36, 5), (9, 38), (11, 1), (2, 8), (35, 31), (15, 14), (19, 36), (29, 41), (17, 6), (27, 6), (19, 34), (17, 26), (39, 40), (35, 29), (2, 34), (22, 27), (29, 2), (38, 39), (34, 34), (11, 31), (32, 27), (21, 40), (20, 32), (22, 6), (37, 6), (36, 34), (26, 31), (27, 26), (13, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 42), (41, 11), (21, 15), (36, 21), (29, 19), (43, 27), (39, 32), (8, 46), (13, 21), (45, 30), (43, 6), (34, 4), (15, 23), (9, 12), (18, 3), (43, 34), (23, 35), (4, 14), (39, 23), (2, 20), (17, 1), (33, 34), (23, 27), (2, 33), (1, 34), (38, 47), (14, 25), (39, 4), (38, 6), (45, 24), (41, 36), (25, 36), (27, 43), (28, 43), (23, 29), (31, 20), (14, 39), (44, 39), (0, 7), (30, 30), (35, 18), (5, 6), (22, 47), (21, 7), (19, 24), (9, 28), (27, 40), (19, 25), (4, 41), (35, 16), (36, 1), (0, 9), (9, 17), (21, 40), (7, 4), (8, 0), (35, 15), (12, 31), (1, 11), (2, 15), (41, 40), (31, 31), (29, 16), (2, 29), (27, 32), (6, 13), (20, 17), (10, 2), (16, 29), (0, 24), (33, 17), (18, 26), (33, 23), (2, 18), (21, 30), (34, 8), (16, 43), (17, 30), (4, 3), (27, 31), (27, 6), (13, 19), (17, 3), (35, 36), (19, 21), (21, 22), (33, 25), (8, 34), (33, 1), (11, 13), (34, 1), (0, 44), (21, 13), (34, 41), (13, 26), (6, 17), (12, 9), (20, 4), (29, 28), (27, 12), (36, 47), (0, 1), (16, 47), (7, 16), (37, 42), (16, 44), (1, 36), (13, 41), (25, 46), (18, 47), (40, 16), (13, 33), (12, 39), (41, 21), (42, 40), (8, 18), (10, 8), (44, 28), (10, 7), (32, 35), (40, 32), (13, 31), (0, 21), (22, 19), (44, 36), (4, 24), (30, 9), (22, 17), (18, 38), (45, 22), (34, 15), (6, 37), (19, 10), (17, 33), (42, 5), (41, 0), (31, 43), (9, 1), (36, 41), (28, 4), (11, 24), (45, 4), (33, 24), (3, 0), (13, 25), (2, 41), (13, 24), (1, 33), (45, 11), (4, 34), (3, 9), (35, 35), (6, 19), (7, 27), (22, 44), (41, 33), (33, 28), (41, 28), (14, 9), (8, 37), (39, 9), (0, 11), (1, 25), (35, 7), (6, 35), (23, 25), (25, 30), (30, 16), (37, 14), (15, 8), (21, 27), (6, 33), (38, 4), (4, 40), (36, 10), (27, 1), (45, 36), (26, 22), (41, 3), (17, 22), (4, 4), (11, 34), (10, 37), (9, 10), (43, 33), (23, 9), (29, 46), (37, 11), (34, 35), (3, 23), (36, 37), (12, 20), (22, 24), (39, 6), (10, 20), (37, 20), (20, 42), (15, 44), (13, 15), (24, 9), (20, 43), (2, 7), (29, 37), (25, 9), (35, 14), (31, 45), (8, 16), (36, 34), (25, 12), (5, 0), (15, 46), (4, 9), (13, 13), (28, 30), (33, 38), (35, 46), (33, 21), (34, 45), (27, 46), (12, 22), (37, 23), (41, 6), (28, 26), (25, 15), (33, 7), (12, 32), (27, 7), (14, 30), (9, 36), (32, 27), (7, 37), (33, 5), (14, 31), (26, 17), (16, 19), (15, 5), (15, 31), (26, 37), (17, 2), (7, 22), (5, 2), (15, 27), (38, 24), (28, 13), (37, 16), (18, 40), (15, 28), (36, 19), (23, 34), (11, 26), (6, 34), (41, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 22), (22, 12), (27, 28), (8, 19), (44, 2), (25, 5), (32, 19), (14, 27), (41, 30), (21, 8), (43, 34), (43, 13), (9, 27), (9, 14), (5, 0), (6, 5), (25, 8), (5, 4), (5, 29), (31, 3), (30, 7), (12, 40), (22, 44), (23, 2), (26, 20), (14, 41), (29, 13), (41, 36), (7, 21), (42, 34), (43, 20), (35, 6), (7, 35), (33, 25), (28, 41), (9, 22), (17, 34), (8, 27), (29, 0), (2, 17), (10, 41), (25, 32), (13, 44), (29, 9), (4, 31), (40, 26), (36, 35), (38, 24), (6, 35), (25, 29), (6, 0), (10, 27), (26, 44), (35, 27), (20, 37), (27, 3), (39, 16), (29, 27), (31, 13), (36, 44), (42, 38), (22, 24), (23, 10), (24, 37), (42, 11), (13, 35), (18, 17), (1, 34), (9, 39), (33, 27), (1, 13), (21, 39), (5, 44), (42, 9), (42, 5), (17, 8), (11, 20), (43, 39), (33, 42), (25, 36), (3, 23), (9, 9), (13, 36), (3, 25), (38, 16), (28, 10), (3, 0), (36, 26), (28, 38), (8, 18), (6, 6), (14, 2), (7, 43), (11, 37), (31, 6), (39, 31), (23, 6), (36, 31), (17, 25), (8, 26), (15, 20), (15, 6), (9, 5), (32, 41), (44, 21), (0, 4), (38, 21), (43, 28), (9, 18), (9, 38), (20, 6), (35, 17), (8, 9), (19, 38), (18, 19), (39, 8), (33, 22), (24, 16), (13, 16), (41, 19), (22, 1), (33, 38), (26, 14), (5, 36), (5, 40), (44, 33), (14, 4), (13, 33), (28, 4), (12, 20), (13, 5), (10, 1), (15, 10), (32, 18), (3, 11), (31, 21), (39, 42), (1, 22), (44, 26), (19, 1), (39, 35), (19, 18), (27, 37), (34, 30), (7, 30), (16, 10), (10, 23), (17, 10), (36, 4), (39, 18), (25, 40), (31, 9), (17, 41), (41, 24), (27, 8), (2, 37), (16, 24), (11, 33), (15, 14), (19, 43), (3, 42), (7, 8), (21, 24), (19, 37), (0, 23), (41, 16), (39, 13), (15, 26), (2, 30), (32, 20), (11, 28), (19, 39), (26, 27), (15, 5), (10, 14), (26, 37), (13, 21), (17, 40), (19, 4), (25, 41), (5, 13), (3, 7), (24, 9), (40, 16), (36, 27), (8, 5), (3, 27), (32, 40), (34, 17), (11, 32), (21, 38), (37, 33), (18, 38), (14, 21), (27, 12), (6, 10), (25, 42), (43, 0), (27, 22), (43, 8), (44, 14), (34, 12), (36, 5), (3, 2), (37, 41), (7, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 32), (16, 15), (18, 13), (9, 5), (40, 22), (33, 17), (25, 9), (34, 11), (15, 24), (33, 19), (31, 2), (29, 24), (36, 13), (27, 2), (2, 30), (26, 2), (26, 22), (22, 12), (24, 3), (23, 40), (15, 27), (8, 17), (38, 31), (25, 11), (26, 26), (36, 16), (38, 38), (22, 25), (2, 4), (26, 38), (40, 10), (20, 34), (13, 13), (12, 0), (41, 24), (22, 6), (1, 26), (27, 34), (21, 36), (18, 1), (32, 40), (25, 5), (21, 23), (7, 12), (9, 3), (36, 9), (26, 15), (38, 23), (36, 38), (16, 11), (23, 34), (6, 33), (7, 1), (2, 2), (30, 7), (4, 29), (30, 31), (31, 7), (12, 16), (2, 13), (19, 3), (14, 39), (3, 15), (16, 30), (13, 40), (3, 23), (26, 0), (31, 34), (28, 15), (2, 33), (2, 9), (1, 35), (18, 3), (5, 38), (5, 40), (39, 1), (8, 9), (20, 23), (40, 1), (15, 9), (16, 2), (1, 9), (28, 16), (6, 13), (3, 39), (35, 15), (28, 23), (37, 5), (7, 39), (38, 1), (40, 12), (30, 16), (5, 23), (21, 16), (18, 40), (28, 41), (41, 12), (1, 22), (17, 39), (21, 37), (33, 35), (39, 7), (17, 1), (24, 23), (23, 29), (10, 1), (9, 18), (15, 25), (12, 8), (16, 0), (10, 28), (17, 36), (11, 3), (6, 24), (12, 29), (2, 31), (33, 32), (31, 15), (19, 18), (41, 1), (36, 6), (20, 9), (32, 21), (34, 32), (17, 21), (14, 18), (12, 20), (35, 14), (10, 0), (1, 6), (25, 16), (2, 20), (17, 40), (20, 27), (36, 39), (24, 18), (21, 31), (38, 16), (32, 28), (37, 0), (24, 29), (39, 8), (0, 13), (31, 9), (16, 3), (3, 11), (4, 19), (34, 26), (10, 4), (26, 12), (20, 19), (15, 3), (13, 34), (32, 3), (27, 28), (29, 33), (15, 36), (38, 15), (34, 1), (37, 30), (9, 8), (12, 4), (18, 11), (22, 18), (24, 5), (40, 17), (14, 38), (27, 33), (20, 14), (38, 17), (39, 33), (14, 5), (38, 22), (6, 15), (1, 21), (19, 19), (31, 31), (19, 31), (0, 3), (14, 40), (1, 38), (21, 24), (33, 13), (19, 4), (0, 35), (19, 34), (5, 28), (39, 19), (41, 11), (34, 19), (12, 7), (39, 36), (3, 1), (15, 22), (0, 25), (26, 27), (0, 31), (29, 10), (25, 23), (40, 24), (22, 8), (11, 27), (24, 25), (33, 36), (5, 25), (30, 41), (32, 4), (19, 33), (32, 25), (17, 5), (32, 38), (27, 7), (21, 27), (23, 8), (19, 37), (3, 4), (19, 12), (20, 17), (37, 39), (29, 11), (28, 8), (30, 10), (14, 29), (12, 14), (13, 1), (21, 34), (18, 24), (34, 2), (26, 11), (32, 24), (14, 7), (32, 30), (21, 35), (18, 36), (25, 6), (0, 30), (14, 31), (8, 7), (13, 18), (38, 30), (36, 26), (36, 5), (24, 0), (21, 1), (15, 13), (39, 16), (28, 40), (25, 2), (40, 8), (33, 5), (5, 1), (28, 18), (13, 19), (1, 40), (21, 18), (15, 14), (5, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 6), (19, 40), (15, 21), (37, 45), (20, 0), (25, 17), (0, 20), (22, 29), (34, 20), (38, 31), (8, 20), (26, 24), (39, 31), (1, 38), (7, 20), (9, 41), (13, 3), (17, 31), (36, 26), (23, 0), (1, 36), (18, 8), (10, 36), (9, 22), (42, 13), (36, 23), (48, 8), (31, 34), (43, 41), (21, 12), (9, 46), (2, 5), (10, 35), (13, 38), (29, 29), (41, 14), (12, 43), (34, 3), (8, 10), (46, 47), (47, 47), (26, 34), (38, 27), (35, 5), (29, 13), (22, 37), (47, 1), (4, 41), (28, 4), (35, 36), (24, 27), (25, 13), (6, 38), (12, 25), (4, 29), (29, 28), (28, 0), (0, 37), (16, 25), (42, 20), (0, 23), (46, 26), (27, 41), (24, 10), (14, 48), (25, 42), (48, 19), (16, 41), (5, 17), (10, 28), (32, 43), (5, 36), (47, 0), (24, 39), (1, 40), (5, 14), (23, 48), (39, 48), (22, 31), (45, 27), (5, 24), (48, 39), (48, 16), (3, 8), (11, 1), (31, 0), (15, 22), (29, 4), (30, 14), (30, 31), (29, 42), (45, 20), (7, 29), (25, 48), (46, 13), (4, 27), (5, 1), (39, 34), (1, 2), (37, 30), (4, 40), (19, 41), (23, 8), (12, 21), (47, 26), (26, 2), (21, 26), (16, 29), (2, 27), (18, 34), (44, 5), (12, 0), (3, 5), (15, 35), (40, 17), (45, 26), (4, 15), (20, 39), (21, 44), (31, 37), (11, 38), (16, 16), (10, 11), (14, 40), (38, 15), (42, 44), (35, 14), (38, 43), (7, 12), (27, 25), (47, 37), (47, 44), (21, 1), (30, 27), (19, 10), (28, 39), (23, 5), (0, 12), (1, 4), (25, 11), (28, 17), (8, 3), (14, 21), (40, 2), (46, 32), (24, 15), (21, 46), (3, 27), (13, 0), (38, 39), (32, 6), (22, 40), (4, 1), (13, 39), (34, 11), (13, 37), (9, 38), (47, 16), (26, 42), (43, 35), (28, 23), (36, 45), (25, 18), (25, 37), (38, 4), (18, 14), (17, 37), (48, 0), (15, 3), (24, 17), (18, 20), (15, 4), (23, 16), (12, 32), (2, 41), (16, 31), (46, 39), (40, 42), (24, 30), (24, 45), (28, 6), (48, 45), (20, 15), (8, 34), (41, 47), (12, 14), (20, 11), (6, 39), (30, 10), (4, 39), (2, 20), (24, 4), (26, 3), (4, 28), (7, 25), (9, 18), (39, 30), (31, 25), (40, 27), (22, 22), (26, 12), (16, 47), (11, 24), (20, 10), (23, 21), (14, 29), (27, 37), (21, 14), (33, 5), (41, 27), (41, 26), (2, 23), (21, 21), (34, 37), (13, 35), (4, 11), (42, 36), (33, 3), (25, 28), (32, 16), (40, 25), (47, 36), (22, 9), (8, 14), (29, 22), (38, 9), (13, 32), (7, 3), (1, 6), (38, 35), (31, 35), (37, 36), (5, 43), (42, 0), (9, 12), (47, 20), (32, 42), (29, 38), (12, 33), (14, 37), (4, 36), (21, 15), (7, 39), (16, 39), (33, 40), (22, 21), (47, 23), (13, 1), (19, 31), (1, 14), (30, 48), (27, 43), (31, 30), (39, 29), (31, 38), (4, 7), (2, 19), (45, 10), (17, 38), (46, 36), (48, 47), (6, 15), (18, 18), (48, 27), (0, 44), (25, 3), (38, 14), (2, 17), (38, 7), (4, 14), (6, 34), (17, 19), (39, 36), (32, 11), (17, 5), (10, 19), (18, 5), (26, 21), (32, 17), (20, 6), (45, 1), (2, 9), (26, 18), (7, 26), (9, 24), (34, 4), (6, 36), (40, 30), (44, 37), (31, 16), (24, 26), (32, 19), (10, 37), (24, 20), (1, 1), (17, 8), (4, 6), (47, 13), (8, 45), (15, 30), (5, 33), (38, 17), (5, 10), (5, 9), (30, 13), (16, 11), (7, 40), (31, 2), (7, 24), (17, 32), (0, 42), (17, 35), (27, 1), (6, 9), (45, 13), (45, 33), (33, 16), (31, 32), (32, 26), (45, 43), (21, 13), (0, 38), (40, 4), (41, 40), (32, 9), (46, 27), (21, 32), (18, 4), (23, 20), (48, 2), (4, 22), (3, 21), (1, 21), (27, 36), (17, 41), (47, 32), (8, 32), (44, 27), (8, 37), (31, 5), (41, 7), (23, 10), (1, 16), (5, 45), (42, 26), (41, 23), (20, 30), (26, 32), (36, 15), (12, 30), (12, 40), (18, 30), (7, 48), (24, 1), (30, 37), (3, 17), (5, 23), (5, 16), (44, 43), (9, 19), (5, 3), (13, 11), (41, 38), (48, 5), (19, 37), (3, 13), (0, 34), (27, 46), (21, 19), (45, 4), (24, 41), (38, 36), (18, 21), (15, 29), (32, 40), (15, 24), (28, 35), (33, 27), (23, 4), (30, 24), (34, 46), (9, 25), (6, 37), (18, 10), (7, 46), (29, 5), (46, 34), (5, 38), (45, 15), (22, 41), (32, 48), (37, 46), (21, 0), (27, 39), (46, 4), (3, 41), (31, 6), (9, 3), (29, 44), (19, 30), (48, 28), (46, 18), (2, 38), (5, 7), (48, 38), (30, 26), (46, 2), (2, 36), (21, 48), (35, 7), (25, 9), (47, 27), (33, 44), (36, 24), (23, 2), (13, 27), (42, 39), (1, 32), (46, 35), (2, 28), (11, 40), (12, 42), (2, 6), (40, 44), (19, 28), (21, 25), (28, 25), (11, 46), (32, 10), (42, 14), (21, 18), (37, 4), (34, 13), (0, 36), (15, 1), (2, 46), (47, 42), (27, 33), (37, 10), (18, 16), (6, 47), (20, 28), (17, 45), (20, 34), (34, 40), (11, 48), (3, 36), (32, 24), (27, 30), (27, 45), (35, 38), (4, 0), (20, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 45), (2, 17), (7, 43), (9, 38), (32, 3), (11, 30), (14, 0), (2, 13), (8, 45), (47, 36), (1, 39), (45, 0), (36, 8), (44, 4), (13, 23), (17, 33), (33, 20), (12, 11), (0, 3), (28, 27), (13, 16), (34, 2), (14, 37), (16, 19), (45, 17), (35, 32), (26, 40), (13, 28), (21, 23), (29, 34), (48, 29), (28, 9), (22, 23), (20, 9), (28, 24), (3, 0), (48, 36), (13, 15), (35, 13), (15, 5), (37, 7), (42, 18), (32, 20), (35, 41), (45, 36), (24, 26), (42, 42), (16, 2), (43, 32), (44, 28), (23, 29), (13, 22), (4, 37), (28, 20), (6, 9), (39, 13), (29, 41), (41, 22), (35, 21), (40, 26), (32, 12), (16, 15), (10, 36), (35, 8), (30, 2), (42, 28), (7, 6), (12, 44), (23, 24), (22, 20), (31, 29), (5, 7), (11, 28), (20, 1), (32, 43), (15, 25), (4, 5), (46, 12), (15, 14), (10, 29), (17, 26), (28, 41), (14, 43), (45, 30), (38, 32), (42, 35), (45, 42), (32, 26), (11, 26), (10, 38), (28, 4), (41, 1), (8, 17), (39, 39), (33, 42), (45, 45), (3, 11), (40, 40), (30, 39), (47, 3), (11, 33), (33, 17), (16, 32), (29, 16), (11, 6), (3, 34), (34, 31), (29, 33), (20, 29), (7, 24), (23, 13), (36, 18), (34, 3), (25, 22), (4, 11), (12, 43), (23, 38), (34, 44), (17, 12), (15, 33), (1, 40), (5, 22), (18, 7), (35, 34), (40, 33), (16, 21), (6, 4), (1, 30), (48, 30), (12, 29), (2, 24), (10, 27), (25, 18), (33, 7), (21, 35), (23, 12), (39, 1), (29, 5), (19, 27), (12, 19), (31, 24), (14, 40), (42, 27), (18, 30), (12, 20), (30, 18), (6, 35), (41, 14), (24, 43), (39, 34), (23, 45), (34, 14), (19, 36), (11, 8), (14, 21), (5, 3), (33, 43), (36, 17), (5, 26), (32, 4), (41, 12), (9, 37), (13, 21), (34, 17), (26, 0), (17, 25), (3, 10), (12, 24), (42, 13), (43, 34), (37, 37), (47, 35), (19, 13), (20, 33), (44, 15), (11, 29), (9, 41), (40, 6), (20, 35), (18, 38), (41, 10), (44, 6), (41, 31), (19, 23), (3, 19), (34, 27), (8, 27), (27, 41), (31, 16), (23, 1), (46, 1), (27, 19), (13, 3), (21, 42), (44, 43), (26, 17), (12, 26), (37, 5), (33, 36), (26, 39), (8, 34), (46, 7), (17, 45), (13, 36), (48, 31), (34, 8), (26, 26), (36, 22), (17, 36), (26, 35), (27, 23), (16, 35), (3, 3), (26, 8), (0, 19), (30, 25), (28, 26), (18, 34), (25, 36), (5, 43), (15, 8), (35, 19), (41, 34), (46, 15), (20, 19), (37, 10), (38, 23), (32, 9), (31, 14), (13, 33), (46, 13), (36, 1), (31, 12), (44, 17), (31, 19), (40, 0), (31, 2), (33, 45), (7, 36), (8, 19), (36, 33), (10, 1), (18, 31), (47, 22), (44, 19), (41, 7), (45, 27), (31, 6), (26, 16), (25, 21), (18, 33), (32, 37), (45, 1), (45, 41), (27, 32), (6, 33), (33, 25), (9, 4), (14, 10), (34, 42), (39, 6), (8, 18), (29, 27), (0, 32), (11, 3), (0, 20), (12, 37), (8, 4), (38, 45), (29, 42), (32, 15), (27, 7), (28, 10), (29, 8), (0, 16), (4, 30), (44, 12), (24, 44), (9, 39), (29, 30), (32, 5), (19, 11), (21, 8), (3, 26), (31, 26), (14, 12), (47, 4), (33, 30), (33, 24), (7, 20), (38, 30), (29, 31), (4, 2), (8, 31), (24, 31), (14, 34), (41, 21), (12, 41), (47, 15), (18, 1), (40, 3), (0, 7), (33, 13), (34, 16), (18, 43), (22, 28), (47, 34), (36, 24), (16, 12), (25, 26), (9, 45), (26, 21), (20, 30), (41, 42), (29, 29), (21, 21), (48, 21), (17, 6), (22, 17), (9, 6), (45, 25), (0, 8), (12, 36), (44, 2), (0, 9), (13, 29), (17, 34), (47, 26), (42, 43), (1, 35), (2, 27), (3, 23), (40, 2), (34, 45), (7, 26), (9, 2), (40, 16), (8, 38), (17, 10), (10, 25), (15, 17), (3, 38), (25, 19), (45, 29), (31, 35), (29, 0), (10, 21), (3, 16), (1, 45), (28, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 22), (7, 20), (10, 36), (21, 28), (43, 17), (15, 24), (34, 28), (29, 7), (22, 36), (32, 2), (20, 45), (44, 44), (2, 27), (18, 13), (19, 10), (45, 10), (27, 33), (14, 1), (45, 46), (29, 41), (41, 26), (11, 44), (42, 24), (2, 42), (7, 30), (33, 9), (11, 18), (37, 22), (39, 36), (18, 38), (37, 7), (1, 8), (0, 4), (35, 44), (35, 36), (46, 24), (14, 18), (40, 32), (21, 8), (29, 44), (23, 37), (3, 9), (20, 46), (37, 43), (21, 27), (40, 26), (13, 7), (44, 38), (12, 38), (15, 43), (18, 20), (4, 6), (0, 8), (36, 32), (48, 3), (20, 33), (32, 9), (10, 18), (34, 25), (19, 12), (12, 37), (47, 4), (44, 13), (29, 18), (14, 27), (14, 19), (23, 39), (8, 17), (44, 14), (42, 34), (28, 34), (11, 40), (6, 17), (22, 9), (1, 22), (43, 23), (34, 1), (25, 40), (1, 18), (28, 45), (7, 7), (24, 33), (6, 22), (19, 14), (46, 0), (9, 44), (35, 23), (34, 34), (4, 2), (9, 19), (35, 37), (32, 22), (9, 36), (32, 45), (38, 7), (9, 20), (10, 23), (31, 13), (28, 28), (17, 9), (32, 38), (17, 28), (28, 27), (39, 1), (36, 23), (12, 32), (3, 19), (0, 14), (33, 15), (25, 17), (37, 25), (9, 2), (13, 2), (36, 33), (10, 22), (0, 5), (12, 43), (24, 10), (6, 14), (47, 9), (4, 24), (47, 6), (12, 35), (30, 36), (0, 36), (12, 10), (39, 15), (35, 7), (29, 13), (44, 10), (14, 26), (47, 42), (10, 21), (23, 9), (17, 21), (17, 3), (44, 25), (11, 27), (21, 26), (28, 40), (39, 45), (3, 37), (12, 2), (16, 38), (19, 17), (47, 12), (48, 32), (18, 29), (5, 5), (7, 5), (32, 29), (43, 27), (21, 14), (11, 36), (34, 0), (41, 41), (40, 39), (47, 31), (18, 22), (37, 33), (2, 9), (23, 36), (45, 31), (21, 37), (3, 10), (8, 6), (0, 43), (19, 41), (18, 43), (48, 16), (34, 23), (42, 41), (32, 16), (42, 45), (15, 13), (45, 19), (7, 23), (11, 15), (39, 30), (46, 32), (35, 39), (42, 11), (27, 37), (12, 34), (1, 38), (22, 26), (21, 6), (27, 21), (9, 22), (28, 6), (34, 10), (15, 37), (2, 6), (12, 44), (29, 34), (5, 26), (24, 45), (22, 27), (31, 7), (15, 5), (34, 21), (22, 4), (26, 44), (14, 14), (8, 20), (29, 9), (11, 35), (23, 40), (47, 19), (5, 31), (17, 27), (8, 9), (45, 24), (22, 18), (45, 26), (40, 35), (48, 24), (35, 46), (3, 18), (6, 16), (9, 31), (1, 34), (4, 1), (48, 31), (20, 39), (17, 22), (6, 38), (20, 8), (9, 38), (32, 21), (25, 29), (46, 8), (40, 2), (19, 19), (32, 23), (33, 34), (24, 21), (12, 24), (2, 18), (27, 16), (48, 41), (48, 0), (47, 10), (34, 35), (14, 35), (42, 31), (19, 18), (42, 2), (0, 42), (41, 2), (39, 27), (19, 35), (31, 28), (41, 6), (17, 17), (32, 15), (11, 1), (26, 5), (26, 46), (19, 45), (38, 19), (10, 35), (18, 35), (29, 14), (30, 33), (1, 2), (13, 18), (26, 13), (33, 14), (25, 45), (0, 28), (11, 10), (29, 15), (9, 0), (47, 0), (5, 40), (48, 8), (46, 10), (34, 15), (18, 30), (33, 4), (16, 8), (37, 13), (12, 39), (16, 6), (3, 16), (33, 17), (18, 9), (3, 36), (1, 46), (45, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 10), (4, 37), (9, 36), (19, 36), (37, 23), (39, 17), (32, 25), (42, 2), (36, 7), (16, 22), (8, 17), (15, 6), (11, 20), (38, 44), (9, 20), (7, 17), (7, 10), (38, 24), (29, 12), (31, 7), (10, 16), (6, 37), (22, 1), (39, 34), (40, 6), (24, 9), (19, 24), (19, 31), (18, 23), (2, 37), (14, 2), (6, 8), (11, 26), (19, 23), (25, 12), (44, 7), (5, 28), (30, 36), (11, 24), (10, 42), (21, 13), (29, 22), (34, 41), (44, 4), (2, 12), (17, 15), (8, 21), (13, 36), (0, 15), (34, 11), (44, 35), (44, 33), (2, 15), (28, 16), (40, 23), (29, 3), (40, 14), (7, 47), (38, 34), (36, 31), (42, 39), (27, 8), (29, 0), (21, 37), (43, 7), (8, 28), (3, 47), (25, 38), (9, 21), (4, 23), (42, 3), (24, 35), (30, 27), (43, 30), (34, 15), (10, 40), (33, 46), (9, 40), (5, 14), (3, 14), (2, 42), (10, 13), (38, 1), (30, 2), (42, 17), (2, 39), (28, 23), (35, 11), (27, 27), (33, 43), (9, 17), (8, 22), (12, 38), (1, 44), (24, 20), (12, 11), (12, 9), (25, 35), (22, 47), (32, 29), (8, 34), (15, 38), (39, 7), (43, 11), (6, 45), (44, 6), (24, 15), (43, 47), (10, 8), (17, 19), (19, 29), (43, 26), (3, 42), (27, 44), (29, 34), (22, 7), (37, 27), (38, 39), (7, 23), (6, 32), (6, 16), (21, 26), (35, 16), (13, 35), (3, 33), (22, 10), (33, 7), (30, 8), (38, 38), (8, 12), (41, 3), (39, 21), (35, 2), (29, 41), (14, 23), (3, 18), (38, 6), (24, 46), (1, 17), (28, 36), (20, 47), (31, 2), (17, 27), (26, 46), (35, 24), (34, 14), (30, 18), (32, 35), (10, 4), (18, 8), (29, 42), (44, 15), (8, 35), (19, 37), (4, 25), (30, 48), (9, 44), (13, 28), (33, 0), (3, 26), (38, 4), (31, 41), (20, 34), (34, 46), (16, 20), (7, 35), (21, 35), (40, 48), (30, 6), (5, 6), (23, 22), (8, 31), (35, 42), (33, 36), (2, 47), (9, 28), (11, 34), (9, 48), (8, 33), (39, 5), (43, 0), (16, 31), (26, 4), (34, 23), (0, 20), (11, 28), (11, 16), (30, 14), (34, 39), (18, 14), (40, 33), (11, 5), (2, 16), (41, 4), (43, 18), (36, 36), (42, 28), (32, 31), (23, 21), (20, 40), (20, 24), (35, 48), (40, 24), (17, 17), (13, 39), (25, 18), (29, 14), (21, 47), (13, 1), (10, 30), (1, 14), (18, 40), (1, 39), (40, 10), (25, 6), (9, 4), (2, 19), (10, 19), (33, 48), (42, 4), (22, 23), (20, 5), (34, 48), (12, 12), (3, 44), (0, 17), (39, 30), (34, 21), (20, 33), (42, 44), (7, 21), (41, 39), (16, 16), (44, 13), (4, 24), (13, 25), (35, 35), (27, 28), (5, 35), (42, 21), (33, 34), (17, 13), (23, 17), (5, 36), (36, 2), (11, 37), (27, 48), (7, 18), (25, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 34), (3, 5), (22, 18), (24, 28), (37, 29), (10, 1), (13, 35), (4, 31), (14, 14), (38, 10), (32, 43), (29, 30), (12, 16), (9, 25), (24, 29), (8, 10), (21, 2), (35, 46), (18, 6), (28, 22), (11, 23), (25, 2), (21, 45), (29, 21), (25, 37), (23, 12), (3, 27), (27, 14), (0, 26), (38, 25), (20, 45), (36, 16), (17, 31), (20, 37), (33, 45), (11, 13), (10, 20), (15, 36), (25, 30), (29, 25), (23, 5), (27, 39), (27, 30), (22, 0), (9, 17), (6, 7), (6, 42), (38, 22), (13, 23), (19, 2), (26, 28), (18, 20), (31, 37), (10, 21), (32, 31), (9, 39), (0, 7), (19, 37), (22, 9), (35, 36), (28, 42), (8, 35), (7, 24), (12, 35), (37, 10), (24, 25), (1, 27), (16, 33), (19, 34), (31, 32), (10, 24), (35, 18), (24, 17), (17, 0), (3, 0), (1, 46), (8, 33), (19, 12), (6, 12), (30, 8), (17, 22), (13, 27), (35, 39), (22, 16), (27, 24), (29, 38), (18, 27), (36, 34), (16, 5), (33, 44), (19, 36), (14, 11), (21, 3), (15, 24), (13, 5), (4, 5), (26, 6), (10, 28), (21, 5), (39, 18), (3, 35), (27, 13), (15, 5), (7, 45), (3, 38), (37, 6), (9, 7), (2, 43), (13, 1), (19, 30), (10, 31), (4, 33), (36, 15), (31, 10), (32, 46), (27, 42), (38, 30), (7, 29), (7, 16), (33, 25), (37, 33), (18, 36), (30, 4), (38, 29), (9, 38), (14, 45), (32, 25), (26, 17), (5, 27), (27, 1), (28, 34), (32, 37), (18, 7), (39, 16), (7, 2), (27, 23), (28, 29), (0, 45), (2, 46), (34, 17), (8, 23), (25, 32), (17, 6), (26, 46), (16, 10), (23, 30), (0, 21), (0, 39), (29, 8), (17, 8), (28, 7), (35, 34), (10, 25), (29, 0), (35, 24), (11, 14), (34, 30), (22, 13), (5, 37), (24, 35), (12, 46), (32, 5), (6, 36), (10, 39), (23, 39), (6, 32), (18, 25), (32, 41), (7, 34), (14, 42), (19, 3), (5, 13), (8, 3), (3, 15), (13, 38), (37, 30), (31, 13), (12, 10), (23, 4), (12, 3), (13, 37), (31, 41), (34, 20), (32, 1), (32, 18), (33, 7), (28, 20), (11, 11), (39, 40), (34, 40), (25, 25), (21, 43), (24, 27), (31, 9), (39, 3), (36, 0), (8, 31), (22, 10), (18, 28), (18, 26), (4, 39), (14, 30), (32, 40), (1, 20), (21, 30), (21, 31), (35, 13), (37, 41), (29, 1), (9, 2), (31, 26), (30, 11), (31, 44), (13, 9), (37, 24), (3, 7), (11, 17), (30, 27), (33, 32), (21, 41), (0, 29), (22, 28), (37, 27), (22, 3), (17, 39), (9, 12), (28, 28), (18, 2), (17, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 13), (14, 34), (8, 8), (14, 2), (5, 20), (4, 39), (18, 4), (32, 9), (27, 10), (4, 1), (10, 27), (7, 14), (27, 1), (36, 2), (28, 18), (10, 23), (34, 37), (31, 6), (7, 25), (36, 4), (12, 6), (31, 13), (30, 22), (28, 35), (35, 11), (23, 6), (29, 37), (21, 7), (20, 1), (36, 38), (22, 30), (38, 36), (37, 27), (22, 23), (25, 20), (33, 36), (30, 39), (16, 11), (9, 2), (14, 13), (31, 20), (28, 22), (32, 28), (5, 23), (25, 18), (12, 21), (25, 0), (22, 33), (5, 7), (14, 30), (34, 25), (6, 25), (7, 20), (8, 15), (3, 33), (38, 2), (30, 10), (23, 26), (27, 30), (1, 36), (18, 38), (29, 6), (33, 2), (21, 32), (23, 32), (18, 33), (15, 11), (29, 14), (3, 35), (30, 24), (39, 24), (0, 14), (11, 34), (11, 33), (12, 17), (28, 0), (18, 2), (4, 9), (18, 35), (0, 24), (14, 6), (34, 10), (0, 17), (11, 1), (27, 34), (21, 33), (38, 20), (26, 19), (35, 27), (34, 31), (27, 5), (34, 15), (7, 27), (13, 32), (0, 20), (15, 17), (11, 0), (38, 30), (14, 23), (0, 23), (0, 4), (30, 38), (23, 36), (0, 21), (26, 17), (32, 31), (37, 14), (17, 38), (16, 40), (7, 22), (20, 11), (0, 12), (9, 12), (33, 26), (29, 20), (17, 27), (38, 10), (34, 32), (18, 36), (22, 36), (24, 29), (10, 13), (34, 22), (11, 31), (1, 15), (24, 40), (1, 29), (19, 37), (29, 21), (16, 27), (7, 8), (13, 16), (27, 31), (28, 38), (24, 26), (36, 28), (32, 23), (7, 37), (22, 5), (13, 27), (20, 27), (16, 14), (33, 7), (13, 35), (13, 17), (9, 5), (8, 39), (38, 7), (28, 21), (25, 17), (5, 33), (36, 3), (35, 33), (33, 4), (0, 3), (22, 14), (4, 15), (29, 4), (31, 38), (36, 0), (32, 37), (26, 25), (27, 22), (29, 33), (20, 0), (5, 36), (34, 0), (13, 40), (37, 12), (5, 10), (5, 18), (14, 32), (8, 32), (37, 40), (10, 39), (7, 23), (18, 0), (21, 26), (24, 39), (23, 28), (20, 9), (9, 20), (35, 26), (9, 22), (30, 8), (17, 0), (3, 19), (6, 37), (31, 25), (0, 26), (23, 34), (24, 38), (6, 9), (11, 37), (24, 33), (5, 37), (11, 36), (33, 29), (13, 20), (19, 27), (8, 28), (18, 15), (8, 4), (0, 9), (32, 3), (27, 18), (29, 36), (32, 11), (28, 4), (30, 1), (37, 11), (4, 19), (33, 32), (1, 8), (9, 31), (5, 3), (37, 9), (1, 23), (10, 33), (27, 36), (29, 34), (31, 19), (18, 7), (18, 6), (2, 26), (30, 28), (11, 14), (8, 30), (5, 38), (39, 36), (36, 18), (9, 14), (39, 13), (11, 32), (3, 39), (11, 23), (3, 26), (10, 21), (12, 4), (12, 32), (27, 0), (4, 10), (11, 40), (7, 29), (36, 31), (13, 1), (14, 26), (8, 20), (1, 3), (10, 36), (1, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 31), (39, 35), (29, 43), (8, 11), (23, 36), (16, 18), (39, 8), (16, 14), (17, 29), (35, 32), (6, 41), (36, 4), (33, 27), (16, 40), (1, 10), (32, 4), (27, 35), (38, 19), (0, 38), (6, 46), (13, 9), (20, 0), (11, 21), (3, 17), (4, 22), (33, 41), (4, 3), (38, 46), (3, 34), (26, 5), (35, 28), (8, 45), (43, 24), (16, 21), (23, 12), (41, 29), (42, 23), (35, 12), (19, 5), (14, 38), (22, 45), (4, 31), (34, 28), (24, 45), (8, 36), (36, 44), (36, 8), (18, 11), (18, 18), (32, 34), (11, 15), (17, 28), (30, 18), (7, 10), (9, 39), (9, 20), (37, 19), (22, 5), (31, 21), (10, 30), (20, 31), (9, 17), (18, 30), (17, 4), (36, 32), (29, 2), (8, 25), (6, 5), (43, 20), (23, 30), (2, 12), (1, 47), (20, 2), (43, 32), (24, 40), (34, 13), (40, 18), (6, 28), (42, 30), (9, 40), (29, 27), (20, 23), (8, 8), (17, 30), (40, 23), (1, 29), (18, 32), (11, 27), (17, 7), (30, 8), (13, 32), (9, 13), (4, 38), (20, 9), (39, 25), (19, 20), (6, 37), (22, 24), (38, 22), (41, 37), (25, 23), (36, 23), (21, 40), (32, 6), (13, 44), (33, 16), (27, 31), (43, 29), (0, 44), (10, 34), (2, 14), (1, 27), (17, 36), (5, 23), (12, 17), (33, 13), (33, 44), (40, 5), (3, 28), (23, 18), (1, 45), (23, 14), (7, 38), (25, 39), (11, 4), (40, 27), (15, 6), (7, 20), (8, 28), (34, 20), (2, 8), (10, 33), (28, 8), (13, 38), (13, 31), (21, 47), (41, 46), (22, 3), (16, 20), (41, 12), (10, 24), (36, 11), (27, 22), (29, 30), (9, 0), (30, 33), (5, 14), (41, 7), (15, 42), (28, 16), (29, 16), (8, 38), (21, 0), (2, 18), (26, 21), (22, 7), (35, 43), (37, 33), (21, 39), (16, 15), (41, 41), (32, 16), (35, 6), (36, 0), (18, 28), (29, 5), (26, 47), (40, 45), (22, 8), (16, 17), (39, 29), (10, 9), (14, 34), (25, 1), (20, 25), (12, 31), (34, 21), (21, 44), (41, 3), (40, 16), (7, 37), (12, 0), (12, 41), (33, 2), (7, 22), (27, 20), (2, 3), (29, 25), (12, 27), (40, 10), (28, 11), (36, 16), (33, 34), (38, 11), (15, 33), (2, 1), (7, 42), (2, 4), (41, 35), (19, 31), (23, 29), (43, 5), (2, 39), (5, 6), (0, 37), (19, 8), (36, 42), (40, 14), (13, 13), (26, 30), (34, 31), (33, 8), (21, 45), (0, 7), (18, 31), (34, 4), (18, 21), (34, 1), (25, 37), (28, 45), (28, 41), (30, 45), (38, 3), (12, 8), (12, 29), (36, 22), (15, 18), (39, 9), (5, 33), (33, 11), (41, 40), (16, 22), (14, 17), (39, 42), (27, 17), (35, 37), (8, 31), (22, 13), (25, 21), (34, 8), (2, 40), (21, 13), (36, 33), (43, 21), (3, 21), (24, 10), (23, 33), (26, 31), (9, 18), (14, 37), (13, 37), (18, 17), (10, 5), (34, 7), (26, 35), (43, 26), (4, 11), (21, 21), (16, 1), (33, 21), (13, 39), (24, 44), (12, 6), (22, 18), (4, 17), (14, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 32), (34, 18), (25, 5), (8, 22), (13, 37), (17, 38), (40, 28), (43, 35), (43, 25), (5, 6), (41, 2), (28, 26), (36, 40), (21, 36), (39, 34), (43, 6), (27, 29), (11, 33), (12, 4), (4, 41), (28, 43), (30, 3), (26, 27), (35, 15), (14, 31), (33, 43), (21, 18), (40, 42), (5, 27), (2, 43), (11, 39), (17, 18), (25, 13), (32, 13), (31, 42), (36, 34), (19, 23), (20, 42), (19, 22), (27, 25), (19, 39), (5, 5), (10, 23), (5, 28), (13, 12), (28, 9), (7, 5), (6, 0), (29, 31), (36, 37), (22, 4), (37, 28), (16, 15), (15, 13), (7, 32), (32, 29), (12, 27), (10, 8), (6, 36), (33, 24), (37, 36), (8, 27), (16, 16), (30, 10), (34, 43), (42, 19), (9, 42), (13, 8), (43, 21), (1, 10), (3, 33), (33, 19), (28, 25), (15, 7), (36, 12), (28, 14), (27, 22), (26, 38), (16, 8), (19, 29), (15, 22), (34, 32), (5, 44), (36, 1), (40, 31), (7, 31), (6, 16), (1, 28), (12, 9), (20, 2), (23, 2), (36, 15), (13, 39), (10, 16), (4, 39), (35, 34), (18, 40), (8, 28), (26, 5), (28, 38), (38, 6), (39, 23), (13, 15), (12, 14), (39, 10), (4, 15), (26, 43), (11, 24), (31, 37), (31, 17), (40, 2), (16, 31), (25, 28), (21, 11), (17, 1), (9, 18), (8, 1), (19, 0), (2, 6), (32, 18), (23, 41), (39, 32), (19, 12), (34, 34), (39, 43), (21, 23), (16, 3), (42, 40), (18, 32), (22, 18), (23, 42), (4, 10), (1, 20), (22, 29), (23, 3), (15, 37), (37, 23), (35, 28), (7, 9), (2, 7), (42, 20), (15, 21), (12, 10), (15, 35), (4, 4), (40, 40), (31, 29), (4, 22), (5, 37), (20, 12), (39, 2), (31, 23), (40, 0), (26, 1), (24, 16), (20, 7), (14, 8), (43, 27), (38, 18), (31, 41), (23, 0), (3, 23), (21, 30), (4, 26), (34, 41), (0, 23), (39, 9), (14, 40), (16, 18), (20, 41), (2, 30), (30, 1), (21, 7), (30, 39), (28, 22), (29, 37), (18, 34), (15, 14), (16, 29), (3, 36), (11, 13), (2, 28), (22, 39), (34, 22), (20, 30), (41, 30), (27, 5), (2, 4), (24, 22), (13, 13), (32, 27), (21, 37), (3, 9), (41, 44), (21, 15), (18, 31), (32, 40), (33, 25), (21, 24), (27, 32), (32, 24), (38, 12), (38, 43), (28, 24), (15, 26), (34, 38), (21, 31), (7, 34), (3, 2), (33, 39), (33, 36), (1, 15), (36, 19), (18, 8), (40, 12), (12, 32), (42, 26), (29, 17), (13, 29), (24, 26), (7, 8), (42, 6), (26, 11), (35, 5), (18, 30), (25, 6), (24, 33), (29, 34), (41, 39), (19, 27), (41, 28), (38, 20), (0, 7), (15, 34), (0, 17), (17, 12), (19, 33), (25, 2), (30, 36), (8, 39), (18, 28), (12, 36), (22, 7), (25, 35), (10, 0), (35, 17), (20, 13), (29, 1), (27, 10), (19, 9), (29, 5), (23, 43), (10, 17), (16, 25), (42, 41), (3, 27), (31, 7), (10, 41), (3, 31), (14, 41), (31, 0), (25, 7), (4, 42), (38, 34), (2, 9), (34, 23), (5, 18), (24, 12), (22, 42), (16, 12), (35, 16), (39, 0), (39, 22), (9, 27), (21, 21), (40, 5), (33, 41), (9, 36), (39, 1), (30, 30), (14, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 43), (25, 32), (40, 29), (17, 19), (19, 24), (39, 0), (38, 26), (15, 14), (21, 31), (42, 7), (26, 37), (34, 27), (18, 26), (8, 4), (5, 37), (21, 25), (32, 14), (41, 5), (9, 13), (3, 43), (15, 4), (6, 6), (12, 44), (17, 27), (43, 32), (19, 25), (39, 24), (10, 30), (0, 28), (37, 24), (35, 11), (26, 40), (11, 40), (30, 11), (13, 12), (15, 36), (13, 21), (21, 26), (36, 21), (24, 8), (28, 35), (43, 8), (38, 28), (37, 9), (37, 0), (29, 33), (25, 16), (2, 15), (15, 42), (35, 34), (22, 19), (28, 18), (42, 39), (1, 44), (2, 34), (32, 11), (41, 21), (19, 38), (37, 10), (18, 18), (9, 14), (9, 26), (35, 29), (17, 28), (29, 25), (36, 43), (26, 11), (23, 38), (5, 38), (39, 15), (26, 25), (30, 40), (37, 29), (24, 36), (16, 12), (40, 15), (18, 24), (29, 36), (8, 13), (33, 2), (16, 30), (31, 37), (27, 0), (41, 12), (43, 33), (41, 16), (25, 38), (12, 24), (28, 6), (33, 28), (11, 23), (19, 13), (3, 0), (20, 12), (0, 23), (10, 19), (41, 10), (14, 38), (27, 3), (14, 37), (43, 19), (33, 21), (36, 9), (13, 39), (37, 22), (6, 5), (43, 39), (26, 13), (30, 41), (27, 35), (17, 37), (2, 9), (3, 16), (17, 16), (33, 31), (34, 23), (21, 35), (21, 7), (18, 23), (2, 38), (1, 17), (41, 11), (15, 8), (18, 15), (35, 0), (11, 4), (7, 20), (9, 38), (2, 17), (10, 0), (40, 32), (14, 13), (7, 17), (32, 40), (1, 16), (37, 12), (13, 0), (41, 23), (35, 13), (40, 20), (4, 15), (16, 22), (5, 35), (17, 20), (4, 2), (20, 34), (3, 3), (5, 25), (43, 14), (18, 8), (30, 14), (4, 8), (1, 40), (22, 28), (3, 7), (22, 15), (42, 9), (34, 9), (7, 15), (41, 30), (20, 5), (23, 7), (38, 7), (37, 13), (3, 13), (20, 23), (9, 28), (4, 29), (25, 5), (7, 21), (27, 29), (16, 21), (4, 34), (22, 34), (9, 30), (34, 13), (1, 28), (33, 27), (36, 36), (2, 40), (33, 16), (34, 35), (0, 22), (33, 34), (8, 1), (29, 16), (14, 41), (6, 20), (39, 5), (9, 4), (8, 22), (42, 26), (1, 38), (30, 23), (5, 44), (31, 4), (34, 37), (35, 6), (25, 37), (6, 21), (25, 21), (30, 12), (29, 44), (7, 26), (4, 44), (28, 9), (37, 2), (31, 44), (37, 38), (39, 32), (43, 37), (42, 35), (17, 26), (25, 9), (15, 25), (8, 29), (6, 24), (10, 5), (21, 13), (7, 29), (8, 3), (3, 19), (36, 42), (28, 30), (17, 25), (8, 36), (19, 14), (40, 9), (15, 39), (26, 31), (6, 1), (9, 23), (28, 31), (33, 41), (5, 12), (36, 22), (19, 8), (36, 26), (27, 13), (10, 36), (18, 32), (6, 19), (5, 18), (0, 18), (36, 44), (6, 28), (6, 40), (8, 42), (34, 0), (36, 1), (26, 9), (28, 21), (37, 30), (28, 16), (39, 41), (5, 5), (38, 0), (13, 20), (31, 33), (11, 31), (30, 16), (3, 37), (5, 8), (0, 25), (18, 12), (1, 32), (40, 18), (41, 32), (38, 6), (36, 41), (33, 15), (33, 19), (29, 17), (4, 19), (7, 37), (2, 22), (20, 41), (14, 25), (4, 24), (31, 42), (22, 35), (1, 12), (34, 3), (20, 6), (9, 16), (5, 30), (6, 34), (10, 23), (19, 40), (2, 37), (15, 33), (34, 28), (12, 0), (21, 39), (39, 31), (19, 19), (29, 29), (38, 18), (7, 2), (5, 20), (11, 14), (33, 36), (25, 39), (27, 43), (30, 13), (21, 6), (39, 44), (17, 22), (23, 35), (24, 21), (12, 34), (27, 17), (11, 15), (13, 22), (30, 5), (38, 13), (33, 0), (31, 41), (5, 14), (10, 13), (1, 26), (43, 42), (23, 6), (8, 32), (25, 40), (40, 23), (42, 34), (10, 39), (20, 32), (23, 2), (2, 44), (40, 17), (22, 12), (20, 8), (14, 8), (26, 0), (21, 27), (37, 27), (5, 39), (24, 14), (15, 5), (11, 11), (42, 22), (20, 13), (3, 39), (39, 11), (2, 16), (33, 14), (5, 36), (32, 39), (25, 24), (18, 13), (35, 1), (13, 26), (16, 13), (13, 5), (12, 29), (39, 27), (17, 34), (40, 25), (27, 16), (29, 28), (17, 33), (5, 29), (18, 42), (23, 28), (42, 4), (42, 0), (43, 43), (26, 3), (32, 29), (0, 36), (18, 36), (16, 17), (30, 18), (16, 7), (26, 24), (18, 30), (29, 7), (15, 15), (39, 40), (41, 13), (19, 39), (5, 31), (18, 40), (0, 37), (39, 23), (36, 12), (30, 30), (30, 33), (40, 4), (13, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 31), (4, 14), (37, 22), (34, 1), (29, 35), (47, 37), (22, 30), (40, 33), (27, 18), (37, 9), (31, 3), (27, 5), (48, 6), (20, 8), (29, 9), (27, 25), (36, 15), (6, 27), (24, 22), (42, 19), (42, 23), (37, 39), (48, 8), (7, 26), (8, 22), (12, 6), (8, 8), (45, 25), (1, 11), (8, 0), (15, 37), (16, 10), (23, 23), (35, 7), (35, 29), (19, 2), (19, 40), (38, 24), (3, 5), (31, 25), (48, 22), (45, 8), (30, 15), (29, 1), (33, 28), (48, 25), (23, 14), (10, 35), (17, 21), (20, 36), (2, 14), (47, 9), (38, 3), (26, 12), (37, 25), (27, 20), (41, 5), (19, 36), (5, 20), (33, 26), (12, 30), (26, 11), (42, 6), (19, 13), (44, 37), (1, 39), (42, 12), (42, 41), (4, 19), (30, 7), (30, 16), (11, 12), (24, 17), (24, 15), (34, 15), (26, 42), (12, 10), (8, 13), (23, 27), (2, 30), (27, 24), (18, 31), (10, 21), (6, 7), (33, 19), (22, 18), (11, 41), (31, 10), (19, 32), (7, 33), (46, 15), (46, 11), (48, 41), (0, 19), (21, 34), (4, 31), (40, 37), (40, 24), (17, 0), (15, 21), (36, 33), (2, 32), (20, 16), (36, 12), (5, 5), (37, 41), (44, 11), (30, 12), (13, 34), (41, 9), (31, 34), (29, 26), (41, 41), (33, 24), (26, 34), (2, 33), (33, 2), (19, 9), (20, 39), (43, 40), (0, 20), (23, 3), (45, 1), (33, 12), (14, 19), (5, 34), (36, 22), (24, 34), (48, 5), (12, 11), (7, 39), (21, 31), (19, 15), (45, 39), (39, 10), (41, 23), (26, 21), (18, 22), (29, 30), (22, 15), (39, 34), (15, 19), (21, 25), (34, 41), (40, 3), (29, 25), (16, 40), (17, 28), (23, 15), (23, 24), (0, 26), (46, 40), (28, 26), (22, 35), (23, 21), (40, 28), (42, 33), (31, 20), (13, 4), (11, 6), (1, 22), (8, 39), (5, 17), (8, 19), (28, 36), (44, 36), (2, 0), (35, 42), (38, 2), (13, 23), (25, 17), (26, 10), (34, 29), (45, 27), (12, 9), (43, 1), (4, 7), (36, 11), (18, 13), (21, 7), (33, 6), (35, 24), (31, 4), (22, 1), (21, 14), (1, 41), (38, 13), (18, 2), (29, 21), (4, 41), (45, 19), (31, 38), (18, 18), (13, 37), (30, 21), (24, 2), (30, 17), (14, 0), (22, 25), (5, 4), (21, 13), (11, 39), (6, 21), (38, 33), (26, 37), (1, 37), (2, 6), (9, 0), (19, 41), (20, 30), (4, 34), (27, 4), (0, 30), (27, 0), (2, 21), (20, 35), (33, 17), (31, 32), (27, 19), (45, 17), (46, 14), (9, 25), (42, 15), (36, 37), (48, 29), (23, 22), (10, 36), (44, 17), (2, 12), (3, 38), (15, 40), (7, 15), (12, 13), (13, 20), (11, 11), (34, 13), (11, 10), (11, 18), (18, 35), (16, 36), (26, 33), (28, 42), (20, 18), (37, 29), (0, 34), (9, 15), (46, 22), (24, 8), (18, 39), (20, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 32), (29, 20), (27, 17), (31, 36), (19, 22), (13, 3), (16, 17), (26, 26), (39, 2), (9, 32), (6, 10), (35, 29), (27, 13), (37, 25), (14, 33), (7, 16), (22, 6), (27, 12), (18, 31), (38, 25), (29, 11), (8, 15), (21, 36), (10, 7), (3, 32), (24, 5), (31, 19), (18, 28), (15, 34), (2, 3), (6, 19), (29, 4), (24, 30), (17, 26), (4, 16), (10, 35), (35, 14), (16, 37), (39, 30), (6, 26), (11, 26), (36, 11), (32, 20), (16, 9), (34, 32), (10, 31), (27, 25), (12, 1), (18, 5), (25, 38), (15, 39), (18, 27), (5, 18), (0, 22), (12, 31), (5, 24), (26, 12), (32, 15), (36, 8), (7, 39), (36, 38), (24, 8), (3, 5), (7, 8), (0, 28), (11, 36), (21, 38), (36, 33), (15, 20), (21, 34), (10, 28), (39, 11), (0, 3), (26, 35), (5, 23), (29, 22), (28, 28), (21, 8), (28, 22), (31, 39), (8, 38), (34, 13), (19, 36), (22, 1), (2, 2), (34, 35), (17, 24), (23, 10), (17, 22), (31, 12), (18, 6), (37, 27), (17, 18), (11, 35), (10, 19), (10, 8), (16, 39), (1, 26), (29, 35), (36, 10), (33, 11), (14, 36), (23, 22), (3, 14), (2, 1), (33, 7), (2, 10), (9, 5), (31, 17), (24, 26), (23, 14), (13, 2), (36, 2), (15, 11), (6, 8), (36, 13), (16, 33), (11, 27), (22, 18), (31, 18), (17, 28), (0, 8), (22, 27), (34, 37), (12, 33), (24, 29), (6, 14), (13, 33), (37, 24), (6, 28), (28, 24), (10, 14), (8, 21), (12, 18), (24, 37), (0, 27), (34, 14), (2, 32), (30, 10), (18, 12), (1, 14), (35, 39), (3, 4), (33, 9), (22, 22), (9, 1), (11, 19), (11, 39), (5, 20), (5, 5), (20, 24), (3, 8), (39, 3), (29, 23), (9, 7), (26, 5), (11, 17), (13, 16), (11, 30), (35, 31), (8, 29), (5, 4), (4, 20), (0, 26), (21, 30), (37, 32), (25, 27), (21, 11), (23, 15), (15, 14), (38, 3), (15, 23), (15, 28), (19, 23), (26, 22), (18, 38), (21, 12), (36, 25), (1, 19), (17, 12), (20, 6), (34, 18), (35, 3), (27, 8), (12, 12), (7, 7), (31, 27), (3, 28), (35, 34), (11, 33), (29, 31), (0, 13), (15, 7), (34, 30), (19, 27), (32, 17), (27, 31), (32, 21), (34, 25), (8, 23), (28, 23), (12, 10), (13, 31), (25, 26), (38, 4), (28, 35), (28, 5), (27, 30), (23, 19), (35, 36), (8, 5), (14, 3), (19, 6), (38, 8), (22, 21), (35, 37), (31, 38), (29, 25), (15, 16), (6, 32), (29, 24), (19, 11), (16, 34), (11, 1), (17, 13), (29, 0), (2, 16), (5, 3), (14, 11), (17, 9), (9, 34), (12, 11), (8, 4), (17, 11), (7, 36), (33, 18), (21, 9), (0, 16), (14, 30), (38, 32), (12, 38), (37, 30), (29, 37), (30, 13), (8, 39), (2, 24), (8, 25), (38, 20), (7, 5), (29, 3), (34, 8), (4, 10), (11, 38), (0, 14), (24, 28), (33, 16), (36, 12), (4, 14), (19, 28), (1, 15), (24, 38), (30, 19), (29, 7), (34, 22), (33, 25), (5, 28), (17, 39), (23, 25), (3, 9), (35, 9), (10, 16), (39, 14), (31, 22), (34, 15), (27, 14), (20, 25), (17, 16), (30, 28), (33, 35), (38, 21), (32, 29), (12, 35), (24, 21), (36, 3), (9, 27), (2, 36), (11, 11), (2, 6), (2, 29), (30, 17), (9, 19), (38, 7), (36, 22), (27, 38), (32, 2), (36, 39), (39, 22), (32, 9), (13, 38), (1, 11), (30, 24), (32, 16), (20, 11), (21, 18), (34, 3), (12, 36), (34, 2), (4, 22), (28, 8), (23, 16), (32, 31), (20, 12), (21, 15), (10, 15), (7, 10), (2, 38), (20, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 33), (16, 14), (11, 14), (34, 13), (15, 34), (39, 3), (37, 18), (37, 41), (28, 2), (34, 38), (43, 45), (33, 42), (8, 42), (19, 37), (44, 33), (7, 39), (1, 10), (31, 3), (31, 38), (16, 40), (20, 13), (9, 36), (25, 18), (32, 5), (14, 8), (9, 0), (5, 31), (4, 26), (37, 33), (35, 24), (26, 45), (2, 23), (18, 42), (13, 0), (41, 28), (16, 29), (8, 17), (20, 34), (29, 36), (41, 31), (17, 5), (34, 14), (18, 23), (35, 25), (41, 16), (7, 30), (37, 14), (8, 46), (16, 9), (30, 10), (40, 19), (44, 2), (44, 30), (42, 45), (39, 7), (11, 30), (28, 31), (25, 40), (37, 31), (14, 46), (22, 7), (35, 32), (40, 0), (19, 13), (22, 5), (23, 36), (3, 31), (12, 11), (2, 32), (10, 34), (33, 45), (23, 4), (37, 39), (7, 17), (24, 38), (15, 15), (40, 14), (32, 7), (9, 42), (13, 26), (34, 8), (39, 34), (8, 37), (31, 30), (18, 25), (36, 8), (12, 5), (10, 41), (7, 14), (0, 25), (19, 35), (39, 26), (9, 29), (29, 38), (4, 3), (25, 26), (22, 33), (44, 35), (43, 18), (27, 24), (32, 20), (31, 14), (30, 41), (9, 18), (38, 41), (28, 35), (20, 0), (19, 4), (28, 1), (37, 9), (43, 41), (8, 20), (41, 9), (24, 3), (9, 15), (19, 21), (42, 42), (27, 36), (10, 22), (27, 2), (36, 3), (41, 45), (19, 11), (42, 16), (12, 30), (43, 15), (9, 20), (41, 26), (0, 19), (29, 29), (43, 5), (5, 45), (24, 2), (29, 30), (13, 23), (20, 43), (2, 19), (34, 1), (43, 34), (44, 13), (4, 36), (1, 8), (18, 32), (22, 4), (20, 20), (43, 33), (10, 42), (14, 30), (0, 31), (20, 7), (42, 34), (32, 9), (2, 34), (13, 28), (17, 15), (38, 33), (14, 43), (20, 27), (16, 28), (26, 4), (0, 42), (1, 31), (27, 1), (7, 20), (10, 20), (31, 32), (5, 20), (31, 4), (29, 33), (8, 2), (29, 3), (36, 28), (16, 10), (36, 43), (27, 26), (42, 20), (38, 17), (28, 25), (5, 34), (40, 9), (36, 46), (16, 39), (22, 40), (16, 1), (3, 14), (34, 18), (11, 5), (20, 45), (1, 41), (43, 28), (40, 23), (41, 15), (4, 21), (16, 46), (16, 34), (31, 25), (32, 24), (42, 1), (4, 33), (31, 43), (24, 24), (36, 23), (5, 39), (29, 43), (23, 33), (11, 37), (20, 17), (20, 42), (39, 41), (42, 22), (17, 6), (22, 9), (32, 39), (5, 18), (24, 34), (15, 0), (42, 23), (32, 36), (8, 35), (28, 3), (14, 19), (4, 10), (24, 17), (36, 11), (8, 18), (10, 44), (16, 2), (10, 4), (30, 7), (32, 26), (20, 18), (26, 29), (33, 3), (20, 1), (6, 19), (18, 7), (15, 40), (21, 11), (28, 18), (37, 15), (11, 43), (6, 35), (42, 12), (27, 22), (12, 20), (21, 5), (41, 41), (20, 26), (26, 9), (40, 41), (26, 42), (3, 25), (17, 23), (19, 20), (23, 5), (14, 2), (39, 12), (2, 41), (8, 24), (33, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 31), (21, 28), (11, 31), (11, 41), (31, 32), (18, 5), (28, 20), (38, 7), (14, 26), (34, 18), (35, 33), (12, 6), (4, 20), (27, 9), (7, 29), (20, 19), (30, 20), (38, 29), (12, 41), (13, 30), (10, 23), (33, 6), (7, 35), (24, 38), (12, 5), (27, 36), (14, 18), (35, 2), (30, 32), (15, 41), (16, 9), (35, 13), (33, 21), (8, 2), (26, 31), (34, 6), (1, 26), (38, 30), (0, 40), (12, 35), (27, 24), (17, 39), (2, 34), (36, 7), (0, 5), (3, 8), (5, 4), (21, 7), (6, 31), (40, 0), (24, 9), (23, 2), (11, 0), (28, 2), (24, 36), (19, 30), (15, 31), (32, 15), (15, 32), (9, 33), (28, 1), (29, 0), (10, 10), (26, 7), (0, 27), (24, 40), (24, 27), (2, 41), (18, 21), (15, 13), (25, 11), (7, 32), (27, 19), (10, 6), (37, 33), (26, 34), (32, 37), (39, 26), (19, 18), (3, 30), (39, 10), (36, 3), (27, 23), (15, 20), (19, 38), (34, 30), (2, 26), (23, 38), (24, 37), (29, 6), (6, 1), (33, 10), (20, 20), (29, 31), (25, 13), (28, 16), (5, 20), (30, 40), (5, 26), (36, 16), (34, 25), (13, 22), (7, 11), (20, 31), (37, 9), (19, 31), (3, 33), (16, 14), (1, 27), (23, 21), (15, 27), (14, 4), (22, 18), (5, 9), (22, 5), (20, 18), (34, 13), (18, 22), (29, 26), (39, 40), (31, 26), (6, 12), (21, 18), (19, 19), (14, 15), (33, 14), (18, 18), (10, 16), (23, 24), (15, 18), (29, 29), (36, 41), (4, 21), (8, 1), (20, 6), (22, 32), (0, 7), (1, 30), (33, 34), (26, 8), (27, 1), (7, 37), (17, 29), (22, 12), (35, 37), (9, 36), (36, 23), (39, 37), (1, 0), (8, 20), (32, 24), (31, 28), (40, 26), (29, 5), (9, 8), (30, 3), (8, 38), (26, 20), (11, 30), (37, 8), (33, 12), (26, 23), (35, 27), (40, 17), (25, 0), (19, 39), (29, 7), (38, 22), (27, 33), (5, 10), (16, 1), (6, 21), (16, 11), (32, 6), (40, 30), (6, 42), (5, 14), (40, 14), (10, 33), (14, 33), (38, 24), (11, 17), (34, 33), (4, 29), (38, 2), (2, 33), (35, 23), (38, 18), (22, 19), (26, 21), (20, 17), (24, 41), (23, 31), (6, 32), (35, 36), (7, 10), (21, 19), (33, 39), (22, 10), (8, 11), (10, 32), (37, 3), (15, 42), (40, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 34), (34, 12), (21, 16), (19, 35), (8, 4), (8, 37), (5, 40), (34, 39), (33, 21), (38, 4), (2, 0), (36, 38), (5, 29), (11, 1), (40, 1), (19, 18), (36, 30), (24, 24), (5, 10), (12, 6), (12, 11), (10, 6), (36, 5), (12, 13), (18, 9), (12, 12), (14, 15), (30, 21), (6, 31), (35, 6), (38, 25), (21, 27), (31, 7), (29, 38), (41, 2), (39, 28), (32, 2), (31, 14), (10, 29), (37, 13), (32, 8), (31, 1), (28, 41), (29, 12), (10, 1), (21, 38), (24, 38), (41, 3), (2, 23), (39, 22), (18, 29), (11, 19), (28, 24), (11, 39), (12, 24), (31, 23), (27, 29), (35, 15), (18, 43), (42, 24), (11, 28), (24, 0), (5, 19), (14, 30), (24, 28), (35, 24), (9, 28), (39, 7), (32, 44), (5, 43), (6, 33), (29, 23), (16, 21), (2, 2), (20, 18), (26, 40), (13, 30), (37, 8), (30, 29), (30, 4), (3, 39), (28, 0), (12, 27), (39, 2), (8, 21), (5, 2), (24, 23), (25, 1), (25, 31), (38, 37), (1, 32), (11, 25), (30, 3), (19, 15), (38, 39), (35, 23), (33, 25), (6, 42), (14, 14), (9, 3), (17, 33), (2, 3), (29, 21), (35, 4), (26, 22), (11, 0), (22, 30), (31, 3), (42, 22), (25, 24), (9, 30), (41, 44), (12, 42), (11, 20), (39, 9), (38, 23), (30, 43), (13, 18), (40, 28), (38, 7), (39, 37), (9, 24), (8, 16), (34, 3), (25, 2), (14, 32), (9, 25), (22, 31), (33, 27), (29, 36), (35, 38), (12, 29), (9, 36), (10, 0), (3, 11), (39, 4), (0, 1), (27, 23), (4, 40), (13, 20), (36, 23), (6, 1), (25, 30), (20, 42), (29, 6), (41, 24), (10, 10), (24, 36), (18, 30), (14, 13), (42, 15), (18, 39), (33, 28), (11, 3), (34, 35), (23, 10), (34, 34), (5, 33), (6, 19), (0, 32), (3, 27), (1, 37), (16, 12), (16, 33), (41, 27), (28, 6), (41, 14), (32, 10), (18, 27), (35, 5), (29, 22), (30, 6), (1, 6), (17, 23), (24, 15), (13, 32), (7, 1), (7, 16), (29, 4), (16, 31), (39, 33), (15, 18), (34, 5), (16, 25), (27, 19), (13, 12), (3, 15), (26, 20), (23, 15), (36, 31), (32, 24), (3, 26), (21, 41), (31, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 12), (3, 4), (40, 39), (41, 6), (40, 37), (36, 30), (28, 24), (41, 30), (34, 7), (14, 23), (9, 21), (8, 40), (21, 23), (34, 16), (23, 30), (30, 40), (29, 30), (36, 28), (38, 24), (17, 21), (23, 7), (15, 35), (8, 25), (38, 26), (6, 1), (11, 2), (39, 26), (18, 15), (16, 0), (20, 1), (35, 1), (19, 27), (30, 18), (34, 4), (36, 39), (22, 2), (16, 11), (21, 10), (18, 11), (10, 23), (27, 6), (10, 28), (14, 22), (38, 36), (33, 4), (13, 20), (29, 22), (8, 35), (8, 20), (3, 29), (16, 40), (36, 12), (30, 16), (37, 19), (36, 1), (22, 27), (28, 9), (20, 11), (27, 37), (23, 37), (3, 26), (10, 4), (19, 37), (12, 10), (37, 29), (22, 24), (33, 18), (2, 26), (21, 24), (34, 28), (20, 5), (38, 1), (11, 3), (32, 40), (25, 21), (11, 23), (32, 39), (12, 40), (37, 30), (23, 14), (33, 2), (14, 8), (36, 10), (34, 15), (23, 0), (17, 34), (21, 5), (30, 9), (13, 21), (41, 16), (10, 25), (23, 40), (14, 32), (22, 40), (40, 23), (3, 9), (16, 36), (35, 6), (20, 21), (36, 40), (3, 37), (3, 35), (15, 25), (1, 33), (40, 22), (29, 8), (23, 22), (5, 7), (32, 37), (31, 29), (3, 16), (1, 11), (21, 2), (21, 22), (11, 30), (3, 18), (5, 26), (37, 13), (28, 29), (16, 27), (38, 19), (26, 39), (33, 27), (29, 34), (38, 33), (32, 10), (12, 16), (23, 32), (2, 20), (36, 29), (20, 40), (30, 34), (10, 10), (15, 2), (4, 38), (21, 18), (20, 0), (5, 20), (40, 2), (37, 40), (32, 6), (36, 8), (13, 36), (1, 12), (40, 31), (29, 20), (38, 21), (6, 8), (12, 14), (32, 33), (11, 36), (1, 39), (7, 39), (8, 26), (33, 3), (16, 23), (0, 15), (12, 24), (27, 26), (5, 5), (30, 15), (17, 35), (10, 9), (29, 3), (19, 4), (16, 24), (5, 37), (30, 38), (4, 27), (17, 23), (3, 6), (37, 4), (7, 15), (20, 37), (11, 18), (24, 37), (15, 6), (8, 30), (36, 33), (25, 7), (37, 1), (10, 29), (12, 13), (41, 8), (5, 34), (14, 16), (40, 25), (26, 6), (11, 38), (3, 7), (31, 10), (30, 21), (14, 5), (30, 24), (13, 33), (28, 22), (19, 21), (7, 40), (11, 21), (35, 5), (18, 1), (22, 4), (13, 4), (2, 30), (23, 20), (40, 20), (15, 3), (33, 28), (34, 10), (6, 38), (2, 2), (36, 36), (1, 7), (2, 16), (28, 36), (23, 8), (3, 32), (36, 16), (17, 6), (10, 6), (41, 22), (31, 13), (7, 35), (16, 5), (22, 37), (31, 39), (28, 16), (4, 8), (30, 5), (22, 33), (23, 16), (31, 21), (24, 16), (36, 20), (20, 14), (21, 1), (27, 17), (34, 22), (7, 27), (6, 35), (40, 40), (41, 13), (19, 26), (21, 27), (28, 3), (21, 33), (13, 30), (34, 30), (25, 4), (35, 4), (41, 24), (8, 8), (24, 30), (32, 9), (18, 35), (22, 29), (36, 0), (35, 37), (25, 37), (23, 4), (22, 8), (1, 18), (38, 13), (39, 8), (25, 34), (8, 1), (37, 35), (34, 3), (12, 37), (41, 31), (37, 38), (6, 6), (15, 17), (4, 3), (4, 7), (39, 13), (6, 23), (8, 14), (26, 5), (30, 30), (21, 9), (29, 6), (13, 28), (9, 29), (22, 31), (28, 40), (22, 19), (8, 18), (41, 35), (9, 11), (15, 1), (6, 21), (37, 14), (33, 1), (27, 13), (14, 12), (23, 23), (2, 23), (38, 10), (13, 29), (23, 15), (6, 13), (6, 26), (36, 37), (18, 14), (13, 26), (2, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 14), (34, 37), (11, 40), (39, 32), (27, 37), (24, 46), (26, 3), (22, 19), (44, 0), (26, 38), (29, 41), (38, 17), (29, 1), (2, 34), (42, 7), (16, 12), (21, 46), (11, 45), (36, 3), (36, 4), (27, 17), (28, 25), (1, 24), (10, 19), (41, 1), (11, 28), (15, 31), (42, 35), (9, 21), (42, 3), (44, 25), (13, 12), (7, 33), (7, 32), (39, 19), (33, 14), (42, 20), (20, 17), (15, 0), (1, 37), (36, 35), (10, 39), (29, 36), (38, 3), (9, 12), (29, 12), (25, 33), (17, 42), (15, 24), (20, 16), (13, 25), (23, 38), (24, 33), (24, 41), (2, 28), (2, 24), (20, 30), (16, 47), (25, 46), (26, 44), (0, 5), (35, 40), (3, 32), (15, 18), (44, 12), (32, 41), (32, 17), (16, 43), (27, 11), (31, 6), (3, 46), (34, 22), (10, 8), (26, 26), (43, 23), (21, 45), (3, 42), (2, 1), (23, 8), (20, 3), (44, 47), (38, 5), (2, 46), (32, 48), (42, 2), (12, 37), (37, 23), (10, 13), (32, 7), (13, 27), (5, 44), (42, 23), (26, 46), (8, 27), (16, 41), (12, 7), (5, 32), (17, 33), (20, 5), (44, 37), (15, 11), (19, 48), (17, 28), (19, 10), (4, 7), (3, 24), (17, 18), (0, 16), (33, 37), (27, 7), (44, 1), (44, 15), (36, 7), (13, 14), (31, 12), (30, 48), (23, 40), (7, 45), (30, 27), (23, 42), (21, 35), (42, 0), (42, 4), (4, 46), (40, 33), (12, 34), (34, 24), (36, 1), (8, 22), (32, 19), (33, 5), (20, 11), (22, 44), (2, 48), (10, 35), (41, 38), (15, 46), (19, 12), (10, 30), (9, 5), (21, 14), (3, 33), (1, 6), (36, 12), (7, 48), (34, 33), (13, 16), (29, 22), (12, 2), (34, 42), (2, 3), (39, 5), (13, 3), (33, 39), (25, 0), (5, 47), (1, 13), (44, 8), (5, 33), (11, 23), (0, 37), (5, 17), (9, 3), (11, 44), (8, 23), (4, 47), (5, 24), (36, 47), (30, 28), (44, 19), (5, 41), (11, 0), (31, 47), (8, 24), (29, 40), (35, 1), (28, 16), (29, 18), (43, 18), (2, 11), (25, 4), (25, 13), (30, 20), (42, 47), (12, 47), (41, 45), (6, 30), (36, 10), (34, 45), (1, 36), (24, 45), (8, 28), (35, 33), (12, 18), (23, 17), (3, 9), (26, 35), (30, 8), (14, 31), (39, 40), (26, 14), (15, 10), (7, 15), (0, 26), (16, 30), (15, 15), (6, 9), (7, 9), (17, 31), (6, 17), (8, 15), (0, 24), (9, 6), (36, 23), (31, 17), (2, 5), (35, 18), (13, 20), (29, 45), (23, 31), (22, 47), (5, 10), (1, 23), (4, 5), (14, 45), (18, 0), (21, 0), (25, 44), (30, 16), (4, 35), (44, 42), (18, 17), (38, 22), (17, 47), (39, 12), (12, 19), (21, 47), (11, 3), (33, 10), (42, 45), (12, 33), (34, 40), (3, 20), (25, 22), (26, 4), (20, 4), (19, 0), (19, 46), (31, 27), (4, 33), (24, 36), (25, 25), (15, 25), (44, 27), (20, 20), (21, 15), (38, 24), (22, 5), (16, 21), (2, 33), (29, 23), (22, 18), (36, 14), (43, 42), (5, 40), (31, 32), (0, 47), (37, 37), (25, 8), (39, 46), (40, 7), (34, 27), (43, 10), (41, 32), (12, 23), (34, 25), (25, 18), (42, 24), (4, 41), (6, 23), (28, 39), (30, 18), (17, 41), (5, 26), (7, 39), (9, 22), (34, 38), (33, 0), (11, 5), (31, 14), (32, 3), (42, 38), (29, 38), (16, 25), (43, 20), (7, 46), (44, 14), (16, 11), (35, 31), (12, 9), (37, 22), (22, 32), (6, 46), (15, 33), (0, 8), (41, 44), (37, 41), (0, 10), (15, 2), (37, 11), (40, 41), (35, 45), (28, 46), (32, 24), (11, 48), (43, 26), (33, 20), (0, 40), (27, 31), (39, 25), (22, 25), (1, 8), (5, 7), (40, 8), (17, 20), (9, 39), (39, 38), (23, 47), (15, 44), (31, 18), (31, 31), (25, 21), (20, 26), (29, 47), (25, 37), (19, 44), (3, 1), (37, 2), (32, 5), (22, 46), (41, 16), (13, 29), (1, 0), (22, 29), (14, 15), (1, 7), (37, 35), (17, 6), (17, 7), (22, 24), (7, 7), (20, 44), (0, 39), (6, 32), (14, 23), (15, 45), (27, 10), (26, 42), (37, 32), (11, 19), (8, 13), (0, 20), (2, 45), (29, 32), (8, 45), (14, 4), (10, 46), (3, 18), (23, 25), (18, 41), (13, 36), (33, 18), (11, 8), (6, 1), (0, 13), (19, 31), (25, 19), (17, 8), (28, 21), (2, 26), (11, 30), (43, 37), (7, 17), (21, 4), (26, 18), (43, 40), (14, 44), (33, 41), (33, 33), (4, 29), (40, 19), (35, 8), (18, 11), (11, 26), (13, 42), (36, 9), (8, 8), (18, 1), (43, 2), (24, 8), (12, 39), (12, 28), (42, 25), (21, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 28), (7, 31), (25, 4), (31, 36), (14, 15), (19, 38), (41, 37), (47, 6), (16, 22), (33, 24), (21, 27), (30, 31), (14, 34), (29, 11), (13, 22), (43, 3), (2, 2), (6, 3), (26, 18), (10, 33), (27, 7), (6, 16), (31, 17), (4, 39), (36, 39), (21, 40), (32, 10), (42, 23), (8, 14), (28, 43), (35, 0), (38, 35), (25, 42), (6, 4), (44, 32), (26, 42), (44, 40), (11, 41), (32, 41), (14, 42), (7, 4), (23, 26), (44, 3), (26, 24), (20, 25), (45, 42), (22, 1), (20, 19), (35, 11), (15, 21), (23, 39), (7, 37), (41, 1), (35, 37), (25, 19), (18, 4), (47, 20), (37, 12), (7, 41), (15, 38), (8, 7), (47, 40), (14, 10), (28, 9), (3, 32), (30, 30), (44, 27), (43, 29), (7, 40), (13, 34), (42, 43), (5, 20), (19, 17), (44, 42), (17, 13), (45, 28), (8, 38), (11, 6), (35, 21), (43, 27), (42, 4), (31, 3), (25, 5), (32, 11), (43, 16), (37, 13), (17, 0), (27, 16), (3, 41), (35, 4), (21, 16), (9, 10), (0, 23), (37, 14), (36, 31), (33, 27), (9, 42), (9, 40), (20, 17), (38, 33), (28, 16), (5, 5), (13, 9), (1, 38), (42, 14), (32, 24), (34, 33), (43, 19), (33, 31), (7, 30), (12, 33), (39, 25), (28, 11), (7, 12), (5, 42), (20, 21), (43, 39), (41, 22), (2, 19), (12, 10), (10, 6), (11, 3), (43, 1), (6, 40), (9, 32), (34, 37), (23, 3), (27, 12), (19, 35), (46, 8), (27, 9), (3, 20), (46, 16), (20, 39), (42, 5), (3, 34), (38, 2), (19, 29), (18, 0), (36, 13), (41, 8), (20, 28), (40, 11), (38, 31), (2, 10), (34, 30), (6, 5), (38, 26), (45, 18), (47, 12), (0, 2), (7, 38), (35, 5), (3, 36), (40, 26), (8, 33), (14, 21), (44, 13), (22, 19), (22, 35), (1, 20), (0, 40), (24, 25), (35, 3), (25, 9), (12, 4), (35, 43), (3, 16), (39, 7), (27, 33), (12, 42), (28, 10), (43, 34), (31, 40), (42, 21), (7, 19), (40, 37), (38, 17), (25, 18), (18, 23), (33, 4), (39, 37), (4, 4), (9, 25), (4, 40), (47, 25), (13, 17), (3, 22), (45, 17), (10, 3), (4, 9), (33, 18), (12, 34), (44, 12), (19, 21), (7, 35), (42, 10), (15, 1), (15, 40), (45, 27), (22, 41), (19, 31), (10, 22), (22, 4), (27, 11), (29, 20), (47, 41), (39, 43), (17, 31), (46, 27), (42, 22), (3, 15), (14, 3), (3, 26), (28, 5), (32, 5), (14, 20), (41, 26), (30, 21), (21, 33), (1, 41), (45, 3), (34, 29), (21, 7), (29, 3), (35, 20), (0, 8), (3, 25), (9, 26), (15, 18), (15, 43), (19, 14), (10, 30), (11, 0), (16, 29), (20, 11), (15, 26), (16, 10), (8, 16), (14, 22), (43, 24), (22, 31), (27, 31), (16, 5), (5, 11), (17, 9), (23, 34), (19, 43), (3, 13), (30, 1), (24, 43), (30, 5), (16, 43), (24, 34), (36, 16), (5, 43), (3, 43), (10, 41), (16, 15), (12, 9), (19, 3), (7, 0), (27, 4), (30, 4), (31, 7), (41, 13), (24, 22), (38, 27), (41, 3), (9, 21), (44, 23), (1, 19), (33, 20), (12, 43), (5, 26), (34, 0), (3, 10), (17, 18), (5, 2), (17, 32), (2, 26), (46, 0), (15, 23), (16, 26), (31, 38), (28, 18), (42, 3), (19, 30), (0, 31), (42, 26), (15, 37), (44, 34), (33, 12), (30, 29), (10, 4), (17, 20), (16, 21), (6, 28), (35, 29), (17, 12), (34, 36), (34, 3), (10, 20), (8, 17), (43, 41), (13, 31), (21, 29), (15, 42), (4, 14), (4, 18), (35, 35), (12, 24), (2, 22), (42, 36), (8, 42), (5, 13), (0, 26), (19, 0), (23, 5), (33, 41), (33, 9), (3, 35), (13, 32), (41, 19), (45, 40), (13, 41), (6, 36), (6, 38), (31, 28), (41, 28), (6, 19), (33, 42), (41, 24), (7, 42), (33, 36), (17, 38), (38, 22), (44, 31), (37, 38), (35, 41), (43, 13), (1, 17), (4, 31), (44, 39), (43, 20), (12, 37), (27, 21), (13, 18), (42, 40), (28, 30), (8, 11), (37, 2), (43, 30), (29, 1), (33, 26), (9, 13), (30, 26), (25, 36), (3, 4), (39, 10), (17, 43), (7, 25), (18, 30), (25, 10), (17, 22), (38, 9), (16, 0), (16, 13), (15, 4), (21, 3), (10, 13), (10, 2), (33, 33), (5, 0), (47, 31), (46, 34), (6, 24), (0, 3), (30, 19), (11, 4), (40, 24), (4, 12), (6, 34), (19, 27), (29, 36), (20, 4), (38, 38), (32, 27), (40, 41), (23, 15), (16, 34), (31, 32), (45, 21), (45, 30), (17, 2), (31, 13), (9, 1), (1, 29), (35, 30), (7, 23), (27, 5), (46, 4), (4, 20), (45, 34), (27, 27), (40, 16), (20, 38), (22, 24), (18, 14), (20, 14), (13, 4), (29, 30), (1, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 21), (10, 42), (4, 33), (38, 24), (19, 25), (14, 41), (13, 40), (37, 5), (33, 21), (3, 35), (23, 27), (15, 19), (14, 24), (40, 46), (4, 27), (8, 5), (42, 43), (3, 8), (24, 19), (19, 44), (15, 28), (36, 3), (7, 9), (33, 34), (0, 4), (14, 44), (27, 15), (1, 36), (13, 32), (3, 38), (8, 30), (6, 13), (21, 46), (40, 35), (19, 37), (28, 1), (8, 16), (3, 19), (41, 26), (12, 37), (21, 4), (5, 32), (14, 10), (8, 37), (37, 19), (10, 30), (34, 43), (6, 12), (7, 3), (23, 32), (27, 7), (38, 32), (33, 10), (5, 34), (14, 17), (30, 8), (11, 13), (13, 14), (16, 29), (27, 30), (19, 45), (33, 46), (18, 17), (12, 0), (15, 14), (21, 19), (39, 5), (9, 2), (13, 17), (13, 26), (30, 37), (1, 33), (9, 26), (7, 12), (6, 30), (35, 35), (32, 8), (25, 5), (30, 24), (23, 44), (22, 31), (32, 5), (29, 17), (19, 21), (39, 13), (22, 36), (33, 32), (11, 28), (16, 16), (7, 23), (21, 25), (33, 35), (13, 39), (22, 37), (12, 16), (42, 0), (32, 30), (18, 45), (27, 42), (25, 0), (40, 26), (35, 36), (15, 43), (12, 23), (30, 28), (39, 41), (10, 1), (37, 4), (35, 6), (19, 6), (6, 33), (12, 15), (30, 10), (30, 20), (15, 6), (32, 10), (32, 27), (14, 19), (35, 46), (10, 28), (22, 3), (22, 9), (15, 4), (4, 17), (20, 26), (34, 26), (33, 8), (42, 35), (36, 15), (11, 1), (8, 34), (6, 21), (12, 8), (29, 33), (1, 10), (36, 12), (23, 14), (38, 19), (12, 36), (22, 18), (28, 11), (24, 18), (3, 26), (16, 20), (10, 11), (27, 8), (39, 35), (16, 14), (30, 1), (34, 16), (41, 13), (38, 36), (12, 20), (5, 36), (1, 21), (8, 19), (17, 14), (19, 10), (3, 20), (37, 39), (37, 12), (35, 25), (16, 33), (10, 23), (2, 1), (11, 39), (22, 42), (28, 18), (38, 38), (14, 30), (17, 13), (38, 14), (40, 2), (2, 26), (32, 42), (14, 3), (0, 41), (21, 8), (10, 26), (38, 9), (5, 4), (1, 23), (21, 17), (16, 28), (42, 36), (16, 30), (26, 26), (9, 34), (10, 16), (4, 8), (34, 2), (27, 36), (32, 32), (41, 42), (11, 29), (1, 34), (20, 45), (39, 22), (40, 5), (3, 0), (7, 41), (23, 18), (29, 26), (27, 9), (41, 34), (19, 4), (14, 26), (23, 37), (26, 17), (13, 30), (38, 30), (19, 27), (10, 38), (32, 33), (25, 34), (3, 14), (11, 42), (36, 41), (4, 28), (1, 25), (18, 19), (27, 17), (16, 7), (35, 26), (14, 28), (13, 4), (11, 14), (33, 18), (13, 12), (29, 16), (19, 39), (27, 44), (23, 3), (6, 0), (10, 20), (25, 7), (26, 36), (24, 41), (42, 7), (9, 40), (29, 10), (37, 40), (8, 35), (28, 22), (14, 9), (42, 19), (35, 40), (9, 3), (17, 7), (25, 29), (19, 8), (3, 28), (17, 31), (36, 1), (30, 16), (31, 0), (31, 43), (13, 38), (18, 14), (17, 35), (5, 37), (4, 7), (23, 26), (0, 14), (23, 30), (22, 33), (2, 10), (19, 19), (41, 46), (33, 31), (29, 32), (26, 35), (30, 14), (41, 45), (20, 23), (5, 41), (40, 45), (10, 3), (42, 32), (21, 39), (28, 15), (33, 24), (8, 0), (27, 21), (14, 29), (15, 42), (18, 18), (14, 6), (0, 35), (39, 11), (7, 6), (8, 41), (16, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 1), (9, 5), (29, 14), (26, 21), (23, 6), (33, 22), (35, 38), (30, 3), (26, 4), (10, 32), (28, 32), (26, 6), (32, 6), (0, 28), (20, 6), (40, 36), (4, 9), (41, 36), (20, 35), (36, 2), (15, 20), (27, 20), (4, 0), (40, 33), (17, 35), (3, 10), (39, 9), (5, 37), (3, 6), (33, 11), (41, 2), (22, 38), (9, 39), (11, 39), (14, 35), (38, 33), (6, 27), (10, 25), (33, 24), (28, 12), (10, 35), (17, 32), (25, 32), (29, 36), (17, 10), (36, 30), (4, 15), (20, 0), (8, 14), (28, 30), (23, 15), (29, 37), (34, 37), (1, 10), (1, 31), (39, 25), (37, 22), (42, 15), (37, 34), (25, 24), (4, 24), (1, 37), (34, 2), (25, 25), (19, 39), (42, 2), (31, 21), (40, 31), (29, 21), (3, 14), (6, 13), (30, 5), (38, 26), (9, 15), (15, 3), (18, 15), (10, 10), (33, 30), (20, 38), (34, 5), (17, 27), (20, 9), (35, 26), (13, 33), (1, 11), (12, 31), (29, 28), (34, 4), (10, 37), (38, 10), (7, 30), (38, 4), (26, 30), (13, 20), (40, 9), (25, 5), (20, 17), (0, 10), (35, 7), (27, 38), (3, 39), (27, 37), (19, 15), (42, 11), (10, 34), (40, 6), (7, 4), (14, 16), (21, 30), (38, 31), (22, 14), (38, 35), (26, 12), (42, 6), (23, 19), (14, 39), (18, 11), (7, 16), (38, 8), (24, 16), (12, 33), (20, 24), (5, 15), (30, 17), (40, 5), (11, 28), (19, 18), (17, 23), (33, 8), (20, 13), (9, 35), (4, 17), (23, 30), (2, 17), (29, 12), (19, 1), (10, 17), (15, 14), (15, 31), (39, 29), (39, 28), (40, 20), (26, 15), (23, 25), (2, 4), (19, 2), (34, 18), (1, 29), (9, 37), (0, 37), (32, 36), (11, 21), (29, 9), (21, 17), (32, 5), (36, 39), (26, 11), (17, 7), (21, 8), (27, 21), (5, 13), (11, 19), (24, 32), (37, 3), (10, 19), (35, 17), (29, 22), (41, 33), (2, 22), (3, 2), (24, 21), (3, 13), (29, 27), (10, 30), (27, 2), (41, 37), (20, 19), (20, 37), (20, 8), (29, 2), (18, 38), (14, 14), (10, 15), (32, 23), (3, 32), (20, 28), (14, 1), (27, 32), (20, 36), (32, 18), (1, 25), (21, 35), (1, 5), (29, 29), (10, 31), (40, 14), (15, 22), (42, 26), (7, 5), (23, 21), (24, 27), (4, 25), (24, 5), (5, 9), (29, 4), (1, 18), (30, 30), (5, 28), (21, 31), (4, 33), (6, 19), (31, 19), (19, 16), (7, 14), (12, 21), (23, 2), (27, 28), (41, 10), (26, 9), (3, 20), (6, 33), (16, 13), (38, 21), (31, 39), (18, 37), (31, 5), (13, 31), (28, 24), (41, 32), (30, 29), (9, 28), (40, 1), (21, 29), (9, 14), (22, 34), (1, 9), (2, 21), (25, 30), (18, 34), (0, 7), (39, 7), (21, 25), (29, 17), (38, 24), (40, 32), (9, 2), (10, 27), (0, 29), (12, 32), (15, 6), (9, 0), (25, 17), (23, 23), (41, 15), (23, 38), (20, 33), (34, 32), (6, 34), (20, 21), (18, 12), (20, 4), (3, 1), (25, 14), (24, 13), (0, 15), (22, 4), (27, 10), (38, 34), (0, 27), (32, 17), (24, 35), (8, 4), (28, 18), (25, 37), (36, 4), (12, 28), (6, 15), (35, 8), (2, 2), (24, 19), (14, 3), (12, 16), (34, 24), (3, 19), (36, 26), (17, 26), (14, 32), (26, 3), (17, 5), (7, 11), (6, 21), (15, 33), (19, 5), (22, 22), (28, 17), (11, 32), (12, 15), (5, 19), (7, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 33), (1, 18), (28, 13), (11, 7), (32, 21), (16, 30), (16, 12), (7, 14), (36, 19), (31, 11), (41, 26), (1, 41), (21, 2), (34, 19), (36, 25), (16, 31), (4, 26), (3, 1), (20, 13), (42, 29), (21, 28), (37, 23), (32, 11), (3, 35), (41, 33), (6, 38), (8, 8), (12, 1), (0, 38), (40, 6), (39, 10), (32, 0), (30, 6), (1, 2), (27, 29), (8, 25), (15, 31), (19, 11), (41, 39), (28, 19), (42, 8), (31, 0), (12, 13), (5, 28), (9, 36), (8, 1), (24, 2), (9, 9), (17, 12), (10, 38), (18, 9), (4, 14), (13, 11), (33, 24), (12, 30), (17, 1), (17, 35), (29, 40), (34, 23), (33, 12), (29, 21), (9, 5), (36, 20), (2, 27), (36, 13), (3, 23), (7, 11), (8, 0), (26, 32), (29, 32), (14, 12), (35, 23), (6, 37), (29, 24), (19, 13), (22, 29), (28, 28), (33, 10), (13, 4), (12, 14), (8, 17), (29, 4), (31, 5), (18, 37), (27, 18), (25, 20), (15, 27), (11, 41), (25, 34), (22, 8), (42, 13), (31, 41), (34, 40), (19, 19), (4, 35), (35, 7), (31, 38), (11, 16), (28, 5), (28, 34), (31, 13), (30, 37), (19, 25), (18, 28), (37, 40), (4, 6), (0, 32), (27, 26), (27, 21), (13, 24), (16, 29), (6, 35), (26, 26), (9, 8), (22, 37), (17, 40), (26, 35), (19, 17), (21, 1), (40, 8), (9, 39), (26, 2), (18, 31), (18, 21), (14, 10), (34, 1), (27, 14), (14, 9), (39, 39), (7, 6), (20, 14), (7, 8), (5, 12), (6, 21), (18, 17), (42, 7), (33, 32), (31, 8), (3, 13), (8, 22), (6, 24), (27, 40), (11, 10), (16, 18), (35, 5), (15, 25), (21, 9), (42, 6), (28, 21), (7, 29), (8, 3), (37, 17), (15, 35), (12, 27), (13, 40), (6, 10), (39, 20), (2, 35), (2, 37), (24, 1), (9, 32), (1, 22), (3, 0), (25, 13), (5, 29), (18, 15), (32, 22), (21, 34), (11, 5), (33, 6), (22, 10), (19, 34), (36, 32), (12, 37), (31, 10), (29, 7), (17, 30), (23, 0), (16, 17), (21, 6), (13, 20), (36, 30), (22, 3), (40, 32), (2, 17), (27, 23), (31, 28), (33, 39), (18, 5), (32, 8), (38, 36), (10, 34), (37, 8), (14, 13), (22, 1), (28, 10), (13, 26), (40, 0), (41, 40), (10, 20), (6, 26), (6, 2), (7, 12), (5, 35), (26, 33), (12, 23), (33, 14), (15, 6), (25, 24), (0, 5), (12, 18), (33, 25), (10, 7), (11, 39), (9, 11), (6, 31), (2, 29), (0, 18), (16, 15), (24, 35), (14, 11), (3, 19), (11, 32), (26, 12), (19, 18), (15, 13), (13, 6), (3, 12), (28, 4), (10, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 42), (35, 40), (11, 8), (3, 24), (40, 35), (3, 15), (21, 39), (27, 13), (6, 27), (22, 26), (25, 35), (24, 14), (30, 13), (7, 25), (26, 30), (4, 27), (46, 41), (3, 5), (17, 37), (0, 3), (16, 4), (8, 27), (48, 18), (14, 11), (41, 15), (39, 6), (35, 7), (14, 30), (11, 29), (9, 27), (48, 21), (7, 5), (47, 41), (22, 33), (28, 43), (34, 45), (48, 34), (24, 6), (40, 14), (47, 44), (9, 35), (9, 9), (20, 26), (27, 35), (48, 35), (46, 36), (6, 5), (41, 33), (14, 44), (7, 6), (19, 9), (26, 10), (15, 36), (26, 3), (8, 15), (19, 45), (35, 17), (8, 43), (47, 22), (7, 48), (12, 9), (30, 10), (34, 37), (40, 36), (34, 6), (16, 34), (18, 34), (38, 9), (44, 10), (22, 28), (40, 43), (26, 28), (37, 21), (23, 31), (16, 23), (16, 41), (16, 44), (6, 12), (9, 34), (21, 27), (9, 6), (2, 20), (19, 15), (48, 37), (38, 45), (33, 31), (35, 9), (3, 12), (39, 29), (26, 17), (35, 19), (9, 0), (4, 32), (14, 41), (43, 34), (43, 31), (39, 14), (46, 3), (40, 31), (15, 27), (24, 48), (18, 13), (41, 13), (1, 24), (46, 31), (36, 40), (32, 43), (34, 47), (38, 14), (27, 17), (40, 17), (39, 11), (0, 15), (35, 30), (17, 19), (32, 11), (16, 2), (22, 45), (4, 3), (18, 44), (13, 42), (15, 22), (48, 22), (27, 37), (12, 6), (17, 10), (18, 16), (27, 0), (44, 16), (1, 16), (32, 45), (45, 34), (17, 7), (14, 18), (40, 7), (26, 4), (48, 24), (12, 35), (6, 48), (11, 31), (4, 37), (45, 27), (32, 0), (27, 21), (35, 39), (26, 24), (8, 36), (15, 9), (43, 48), (4, 47), (43, 0), (38, 31), (35, 45), (35, 8), (1, 39), (45, 15), (43, 6), (16, 15), (44, 41), (30, 32), (12, 3), (35, 42), (8, 9), (17, 8), (16, 9), (31, 37), (41, 19), (34, 32), (44, 42), (38, 40), (45, 5), (39, 35), (36, 28), (31, 2), (5, 41), (32, 47), (32, 19), (12, 19), (24, 2), (37, 44), (8, 47), (38, 3), (21, 12), (26, 19), (18, 7), (30, 5), (29, 5), (38, 48), (9, 29), (40, 6), (41, 35), (0, 30), (5, 48), (30, 29), (36, 11), (15, 11), (27, 41), (48, 29), (6, 35), (28, 44), (38, 25), (36, 2), (34, 12), (0, 21), (30, 43), (28, 35), (26, 44), (26, 42), (9, 25), (24, 23), (1, 23), (4, 23), (45, 7), (18, 2), (26, 16), (35, 10), (4, 10), (35, 38), (42, 48), (19, 7), (47, 4), (2, 37), (22, 31), (24, 36), (39, 46), (36, 3), (21, 28), (28, 1), (31, 0), (39, 22), (15, 6), (26, 20), (16, 32), (47, 9), (7, 10), (15, 48), (20, 25), (13, 13), (36, 41), (38, 44), (15, 1), (22, 27), (25, 33), (36, 36), (21, 30), (9, 17), (17, 35), (38, 12), (10, 25), (0, 8), (36, 16), (34, 7), (42, 14), (8, 26), (35, 18), (6, 46), (37, 12), (27, 32), (32, 33), (27, 33), (9, 19), (36, 7), (5, 11), (8, 45), (11, 23), (2, 43), (41, 32), (25, 29), (0, 32), (31, 25), (6, 29), (15, 29), (27, 44), (16, 27), (12, 40), (22, 14), (25, 5), (2, 41), (14, 29), (18, 47), (33, 37), (15, 14), (30, 7), (23, 17), (40, 21), (4, 17), (16, 37), (6, 25), (15, 13), (31, 47), (31, 3), (48, 6), (17, 26), (8, 21), (8, 5), (27, 45), (33, 45), (33, 9), (13, 10), (2, 28), (35, 12), (15, 40), (25, 13), (13, 9), (17, 36), (5, 47), (8, 14), (29, 39), (18, 33), (13, 0), (25, 11), (26, 33), (39, 13), (12, 5), (4, 8), (6, 26), (3, 25), (0, 39), (21, 43), (2, 27), (32, 48), (13, 40), (22, 20), (27, 31), (5, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 9), (11, 1), (33, 5), (15, 11), (32, 14), (23, 36), (28, 6), (21, 28), (28, 20), (4, 26), (29, 3), (23, 24), (17, 12), (9, 1), (28, 4), (7, 8), (25, 39), (12, 21), (25, 21), (35, 14), (36, 32), (0, 6), (14, 19), (35, 3), (23, 7), (17, 27), (16, 4), (16, 8), (29, 4), (32, 12), (37, 33), (16, 22), (2, 24), (38, 24), (10, 34), (21, 19), (21, 31), (19, 19), (19, 32), (22, 19), (8, 40), (14, 12), (6, 14), (26, 30), (22, 26), (1, 13), (4, 21), (36, 28), (20, 39), (4, 8), (36, 22), (25, 19), (12, 40), (31, 28), (32, 5), (31, 20), (15, 15), (22, 16), (13, 2), (28, 28), (35, 33), (20, 26), (12, 17), (3, 25), (15, 34), (35, 6), (30, 21), (24, 17), (27, 4), (7, 40), (5, 5), (37, 12), (10, 6), (25, 32), (35, 5), (29, 18), (30, 24), (1, 24), (27, 23), (20, 23), (3, 19), (26, 3), (22, 23), (14, 0), (33, 39), (1, 3), (35, 16), (38, 27), (12, 22), (25, 35), (18, 16), (23, 8), (34, 31), (24, 30), (15, 25), (14, 32), (33, 14), (22, 28), (12, 39), (0, 40), (1, 17), (26, 39), (27, 26), (0, 38), (35, 19), (28, 27), (28, 25), (13, 27), (4, 11), (21, 2), (39, 26), (6, 2), (1, 6), (29, 11), (20, 5), (15, 29), (20, 19), (10, 29), (37, 21), (32, 19), (14, 22), (8, 34), (14, 4), (2, 12), (39, 34), (39, 24), (7, 19), (9, 35), (39, 0), (31, 26), (12, 6), (3, 37), (6, 17), (36, 35), (14, 11), (4, 5), (29, 20), (0, 24), (27, 7), (0, 14), (5, 4), (3, 10), (0, 8), (13, 37), (9, 9), (22, 13), (37, 23), (29, 10), (0, 12), (2, 10), (36, 17), (23, 4), (13, 14), (30, 16), (19, 15), (26, 5), (20, 0), (2, 6), (37, 40), (15, 5), (3, 20), (13, 24), (33, 23), (20, 11), (9, 7), (6, 36), (7, 0), (26, 2), (13, 35), (36, 27), (36, 7), (31, 13), (5, 16), (8, 32), (18, 35), (39, 8), (0, 2), (15, 14), (19, 23), (29, 23), (33, 21), (24, 32), (25, 3), (39, 35), (8, 14), (11, 9), (21, 11), (4, 13), (21, 23), (27, 25), (21, 33), (1, 4), (13, 40), (10, 15), (3, 0), (7, 20), (15, 12), (11, 28), (29, 31), (35, 20), (28, 14), (18, 1), (11, 11), (31, 15), (22, 33), (17, 7), (2, 4), (9, 28), (27, 27), (22, 38), (13, 30), (10, 24), (37, 19), (37, 37), (17, 26), (6, 40), (34, 29), (31, 31), (6, 8), (8, 13), (35, 2), (19, 5), (16, 3), (32, 23), (33, 15), (0, 21), (27, 37), (27, 21), (16, 28), (4, 10), (10, 20), (39, 37), (20, 28), (2, 1), (34, 3), (27, 35), (20, 17), (15, 17), (24, 7), (21, 10), (31, 6), (28, 23), (29, 0), (0, 27), (20, 37), (7, 17), (17, 37), (24, 15), (32, 28), (22, 4), (17, 8), (11, 14), (27, 16), (39, 23), (18, 26), (9, 18), (10, 19), (17, 10), (10, 39), (8, 18), (13, 0), (5, 3), (29, 33), (28, 35), (22, 0), (39, 21), (0, 18), (8, 39), (31, 24), (28, 7), (13, 33), (4, 23), (9, 0), (22, 15), (25, 27), (32, 2), (1, 8), (15, 2), (36, 5), (16, 11), (22, 8), (36, 15), (12, 26), (18, 23), (36, 26), (5, 40), (16, 13), (5, 11), (39, 4), (17, 4), (17, 14), (36, 14), (39, 33), (12, 28), (24, 27), (5, 31), (7, 31), (7, 38), (29, 21), (32, 40), (8, 0), (10, 17), (13, 4), (37, 7), (0, 16), (1, 21), (19, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 13), (23, 30), (7, 25), (34, 1), (28, 35), (28, 36), (3, 26), (18, 18), (15, 1), (35, 17), (28, 7), (19, 31), (5, 8), (36, 3), (15, 45), (5, 41), (15, 5), (14, 20), (3, 0), (35, 26), (26, 16), (12, 25), (8, 34), (34, 19), (31, 44), (9, 36), (3, 44), (31, 14), (26, 11), (37, 42), (20, 41), (32, 23), (11, 31), (15, 22), (16, 44), (14, 15), (15, 12), (2, 5), (0, 14), (35, 4), (0, 12), (14, 23), (18, 40), (36, 6), (18, 10), (26, 34), (7, 32), (17, 26), (20, 1), (25, 21), (15, 15), (36, 1), (38, 32), (39, 11), (31, 20), (9, 6), (29, 40), (18, 13), (34, 22), (28, 44), (23, 43), (3, 10), (37, 7), (6, 9), (19, 13), (19, 7), (18, 9), (30, 31), (22, 14), (11, 14), (33, 23), (20, 4), (31, 25), (6, 15), (7, 24), (27, 10), (24, 10), (21, 43), (36, 38), (38, 35), (19, 19), (19, 20), (1, 44), (15, 27), (0, 28), (38, 1), (38, 27), (23, 32), (35, 11), (24, 38), (9, 0), (32, 34), (10, 10), (31, 45), (23, 42), (22, 20), (39, 24), (38, 15), (30, 16), (10, 20), (27, 44), (4, 3), (32, 31), (26, 22), (36, 22), (15, 42), (25, 8), (5, 35), (7, 35), (16, 33), (27, 16), (6, 10), (5, 45), (11, 27), (36, 16), (33, 24), (27, 15), (19, 44), (17, 3), (37, 34), (6, 7), (8, 9), (27, 34), (4, 28), (35, 41), (14, 27), (2, 30), (4, 15), (36, 2), (9, 29), (24, 5), (25, 37), (15, 28), (36, 9), (27, 30), (38, 45), (6, 8), (17, 27), (31, 32), (16, 3), (30, 33), (23, 19), (22, 39), (9, 37), (20, 37), (35, 42), (17, 0), (25, 33), (11, 32), (15, 33), (1, 23), (23, 20), (20, 17), (36, 45), (10, 28), (33, 14), (11, 35), (21, 25), (13, 8), (28, 22), (16, 37), (3, 11), (27, 33), (19, 2), (33, 10), (22, 23), (29, 22), (36, 44), (26, 10), (9, 41), (21, 10), (4, 35), (13, 4), (1, 8), (9, 34), (3, 12), (14, 33), (34, 6), (35, 6), (32, 43), (4, 2), (39, 36), (2, 41), (34, 25), (35, 32), (8, 0), (31, 17), (0, 22), (14, 44), (2, 13), (16, 36), (11, 34), (13, 0), (5, 13), (39, 6), (8, 35), (9, 33), (8, 39), (3, 2), (14, 24), (39, 35), (18, 44), (7, 42), (5, 20), (32, 32), (11, 2), (11, 1), (5, 39), (13, 13), (24, 27), (32, 6), (26, 31), (3, 25), (37, 18), (23, 45), (9, 1), (35, 34), (13, 12), (8, 11), (1, 3), (9, 27), (1, 27), (15, 43), (4, 43), (26, 38), (18, 16), (36, 30), (22, 28), (2, 38), (29, 8), (7, 18), (6, 1), (38, 38), (11, 38), (39, 41), (10, 21), (17, 7), (13, 7), (8, 5), (18, 20), (16, 11), (28, 30), (10, 45), (6, 42), (24, 42), (4, 29), (33, 19), (22, 44), (8, 38), (11, 4), (17, 1), (33, 15), (31, 21), (26, 6), (28, 23), (27, 28), (17, 19), (18, 11), (35, 13), (5, 44), (37, 22), (16, 12), (17, 22), (30, 29), (20, 16), (38, 25), (6, 16), (18, 1), (1, 21), (11, 22), (26, 17), (10, 33), (0, 35), (33, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 32), (18, 17), (11, 1), (34, 25), (40, 4), (21, 25), (34, 5), (18, 23), (29, 27), (34, 30), (26, 20), (32, 34), (41, 40), (0, 22), (4, 29), (0, 21), (1, 14), (39, 22), (9, 38), (43, 37), (32, 15), (46, 26), (46, 6), (25, 13), (25, 32), (4, 2), (10, 2), (44, 31), (20, 17), (40, 15), (22, 16), (2, 3), (0, 13), (7, 10), (14, 15), (32, 3), (37, 14), (38, 16), (0, 24), (10, 32), (11, 22), (4, 21), (16, 13), (16, 24), (10, 12), (0, 29), (30, 2), (35, 39), (38, 18), (25, 41), (0, 26), (16, 36), (41, 28), (21, 4), (0, 32), (22, 22), (28, 36), (33, 6), (3, 39), (23, 1), (15, 38), (27, 9), (27, 18), (21, 2), (19, 27), (12, 22), (12, 35), (47, 39), (30, 11), (22, 10), (23, 23), (8, 17), (44, 9), (8, 4), (45, 14), (31, 0), (24, 36), (46, 31), (31, 15), (7, 19), (39, 21), (10, 0), (33, 25), (41, 21), (41, 22), (13, 13), (27, 11), (35, 1), (0, 5), (34, 11), (23, 30), (28, 37), (25, 17), (39, 38), (2, 2), (14, 16), (11, 24), (8, 10), (34, 20), (12, 3), (37, 21), (9, 7), (22, 12), (12, 32), (36, 23), (40, 38), (45, 20), (4, 28), (40, 17), (30, 41), (21, 13), (26, 4), (10, 6), (3, 40), (32, 16), (36, 41), (27, 21), (46, 16), (32, 17), (46, 35), (24, 31), (5, 16), (26, 36), (2, 26), (34, 17), (12, 40), (27, 31), (4, 41), (40, 37), (14, 31), (32, 0), (38, 8), (16, 18), (3, 0), (10, 10), (14, 28), (41, 0), (14, 27), (28, 9), (40, 24), (14, 14), (18, 9), (41, 6), (10, 25), (6, 40), (1, 25), (42, 27), (18, 4), (13, 40), (37, 20), (17, 38), (7, 7), (1, 28), (23, 38), (19, 36), (44, 28), (5, 2), (10, 1), (41, 30), (18, 27), (16, 21), (5, 31), (1, 3), (41, 41), (38, 12), (38, 21), (22, 33), (7, 20), (6, 26), (23, 12), (41, 36), (27, 12), (39, 7), (29, 25), (6, 30), (6, 31), (13, 32), (32, 28), (28, 22), (22, 39), (35, 18), (39, 26), (4, 13), (37, 1), (40, 10), (32, 8), (21, 27), (31, 3), (23, 37), (20, 26), (25, 30), (22, 30), (29, 9), (41, 17), (2, 28), (18, 12), (35, 14), (19, 33), (14, 34), (16, 1), (25, 14), (13, 41), (9, 39), (29, 7), (22, 17), (26, 22), (9, 17), (45, 30), (33, 40), (16, 12), (20, 1), (35, 34), (11, 16), (32, 22), (29, 21), (29, 1), (30, 21), (0, 25), (19, 31), (33, 15), (39, 34), (18, 35), (34, 6), (27, 27), (13, 8), (32, 7), (6, 13), (9, 41), (45, 39), (32, 2), (25, 36), (15, 18), (41, 2), (11, 33), (36, 1), (46, 21), (20, 38), (30, 39), (12, 5), (19, 20), (40, 35), (24, 5), (27, 35), (2, 33), (40, 14), (5, 22), (9, 28), (42, 33), (43, 13), (8, 6), (26, 29), (40, 40), (47, 35), (24, 15), (40, 23), (7, 17), (44, 1), (30, 12), (46, 1), (1, 0), (41, 7), (34, 23), (39, 0), (25, 39), (29, 29), (7, 41), (21, 24), (8, 7), (23, 14), (1, 9), (44, 24), (6, 2), (22, 36), (34, 35), (30, 14), (9, 4), (45, 0), (21, 35), (28, 2), (6, 3), (46, 8), (15, 26), (3, 21), (13, 25), (22, 11), (16, 37), (33, 4), (1, 38), (9, 19), (23, 21), (29, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 17), (38, 3), (39, 32), (24, 16), (14, 29), (31, 0), (15, 13), (6, 40), (14, 25), (36, 20), (36, 40), (15, 23), (6, 32), (35, 39), (42, 8), (20, 3), (24, 14), (19, 33), (34, 10), (31, 34), (19, 6), (0, 35), (17, 27), (12, 21), (23, 22), (5, 7), (24, 25), (22, 22), (0, 23), (24, 40), (36, 32), (14, 9), (7, 40), (26, 20), (40, 17), (8, 31), (27, 26), (13, 40), (4, 5), (41, 33), (23, 14), (38, 34), (29, 39), (4, 32), (5, 38), (16, 0), (37, 25), (13, 14), (6, 31), (27, 20), (1, 22), (12, 23), (30, 21), (5, 10), (43, 21), (11, 7), (30, 8), (8, 27), (23, 5), (40, 9), (25, 11), (35, 30), (30, 17), (14, 20), (8, 24), (42, 19), (28, 34), (6, 38), (8, 22), (2, 21), (37, 19), (15, 18), (41, 28), (28, 5), (35, 13), (18, 34), (26, 28), (43, 0), (1, 5), (43, 24), (4, 20), (17, 35), (2, 39), (35, 7), (13, 36), (3, 28), (39, 12), (18, 21), (3, 10), (19, 15), (3, 4), (1, 3), (6, 14), (7, 37), (8, 1), (3, 37), (36, 26), (14, 17), (3, 16), (23, 40), (5, 37), (7, 15), (41, 15), (20, 39), (19, 13), (9, 27), (34, 2), (24, 41), (21, 19), (5, 18), (17, 39), (1, 6), (43, 18), (27, 10), (12, 28), (22, 34), (17, 29), (2, 12), (19, 39), (8, 3), (15, 15), (31, 12), (26, 25), (20, 10), (2, 23), (10, 35), (9, 30), (7, 14), (41, 21), (35, 16), (16, 5), (19, 22), (16, 2), (30, 12), (17, 12), (35, 15), (23, 15), (10, 2), (31, 6), (38, 29), (42, 2), (4, 11), (12, 13), (35, 40), (29, 23), (24, 10), (10, 29), (7, 24), (43, 9), (15, 16), (21, 5), (25, 31), (26, 39), (27, 2), (10, 40), (35, 34), (16, 41), (38, 2), (27, 13), (37, 30), (3, 17), (24, 12), (41, 24), (31, 5), (35, 29), (26, 15), (39, 16), (13, 16), (23, 39), (27, 12), (17, 37), (1, 17), (24, 36), (13, 30), (5, 21), (18, 40), (29, 20), (12, 14), (16, 28), (39, 22), (5, 36), (25, 5), (25, 20), (27, 11), (22, 25), (39, 8), (6, 5), (39, 30), (33, 32), (6, 11), (21, 15), (29, 2), (33, 21), (4, 3), (35, 35), (29, 24), (20, 33), (40, 12), (28, 10), (42, 28), (11, 13), (42, 6), (15, 27), (1, 20), (12, 16), (12, 40), (41, 40), (24, 3), (17, 36), (7, 31), (10, 19), (22, 24), (14, 14), (22, 18), (4, 18), (18, 33), (15, 39), (29, 41), (5, 40), (8, 25), (30, 38), (10, 32), (37, 28), (24, 27), (28, 23), (29, 15), (31, 17), (9, 34), (12, 37), (28, 32), (37, 12), (38, 37), (28, 9), (32, 2), (9, 17), (17, 28), (16, 38), (15, 30), (37, 24), (2, 19), (20, 32), (27, 27), (17, 38), (2, 27), (27, 7), (16, 26), (30, 25), (21, 17), (20, 23), (32, 23), (41, 5), (1, 31), (33, 37), (19, 23), (3, 35), (19, 20), (22, 31), (22, 21), (14, 28), (19, 21), (21, 14), (3, 12), (39, 26), (36, 11), (31, 40), (3, 0), (1, 14), (41, 13), (11, 38), (17, 6), (43, 6), (4, 17), (39, 15), (14, 7), (22, 14), (29, 13), (20, 1), (33, 31), (8, 9), (5, 25), (25, 25), (18, 10), (13, 25), (35, 1), (17, 34), (13, 8), (0, 3), (11, 16), (36, 41), (18, 16), (38, 19), (10, 31), (39, 25), (41, 22), (42, 17), (0, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (4, 24), (13, 30), (15, 23), (36, 15), (1, 20), (36, 9), (28, 6), (39, 41), (22, 31), (30, 21), (30, 32), (28, 45), (1, 44), (40, 37), (20, 9), (10, 6), (39, 10), (15, 37), (39, 34), (34, 7), (45, 3), (0, 30), (29, 31), (8, 44), (26, 9), (13, 23), (18, 28), (33, 21), (46, 4), (26, 14), (12, 19), (45, 21), (33, 42), (40, 42), (24, 6), (7, 13), (23, 10), (16, 45), (5, 39), (32, 13), (26, 10), (34, 39), (44, 36), (34, 10), (20, 0), (3, 25), (9, 11), (37, 40), (38, 5), (36, 20), (29, 7), (8, 31), (43, 14), (26, 7), (3, 36), (22, 38), (29, 39), (40, 22), (1, 23), (37, 31), (26, 43), (40, 21), (12, 36), (38, 40), (29, 6), (37, 33), (13, 33), (21, 35), (31, 5), (26, 40), (38, 14), (2, 5), (26, 19), (37, 37), (41, 13), (4, 33), (19, 7), (2, 0), (13, 15), (5, 7), (24, 9), (30, 1), (34, 8), (18, 42), (12, 29), (18, 12), (40, 4), (23, 39), (37, 7), (27, 31), (2, 24), (29, 29), (26, 24), (17, 33), (23, 36), (25, 40), (9, 24), (0, 32), (8, 39), (33, 31), (20, 1), (0, 23), (21, 12), (19, 40), (20, 10), (8, 14), (14, 16), (29, 11), (4, 4), (34, 16), (12, 45), (20, 13), (2, 12), (0, 11), (40, 10), (15, 9), (3, 17), (9, 25), (28, 30), (29, 26), (7, 35), (43, 4), (2, 40), (16, 24), (27, 7), (36, 2), (31, 19), (4, 44), (16, 10), (21, 3), (5, 3), (3, 34), (34, 23), (15, 42), (42, 36), (13, 27), (10, 20), (36, 32), (41, 11), (23, 38), (5, 12), (4, 31), (27, 5), (19, 19), (15, 2), (25, 12), (3, 3), (22, 0), (40, 26), (20, 41), (3, 23), (36, 21), (10, 8), (27, 45), (16, 23), (15, 30), (6, 13), (3, 35), (4, 29), (12, 16), (16, 0), (21, 0), (0, 3), (0, 19), (46, 43), (24, 15), (17, 9), (46, 28), (9, 19), (28, 14), (23, 16), (1, 24), (46, 21), (24, 8), (10, 30), (14, 36), (23, 11), (38, 22), (18, 22), (4, 21), (25, 14), (42, 8), (18, 31), (20, 37), (18, 33), (10, 26), (36, 14), (24, 37), (20, 2), (24, 18), (28, 7), (21, 19), (8, 45), (31, 29), (3, 29), (8, 42), (30, 10), (30, 27), (32, 5), (34, 43), (23, 35), (38, 36), (22, 32), (13, 2), (18, 39), (36, 45), (15, 28), (15, 27), (3, 39), (22, 15), (19, 27), (33, 44), (17, 14), (33, 20), (35, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 6), (45, 30), (19, 22), (14, 32), (22, 17), (35, 32), (36, 18), (8, 15), (26, 42), (10, 39), (21, 13), (13, 10), (43, 23), (37, 39), (9, 18), (14, 7), (31, 19), (17, 33), (21, 38), (14, 14), (21, 17), (33, 39), (40, 42), (22, 24), (41, 16), (22, 3), (31, 20), (38, 16), (39, 5), (3, 16), (14, 11), (44, 37), (2, 16), (25, 23), (37, 10), (12, 10), (16, 4), (23, 34), (3, 38), (27, 16), (25, 10), (43, 19), (20, 31), (37, 35), (18, 21), (17, 34), (40, 10), (5, 3), (11, 11), (24, 39), (25, 14), (8, 28), (37, 37), (18, 37), (32, 40), (41, 9), (30, 21), (32, 28), (37, 41), (24, 32), (4, 36), (43, 17), (21, 14), (41, 36), (28, 10), (13, 4), (32, 3), (9, 16), (3, 29), (9, 25), (4, 40), (8, 32), (7, 29), (23, 32), (27, 30), (33, 41), (37, 19), (10, 43), (42, 39), (17, 9), (8, 36), (41, 33), (17, 19), (12, 5), (39, 34), (33, 11), (27, 41), (16, 19), (12, 36), (11, 32), (6, 27), (6, 11), (9, 27), (38, 26), (43, 16), (33, 15), (3, 33), (35, 15), (7, 19), (0, 17), (18, 5), (5, 19), (47, 7), (25, 31), (27, 33), (34, 8), (22, 41), (37, 21), (6, 15), (36, 1), (3, 37), (44, 1), (2, 24), (20, 39), (34, 19), (16, 29), (24, 30), (21, 0), (16, 11), (8, 1), (41, 18), (33, 6), (1, 32), (44, 30), (20, 0), (15, 27), (45, 17), (29, 10), (23, 35), (30, 10), (27, 19), (23, 21), (38, 27), (33, 3), (5, 2), (22, 29), (33, 9), (8, 31), (10, 7), (19, 43), (22, 34), (7, 25), (32, 0), (20, 28), (41, 35), (18, 30), (30, 11), (32, 39), (26, 43), (12, 21), (47, 29), (29, 0), (3, 7), (45, 14), (33, 21), (21, 32), (1, 11), (28, 38), (45, 22), (37, 1), (43, 43), (30, 13), (44, 34), (39, 6), (44, 27), (47, 9), (9, 8), (6, 34), (37, 9), (42, 41), (9, 7), (32, 19), (17, 5), (23, 7), (31, 39), (24, 29), (9, 4), (27, 12), (33, 27), (24, 11), (47, 32), (34, 1), (35, 16), (28, 7), (23, 41), (22, 25), (4, 41), (8, 34), (40, 3), (29, 40), (47, 25), (20, 2), (37, 22), (12, 25), (25, 26), (33, 40), (18, 7), (22, 40), (35, 12), (16, 3), (42, 28), (41, 25), (39, 29), (4, 37), (22, 2), (22, 19), (9, 6), (45, 41), (46, 28), (28, 9), (29, 15), (13, 41), (7, 2), (47, 23), (2, 29), (41, 24), (28, 23), (31, 1), (16, 40), (26, 21), (18, 25), (24, 7), (7, 37), (11, 19), (24, 9), (42, 37), (24, 40), (47, 33), (47, 18), (37, 15), (26, 1), (28, 18), (45, 18), (37, 7), (45, 40), (18, 33), (44, 32), (19, 13), (35, 2), (43, 9), (42, 19), (38, 12), (32, 14), (23, 8), (9, 19), (3, 11), (34, 28), (3, 26), (29, 35), (0, 38), (22, 36), (16, 39), (10, 40), (36, 10), (40, 24), (42, 22), (8, 3), (4, 18), (17, 24), (31, 27), (39, 28), (4, 20), (45, 35), (22, 16), (37, 16), (9, 26), (11, 24), (17, 0), (33, 23), (26, 3), (20, 5), (2, 31), (42, 6), (25, 20), (2, 32), (11, 30), (27, 8), (20, 4), (3, 32), (36, 29), (13, 8), (41, 21), (42, 24), (46, 32), (4, 13), (41, 42), (19, 6), (46, 16), (43, 4), (37, 11), (20, 14), (13, 6), (12, 43), (9, 0), (3, 36), (0, 6), (25, 8), (1, 36), (10, 28), (32, 10), (25, 39), (15, 10), (26, 40), (0, 32), (1, 0), (1, 34), (43, 35), (34, 29), (34, 24), (45, 21), (10, 34), (19, 11), (3, 35), (38, 11), (43, 26), (36, 36), (26, 38), (21, 41), (31, 11), (32, 33), (1, 33), (10, 2), (0, 11), (0, 8), (3, 6), (9, 39), (39, 26), (0, 41), (47, 24), (39, 14), (1, 13), (20, 17), (2, 34), (45, 11), (46, 31), (31, 24), (37, 38), (8, 20), (19, 12), (45, 23), (13, 28), (21, 42), (32, 17), (15, 4), (38, 3), (18, 9), (13, 22), (10, 22), (44, 2), (42, 34), (32, 36), (30, 20), (15, 15), (8, 6), (23, 39), (39, 3), (6, 26), (22, 28), (42, 2), (31, 22), (2, 1), (46, 26), (33, 13), (34, 35), (29, 12), (35, 10), (40, 40), (36, 19), (12, 24), (9, 30), (20, 37), (45, 20), (5, 7), (22, 38), (26, 27), (0, 19), (33, 0), (40, 1), (45, 4), (32, 5), (29, 38), (36, 2), (41, 40), (30, 28), (47, 5), (18, 39), (12, 19), (3, 15), (25, 30), (20, 9), (9, 3), (40, 33), (37, 5), (23, 33), (21, 34), (24, 20), (41, 20), (23, 42), (44, 23), (42, 9), (15, 35), (4, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 26), (26, 31), (18, 19), (30, 30), (13, 8), (21, 17), (32, 28), (17, 19), (30, 23), (8, 13), (24, 28), (23, 15), (1, 4), (0, 26), (41, 7), (34, 13), (21, 43), (22, 42), (22, 12), (19, 32), (3, 15), (7, 25), (46, 12), (43, 40), (43, 29), (24, 25), (6, 27), (32, 42), (6, 23), (3, 25), (44, 8), (10, 17), (17, 34), (3, 10), (9, 37), (31, 37), (20, 39), (42, 36), (19, 27), (30, 13), (19, 16), (2, 11), (2, 29), (44, 37), (32, 18), (4, 0), (3, 36), (8, 19), (6, 0), (12, 21), (11, 27), (26, 11), (10, 28), (9, 3), (43, 30), (16, 30), (43, 14), (37, 42), (44, 32), (39, 9), (37, 41), (20, 34), (14, 23), (24, 40), (43, 38), (26, 43), (35, 35), (34, 10), (17, 13), (40, 38), (10, 16), (36, 3), (36, 17), (36, 23), (34, 7), (41, 3), (37, 6), (2, 1), (14, 16), (35, 23), (23, 18), (45, 18), (40, 3), (7, 17), (36, 8), (32, 36), (5, 30), (32, 32), (39, 3), (20, 20), (35, 10), (43, 8), (30, 14), (20, 42), (1, 33), (6, 9), (23, 9), (22, 36), (0, 46), (11, 18), (46, 27), (13, 43), (39, 24), (23, 43), (32, 22), (5, 5), (29, 42), (24, 18), (9, 17), (17, 17), (23, 17), (19, 35), (6, 17), (46, 20), (29, 12), (1, 45), (25, 18), (27, 5), (2, 32), (9, 10), (9, 1), (32, 25), (3, 42), (27, 8), (36, 2), (24, 27), (11, 39), (24, 29), (0, 37), (38, 26), (33, 11), (7, 34), (16, 28), (21, 8), (20, 14), (15, 27), (25, 15), (41, 25), (46, 39), (11, 25), (22, 11), (23, 27), (42, 0), (6, 25), (16, 25), (27, 32), (10, 25), (2, 16), (41, 36), (12, 46), (24, 31), (3, 38), (19, 28), (43, 28), (35, 19), (4, 21), (35, 21), (40, 7), (35, 24), (29, 25), (24, 42), (25, 34), (14, 39), (37, 43), (39, 18), (22, 25), (18, 31), (34, 35), (42, 14), (13, 13), (33, 4), (22, 13), (39, 19), (38, 45), (44, 24), (16, 11), (34, 3), (19, 40), (20, 16), (43, 19), (44, 9), (18, 23), (42, 44), (37, 23), (24, 1), (14, 32), (5, 14), (18, 43), (3, 45), (31, 24), (13, 21), (21, 29), (25, 44), (0, 19), (33, 21), (4, 4), (34, 44), (0, 33), (2, 18), (28, 5), (1, 36), (26, 6), (27, 29), (38, 8), (33, 36), (43, 3), (40, 36), (31, 16), (45, 17), (27, 28), (44, 2), (34, 12), (5, 8), (35, 46), (13, 15), (31, 12), (29, 0), (1, 37), (20, 12), (21, 13), (41, 34), (13, 30), (28, 27), (11, 5), (1, 23), (26, 36), (4, 39), (7, 4), (34, 26), (15, 43), (2, 41), (17, 1), (27, 38), (21, 31), (29, 3), (25, 43), (36, 22), (43, 36), (30, 42), (38, 29), (0, 42), (0, 13), (41, 33), (6, 6), (41, 10), (34, 45), (7, 19), (31, 5), (23, 0), (18, 16), (28, 22), (4, 29), (23, 16), (41, 13), (31, 8), (40, 25), (4, 44), (7, 14), (20, 30), (0, 5), (34, 6), (36, 10), (32, 4), (1, 35), (27, 40), (33, 43), (10, 34), (8, 9), (7, 16), (27, 12), (44, 25), (11, 45), (45, 13), (19, 38), (3, 20), (21, 36), (16, 33), (28, 41), (40, 43), (3, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 20), (17, 4), (10, 27), (28, 8), (38, 6), (8, 40), (6, 12), (2, 18), (36, 35), (29, 41), (16, 20), (34, 5), (5, 16), (12, 18), (7, 27), (19, 33), (30, 36), (0, 31), (33, 0), (37, 43), (2, 30), (17, 7), (30, 40), (5, 39), (10, 35), (0, 40), (6, 9), (10, 31), (23, 28), (36, 36), (32, 29), (31, 20), (17, 0), (39, 11), (26, 12), (8, 19), (37, 7), (0, 13), (13, 37), (18, 23), (1, 23), (16, 37), (14, 9), (12, 34), (18, 17), (11, 41), (26, 26), (18, 31), (33, 23), (36, 23), (30, 34), (35, 27), (13, 32), (11, 21), (22, 9), (4, 8), (35, 17), (36, 12), (13, 29), (3, 2), (11, 11), (10, 5), (29, 3), (23, 12), (38, 37), (39, 36), (2, 8), (36, 15), (5, 8), (39, 13), (34, 27), (23, 3), (5, 5), (31, 5), (19, 39), (0, 17), (5, 15), (19, 22), (28, 9), (38, 39), (1, 43), (22, 30), (17, 26), (18, 41), (3, 39), (0, 38), (38, 32), (14, 41), (21, 25), (31, 38), (14, 18), (0, 1), (13, 19), (34, 26), (15, 15), (3, 34), (12, 8), (34, 43), (33, 34), (5, 37), (26, 24), (38, 1), (36, 40), (35, 26), (35, 35), (4, 6), (8, 23), (32, 24), (0, 41), (9, 22), (19, 11), (11, 23), (34, 11), (31, 2), (35, 30), (35, 37), (21, 19), (32, 26), (5, 36), (21, 24), (25, 11), (36, 0), (7, 30), (4, 24), (3, 15), (11, 27), (30, 37), (21, 1), (22, 23), (2, 14), (31, 6), (14, 4), (19, 31), (35, 18), (17, 40), (10, 17), (36, 6), (31, 18), (15, 35), (27, 8), (24, 30), (10, 7), (16, 12), (3, 1), (21, 15), (30, 33), (25, 17), (33, 27), (14, 38), (24, 6), (3, 22), (25, 39), (23, 32), (38, 10), (27, 42), (26, 43), (26, 17), (22, 8), (21, 0), (38, 13), (27, 23), (2, 19), (25, 31), (6, 1), (21, 6), (7, 1), (36, 39), (22, 12), (37, 14), (35, 42), (17, 2), (6, 23), (30, 13), (35, 43), (27, 17), (9, 9), (28, 43), (38, 43), (7, 14), (12, 6), (16, 7), (31, 37), (27, 25), (18, 15), (14, 8), (34, 24), (5, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (33, 34), (18, 26), (2, 11), (40, 19), (41, 12), (38, 22), (1, 38), (43, 3), (14, 32), (41, 32), (9, 11), (36, 21), (33, 31), (41, 27), (40, 29), (43, 5), (33, 30), (0, 22), (30, 28), (14, 33), (10, 37), (23, 30), (24, 35), (4, 36), (12, 30), (13, 22), (0, 34), (9, 41), (5, 8), (27, 26), (19, 31), (41, 31), (32, 18), (33, 40), (40, 34), (2, 24), (12, 32), (8, 13), (26, 35), (33, 22), (19, 18), (28, 6), (38, 27), (38, 25), (36, 27), (11, 38), (18, 5), (17, 17), (23, 12), (29, 24), (20, 26), (32, 30), (2, 1), (38, 30), (2, 7), (16, 20), (16, 16), (35, 13), (10, 39), (32, 2), (14, 34), (2, 17), (38, 0), (12, 7), (42, 3), (9, 24), (38, 3), (40, 40), (15, 37), (42, 29), (36, 14), (35, 27), (10, 20), (31, 16), (39, 0), (37, 7), (9, 38), (39, 13), (0, 19), (3, 13), (38, 20), (26, 9), (13, 4), (32, 37), (5, 38), (36, 24), (33, 13), (27, 35), (8, 8), (9, 12), (42, 37), (2, 5), (22, 6), (4, 24), (24, 6), (1, 19), (8, 12), (20, 2), (23, 22), (27, 27), (3, 36), (12, 34), (5, 0), (14, 18), (12, 5), (37, 21), (25, 14), (3, 25), (31, 29), (11, 2), (16, 34), (16, 40), (28, 25), (33, 33), (38, 24), (14, 2), (30, 0), (18, 20), (3, 0), (42, 5), (42, 17), (15, 7), (21, 39), (5, 6), (29, 15), (4, 20), (25, 13), (1, 17), (30, 11), (1, 2), (12, 0), (13, 29), (18, 17), (29, 34), (28, 16), (33, 19), (25, 4), (17, 0), (40, 25), (9, 35), (19, 28), (2, 15), (18, 39), (30, 1), (42, 25), (18, 32), (28, 27), (7, 28), (37, 34), (42, 11), (36, 35), (20, 5), (6, 34), (22, 17), (24, 33), (21, 40), (43, 32), (31, 40), (7, 33), (34, 35), (10, 19), (23, 3), (36, 32), (12, 4), (21, 9), (14, 16), (13, 32), (0, 27), (14, 36), (31, 14), (13, 19), (33, 21), (13, 0), (36, 26), (17, 3), (21, 1), (20, 22), (41, 19), (28, 33), (7, 38), (6, 26), (21, 18), (40, 22), (39, 2), (28, 38), (38, 13), (22, 28), (31, 19), (39, 33), (27, 11), (29, 16), (3, 20), (29, 31), (17, 13), (20, 12), (1, 23), (22, 35), (27, 18), (31, 5), (27, 28), (43, 22), (12, 35), (0, 17), (0, 38), (12, 20), (14, 26), (4, 22), (33, 23), (5, 30), (23, 9), (16, 38), (35, 8), (37, 16), (8, 25), (16, 18), (27, 10), (18, 15), (22, 14), (7, 32), (23, 28), (25, 8), (41, 33), (34, 1), (28, 30), (8, 36), (38, 6), (18, 40), (2, 38), (32, 21), (26, 11), (41, 15), (13, 35), (8, 29), (9, 36), (21, 26), (26, 15), (24, 17), (16, 5), (15, 3), (39, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 37), (41, 29), (43, 34), (35, 38), (2, 40), (39, 8), (45, 14), (7, 3), (3, 33), (21, 6), (39, 5), (29, 16), (39, 24), (45, 12), (2, 27), (17, 31), (4, 8), (10, 10), (12, 22), (45, 18), (5, 26), (3, 41), (27, 18), (8, 21), (32, 34), (35, 27), (29, 21), (16, 15), (38, 4), (31, 39), (22, 12), (21, 42), (5, 19), (8, 40), (3, 37), (26, 42), (36, 11), (34, 39), (11, 22), (32, 19), (18, 1), (7, 28), (25, 13), (4, 15), (41, 0), (3, 4), (43, 7), (3, 26), (12, 19), (46, 11), (3, 22), (34, 12), (34, 23), (42, 27), (39, 30), (42, 0), (26, 27), (32, 22), (40, 2), (24, 18), (38, 31), (45, 44), (19, 16), (18, 26), (30, 9), (24, 16), (3, 44), (5, 39), (9, 17), (45, 31), (41, 1), (36, 35), (45, 33), (28, 41), (28, 17), (9, 8), (7, 41), (26, 10), (37, 22), (9, 23), (18, 21), (27, 28), (5, 20), (8, 14), (3, 15), (36, 12), (23, 16), (23, 42), (22, 0), (12, 40), (7, 4), (10, 40), (42, 21), (39, 41), (33, 0), (42, 29), (24, 29), (5, 32), (18, 16), (17, 24), (15, 35), (12, 20), (5, 21), (6, 29), (39, 14), (38, 20), (32, 9), (15, 22), (29, 11), (0, 17), (43, 11), (20, 28), (11, 0), (17, 42), (37, 41), (7, 5), (20, 29), (32, 32), (22, 21), (8, 33), (27, 33), (39, 18), (21, 27), (1, 22), (4, 23), (33, 7), (0, 4), (20, 30), (42, 34), (42, 43), (3, 16), (7, 1), (25, 28), (14, 34), (15, 32), (8, 29), (28, 36), (41, 20), (10, 29), (7, 11), (11, 3), (22, 22), (40, 4), (42, 17), (23, 22), (30, 39), (24, 42), (7, 0), (34, 10), (28, 37), (39, 27), (15, 12), (23, 36), (43, 33), (46, 16), (23, 19), (27, 11), (38, 23), (11, 6), (8, 24), (36, 26), (46, 5), (10, 8), (27, 25), (31, 18), (5, 0), (9, 1), (6, 40), (9, 37), (12, 39), (37, 38), (40, 20), (11, 42), (2, 15), (11, 38), (36, 19), (30, 25), (21, 15), (12, 27), (12, 10), (37, 32), (10, 22), (6, 38), (1, 18), (33, 24), (10, 4), (40, 13), (35, 17), (35, 18), (38, 0), (46, 41), (33, 25), (33, 1), (41, 38), (30, 27), (14, 19), (46, 40), (43, 31), (29, 8), (10, 18), (23, 24), (18, 20), (39, 12), (27, 4), (13, 13), (19, 39), (27, 38), (7, 2), (45, 24), (38, 35), (0, 44), (10, 20), (4, 42), (26, 39), (30, 41), (1, 28), (25, 35), (12, 16), (5, 9), (24, 27), (6, 6), (45, 32), (35, 0), (39, 42), (13, 33), (29, 9), (39, 10), (39, 9), (21, 23), (29, 31), (1, 1), (42, 4), (37, 40), (7, 35), (15, 20), (11, 31), (0, 11), (25, 6), (26, 13), (18, 43), (30, 38), (42, 30), (3, 17), (16, 35), (10, 43), (7, 13), (44, 6), (39, 6), (23, 43), (36, 29), (33, 22), (16, 31), (8, 36), (6, 2), (5, 38), (5, 18), (38, 33), (5, 29), (34, 7), (16, 20), (5, 3), (32, 2), (34, 1), (21, 44), (3, 30), (40, 15), (26, 23), (9, 19), (25, 32), (7, 30), (24, 30), (44, 38), (36, 21), (21, 1), (9, 29), (0, 42), (38, 40), (27, 12), (23, 1), (9, 44), (25, 26), (33, 19), (24, 19), (17, 29), (23, 33), (10, 23), (24, 35), (18, 4), (27, 41), (15, 41), (2, 13), (34, 5), (20, 31), (41, 9), (7, 8), (0, 34), (7, 34), (29, 7), (31, 9), (0, 38), (41, 24), (46, 15), (30, 1), (28, 14), (3, 27), (27, 30), (29, 34), (27, 36), (0, 9), (14, 39), (44, 44), (31, 15), (20, 9), (33, 18), (32, 23), (22, 28), (39, 25), (42, 23), (35, 8), (4, 44), (21, 19), (0, 36), (27, 27), (2, 23), (4, 32), (44, 1), (24, 23), (19, 11), (30, 29), (13, 26), (19, 2), (22, 5), (18, 37), (10, 39), (23, 14), (33, 38), (31, 0), (45, 7), (43, 14), (16, 43), (12, 12), (37, 28), (21, 26), (0, 10), (43, 43), (13, 31), (22, 2), (11, 29), (16, 14), (40, 24), (11, 23), (22, 10), (18, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 19), (38, 13), (9, 21), (31, 41), (36, 16), (29, 13), (36, 39), (10, 33), (29, 43), (23, 43), (10, 30), (25, 26), (27, 48), (20, 23), (21, 30), (17, 22), (37, 14), (5, 43), (32, 34), (23, 11), (17, 20), (23, 10), (19, 6), (23, 46), (29, 31), (0, 33), (33, 42), (7, 19), (2, 35), (14, 13), (17, 32), (18, 42), (34, 23), (23, 7), (11, 38), (11, 18), (19, 26), (16, 20), (21, 32), (20, 44), (2, 34), (12, 38), (42, 12), (2, 27), (10, 39), (33, 12), (6, 8), (24, 10), (18, 39), (21, 14), (13, 47), (42, 20), (20, 33), (31, 1), (33, 31), (28, 10), (40, 48), (41, 16), (14, 35), (19, 29), (32, 0), (27, 22), (32, 22), (20, 15), (34, 20), (38, 2), (27, 29), (28, 1), (1, 47), (15, 46), (17, 39), (27, 21), (31, 28), (39, 27), (4, 15), (6, 16), (34, 6), (37, 17), (11, 1), (37, 36), (15, 13), (12, 48), (28, 36), (12, 10), (41, 41), (33, 41), (21, 2), (8, 40), (2, 22), (33, 0), (4, 37), (31, 30), (2, 20), (37, 16), (25, 17), (18, 31), (15, 19), (31, 7), (13, 11), (35, 26), (13, 29), (2, 7), (34, 8), (29, 5), (18, 4), (16, 35), (10, 45), (17, 15), (30, 33), (28, 33), (33, 34), (10, 17), (33, 26), (14, 28), (41, 29), (41, 23), (39, 13), (15, 22), (0, 38), (11, 4), (18, 7), (22, 22), (23, 30), (3, 6), (34, 4), (15, 4), (32, 13), (13, 32), (34, 32), (32, 31), (30, 34), (41, 1), (10, 31), (38, 42), (17, 16), (35, 43), (24, 5), (31, 38), (2, 23), (15, 20), (24, 2), (18, 15), (13, 21), (12, 28), (17, 17), (2, 39), (40, 46), (38, 10), (30, 5), (5, 1), (8, 22), (8, 43), (0, 34), (25, 41), (14, 9), (36, 6), (24, 31), (37, 30), (9, 4), (13, 40), (30, 9), (26, 29), (16, 7), (9, 48), (26, 19), (6, 36), (7, 1), (13, 10), (15, 38), (23, 14), (16, 19), (9, 25), (26, 22), (30, 36), (29, 10), (25, 29), (22, 9), (42, 22), (10, 34), (10, 28), (5, 20), (3, 47), (6, 19), (2, 2), (36, 47), (11, 14), (8, 48), (32, 10), (1, 10), (20, 1), (4, 34), (32, 43), (15, 34), (36, 23), (12, 3), (21, 8), (16, 31), (32, 41), (0, 48), (15, 16), (5, 29), (4, 24), (1, 20), (8, 27), (38, 17), (20, 5), (39, 28), (38, 34), (35, 6), (27, 8), (26, 6), (36, 46), (14, 10), (28, 43), (11, 39), (28, 4), (26, 36), (27, 45), (0, 7), (4, 23), (30, 15), (12, 35), (12, 39), (36, 1), (40, 33), (4, 6), (9, 45), (42, 5), (12, 29), (2, 16), (21, 47), (25, 27), (18, 19), (21, 11), (25, 32), (39, 33), (42, 24), (7, 23), (31, 8), (4, 40), (29, 25), (38, 21), (32, 36), (4, 29), (40, 1), (0, 27), (0, 25), (11, 33), (31, 11), (21, 0), (3, 18), (7, 48), (24, 44), (36, 36), (41, 39), (28, 31), (22, 0), (4, 18), (32, 44), (27, 33), (33, 8), (4, 45), (36, 40), (0, 20), (29, 1), (6, 38), (7, 29), (38, 47), (0, 41), (37, 0), (30, 13), (21, 5), (33, 1), (41, 17), (32, 39), (40, 45), (24, 46), (18, 44), (12, 46), (11, 23), (25, 21), (42, 38), (15, 8), (7, 15), (35, 5), (13, 23), (40, 40), (28, 12), (17, 29), (16, 26), (22, 4), (4, 39), (40, 34), (8, 32), (27, 12), (39, 15), (42, 21), (17, 25), (33, 20), (18, 30), (25, 2), (38, 28), (10, 41), (4, 32), (16, 16), (18, 14), (42, 8), (28, 30), (41, 15), (33, 15), (13, 15), (6, 29), (37, 42), (35, 14), (17, 44), (30, 23), (26, 35), (38, 4), (38, 41), (13, 18), (22, 48), (36, 31), (36, 0), (35, 27), (8, 30), (14, 36), (25, 31), (32, 32), (22, 32), (5, 0), (0, 1), (2, 21), (15, 25), (27, 31), (1, 4), (35, 23), (23, 0), (37, 7), (28, 0), (10, 14), (9, 16), (7, 47), (27, 37), (37, 5), (26, 41), (37, 44), (7, 37), (11, 47), (12, 31), (12, 17), (5, 23), (14, 42), (11, 25), (26, 4), (35, 17), (31, 43), (24, 28), (16, 48), (21, 1), (5, 19), (33, 46), (24, 7), (41, 0), (3, 0), (28, 28), (40, 39), (16, 6), (24, 23), (4, 47), (24, 1), (32, 15), (30, 18), (17, 23), (13, 46), (18, 1), (32, 35), (12, 25), (25, 11), (29, 20), (30, 17), (12, 1), (2, 0), (26, 15), (35, 35), (20, 29), (15, 5), (37, 20), (13, 4), (21, 29), (14, 30), (32, 14), (8, 4), (4, 44), (15, 1), (35, 22), (40, 31), (29, 7), (35, 48), (30, 11), (38, 37), (24, 16), (5, 27), (19, 22), (36, 10), (24, 36), (26, 48), (5, 5), (24, 12), (4, 10), (3, 46), (39, 44), (0, 18), (9, 47), (27, 43), (5, 42), (31, 37), (19, 13), (18, 37), (28, 47), (22, 17), (42, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 28), (39, 37), (32, 20), (25, 38), (32, 21), (22, 11), (11, 4), (38, 6), (19, 18), (3, 9), (19, 29), (23, 20), (20, 10), (31, 31), (12, 5), (13, 8), (5, 5), (20, 17), (5, 38), (17, 3), (31, 3), (28, 5), (2, 8), (25, 27), (27, 41), (39, 35), (4, 28), (14, 37), (31, 10), (27, 5), (20, 39), (27, 20), (2, 20), (12, 36), (2, 3), (19, 36), (6, 18), (30, 42), (35, 23), (19, 0), (27, 6), (25, 42), (8, 1), (20, 12), (25, 11), (17, 17), (14, 14), (37, 16), (23, 17), (9, 37), (2, 6), (38, 5), (34, 42), (8, 31), (37, 39), (28, 6), (23, 40), (29, 6), (6, 12), (42, 20), (29, 13), (1, 24), (5, 29), (36, 10), (0, 20), (35, 14), (35, 16), (9, 16), (27, 36), (40, 6), (3, 0), (30, 27), (14, 13), (5, 6), (33, 43), (22, 26), (14, 18), (13, 28), (6, 0), (36, 12), (32, 42), (29, 14), (11, 41), (5, 42), (22, 17), (24, 21), (3, 38), (5, 21), (0, 24), (31, 21), (23, 31), (43, 8), (33, 31), (10, 20), (8, 12), (39, 13), (40, 12), (25, 20), (40, 39), (7, 28), (0, 26), (39, 8), (20, 6), (5, 30), (17, 15), (17, 19), (38, 43), (19, 9), (16, 11), (43, 17), (1, 20), (42, 1), (6, 38), (17, 34), (36, 21), (34, 2), (26, 10), (21, 3), (37, 6), (40, 38), (10, 4), (39, 0), (34, 9), (14, 30), (4, 29), (22, 33), (37, 3), (9, 23), (29, 11), (43, 25), (30, 43), (23, 27), (24, 32), (6, 20), (35, 21), (41, 21), (18, 6), (21, 41), (20, 16), (40, 0), (39, 21), (35, 18), (7, 38), (28, 43), (42, 19), (30, 14), (25, 15), (19, 21), (7, 20), (24, 10), (31, 16), (8, 7), (38, 8), (26, 43), (4, 13), (43, 31), (38, 38), (4, 17), (1, 29), (7, 25), (3, 1), (10, 25), (8, 27), (12, 0), (1, 23), (34, 40), (27, 39), (31, 36), (43, 6), (15, 22), (41, 20), (33, 5), (7, 27), (31, 13), (23, 38), (24, 16), (42, 40), (20, 26), (29, 36), (0, 33), (39, 1), (18, 30), (12, 42), (0, 12), (21, 28), (4, 15), (10, 11), (40, 21), (12, 4), (41, 2), (30, 16), (22, 13), (40, 35), (4, 7), (22, 18), (16, 10), (6, 11), (20, 19), (35, 4), (42, 21), (23, 30), (33, 2), (31, 14), (16, 30), (37, 30), (12, 26), (31, 34), (8, 29), (43, 19), (0, 1), (0, 18), (13, 20), (43, 42), (15, 25), (40, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (1, 15), (29, 20), (43, 39), (31, 3), (20, 4), (26, 31), (20, 48), (4, 31), (7, 39), (25, 20), (27, 27), (12, 12), (20, 42), (10, 9), (25, 44), (41, 16), (19, 41), (34, 12), (44, 17), (35, 45), (1, 5), (21, 13), (10, 27), (43, 22), (9, 31), (13, 3), (12, 17), (13, 28), (22, 39), (25, 31), (3, 9), (8, 23), (37, 37), (31, 16), (30, 21), (31, 37), (20, 36), (3, 29), (22, 44), (9, 22), (30, 34), (44, 22), (31, 17), (26, 43), (16, 5), (20, 1), (38, 45), (42, 45), (4, 7), (20, 26), (1, 2), (38, 47), (39, 17), (7, 13), (8, 27), (22, 19), (35, 19), (34, 25), (41, 1), (21, 17), (20, 23), (10, 15), (40, 43), (16, 47), (29, 44), (7, 12), (26, 6), (26, 39), (42, 28), (35, 35), (3, 26), (20, 45), (1, 44), (15, 8), (17, 44), (4, 41), (28, 30), (21, 18), (43, 32), (18, 48), (8, 8), (22, 41), (23, 33), (22, 37), (16, 8), (23, 34), (40, 48), (16, 48), (33, 2), (29, 9), (19, 10), (12, 33), (32, 0), (26, 46), (35, 16), (14, 14), (33, 17), (0, 25), (8, 21), (0, 16), (30, 24), (32, 13), (11, 25), (5, 19), (13, 6), (9, 19), (11, 22), (32, 48), (13, 0), (15, 23), (33, 22), (40, 47), (27, 13), (32, 38), (0, 5), (11, 2), (43, 21), (6, 19), (18, 15), (12, 21), (35, 43), (19, 15), (40, 18), (16, 39), (9, 46), (41, 21), (44, 30), (17, 16), (32, 30), (38, 12), (27, 24), (43, 9), (13, 23), (38, 28), (5, 26), (26, 40), (42, 46), (23, 43), (10, 37), (39, 0), (40, 22), (7, 37), (20, 17), (31, 10), (13, 5), (30, 27), (17, 36), (4, 16), (25, 29), (14, 33), (1, 33), (4, 22), (31, 42), (35, 37), (1, 38), (5, 25), (2, 25), (8, 32), (15, 2), (25, 32), (0, 1), (24, 28), (36, 2), (43, 48), (33, 19), (15, 5), (9, 37), (21, 24), (10, 43), (17, 27), (12, 6), (38, 19), (37, 11), (21, 27), (42, 14), (0, 21), (28, 16), (11, 34), (15, 10), (20, 46), (11, 18), (21, 33), (33, 28), (23, 21), (31, 44), (42, 39), (26, 16), (31, 2), (29, 18), (37, 4), (3, 31), (41, 15), (33, 1), (26, 27), (2, 31), (34, 1), (36, 25), (40, 23), (32, 39), (34, 27), (22, 21), (0, 22), (41, 46), (38, 15), (25, 6), (35, 12), (29, 6), (21, 25), (37, 17), (1, 32), (8, 3), (34, 43), (6, 21), (24, 31), (43, 27), (41, 48), (37, 28), (17, 4), (43, 10), (13, 41), (35, 39), (19, 2), (17, 34), (34, 29), (5, 42), (2, 36), (0, 48), (30, 11), (10, 4), (18, 40), (5, 34), (39, 41), (35, 20), (19, 42), (7, 29), (14, 4), (32, 36), (9, 20), (8, 39), (22, 20), (41, 40), (19, 45), (3, 24), (16, 20), (12, 18), (12, 14), (39, 48), (7, 9), (18, 42), (41, 0), (14, 3), (20, 44), (14, 48), (17, 7), (36, 18), (18, 39), (40, 20), (29, 21), (1, 37), (21, 16), (7, 36), (13, 19), (30, 30), (32, 7), (29, 2), (28, 6), (6, 14), (26, 11), (20, 8), (36, 22), (15, 0), (20, 9), (44, 43), (31, 35), (28, 35), (22, 4), (44, 28), (41, 10), (36, 8), (0, 39), (8, 16), (33, 8), (37, 44), (0, 12), (30, 7), (41, 37), (24, 2), (23, 10), (9, 36), (25, 35), (11, 3), (26, 12), (23, 38), (29, 13), (38, 2), (21, 30), (8, 38), (38, 4), (41, 6), (16, 29), (6, 12), (42, 48), (11, 36), (30, 25), (27, 16), (18, 34), (37, 34), (36, 36), (27, 34), (2, 41), (15, 43), (32, 28), (34, 48), (8, 44), (20, 27), (44, 19), (44, 25), (24, 36), (15, 42), (15, 29), (24, 41), (19, 38), (4, 25), (1, 28), (42, 22), (25, 0), (41, 24), (31, 29), (28, 21), (5, 46), (19, 33), (33, 7), (38, 48), (6, 42), (4, 20), (33, 5), (10, 19), (44, 13), (42, 47), (3, 38), (29, 7), (9, 4), (14, 45), (37, 16), (9, 1), (4, 10), (13, 10), (43, 24), (11, 19), (36, 4), (14, 18), (14, 22), (34, 44), (12, 5), (18, 26), (4, 42), (22, 16), (5, 45), (44, 38), (23, 0), (36, 41), (28, 4), (43, 8), (36, 9), (35, 22), (10, 26), (6, 17), (20, 33), (43, 28), (0, 47), (31, 48), (23, 28), (18, 37), (10, 16), (12, 47), (7, 34), (20, 28), (32, 15), (12, 9), (37, 47), (21, 46), (2, 10), (19, 29), (4, 44), (22, 12), (2, 18), (22, 40), (33, 46), (36, 26), (27, 21), (7, 20), (9, 17), (11, 35), (32, 34), (4, 9), (3, 41), (33, 24), (0, 10), (12, 4), (33, 18), (43, 38), (9, 8), (20, 31), (18, 31), (13, 40), (40, 8), (33, 25), (14, 11), (29, 17), (21, 31), (8, 5), (31, 15), (16, 23), (1, 16), (28, 40), (42, 34), (40, 28), (36, 6), (2, 28), (26, 24), (25, 42), (24, 16), (25, 11), (36, 38), (38, 30), (0, 41), (7, 47), (39, 9), (34, 20), (31, 43), (15, 34), (9, 47), (37, 46), (9, 12), (39, 32), (22, 18), (33, 15), (32, 12), (43, 0), (27, 10), (30, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 35), (29, 37), (31, 26), (35, 4), (28, 30), (17, 7), (12, 43), (26, 24), (0, 37), (28, 14), (29, 28), (20, 41), (27, 10), (37, 3), (18, 14), (29, 14), (4, 43), (38, 5), (0, 29), (27, 43), (37, 20), (10, 8), (6, 44), (14, 46), (36, 36), (28, 26), (20, 39), (20, 38), (32, 34), (0, 46), (31, 4), (15, 22), (34, 39), (7, 8), (6, 28), (8, 2), (39, 16), (18, 24), (33, 24), (22, 28), (37, 38), (10, 15), (13, 41), (12, 24), (29, 8), (24, 32), (32, 10), (13, 26), (23, 37), (41, 22), (34, 17), (3, 16), (3, 43), (6, 0), (41, 12), (33, 33), (34, 13), (37, 1), (27, 40), (36, 13), (22, 14), (14, 17), (35, 16), (9, 23), (23, 24), (18, 19), (5, 42), (1, 40), (25, 39), (19, 1), (15, 5), (39, 3), (32, 8), (34, 15), (21, 38), (11, 5), (18, 26), (34, 18), (11, 26), (0, 3), (3, 36), (7, 1), (20, 1), (34, 1), (33, 12), (2, 30), (23, 21), (30, 30), (29, 17), (27, 39), (28, 44), (5, 36), (3, 28), (15, 15), (27, 42), (41, 41), (26, 29), (0, 6), (39, 20), (26, 33), (31, 31), (19, 5), (19, 3), (35, 40), (9, 24), (18, 11), (11, 30), (10, 11), (38, 2), (13, 14), (39, 46), (22, 38), (8, 37), (37, 40), (22, 21), (26, 45), (4, 17), (11, 22), (34, 33), (12, 32), (37, 9), (30, 4), (40, 31), (37, 18), (8, 8), (33, 42), (28, 22), (28, 28), (9, 0), (10, 16), (3, 23), (25, 18), (28, 4), (25, 8), (15, 23), (22, 4), (10, 5), (12, 46), (26, 25), (36, 7), (10, 18), (17, 46), (41, 19), (0, 42), (4, 44), (5, 25), (25, 25), (30, 21), (40, 1), (19, 35), (28, 43), (24, 18), (29, 5), (17, 43), (15, 14), (41, 35), (38, 33), (27, 44), (2, 27), (25, 21), (29, 18), (6, 21), (15, 39), (32, 39), (4, 39), (24, 14), (19, 10), (26, 6), (41, 44), (36, 9), (12, 17), (30, 3), (22, 44), (30, 26), (9, 19), (22, 39), (39, 26), (21, 4), (21, 20), (28, 12), (30, 43), (19, 42), (0, 8), (14, 37), (35, 18), (22, 17), (37, 28), (37, 11), (0, 30), (14, 39), (0, 7), (12, 7), (25, 40), (4, 21), (11, 23), (4, 42), (29, 27), (21, 1), (14, 16), (18, 29), (41, 16), (1, 34), (30, 8), (9, 3), (40, 8), (40, 22), (16, 2), (6, 11), (26, 14), (17, 24), (24, 1), (12, 29), (21, 9), (10, 44), (3, 0), (7, 6), (29, 39), (32, 23), (13, 11), (17, 38), (36, 2), (17, 1), (17, 16), (30, 44), (40, 28), (5, 28), (35, 46), (29, 21), (12, 4), (34, 25), (30, 36), (39, 29), (23, 15), (24, 13), (34, 9), (13, 2), (7, 30), (8, 18), (5, 9), (27, 21), (10, 34), (1, 45), (26, 39), (1, 0), (40, 26), (22, 41), (29, 12), (27, 20), (14, 36), (23, 20), (14, 20), (23, 33), (36, 29), (15, 1), (3, 7), (17, 0), (37, 13), (9, 7), (21, 27), (18, 27), (36, 28), (2, 11), (11, 15), (20, 28), (26, 46), (40, 17), (16, 40), (8, 40), (32, 18), (17, 13), (13, 18), (31, 18), (15, 2), (38, 44), (32, 26), (22, 23), (33, 17), (32, 3), (16, 20), (6, 23), (41, 31), (40, 4), (33, 32), (7, 4), (6, 17), (25, 20), (27, 30), (30, 39), (32, 11), (34, 41), (34, 29), (26, 2), (10, 10), (33, 40), (1, 35), (27, 25), (8, 31), (4, 20), (1, 4), (24, 15), (23, 1), (5, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 14), (6, 0), (11, 36), (28, 10), (16, 6), (20, 20), (9, 3), (0, 12), (1, 13), (35, 2), (45, 38), (10, 23), (25, 38), (19, 15), (30, 41), (44, 3), (16, 27), (46, 35), (12, 37), (20, 19), (24, 29), (11, 32), (19, 20), (45, 30), (35, 30), (22, 14), (22, 5), (6, 27), (15, 41), (45, 39), (13, 3), (10, 8), (2, 29), (14, 7), (26, 41), (33, 19), (39, 22), (13, 42), (27, 39), (26, 10), (3, 31), (39, 8), (3, 37), (41, 1), (32, 9), (5, 35), (6, 22), (43, 36), (34, 35), (1, 28), (18, 12), (41, 40), (28, 31), (32, 23), (10, 43), (43, 13), (11, 24), (4, 4), (3, 22), (35, 36), (6, 43), (25, 26), (36, 5), (38, 14), (12, 15), (5, 25), (42, 6), (8, 33), (11, 43), (5, 22), (40, 16), (1, 5), (24, 9), (14, 37), (43, 17), (44, 12), (15, 30), (41, 28), (40, 29), (21, 39), (25, 34), (17, 6), (6, 15), (35, 29), (31, 16), (25, 11), (17, 33), (28, 24), (2, 25), (40, 23), (29, 27), (46, 25), (39, 26), (29, 24), (35, 33), (27, 28), (21, 37), (18, 24), (2, 37), (22, 12), (30, 10), (19, 2), (44, 35), (34, 7), (3, 17), (40, 44), (19, 32), (16, 37), (32, 4), (33, 11), (45, 11), (12, 1), (44, 43), (22, 2), (21, 40), (19, 9), (9, 26), (29, 3), (28, 5), (4, 1), (5, 40), (25, 8), (27, 30), (30, 6), (20, 16), (40, 38), (4, 38), (3, 25), (24, 8), (40, 19), (26, 29), (28, 12), (14, 13), (34, 11), (46, 16), (2, 24), (40, 28), (19, 5), (32, 7), (45, 13), (34, 26), (24, 44), (45, 37), (28, 4), (25, 37), (34, 33), (40, 43), (29, 11), (8, 40), (15, 9), (13, 41), (9, 20), (29, 40), (29, 7), (6, 11), (22, 16), (20, 1), (10, 38), (26, 28), (31, 43), (26, 39), (37, 12), (30, 21), (36, 26), (25, 43), (15, 28), (23, 26), (46, 36), (10, 24), (16, 41), (32, 11), (25, 40), (35, 41), (17, 37), (26, 37), (5, 15), (9, 36), (9, 19), (5, 20), (30, 24), (12, 19), (33, 42), (37, 3), (32, 8), (18, 33), (1, 38), (42, 20), (25, 7), (11, 29), (8, 35), (14, 11), (15, 27), (21, 17), (22, 43), (40, 31), (34, 20), (0, 23), (10, 19), (12, 2), (37, 40), (3, 36), (3, 19), (35, 22), (24, 3), (37, 30), (20, 40), (38, 11), (6, 2), (23, 17), (16, 26), (4, 42), (33, 9), (33, 37), (45, 12), (11, 40), (1, 21), (8, 36), (16, 8), (10, 10), (22, 18), (21, 24), (33, 29), (39, 44), (29, 16), (24, 36), (12, 31), (42, 37), (42, 14), (12, 27), (24, 4), (30, 25), (7, 0), (9, 43), (34, 21), (24, 10), (45, 20), (41, 24), (41, 39), (8, 30), (26, 26), (31, 22), (2, 33), (33, 15), (9, 13), (42, 32), (25, 44), (28, 39), (0, 37), (9, 40), (12, 32), (30, 9), (45, 43), (38, 18), (5, 1), (44, 16), (8, 3), (45, 14), (3, 42), (21, 3), (27, 16), (34, 6), (31, 15), (8, 7), (20, 4), (2, 0), (46, 11), (4, 37), (14, 3), (5, 34), (34, 30), (3, 38), (10, 14), (25, 18), (11, 25), (30, 8), (36, 30), (28, 1), (3, 27), (14, 38), (36, 43), (25, 41), (3, 32), (7, 25), (45, 35), (33, 16), (37, 18), (29, 4), (37, 14), (18, 41), (6, 28), (13, 31), (39, 35), (40, 21), (20, 36), (22, 30), (17, 32), (10, 37), (12, 0), (35, 38), (3, 30), (30, 27), (12, 41), (46, 23), (6, 14), (0, 13), (46, 41), (3, 18), (37, 24), (3, 44), (22, 39), (40, 9), (21, 12), (0, 8), (5, 31), (19, 23), (32, 43), (2, 10), (43, 16), (18, 9), (46, 27), (10, 6), (1, 42), (19, 17), (21, 35), (2, 9), (6, 44), (11, 11), (6, 16), (37, 16), (1, 17), (42, 11), (20, 43), (32, 3), (18, 14), (26, 19), (35, 40), (6, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 22), (21, 18), (46, 33), (8, 4), (1, 30), (42, 24), (34, 12), (18, 25), (27, 15), (1, 12), (5, 22), (0, 22), (33, 17), (26, 7), (38, 10), (30, 9), (42, 23), (29, 22), (31, 42), (43, 24), (12, 29), (13, 15), (30, 47), (8, 7), (11, 14), (19, 26), (31, 25), (39, 12), (6, 26), (16, 40), (39, 10), (17, 3), (26, 18), (30, 36), (21, 26), (7, 19), (31, 17), (43, 19), (35, 29), (0, 28), (15, 36), (3, 8), (21, 8), (5, 47), (22, 25), (27, 7), (9, 46), (42, 19), (36, 5), (3, 17), (38, 27), (32, 35), (17, 22), (34, 20), (16, 22), (41, 28), (38, 37), (36, 43), (16, 46), (24, 12), (29, 12), (5, 5), (31, 21), (24, 26), (30, 0), (9, 36), (37, 47), (22, 21), (3, 40), (46, 5), (24, 34), (28, 28), (31, 47), (8, 1), (4, 41), (20, 24), (12, 45), (43, 21), (30, 46), (27, 9), (27, 40), (21, 9), (20, 22), (28, 4), (43, 29), (33, 32), (39, 33), (13, 2), (2, 4), (43, 33), (13, 43), (12, 15), (14, 11), (13, 45), (8, 35), (43, 9), (34, 34), (19, 44), (30, 19), (0, 44), (5, 14), (21, 16), (10, 2), (14, 44), (33, 22), (33, 37), (39, 35), (34, 17), (14, 46), (37, 36), (9, 19), (40, 25), (39, 27), (1, 7), (7, 2), (16, 8), (25, 35), (14, 19), (35, 19), (33, 26), (27, 20), (3, 14), (9, 32), (16, 11), (27, 10), (10, 35), (38, 32), (43, 13), (35, 12), (6, 17), (5, 29), (13, 21), (33, 31), (29, 0), (27, 25), (18, 29), (3, 9), (6, 27), (33, 18), (37, 45), (41, 44), (23, 35), (41, 29), (2, 14), (10, 28), (10, 23), (6, 30), (25, 15), (7, 24), (16, 10), (33, 0), (31, 44), (24, 6), (27, 17), (39, 40), (10, 3), (39, 31), (11, 39), (3, 44), (19, 7), (37, 10), (31, 9), (43, 34), (13, 10), (11, 40), (26, 2), (1, 28), (0, 38), (22, 33), (41, 5), (33, 20), (29, 1), (1, 15), (7, 41), (17, 28), (5, 39), (27, 23), (44, 10), (28, 46), (34, 7), (41, 22), (1, 41), (24, 24), (32, 43), (22, 18), (31, 6), (13, 8), (26, 41), (36, 11), (34, 3), (21, 21), (11, 12), (43, 47), (32, 7), (14, 33), (35, 33), (30, 17), (38, 28), (44, 27), (20, 39), (26, 47), (21, 46), (39, 42), (38, 4), (8, 26), (7, 14), (30, 38), (33, 35), (9, 2), (13, 38), (11, 13), (21, 43), (29, 44), (5, 27), (32, 29), (13, 29), (21, 45), (35, 23), (12, 42), (1, 20), (40, 28), (14, 24), (46, 18), (19, 37), (30, 14), (38, 31), (45, 6), (7, 38), (21, 35), (45, 7), (4, 26), (16, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 10), (12, 7), (37, 15), (25, 42), (10, 44), (36, 24), (27, 37), (6, 11), (14, 32), (20, 1), (6, 21), (29, 41), (0, 32), (15, 27), (41, 8), (3, 6), (27, 12), (2, 0), (30, 26), (42, 44), (17, 21), (1, 20), (11, 43), (33, 6), (44, 19), (40, 37), (23, 25), (1, 25), (0, 8), (43, 24), (33, 32), (13, 4), (24, 32), (44, 5), (23, 7), (22, 8), (30, 27), (37, 13), (16, 0), (15, 3), (27, 46), (43, 16), (0, 23), (7, 5), (46, 18), (46, 10), (28, 39), (27, 11), (29, 27), (18, 20), (44, 14), (15, 36), (34, 16), (43, 33), (20, 2), (44, 11), (32, 10), (37, 4), (22, 5), (8, 22), (30, 35), (11, 1), (23, 37), (29, 24), (0, 35), (4, 28), (26, 16), (30, 34), (18, 34), (26, 39), (26, 5), (9, 6), (17, 23), (30, 37), (31, 12), (42, 20), (6, 28), (28, 38), (35, 30), (26, 28), (20, 46), (46, 28), (14, 42), (17, 42), (35, 40), (7, 37), (2, 4), (16, 6), (3, 7), (31, 6), (23, 33), (16, 28), (27, 20), (12, 39), (23, 13), (3, 33), (12, 32), (37, 14), (30, 24), (33, 24), (38, 20), (11, 20), (12, 11), (32, 21), (40, 5), (18, 39), (28, 13), (36, 32), (37, 30), (25, 7), (43, 42), (24, 12), (18, 37), (9, 13), (41, 18), (37, 26), (44, 38), (9, 23), (34, 18), (13, 14), (26, 24), (34, 8), (0, 27), (5, 6), (19, 3), (39, 23), (17, 3), (5, 19), (18, 10), (3, 5), (0, 3), (11, 25), (8, 12), (28, 25), (27, 44), (39, 15), (44, 26), (28, 4), (18, 8), (40, 24), (39, 12), (7, 25), (3, 25), (17, 6), (42, 1), (19, 9), (30, 17), (42, 33), (14, 7), (27, 42), (0, 40), (16, 46), (36, 26), (40, 28), (29, 21), (16, 25), (45, 35), (41, 32), (9, 4), (3, 18), (32, 24), (35, 5), (22, 42), (36, 30), (4, 34), (19, 42), (18, 3), (33, 42), (12, 28), (37, 23), (7, 36), (20, 13), (29, 19), (1, 14), (28, 40), (8, 33), (44, 3), (5, 45), (6, 44), (22, 6), (8, 31), (32, 2), (15, 33), (20, 21), (33, 12), (15, 37), (22, 43), (24, 40), (8, 6), (2, 12), (29, 17), (7, 44), (2, 1), (5, 17), (2, 8), (10, 2), (11, 14), (31, 40), (34, 13), (11, 46), (34, 12), (19, 12), (13, 46), (8, 42), (29, 36), (35, 7), (16, 19), (16, 21), (32, 9), (13, 37), (34, 14), (40, 38), (25, 32), (39, 24), (11, 21), (6, 9), (40, 7), (40, 11), (19, 37), (2, 18), (12, 29), (46, 41), (28, 12), (9, 21), (7, 26), (18, 4), (7, 13), (1, 17), (30, 42), (34, 46), (11, 26), (3, 42), (43, 44), (27, 28), (41, 4), (21, 4), (14, 22), (34, 39), (1, 37), (3, 22), (27, 16), (22, 34), (16, 41), (23, 24), (23, 39), (6, 15), (19, 5), (32, 37), (3, 13), (23, 30), (31, 9), (27, 25), (28, 36), (46, 29), (13, 22), (38, 8), (24, 8), (6, 19), (25, 30), (26, 4), (8, 20), (4, 43), (6, 45), (46, 15), (1, 5), (46, 9), (18, 32), (6, 6), (9, 25), (31, 5), (45, 30), (16, 33), (45, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 15), (9, 4), (3, 31), (11, 3), (7, 27), (2, 20), (7, 35), (20, 11), (39, 9), (27, 10), (31, 34), (32, 39), (20, 0), (24, 19), (32, 33), (24, 27), (8, 8), (39, 3), (18, 12), (32, 14), (33, 2), (34, 37), (30, 28), (3, 5), (13, 1), (8, 18), (32, 36), (17, 36), (18, 33), (13, 29), (15, 33), (11, 40), (29, 41), (15, 3), (25, 4), (22, 8), (8, 31), (35, 2), (25, 7), (21, 39), (36, 27), (40, 20), (5, 35), (29, 29), (19, 38), (23, 23), (36, 4), (3, 29), (20, 38), (0, 29), (25, 38), (13, 33), (29, 43), (6, 22), (0, 27), (39, 17), (5, 44), (39, 35), (25, 21), (18, 15), (8, 23), (4, 18), (2, 13), (1, 2), (30, 41), (31, 2), (5, 37), (7, 7), (28, 19), (39, 21), (13, 8), (30, 36), (3, 18), (1, 4), (17, 3), (11, 26), (19, 14), (2, 8), (28, 2), (40, 19), (28, 26), (18, 40), (9, 15), (3, 30), (11, 9), (22, 18), (1, 40), (13, 36), (0, 12), (26, 42), (2, 22), (20, 41), (6, 29), (3, 17), (32, 20), (37, 25), (18, 21), (38, 39), (4, 14), (25, 16), (26, 10), (19, 26), (12, 7), (8, 42), (30, 20), (19, 1), (9, 32), (26, 7), (15, 37), (33, 43), (12, 37), (38, 1), (6, 30), (33, 18), (0, 35), (3, 16), (21, 38), (31, 43), (18, 23), (22, 32), (4, 4), (30, 33), (4, 41), (9, 6), (12, 39), (1, 14), (6, 34), (14, 35), (26, 37), (26, 1), (13, 44), (7, 1), (36, 11), (20, 17), (6, 6), (1, 8), (33, 10), (29, 40), (9, 29), (19, 11), (32, 2), (29, 9), (26, 14), (11, 39), (2, 41), (8, 25), (12, 29), (10, 26), (23, 17), (3, 21), (5, 43), (27, 11), (24, 35), (10, 4), (25, 36), (1, 11), (34, 42), (35, 40), (39, 43), (6, 1), (24, 24), (22, 14), (39, 16), (9, 31), (14, 5), (5, 1), (33, 24), (17, 28), (17, 39), (30, 37), (3, 41), (18, 6), (10, 3), (9, 44), (0, 33), (25, 9), (37, 8), (22, 42), (9, 21), (21, 8), (1, 44), (36, 16), (0, 3), (2, 4), (32, 38), (4, 16), (18, 7), (18, 39), (6, 31), (0, 31), (12, 26), (13, 43), (31, 21), (36, 14), (0, 9), (1, 31), (25, 20), (39, 20), (24, 11), (25, 12), (0, 5), (35, 16), (19, 21), (10, 8), (27, 40), (22, 30), (4, 1), (12, 2), (9, 5), (32, 17), (28, 38), (36, 22), (14, 19), (5, 36), (31, 12), (16, 12), (19, 12), (25, 3), (27, 43), (18, 24), (25, 25), (38, 26), (17, 41), (40, 31), (40, 12), (7, 25), (17, 9), (3, 32), (9, 30), (25, 24), (15, 6), (26, 23), (26, 20), (1, 15), (37, 16), (34, 34), (40, 41), (4, 38), (33, 36), (18, 37), (29, 14), (23, 18), (26, 27), (2, 3), (24, 42), (18, 0), (24, 20), (1, 42), (38, 6), (19, 30), (18, 19), (8, 28), (11, 11), (1, 25), (34, 44), (23, 21), (34, 16), (34, 33), (7, 39), (37, 3), (33, 17), (29, 28), (37, 33), (23, 22), (16, 14), (3, 3), (1, 6), (14, 29), (12, 40), (29, 35), (11, 5), (1, 26), (12, 38), (23, 44), (20, 13), (21, 19), (11, 0), (31, 37), (28, 27), (7, 20), (38, 20), (23, 34), (15, 4), (28, 42), (6, 8), (3, 1), (8, 17), (19, 40), (35, 1), (2, 18), (22, 44), (5, 5), (17, 23), (37, 4), (5, 0), (26, 12), (38, 38), (10, 9), (5, 28), (30, 3), (25, 14), (24, 44), (9, 12), (10, 15), (21, 29), (0, 19), (22, 15), (24, 38), (20, 20), (29, 6), (34, 32), (39, 1), (10, 38), (39, 29), (3, 20), (36, 9), (39, 28), (22, 27), (34, 12), (37, 22), (1, 43), (13, 2), (5, 21), (19, 20), (14, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 46x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 43), (1, 24), (29, 21), (40, 34), (35, 18), (2, 26), (9, 16), (22, 1), (22, 24), (34, 6), (35, 1), (19, 18), (37, 6), (38, 42), (7, 39), (27, 4), (28, 1), (37, 37), (0, 35), (20, 24), (19, 27), (18, 15), (42, 30), (22, 34), (44, 28), (30, 29), (25, 1), (13, 38), (0, 44), (11, 16), (44, 21), (31, 26), (20, 10), (26, 15), (19, 19), (32, 13), (35, 10), (8, 13), (3, 16), (44, 26), (30, 9), (33, 40), (0, 21), (30, 3), (21, 27), (11, 11), (10, 0), (15, 26), (40, 24), (16, 45), (28, 0), (38, 2), (14, 26), (11, 36), (23, 15), (34, 18), (19, 1), (45, 37), (25, 21), (37, 38), (30, 13), (39, 3), (43, 17), (2, 3), (2, 9), (34, 12), (8, 21), (40, 21), (15, 28), (26, 43), (35, 20), (9, 41), (17, 43), (10, 36), (3, 0), (45, 11), (22, 19), (26, 29), (28, 24), (20, 2), (1, 15), (24, 1), (37, 41), (20, 30), (24, 8), (20, 22), (2, 39), (30, 31), (40, 6), (2, 6), (45, 42), (25, 22), (20, 17), (26, 2), (39, 23), (4, 45), (27, 22), (44, 9), (45, 16), (31, 10), (38, 26), (31, 30), (0, 11), (4, 17), (8, 26), (31, 12), (19, 20), (5, 14), (18, 23), (15, 24), (36, 17), (32, 40), (6, 31), (15, 37), (20, 43), (39, 4), (27, 41), (26, 18), (14, 22), (32, 22), (29, 19), (41, 45), (27, 26), (45, 32), (37, 40), (2, 1), (2, 44), (45, 34), (20, 16), (41, 11), (41, 31), (14, 15), (45, 24), (2, 40), (12, 20), (41, 40), (29, 24), (34, 41), (25, 20), (25, 4), (41, 33), (10, 4), (26, 19), (33, 26), (1, 11), (12, 19), (27, 14), (34, 2), (6, 24), (36, 8), (15, 45), (1, 4), (38, 39), (25, 35), (19, 22), (42, 3), (38, 31), (22, 13), (8, 1), (33, 12), (6, 9), (22, 6), (9, 5), (6, 14), (16, 30), (31, 9), (7, 22), (23, 44), (10, 19), (23, 43), (11, 2), (35, 37), (35, 13), (43, 21), (0, 4), (19, 39), (40, 27), (3, 6), (4, 42), (7, 16), (26, 13), (38, 36), (13, 0), (3, 34), (11, 44), (2, 28), (11, 24), (29, 12), (35, 27), (19, 42), (37, 42), (14, 12), (32, 6), (9, 28), (19, 28), (8, 25), (15, 35), (33, 35), (37, 8), (21, 45), (5, 34), (6, 25), (3, 8), (45, 4), (23, 14), (16, 15), (18, 2), (12, 11), (16, 44), (10, 38), (12, 43), (8, 17), (39, 42), (10, 10), (38, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 33), (12, 41), (31, 28), (8, 34), (30, 4), (34, 38), (4, 8), (24, 20), (4, 16), (30, 13), (33, 23), (36, 25), (10, 34), (0, 21), (23, 31), (11, 15), (11, 16), (19, 34), (20, 23), (3, 12), (36, 13), (7, 9), (5, 27), (7, 40), (16, 31), (24, 10), (10, 24), (14, 41), (23, 6), (1, 22), (40, 4), (3, 3), (29, 21), (11, 41), (10, 21), (37, 6), (35, 24), (25, 6), (0, 18), (13, 16), (25, 34), (11, 4), (28, 14), (22, 31), (37, 25), (34, 6), (34, 30), (8, 12), (24, 16), (9, 25), (27, 29), (28, 22), (4, 37), (11, 28), (0, 16), (16, 0), (27, 28), (25, 11), (20, 24), (0, 8), (0, 35), (20, 19), (39, 3), (38, 29), (11, 37), (40, 40), (8, 41), (19, 30), (38, 32), (25, 33), (16, 10), (21, 2), (25, 39), (1, 15), (23, 35), (32, 9), (9, 4), (5, 21), (28, 29), (30, 17), (34, 34), (16, 6), (5, 23), (33, 41), (23, 42), (32, 18), (12, 0), (28, 37), (15, 36), (24, 14), (23, 28), (36, 1), (19, 15), (22, 37), (7, 13), (28, 25), (18, 12), (19, 36), (15, 38), (32, 12), (1, 9), (27, 11), (21, 37), (39, 2), (4, 6), (5, 25), (38, 31), (9, 22), (13, 39), (30, 7), (0, 12), (38, 7), (14, 2), (22, 12), (12, 5), (9, 34), (2, 29), (24, 30), (6, 23), (26, 22), (13, 17), (40, 28), (34, 23), (37, 7), (22, 15), (33, 7), (23, 1), (18, 5), (31, 19), (40, 23), (13, 6), (7, 23), (17, 30), (9, 15), (14, 27), (1, 24), (38, 10), (10, 33), (29, 12), (31, 17), (6, 35), (18, 36), (29, 40), (29, 32), (24, 34), (14, 30), (2, 1), (22, 26), (33, 2), (26, 33), (41, 28), (12, 36), (28, 34), (31, 32), (14, 25), (17, 11), (6, 16), (39, 25), (7, 3), (34, 33), (37, 8), (35, 39), (6, 2), (17, 6), (20, 32), (23, 5), (6, 14), (35, 31), (16, 40), (34, 17), (32, 35), (28, 4), (24, 11), (4, 39), (7, 30), (1, 5), (21, 42), (35, 30), (1, 26), (26, 41), (35, 23), (5, 32), (15, 31), (6, 24), (3, 30), (32, 23), (36, 16), (7, 18), (34, 14), (0, 39), (26, 19), (41, 25), (14, 36), (31, 0), (2, 38), (7, 24), (41, 3), (6, 12), (23, 30), (19, 4), (8, 6), (10, 20), (4, 11), (25, 9), (5, 11), (36, 3), (38, 14), (13, 23), (2, 4), (16, 28), (24, 6), (39, 28), (17, 5), (35, 40), (30, 29), (27, 23), (8, 35), (28, 30), (18, 9), (31, 30), (26, 38), (12, 31), (5, 28), (39, 9), (33, 33), (9, 20), (9, 37), (17, 3), (41, 16), (21, 20), (22, 7), (8, 30), (40, 9), (34, 18), (19, 6), (30, 37), (11, 14), (2, 2), (4, 36), (40, 38), (28, 0), (34, 10), (39, 39), (36, 15), (26, 31), (28, 11), (2, 31), (2, 36), (40, 29), (6, 4), (32, 14), (13, 36), (21, 18), (30, 32), (11, 33), (41, 41), (31, 25), (38, 22), (8, 16), (27, 4), (23, 41), (11, 30), (14, 34), (7, 10), (41, 31), (4, 40), (27, 30), (11, 38), (25, 24), (7, 20), (0, 13), (1, 38), (15, 10), (23, 15), (34, 3), (36, 10), (19, 9), (27, 32), (17, 41), (11, 5), (21, 15), (39, 36), (41, 22), (18, 6), (29, 30), (20, 37), (37, 13), (32, 1), (9, 28), (1, 8), (8, 7), (9, 12), (34, 26), (31, 13), (11, 39), (35, 27), (20, 13), (38, 16), (40, 21), (15, 1), (38, 30), (3, 31), (16, 12), (19, 3), (28, 23), (29, 8), (25, 29), (32, 41), (30, 36), (40, 18), (19, 39), (25, 16), (4, 28), (22, 20), (40, 7), (19, 26), (29, 2), (35, 19), (12, 7), (17, 24), (13, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 25), (21, 0), (26, 21), (40, 21), (8, 21), (21, 3), (30, 19), (28, 38), (17, 38), (39, 32), (37, 16), (3, 19), (18, 0), (37, 5), (7, 2), (16, 23), (15, 20), (21, 22), (2, 34), (21, 7), (28, 11), (34, 24), (10, 40), (22, 34), (37, 40), (18, 4), (2, 1), (18, 42), (10, 18), (32, 39), (1, 10), (6, 30), (9, 28), (7, 37), (4, 33), (2, 40), (32, 33), (17, 4), (3, 3), (38, 35), (26, 25), (36, 30), (9, 40), (32, 30), (28, 12), (33, 25), (6, 1), (32, 29), (2, 35), (16, 30), (15, 36), (6, 36), (26, 13), (6, 37), (4, 36), (39, 35), (37, 24), (5, 5), (35, 14), (33, 14), (26, 42), (6, 6), (30, 20), (17, 1), (22, 13), (30, 2), (29, 6), (17, 30), (8, 2), (2, 17), (19, 38), (21, 21), (0, 40), (3, 41), (13, 11), (24, 18), (30, 38), (35, 36), (34, 33), (31, 5), (20, 15), (22, 14), (37, 37), (32, 20), (17, 17), (12, 9), (10, 26), (19, 0), (6, 21), (12, 42), (35, 17), (33, 38), (32, 25), (32, 16), (30, 42), (30, 9), (29, 24), (33, 15), (34, 15), (5, 36), (31, 15), (38, 39), (32, 11), (10, 3), (37, 14), (5, 31), (39, 33), (26, 11), (2, 29), (3, 13), (16, 4), (14, 2), (10, 4), (33, 16), (34, 29), (12, 19), (23, 32), (40, 31), (12, 36), (10, 21), (15, 32), (35, 41), (0, 1), (3, 26), (34, 3), (33, 1), (9, 42), (2, 15), (7, 35), (14, 38), (12, 25), (17, 26), (26, 27), (33, 40), (26, 36), (35, 10), (24, 13), (38, 26), (28, 20), (12, 6), (30, 29), (9, 10), (39, 34), (0, 28), (20, 16), (33, 35), (18, 35), (13, 7), (0, 33), (36, 9), (4, 40), (3, 10), (7, 40), (18, 26), (3, 1), (38, 32), (20, 10), (3, 7), (21, 32), (27, 9), (29, 9), (38, 34), (35, 22), (36, 10), (21, 42), (32, 4), (29, 31), (22, 0), (6, 10), (8, 8), (24, 38), (31, 36), (34, 36), (37, 0), (28, 25), (40, 36), (14, 20), (36, 26), (35, 35), (2, 0), (3, 9), (10, 32), (28, 15), (31, 16), (11, 19), (20, 29), (15, 18), (22, 11), (12, 10), (35, 7), (9, 27), (7, 23), (14, 8), (26, 35), (15, 0), (35, 25), (38, 11), (18, 20), (8, 9), (24, 36), (0, 6), (28, 30), (15, 34), (10, 9), (24, 14), (10, 39), (3, 5), (25, 39), (38, 21), (29, 22), (25, 17), (20, 22), (23, 20), (25, 13), (6, 8), (23, 19), (23, 22), (10, 37), (31, 40), (34, 42), (11, 37), (40, 13), (10, 17), (9, 22), (16, 28), (8, 16), (9, 26), (36, 11), (29, 42), (40, 41), (24, 31), (10, 23), (21, 19), (19, 40), (15, 41), (31, 4), (26, 24), (33, 19), (22, 3), (35, 13), (30, 31), (5, 42), (4, 24), (2, 20), (7, 12), (37, 36), (7, 18), (16, 37), (24, 16), (18, 7), (11, 9), (18, 21), (31, 33), (26, 6), (0, 2), (33, 23), (7, 11), (16, 9), (15, 9), (5, 39), (8, 31), (17, 6), (19, 33), (6, 35), (8, 20), (8, 41), (23, 42), (36, 2), (10, 2), (31, 39), (30, 40), (21, 29), (30, 32), (32, 1), (17, 29), (27, 34), (36, 21), (25, 18), (23, 29), (33, 18), (38, 22), (21, 18), (10, 10), (33, 7), (37, 9), (14, 41), (12, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 32), (37, 32), (17, 21), (27, 7), (29, 9), (29, 35), (26, 33), (10, 31), (22, 8), (23, 35), (20, 17), (21, 37), (16, 37), (18, 29), (8, 9), (0, 11), (12, 16), (0, 25), (6, 27), (7, 33), (1, 33), (20, 22), (20, 11), (27, 18), (30, 36), (37, 20), (9, 21), (38, 29), (17, 32), (3, 10), (33, 3), (38, 28), (37, 23), (34, 18), (4, 0), (17, 29), (0, 37), (3, 12), (6, 37), (23, 6), (26, 19), (15, 9), (35, 11), (28, 23), (34, 35), (5, 4), (29, 25), (38, 25), (38, 12), (34, 25), (7, 13), (2, 19), (16, 17), (33, 24), (36, 35), (21, 26), (2, 38), (13, 6), (17, 17), (32, 9), (29, 14), (24, 16), (11, 0), (7, 31), (25, 28), (5, 12), (14, 8), (6, 38), (3, 7), (4, 15), (30, 31), (17, 34), (0, 20), (1, 19), (21, 38), (37, 18), (7, 15), (5, 36), (25, 7), (7, 20), (13, 1), (22, 15), (7, 2), (31, 14), (5, 28), (14, 0), (7, 29), (20, 16), (32, 2), (37, 9), (8, 31), (14, 34), (2, 16), (1, 6), (19, 11), (29, 20), (39, 19), (39, 0), (30, 13), (5, 37), (24, 30), (7, 4), (25, 17), (2, 11), (22, 16), (29, 0), (35, 13), (6, 25), (38, 19), (5, 8), (22, 30), (21, 31), (24, 4), (17, 3), (22, 24), (28, 21), (8, 25), (3, 27), (35, 33), (3, 28), (35, 1), (33, 22), (38, 39), (4, 2), (26, 2), (26, 5), (17, 7), (7, 11), (10, 35), (18, 25), (19, 1), (15, 11), (39, 21), (28, 19), (7, 0), (32, 18), (8, 26), (0, 35), (13, 3), (35, 35), (13, 19), (32, 37), (18, 32), (36, 3), (10, 3), (28, 0), (23, 17), (18, 18), (37, 10), (36, 24), (29, 22), (38, 13), (23, 24), (20, 24), (39, 36), (9, 10), (34, 36), (27, 16), (1, 22), (16, 5), (6, 0), (29, 6), (29, 39), (11, 7), (31, 5), (30, 28), (13, 28), (4, 24), (26, 12), (23, 26), (14, 2), (22, 25), (6, 34), (31, 3), (10, 26), (34, 11), (16, 18), (27, 1), (25, 18), (10, 19), (5, 16), (1, 5), (4, 23), (18, 34), (1, 32), (3, 26), (9, 18), (18, 33), (28, 34), (28, 29), (25, 21), (6, 1), (24, 31), (20, 31), (15, 18), (8, 18), (36, 32), (27, 14), (18, 23), (7, 17), (6, 7), (2, 30), (31, 38), (7, 5), (34, 24), (35, 7), (18, 38), (27, 8), (21, 10), (33, 26), (0, 27), (18, 39), (32, 23), (34, 22), (1, 14), (11, 13), (23, 20), (15, 26), (9, 17), (20, 12), (9, 8), (15, 33), (14, 23), (5, 3), (9, 2), (33, 13), (30, 15), (13, 39), (25, 36), (2, 33), (8, 39), (39, 33), (28, 3), (31, 30), (32, 38), (37, 8), (10, 0), (1, 38), (37, 26), (31, 4), (36, 1), (35, 4), (16, 12), (37, 19), (13, 22), (3, 14), (11, 29), (31, 27), (20, 29), (38, 8), (10, 33), (2, 17), (12, 35), (26, 38), (19, 28), (34, 29), (29, 27), (37, 34), (33, 34), (2, 25), (5, 1), (21, 20), (8, 38), (17, 18), (6, 28), (15, 39), (34, 20), (21, 22), (21, 2), (6, 36), (9, 39), (22, 19), (30, 7), (18, 3), (27, 25), (27, 13), (10, 27), (15, 31), (6, 35), (28, 7), (24, 35), (20, 25), (13, 33), (7, 14), (7, 23), (6, 23), (23, 22), (13, 27), (22, 21), (34, 1), (11, 39), (1, 25), (13, 34), (24, 2), (23, 12), (2, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 32), (4, 25), (8, 1), (21, 29), (34, 34), (1, 31), (39, 33), (40, 8), (8, 5), (38, 2), (29, 19), (6, 43), (30, 28), (21, 20), (7, 28), (2, 2), (10, 33), (43, 17), (18, 29), (29, 22), (26, 9), (41, 11), (43, 4), (28, 4), (33, 29), (25, 9), (8, 16), (16, 38), (1, 28), (31, 6), (28, 1), (24, 27), (4, 34), (25, 3), (37, 15), (5, 33), (17, 18), (32, 3), (17, 29), (3, 7), (3, 0), (12, 44), (22, 22), (35, 34), (32, 7), (22, 2), (43, 41), (8, 3), (42, 13), (21, 0), (1, 44), (21, 38), (13, 28), (33, 20), (18, 18), (30, 38), (10, 19), (3, 14), (12, 0), (22, 11), (15, 2), (24, 20), (22, 18), (39, 26), (19, 8), (4, 13), (21, 30), (11, 23), (30, 17), (33, 16), (35, 9), (41, 19), (5, 39), (10, 8), (39, 2), (36, 5), (37, 5), (43, 16), (18, 37), (12, 5), (19, 39), (2, 26), (18, 35), (27, 14), (42, 16), (41, 44), (11, 5), (7, 10), (10, 27), (11, 34), (32, 4), (6, 35), (5, 29), (21, 22), (33, 17), (32, 37), (9, 21), (34, 11), (8, 35), (43, 22), (26, 44), (4, 21), (35, 32), (21, 41), (25, 32), (29, 39), (27, 21), (2, 8), (27, 11), (31, 14), (8, 7), (43, 0), (14, 13), (18, 28), (15, 34), (32, 14), (5, 21), (24, 2), (24, 36), (36, 10), (32, 0), (30, 36), (37, 3), (30, 21), (41, 4), (28, 16), (3, 26), (34, 20), (17, 13), (36, 27), (10, 11), (5, 24), (21, 31), (34, 39), (16, 30), (13, 37), (1, 0), (43, 13), (40, 32), (12, 22), (32, 28), (15, 20), (36, 7), (0, 11), (8, 18), (35, 3), (35, 11), (19, 29), (11, 15), (18, 23), (1, 13), (39, 24), (37, 13), (23, 4), (2, 13), (34, 24), (43, 6), (7, 27), (10, 24), (41, 2), (27, 20), (22, 40), (38, 22), (9, 36), (6, 29), (21, 1), (37, 31), (10, 7), (26, 2), (36, 36), (25, 22), (32, 11), (3, 2), (34, 25), (6, 20), (41, 20), (29, 14), (5, 9), (1, 5), (14, 41), (36, 12), (41, 16), (40, 1), (36, 2), (24, 19), (20, 3), (16, 20), (26, 15), (33, 12), (30, 16), (27, 2), (12, 34), (21, 3), (36, 30), (0, 19), (3, 30), (8, 10), (6, 8), (0, 39), (16, 0), (42, 9), (43, 24), (6, 42), (0, 23), (12, 20), (40, 40), (23, 27), (5, 10), (17, 8), (27, 36), (18, 40), (32, 21), (9, 37), (20, 44), (23, 14), (27, 1), (14, 25), (4, 11), (0, 7), (11, 40), (9, 22), (25, 21), (20, 6), (6, 40), (43, 14), (33, 24), (6, 31), (43, 37), (1, 7), (8, 8), (34, 37), (2, 36), (42, 38), (1, 16), (29, 38), (37, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 41), (40, 1), (36, 15), (22, 20), (11, 40), (5, 9), (12, 25), (2, 37), (12, 33), (22, 44), (33, 0), (20, 41), (13, 29), (13, 28), (4, 33), (2, 36), (12, 7), (13, 32), (4, 30), (33, 10), (14, 13), (1, 38), (24, 26), (29, 25), (44, 20), (45, 37), (37, 26), (19, 39), (47, 34), (20, 17), (36, 10), (27, 0), (14, 18), (35, 31), (42, 34), (12, 36), (37, 20), (42, 5), (17, 24), (3, 19), (15, 26), (16, 11), (1, 35), (2, 20), (44, 27), (8, 28), (44, 6), (29, 44), (3, 38), (8, 39), (25, 29), (6, 41), (38, 12), (11, 10), (41, 38), (2, 9), (19, 28), (33, 3), (14, 33), (28, 0), (11, 43), (13, 23), (14, 0), (0, 21), (25, 20), (31, 27), (8, 13), (3, 30), (0, 1), (2, 29), (12, 1), (24, 38), (16, 32), (38, 42), (8, 31), (24, 18), (34, 6), (17, 13), (17, 26), (5, 16), (38, 4), (29, 7), (12, 28), (17, 16), (43, 43), (24, 36), (31, 14), (20, 10), (36, 31), (28, 22), (0, 44), (23, 44), (36, 7), (16, 36), (42, 18), (48, 32), (26, 1), (2, 24), (42, 39), (37, 42), (32, 5), (2, 7), (39, 40), (36, 43), (36, 22), (24, 37), (34, 20), (39, 31), (17, 40), (40, 25), (41, 26), (19, 34), (12, 5), (11, 29), (20, 7), (9, 11), (22, 33), (15, 5), (32, 13), (4, 6), (31, 17), (32, 32), (8, 35), (46, 39), (32, 22), (29, 2), (13, 27), (16, 10), (0, 30), (24, 17), (45, 39), (0, 18), (25, 13), (48, 13), (27, 3), (36, 36), (35, 5), (42, 4), (12, 13), (30, 3), (37, 8), (44, 19), (31, 16), (29, 26), (39, 44), (24, 20), (16, 26), (40, 12), (20, 27), (14, 2), (12, 16), (9, 33), (31, 19), (15, 0), (39, 17), (29, 6), (36, 9), (36, 4), (15, 42), (40, 17), (2, 33), (43, 9), (7, 41), (30, 2), (25, 34), (36, 1), (12, 20), (23, 43), (3, 27), (31, 28), (27, 39), (20, 6), (7, 35), (18, 21), (25, 38), (4, 16), (35, 37), (14, 38), (23, 20), (9, 20), (41, 27), (18, 36), (21, 30), (4, 17), (21, 10), (43, 15), (21, 41), (30, 30), (3, 13), (25, 23), (7, 16), (35, 30), (45, 9), (28, 11), (10, 4), (43, 35), (40, 6), (14, 19), (32, 35), (20, 26), (32, 41), (0, 42), (17, 11), (37, 14), (9, 37), (42, 37), (8, 19), (6, 31), (37, 39), (15, 29), (34, 15), (30, 28), (1, 39), (31, 39), (26, 19), (3, 34), (39, 35), (14, 40), (6, 18), (9, 40), (22, 36), (10, 13), (0, 39), (1, 14), (46, 41), (10, 36), (6, 33), (30, 38), (41, 11), (28, 25), (32, 18), (3, 23), (11, 44), (26, 40), (1, 21), (48, 16), (9, 6), (3, 28), (38, 10), (27, 19), (36, 42), (16, 37), (23, 21), (46, 26), (33, 12), (47, 42), (42, 19), (35, 4), (10, 16), (39, 14), (12, 27), (11, 33), (46, 0), (48, 33), (25, 25), (20, 1), (11, 5), (36, 13), (8, 36), (41, 8), (42, 32), (25, 9), (15, 24), (33, 44), (34, 22), (21, 32), (5, 2), (38, 26), (39, 1), (1, 33), (18, 30), (28, 7), (3, 33), (37, 11), (31, 33), (42, 16), (47, 24), (3, 9), (7, 0), (34, 43), (26, 5), (44, 8), (18, 15), (46, 28), (36, 3), (41, 18), (31, 34), (35, 16), (19, 35), (8, 22), (36, 40), (21, 2), (0, 29), (39, 25), (38, 16), (47, 4), (44, 13), (13, 12), (28, 43), (4, 12), (8, 1), (18, 37), (25, 35), (33, 38), (6, 17), (36, 8), (35, 10), (3, 7), (41, 6), (21, 27), (26, 36), (36, 37), (20, 18), (40, 23), (45, 7), (37, 29), (43, 37), (0, 15), (16, 1), (5, 44), (2, 2), (17, 33), (34, 12), (1, 27), (9, 9), (12, 14), (10, 30), (15, 10), (42, 13), (13, 38), (32, 11), (29, 33), (21, 13), (26, 27), (16, 7), (45, 2), (27, 35), (6, 19), (23, 30), (9, 43), (7, 6), (0, 11), (28, 2), (25, 7), (45, 36), (6, 15), (40, 19), (18, 1), (34, 32), (29, 42), (31, 6), (45, 29), (23, 9), (24, 35), (32, 31), (20, 8), (22, 38), (26, 43), (40, 15), (43, 1), (9, 12), (26, 17), (37, 19), (21, 39), (7, 14), (15, 33), (35, 18), (22, 27), (8, 41), (26, 12), (13, 33), (10, 1), (41, 5), (8, 11), (45, 34), (13, 3), (26, 38), (25, 10), (10, 35), (31, 15), (5, 36), (14, 35), (22, 17), (17, 9), (24, 44), (32, 36), (48, 39), (17, 20), (30, 42), (34, 16), (15, 25), (44, 10), (43, 11), (0, 37), (42, 2), (15, 36), (43, 7), (39, 9), (43, 3), (5, 25), (40, 14), (16, 34), (11, 24), (25, 36), (12, 30), (5, 20), (17, 30), (44, 12), (4, 34), (6, 5), (41, 16), (15, 43), (13, 5), (7, 44), (3, 41), (47, 20), (34, 25), (4, 7), (1, 26), (23, 15), (10, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 4), (16, 33), (3, 27), (26, 16), (38, 30), (20, 31), (2, 32), (25, 37), (17, 36), (18, 27), (8, 36), (9, 8), (24, 19), (25, 14), (26, 41), (3, 24), (42, 7), (25, 8), (15, 18), (5, 18), (17, 6), (44, 35), (9, 19), (41, 12), (40, 15), (36, 42), (10, 8), (14, 27), (6, 39), (35, 40), (8, 0), (43, 29), (2, 23), (15, 9), (31, 38), (1, 14), (41, 10), (5, 3), (0, 3), (2, 2), (15, 40), (30, 37), (20, 5), (6, 16), (25, 36), (29, 1), (33, 26), (5, 8), (23, 3), (29, 25), (38, 40), (26, 42), (30, 4), (16, 15), (12, 7), (10, 17), (45, 35), (35, 19), (33, 5), (39, 19), (24, 34), (39, 40), (31, 33), (20, 8), (7, 1), (17, 32), (17, 21), (36, 39), (2, 15), (23, 29), (44, 16), (9, 5), (16, 32), (22, 10), (24, 5), (13, 41), (45, 0), (10, 36), (27, 39), (18, 18), (38, 12), (15, 0), (6, 19), (29, 39), (3, 15), (40, 10), (32, 41), (41, 16), (18, 3), (3, 28), (4, 24), (44, 5), (23, 42), (12, 24), (6, 41), (15, 20), (37, 15), (19, 23), (40, 30), (12, 32), (7, 12), (20, 19), (18, 22), (19, 13), (39, 12), (26, 1), (4, 26), (36, 8), (18, 7), (1, 29), (6, 11), (41, 25), (15, 14), (21, 8), (41, 9), (33, 16), (26, 36), (3, 30), (43, 25), (23, 33), (18, 8), (25, 17), (0, 41), (13, 21), (2, 14), (7, 18), (24, 29), (33, 3), (5, 44), (30, 42), (43, 38), (39, 9), (25, 6), (3, 17), (29, 23), (4, 36), (6, 5), (12, 38), (5, 25), (33, 25), (29, 19), (18, 13), (5, 6), (22, 23), (44, 39), (5, 37), (10, 1), (14, 33), (27, 13), (41, 5), (39, 7), (5, 2), (35, 28), (36, 31), (20, 38), (19, 44), (35, 37), (39, 37), (42, 19), (35, 24), (2, 29), (41, 1), (38, 10), (11, 17), (16, 3), (26, 43), (32, 14), (26, 13), (0, 29), (15, 24), (0, 43), (3, 39), (42, 20), (15, 36), (13, 9), (1, 41), (15, 41), (6, 3), (31, 32), (12, 14), (33, 24), (11, 5), (2, 24), (27, 2), (10, 21), (8, 16), (9, 10), (35, 33), (14, 10), (0, 12), (19, 19), (35, 36), (42, 34), (37, 25), (6, 22), (13, 37), (16, 35), (40, 1), (22, 29), (29, 11), (31, 35), (35, 15), (39, 24), (23, 43), (11, 38), (6, 38), (34, 35), (21, 7), (26, 10), (44, 0), (35, 23), (44, 7), (17, 8), (9, 15), (7, 44), (7, 27), (34, 42), (12, 20), (6, 37), (25, 23), (34, 38), (34, 30), (5, 0), (9, 34), (5, 41), (45, 9), (0, 15), (30, 28), (9, 42), (24, 11), (6, 25), (8, 10), (21, 36), (2, 31), (7, 6), (10, 37), (2, 43), (39, 34), (41, 37), (33, 38), (24, 28), (19, 11), (22, 19), (10, 11), (5, 42), (38, 28), (37, 33), (11, 27), (21, 20), (11, 3), (38, 26), (4, 7), (44, 4), (41, 43), (42, 5), (21, 41), (44, 27), (44, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 43x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 13), (14, 43), (3, 12), (35, 7), (18, 32), (17, 26), (1, 17), (13, 40), (19, 23), (19, 25), (20, 45), (21, 42), (25, 7), (15, 27), (42, 34), (5, 18), (18, 34), (34, 39), (0, 34), (5, 33), (8, 27), (14, 1), (2, 2), (8, 36), (1, 38), (23, 20), (39, 32), (41, 3), (14, 4), (16, 15), (23, 22), (19, 18), (11, 39), (5, 44), (37, 40), (22, 6), (41, 10), (38, 13), (3, 22), (24, 28), (33, 16), (33, 37), (16, 13), (17, 28), (10, 20), (28, 15), (7, 10), (10, 5), (23, 11), (0, 44), (21, 34), (13, 25), (34, 21), (31, 8), (14, 30), (9, 3), (41, 39), (40, 19), (1, 29), (36, 23), (22, 9), (38, 10), (19, 7), (34, 38), (28, 43), (4, 44), (11, 38), (3, 30), (14, 29), (8, 24), (15, 19), (15, 5), (31, 15), (27, 36), (31, 10), (32, 10), (8, 11), (8, 25), (18, 9), (32, 0), (11, 40), (34, 27), (36, 35), (12, 22), (13, 15), (4, 38), (6, 25), (7, 7), (6, 45), (18, 42), (25, 24), (5, 36), (39, 1), (0, 19), (32, 20), (34, 42), (33, 3), (28, 9), (13, 17), (34, 12), (0, 33), (25, 5), (4, 29), (39, 15), (7, 41), (10, 18), (15, 41), (15, 10), (41, 13), (6, 27), (21, 36), (40, 30), (1, 8), (32, 41), (27, 12), (0, 28), (31, 17), (3, 14), (26, 44), (11, 6), (18, 13), (3, 15), (41, 29), (34, 24), (17, 33), (8, 21), (11, 8), (32, 27), (22, 39), (28, 7), (7, 21), (18, 31), (28, 20), (33, 36), (1, 5), (19, 27), (39, 27), (27, 45), (12, 2), (35, 1), (38, 3), (9, 24), (37, 14), (32, 28), (29, 36), (0, 22), (37, 23), (36, 6), (30, 45), (40, 11), (16, 1), (15, 16), (21, 28), (3, 41), (15, 21), (12, 21), (34, 0), (33, 33), (1, 19), (40, 36), (41, 33), (29, 28), (21, 11), (37, 21), (8, 7), (15, 35), (36, 20), (0, 20), (19, 6), (22, 43), (16, 30), (24, 6), (28, 27), (30, 5), (3, 46), (33, 8), (11, 29), (35, 17), (2, 1), (21, 39), (6, 46), (40, 37), (42, 5), (15, 6), (14, 18), (12, 27), (23, 6), (13, 38), (26, 6), (42, 21), (6, 5), (8, 17), (18, 14), (12, 29), (8, 40), (31, 19), (35, 30), (3, 20), (20, 46), (7, 29), (41, 41), (31, 0), (7, 42), (12, 15), (41, 38), (15, 30), (21, 8), (9, 37), (27, 8), (4, 18), (17, 15), (11, 32), (22, 13), (39, 36), (14, 24), (35, 29), (37, 3), (6, 43), (22, 11), (13, 21), (22, 5), (9, 46), (42, 36), (41, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 38), (17, 2), (29, 38), (27, 8), (33, 47), (31, 47), (11, 33), (7, 43), (10, 5), (36, 46), (16, 26), (23, 26), (35, 26), (25, 1), (29, 4), (41, 33), (6, 19), (15, 9), (41, 44), (31, 22), (36, 19), (10, 33), (5, 17), (30, 36), (23, 35), (36, 22), (1, 15), (18, 8), (20, 18), (39, 24), (27, 22), (33, 39), (3, 13), (18, 44), (6, 45), (6, 15), (24, 30), (30, 15), (4, 9), (22, 17), (31, 32), (13, 31), (16, 24), (14, 27), (2, 24), (11, 4), (34, 31), (23, 37), (11, 35), (10, 21), (24, 34), (15, 22), (26, 21), (0, 9), (21, 23), (38, 28), (0, 40), (5, 34), (17, 46), (26, 47), (17, 39), (32, 22), (8, 10), (28, 32), (38, 27), (27, 46), (28, 11), (12, 11), (38, 19), (35, 14), (12, 19), (35, 9), (24, 25), (35, 38), (6, 30), (27, 12), (33, 29), (40, 28), (25, 11), (4, 41), (29, 47), (40, 16), (12, 20), (4, 10), (10, 46), (16, 31), (34, 45), (10, 30), (5, 4), (33, 30), (29, 30), (21, 6), (40, 9), (37, 40), (15, 1), (33, 34), (17, 22), (17, 18), (2, 37), (16, 47), (9, 8), (23, 46), (12, 6), (9, 9), (6, 6), (3, 12), (37, 23), (25, 13), (28, 36), (18, 45), (17, 29), (29, 44), (12, 44), (7, 41), (34, 43), (37, 36), (33, 10), (1, 44), (36, 27), (7, 37), (15, 36), (18, 19), (37, 11), (17, 26), (3, 32), (12, 12), (37, 26), (3, 6), (13, 32), (24, 21), (2, 28), (0, 37), (33, 26), (38, 4), (39, 38), (12, 26), (38, 31), (16, 25), (3, 20), (33, 14), (41, 22), (34, 10), (3, 14), (13, 47), (35, 1), (6, 9), (21, 42), (3, 41), (41, 6), (3, 23), (8, 43), (21, 22), (16, 15), (8, 7), (30, 37), (11, 37), (16, 4), (41, 15), (25, 23), (2, 27), (29, 18), (21, 5), (14, 30), (38, 37), (14, 37), (10, 40), (2, 40), (27, 13), (6, 1), (15, 43), (3, 0), (24, 2), (15, 16), (35, 4), (11, 26), (14, 15), (15, 30), (40, 10), (19, 26), (38, 14), (40, 5), (26, 37), (13, 17), (0, 16), (7, 11), (39, 31), (38, 21), (11, 43), (41, 20), (9, 41), (32, 14), (14, 14), (5, 27), (36, 25), (28, 19), (17, 0), (9, 33), (5, 37), (11, 38), (19, 15), (35, 46), (12, 40), (6, 13), (39, 9), (34, 46), (8, 37), (24, 3), (14, 44), (10, 28), (8, 23), (17, 15), (32, 33), (14, 16), (4, 31), (28, 30), (11, 19), (24, 17), (21, 39), (2, 44), (14, 12), (20, 25), (14, 38), (37, 42), (32, 40), (6, 28), (33, 22), (4, 11), (25, 8), (35, 11), (29, 32), (1, 14), (1, 21), (16, 7), (19, 31), (16, 22), (2, 8), (7, 14), (26, 12), (11, 8), (29, 36), (21, 45), (6, 42), (31, 21), (29, 16), (22, 9), (0, 25), (27, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 43), (9, 18), (26, 30), (10, 35), (9, 24), (28, 4), (4, 20), (38, 11), (13, 3), (25, 40), (29, 6), (30, 20), (40, 30), (20, 36), (25, 1), (31, 27), (27, 4), (26, 31), (24, 7), (11, 14), (39, 43), (13, 15), (11, 0), (11, 7), (27, 14), (23, 12), (17, 37), (21, 9), (35, 2), (39, 17), (25, 23), (23, 11), (33, 4), (32, 35), (5, 41), (18, 8), (37, 40), (8, 6), (41, 20), (34, 43), (35, 31), (16, 25), (12, 25), (41, 39), (13, 41), (23, 34), (8, 27), (16, 2), (41, 35), (10, 10), (31, 41), (23, 32), (29, 4), (10, 12), (6, 1), (29, 11), (18, 41), (34, 29), (13, 29), (11, 17), (15, 36), (6, 16), (0, 11), (24, 44), (14, 34), (10, 23), (22, 29), (9, 11), (20, 41), (10, 36), (20, 12), (15, 29), (30, 1), (35, 36), (14, 38), (7, 31), (7, 3), (32, 28), (15, 44), (19, 40), (29, 8), (26, 2), (41, 7), (25, 10), (17, 38), (36, 3), (27, 6), (3, 26), (40, 10), (23, 8), (19, 19), (22, 0), (25, 21), (20, 43), (37, 22), (18, 33), (38, 23), (28, 32), (29, 24), (18, 0), (6, 20), (30, 38), (2, 12), (6, 36), (24, 22), (8, 38), (14, 9), (0, 34), (34, 32), (35, 40), (33, 8), (34, 30), (25, 37), (21, 44), (6, 44), (11, 36), (20, 25), (17, 3), (33, 15), (23, 16), (7, 37), (31, 25), (32, 33), (23, 7), (31, 22), (12, 1), (38, 7), (31, 13), (31, 23), (7, 32), (40, 1), (3, 27), (10, 2), (10, 14), (41, 41), (22, 8), (35, 28), (23, 37), (31, 39), (30, 3), (38, 34), (40, 16), (13, 39), (30, 6), (23, 44), (7, 15), (38, 30), (4, 38), (39, 21), (23, 36), (14, 24), (17, 43), (19, 37), (13, 28), (1, 33), (10, 43), (1, 42), (14, 4), (30, 7), (35, 5), (11, 25), (11, 4), (8, 34), (41, 0), (32, 22), (25, 29), (31, 29), (33, 19), (19, 44), (22, 25), (25, 4), (3, 7), (14, 21), (8, 11), (23, 5), (37, 15), (28, 19), (9, 27), (23, 43), (8, 10), (16, 30), (2, 4), (5, 8), (17, 23), (27, 35), (15, 4), (1, 28), (36, 13), (7, 14), (17, 2), (28, 28), (0, 36), (36, 19), (40, 14), (23, 13), (24, 23), (19, 13), (26, 17), (12, 41), (28, 5), (13, 16), (16, 1), (35, 27), (5, 42), (37, 36), (24, 40), (30, 9), (14, 12), (26, 24), (41, 36), (5, 40), (1, 31), (35, 6), (29, 16), (4, 9), (12, 37), (30, 14), (32, 13), (28, 3), (16, 29), (31, 17), (3, 20), (24, 33), (38, 36), (35, 4), (33, 22), (37, 2), (30, 30), (8, 13), (13, 21), (40, 43), (36, 36), (3, 34), (12, 29), (27, 18), (27, 12), (20, 26), (12, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 17), (21, 4), (20, 28), (38, 27), (10, 5), (36, 36), (8, 36), (10, 1), (19, 42), (35, 38), (31, 29), (23, 3), (29, 27), (13, 7), (14, 27), (1, 2), (1, 3), (16, 22), (27, 43), (20, 7), (39, 22), (29, 18), (7, 8), (20, 45), (2, 34), (23, 32), (1, 11), (3, 9), (21, 37), (32, 0), (14, 13), (10, 20), (15, 15), (30, 0), (17, 4), (0, 7), (38, 22), (20, 34), (34, 6), (2, 0), (6, 13), (37, 17), (37, 38), (8, 43), (0, 37), (34, 12), (13, 17), (9, 23), (34, 32), (7, 10), (22, 13), (30, 15), (30, 16), (1, 34), (18, 20), (6, 28), (33, 24), (27, 42), (31, 33), (27, 36), (9, 5), (30, 3), (8, 12), (24, 15), (23, 24), (10, 38), (35, 18), (35, 15), (10, 40), (0, 15), (5, 14), (3, 40), (37, 34), (25, 0), (25, 11), (37, 26), (21, 35), (9, 4), (26, 44), (5, 26), (5, 8), (32, 24), (6, 30), (26, 9), (32, 10), (32, 2), (9, 19), (19, 11), (15, 6), (27, 38), (33, 27), (35, 8), (36, 7), (0, 1), (12, 37), (1, 14), (11, 37), (28, 40), (16, 28), (21, 28), (5, 10), (7, 38), (27, 41), (25, 40), (9, 24), (22, 0), (0, 13), (9, 42), (6, 32), (23, 15), (25, 19), (17, 40), (12, 8), (3, 32), (11, 29), (39, 35), (16, 5), (9, 10), (2, 33), (27, 27), (26, 7), (18, 19), (5, 13), (13, 14), (13, 31), (4, 33), (10, 42), (31, 45), (8, 34), (26, 43), (29, 24), (3, 7), (11, 23), (36, 19), (21, 18), (34, 16), (38, 20), (21, 5), (32, 16), (25, 2), (25, 16), (39, 33), (23, 8), (15, 20), (1, 43), (6, 39), (32, 9), (21, 33), (7, 1), (17, 22), (17, 2), (25, 5), (15, 18), (13, 16), (16, 19), (22, 16), (12, 17), (19, 3), (5, 38), (36, 29), (18, 43), (7, 26), (31, 19), (17, 35), (0, 25), (6, 41), (35, 23), (23, 14), (8, 1), (12, 28), (27, 2), (35, 0), (33, 42), (37, 15), (14, 33), (10, 45), (28, 42), (7, 30), (2, 19), (10, 32), (31, 35), (36, 26), (14, 21), (0, 32), (38, 28), (14, 41), (16, 41), (23, 28), (35, 30), (9, 22), (36, 11), (38, 9), (24, 44), (7, 36), (27, 10), (11, 34), (10, 16), (18, 30), (21, 17), (24, 17), (35, 11), (8, 30), (8, 35), (33, 8), (20, 39), (14, 38), (1, 32), (21, 11), (37, 39), (14, 29), (35, 40), (14, 7), (16, 8), (3, 6), (7, 18), (36, 20), (32, 21), (17, 29), (36, 14), (12, 44), (38, 14), (11, 31), (9, 44), (5, 39), (14, 16), (2, 11), (39, 2), (15, 37), (34, 18), (32, 27), (3, 24), (24, 41), (34, 37), (10, 33), (23, 33), (10, 7), (10, 30), (31, 8), (39, 9), (38, 1), (32, 34), (8, 38), (23, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 20), (7, 32), (28, 14), (27, 29), (19, 0), (26, 34), (14, 10), (1, 15), (33, 14), (24, 8), (26, 4), (31, 27), (31, 36), (30, 4), (40, 13), (40, 7), (30, 9), (21, 4), (0, 35), (13, 22), (15, 35), (27, 28), (36, 42), (40, 43), (31, 26), (5, 34), (29, 16), (37, 22), (39, 42), (37, 21), (24, 4), (23, 6), (2, 32), (26, 33), (21, 41), (7, 27), (3, 14), (10, 9), (1, 42), (35, 12), (36, 30), (1, 9), (18, 0), (3, 39), (22, 31), (24, 32), (15, 29), (15, 43), (10, 37), (10, 41), (5, 14), (25, 40), (16, 34), (0, 2), (21, 11), (2, 14), (30, 41), (30, 1), (20, 33), (29, 22), (24, 7), (36, 33), (16, 21), (3, 40), (22, 36), (9, 8), (7, 41), (40, 12), (24, 13), (11, 27), (0, 38), (39, 36), (19, 19), (31, 22), (16, 35), (39, 37), (35, 16), (27, 15), (3, 35), (29, 19), (19, 33), (9, 27), (9, 38), (4, 9), (6, 26), (22, 35), (9, 31), (21, 8), (16, 32), (25, 1), (26, 22), (19, 9), (1, 39), (24, 15), (22, 17), (9, 14), (4, 3), (25, 19), (6, 32), (12, 18), (30, 24), (8, 40), (25, 42), (19, 14), (10, 16), (12, 15), (6, 16), (30, 25), (15, 6), (23, 19), (8, 22), (36, 41), (24, 22), (31, 28), (14, 11), (33, 42), (0, 23), (0, 16), (14, 14), (35, 42), (5, 38), (14, 13), (35, 41), (26, 35), (23, 11), (32, 12), (30, 6), (37, 29), (9, 29), (18, 17), (31, 30), (24, 0), (25, 23), (36, 32), (28, 9), (0, 44), (34, 41), (24, 1), (28, 10), (17, 39), (28, 28), (3, 1), (23, 8), (39, 19), (22, 10), (17, 43), (28, 19), (22, 6), (17, 19), (10, 15), (36, 39), (31, 19), (20, 0), (32, 14), (12, 31), (39, 21), (38, 32), (15, 13), (11, 7), (35, 37), (20, 23), (30, 0), (22, 22), (9, 34), (40, 11), (11, 35), (26, 25), (4, 41), (13, 16), (17, 25), (4, 19), (21, 12), (18, 32), (28, 7), (32, 2), (6, 9), (28, 5), (22, 4), (12, 43), (26, 24), (15, 4), (15, 18), (32, 13), (2, 42), (33, 40), (34, 1), (19, 5), (15, 32), (10, 6), (1, 25), (21, 43), (13, 28), (5, 10), (39, 4), (16, 2), (40, 17), (11, 6), (37, 30), (6, 39), (20, 31), (10, 35), (6, 13), (22, 7), (20, 32), (32, 1), (1, 28), (19, 40), (38, 29), (1, 32), (12, 35), (19, 27), (21, 17), (24, 25), (29, 1), (23, 0), (19, 24), (17, 42), (23, 39), (37, 17), (13, 31), (29, 17), (19, 22), (14, 42), (18, 8), (10, 8), (14, 6), (11, 24), (15, 19), (40, 32), (29, 41), (39, 8), (17, 7), (9, 22), (10, 13), (11, 29), (39, 18), (20, 30), (30, 30), (8, 25), (3, 22), (21, 7), (37, 40), (18, 4), (15, 7), (10, 21), (26, 12), (25, 10), (14, 15), (32, 17), (25, 3), (15, 23), (30, 37), (33, 21), (37, 31), (15, 34), (4, 7), (23, 30), (3, 13), (12, 44), (24, 30), (40, 22), (17, 24), (8, 7), (29, 24), (1, 18), (25, 20), (34, 14), (17, 29), (23, 33), (32, 21), (31, 1), (39, 6), (32, 25), (40, 14), (16, 26), (36, 11), (2, 15), (23, 32), (38, 13), (37, 16), (13, 34), (16, 29), (4, 18), (26, 19), (35, 34), (29, 29), (29, 2), (36, 28), (38, 25), (13, 40), (33, 18), (38, 43), (3, 29), (33, 31), (16, 28), (11, 10), (33, 6), (11, 17), (0, 10), (14, 29), (1, 36), (4, 0), (12, 16), (18, 30), (31, 13), (9, 18), (22, 25), (8, 38), (14, 9), (34, 43), (22, 21), (20, 26), (38, 4), (21, 35), (15, 20), (25, 11), (10, 20), (26, 38), (28, 36), (14, 38), (3, 3), (16, 18), (33, 36), (4, 15), (40, 40), (34, 28), (8, 32), (28, 39), (15, 27), (36, 16), (34, 12), (16, 42), (1, 0), (36, 36), (32, 18), (10, 4), (10, 14), (37, 33), (37, 1), (30, 13), (14, 16), (1, 29), (30, 17), (6, 17), (40, 34), (9, 10), (30, 16), (18, 25), (25, 44), (12, 37), (30, 8), (23, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 34), (5, 23), (19, 37), (31, 13), (22, 4), (6, 34), (11, 9), (37, 17), (39, 24), (24, 11), (32, 27), (37, 39), (16, 32), (43, 33), (2, 43), (18, 28), (2, 22), (16, 22), (44, 21), (28, 15), (33, 6), (22, 33), (24, 1), (7, 34), (24, 22), (22, 11), (22, 40), (9, 31), (5, 41), (21, 15), (30, 27), (43, 23), (13, 11), (31, 24), (26, 0), (35, 27), (35, 24), (11, 42), (26, 37), (41, 41), (32, 12), (22, 5), (7, 40), (7, 35), (14, 37), (17, 40), (32, 4), (38, 34), (1, 36), (10, 6), (1, 24), (24, 39), (37, 31), (5, 17), (15, 6), (38, 43), (40, 37), (11, 39), (18, 23), (18, 39), (36, 7), (9, 8), (15, 10), (0, 26), (1, 28), (32, 19), (9, 11), (27, 24), (17, 39), (16, 37), (29, 39), (38, 37), (23, 19), (39, 5), (10, 23), (15, 27), (7, 36), (7, 2), (24, 20), (25, 14), (39, 3), (19, 29), (19, 14), (28, 0), (42, 43), (12, 30), (10, 29), (9, 27), (5, 11), (30, 31), (4, 28), (23, 17), (18, 10), (1, 37), (32, 3), (23, 21), (29, 26), (15, 25), (8, 22), (26, 31), (17, 0), (7, 13), (2, 26), (24, 41), (1, 1), (15, 15), (6, 21), (44, 22), (28, 19), (3, 35), (20, 13), (42, 22), (1, 9), (18, 15), (34, 35), (28, 34), (9, 26), (0, 31), (4, 41), (33, 21), (36, 20), (34, 41), (33, 31), (5, 25), (40, 31), (15, 21), (41, 22), (22, 15), (33, 41), (25, 39), (41, 12), (44, 1), (9, 15), (19, 40), (41, 18), (36, 11), (15, 16), (30, 4), (19, 21), (15, 29), (1, 19), (18, 41), (40, 10), (37, 24), (26, 7), (35, 40), (15, 14), (7, 42), (34, 28), (33, 29), (10, 4), (44, 13), (21, 1), (37, 18), (4, 34), (38, 22), (44, 7), (26, 21), (22, 32), (33, 13), (30, 25), (12, 17), (11, 14), (18, 35), (1, 35), (19, 7), (32, 26), (3, 25), (19, 32), (41, 36), (35, 15), (26, 5), (11, 4), (16, 20), (31, 12), (31, 14), (16, 7), (7, 24), (6, 18), (36, 23), (26, 1), (41, 10), (3, 1), (5, 15), (31, 17), (37, 14), (35, 37), (32, 25), (32, 17), (2, 15), (29, 1), (32, 39), (17, 18), (15, 2), (36, 6), (6, 7), (8, 2), (38, 39), (39, 36), (41, 7), (8, 42), (19, 43), (42, 36), (28, 29), (34, 2), (33, 33), (22, 17), (21, 7), (21, 43), (44, 18), (23, 6), (12, 42), (19, 12), (24, 33), (1, 12), (40, 17), (6, 16), (7, 38), (2, 16), (37, 29), (38, 9), (9, 3), (11, 43), (9, 43), (32, 34), (24, 10), (22, 30), (5, 28), (41, 43), (13, 9), (35, 4), (15, 41), (29, 21), (9, 41), (32, 6), (17, 20), (42, 29), (31, 22), (0, 25), (0, 36), (32, 29), (18, 33), (23, 2), (38, 35), (11, 8), (29, 31), (10, 34), (18, 9), (17, 42), (33, 14), (3, 9), (11, 18), (12, 21), (2, 28), (19, 17), (25, 5), (28, 4), (38, 2), (43, 18), (12, 38), (24, 30), (31, 1), (18, 31), (35, 3), (30, 35), (0, 39), (2, 19), (5, 18), (10, 25), (4, 32), (9, 19), (14, 23), (7, 37), (25, 11), (15, 31), (12, 23), (35, 23), (41, 24), (38, 26), (28, 26), (17, 33), (5, 13), (33, 12), (15, 33), (10, 20), (30, 3), (5, 43), (3, 7), (43, 16), (37, 40), (16, 42), (11, 0), (17, 41), (42, 37), (38, 13), (29, 27), (17, 36), (33, 26), (28, 2), (34, 37), (14, 43), (10, 31), (17, 15), (19, 13), (3, 32), (2, 7), (28, 27), (32, 37), (23, 18), (31, 23), (8, 34), (27, 22), (28, 1), (43, 19), (1, 38), (27, 28), (17, 21), (20, 31), (31, 39), (27, 8), (31, 32), (38, 32), (22, 19), (4, 33), (2, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 25), (26, 12), (7, 41), (26, 14), (8, 20), (5, 0), (27, 25), (25, 41), (10, 16), (4, 44), (44, 43), (42, 34), (40, 38), (38, 27), (41, 6), (27, 38), (12, 14), (0, 27), (24, 23), (8, 43), (12, 41), (44, 26), (14, 20), (38, 34), (39, 41), (2, 3), (20, 18), (40, 42), (1, 4), (17, 24), (12, 35), (24, 27), (7, 43), (10, 17), (12, 22), (28, 26), (44, 36), (43, 21), (6, 41), (19, 22), (5, 33), (38, 22), (23, 11), (33, 11), (38, 44), (17, 15), (21, 17), (32, 17), (40, 30), (4, 13), (16, 20), (3, 43), (2, 7), (28, 22), (39, 2), (39, 35), (40, 20), (32, 23), (40, 13), (35, 43), (40, 39), (15, 28), (35, 25), (24, 28), (23, 42), (29, 40), (26, 20), (27, 15), (0, 9), (15, 20), (14, 9), (4, 33), (14, 3), (14, 25), (11, 27), (31, 10), (20, 19), (2, 10), (42, 19), (8, 0), (3, 15), (38, 30), (34, 14), (22, 33), (8, 18), (14, 41), (43, 40), (14, 32), (24, 8), (25, 18), (0, 24), (21, 3), (19, 28), (42, 36), (36, 7), (32, 8), (30, 34), (31, 24), (13, 1), (1, 39), (33, 33), (22, 18), (23, 20), (11, 41), (37, 9), (7, 4), (16, 12), (0, 42), (31, 38), (43, 25), (1, 21), (42, 28), (41, 44), (30, 21), (8, 41), (33, 35), (38, 29), (42, 40), (21, 5), (1, 14), (26, 19), (30, 14), (38, 17), (28, 35), (9, 28), (37, 1), (14, 12), (29, 41), (43, 0), (41, 20), (35, 39), (1, 13), (7, 19), (19, 20), (21, 30), (33, 27), (17, 22), (2, 6), (35, 5), (17, 4), (39, 16), (34, 12), (35, 16), (44, 0), (5, 32), (19, 7), (14, 42), (2, 36), (13, 30), (20, 28), (1, 42), (17, 41), (20, 15), (7, 14), (10, 13), (12, 28), (42, 41), (2, 44), (26, 25), (14, 23), (21, 29), (8, 8), (38, 14), (44, 15), (6, 14), (30, 5), (4, 16), (2, 26), (0, 13), (16, 27), (37, 34), (13, 23), (38, 15), (17, 28), (19, 29), (3, 39), (2, 0), (28, 27), (26, 24), (0, 38), (37, 2), (5, 26), (2, 11), (25, 13), (37, 26), (7, 28), (35, 2), (40, 16), (19, 6), (5, 23), (43, 1), (26, 41), (0, 34), (24, 43), (28, 4), (37, 44), (35, 15), (41, 5), (5, 14), (32, 36), (9, 2), (44, 4), (8, 31), (23, 0), (7, 10), (40, 28), (40, 41), (39, 34), (37, 19), (41, 26), (41, 4), (12, 18), (6, 33), (30, 22), (27, 28), (22, 8), (29, 29), (24, 15), (20, 26), (44, 31), (33, 23), (23, 12), (6, 9), (27, 7), (4, 7), (41, 3), (20, 25), (32, 24), (4, 23), (32, 11), (6, 15), (0, 20), (17, 11), (0, 43), (17, 32), (1, 20), (17, 44), (3, 29), (44, 7), (4, 21), (4, 41), (26, 0), (25, 25), (36, 15), (20, 13), (30, 18), (32, 41), (36, 3), (14, 30), (25, 35), (21, 28), (44, 13), (0, 39), (23, 40), (31, 44), (11, 6), (2, 14), (12, 32), (2, 17), (16, 8), (4, 15), (37, 43), (24, 29), (7, 25), (39, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 11), (40, 34), (27, 25), (31, 31), (46, 37), (46, 16), (23, 14), (4, 23), (40, 9), (34, 10), (5, 34), (44, 25), (38, 22), (36, 21), (44, 28), (39, 16), (19, 0), (41, 8), (16, 26), (11, 11), (48, 7), (6, 13), (48, 39), (23, 27), (7, 11), (28, 33), (12, 7), (47, 23), (23, 21), (34, 39), (26, 25), (4, 35), (25, 8), (31, 21), (42, 3), (23, 32), (47, 30), (19, 14), (16, 16), (36, 35), (14, 33), (0, 12), (33, 25), (5, 2), (33, 12), (3, 28), (29, 40), (24, 29), (35, 28), (13, 1), (20, 18), (19, 28), (6, 27), (33, 19), (8, 17), (47, 18), (16, 24), (24, 28), (10, 38), (24, 37), (1, 20), (35, 39), (45, 25), (3, 26), (13, 21), (36, 37), (38, 19), (43, 14), (34, 21), (33, 37), (37, 7), (39, 25), (37, 19), (18, 27), (18, 33), (12, 40), (16, 15), (0, 22), (42, 15), (16, 12), (25, 13), (36, 19), (31, 5), (23, 29), (31, 9), (31, 36), (34, 1), (35, 2), (3, 39), (28, 7), (34, 19), (6, 11), (22, 10), (43, 0), (14, 12), (2, 15), (24, 11), (48, 35), (2, 34), (4, 38), (8, 21), (19, 11), (19, 2), (19, 7), (33, 28), (9, 28), (22, 4), (20, 37), (26, 27), (46, 14), (5, 30), (11, 21), (10, 22), (38, 38), (0, 36), (19, 19), (2, 27), (10, 27), (15, 40), (32, 36), (7, 33), (34, 30), (46, 7), (20, 21), (14, 30), (43, 1), (26, 33), (34, 6), (10, 4), (14, 10), (16, 18), (48, 30), (32, 30), (6, 37), (46, 5), (17, 30), (16, 0), (6, 24), (1, 33), (20, 35), (36, 6), (10, 0), (16, 10), (34, 0), (9, 16), (32, 25), (11, 22), (45, 16), (37, 18), (9, 9), (0, 17), (43, 31), (5, 25), (27, 39), (48, 4), (30, 32), (12, 35), (9, 27), (26, 23), (46, 10), (25, 37), (31, 32), (37, 23), (1, 24), (41, 21), (42, 9), (42, 18), (13, 3), (3, 7), (44, 23), (3, 14), (16, 29), (36, 5), (29, 38), (32, 28), (19, 34), (22, 29), (33, 4), (18, 34), (27, 20), (10, 9), (41, 25), (38, 1), (42, 19), (37, 28), (45, 6), (15, 29), (30, 18), (20, 28), (8, 16), (5, 15), (43, 15), (8, 1), (6, 23), (16, 4), (36, 27), (21, 25), (8, 9), (34, 22), (41, 1), (40, 17), (23, 31), (7, 2), (31, 27), (29, 1), (24, 20), (22, 40), (23, 7), (7, 23), (30, 2), (42, 27), (4, 28), (15, 39), (10, 37), (26, 13), (9, 39), (33, 39), (0, 26), (6, 22), (31, 19), (2, 0), (34, 12), (24, 19), (45, 21), (36, 7), (32, 22), (2, 2), (43, 24), (39, 23), (24, 4), (15, 37), (19, 4), (44, 33), (2, 28), (2, 24), (6, 38), (4, 29), (41, 20), (32, 3), (33, 15), (22, 18), (2, 11), (17, 2), (45, 31), (3, 24), (19, 5), (29, 10), (4, 13), (37, 20), (29, 6), (34, 13), (32, 11), (14, 4), (23, 40), (2, 14), (25, 40), (7, 3), (26, 12), (11, 36), (42, 6), (1, 21), (11, 31), (38, 25), (15, 32), (24, 0), (17, 22), (11, 0), (21, 32), (31, 29), (43, 20), (34, 14), (24, 23), (22, 11), (40, 10), (30, 19), (37, 24), (26, 15), (38, 24), (27, 12), (3, 1), (45, 17), (4, 3), (47, 14), (19, 33), (37, 38), (21, 0), (9, 0), (3, 29), (15, 26), (41, 11), (10, 6), (48, 37), (15, 28), (34, 34), (48, 14), (20, 22), (44, 1), (32, 7), (28, 39), (0, 28), (2, 33), (48, 25), (38, 39), (2, 8), (14, 34), (39, 14), (24, 15), (48, 22), (22, 27), (28, 1), (18, 25), (47, 9), (29, 12), (13, 35), (42, 16), (16, 8), (27, 29), (44, 7), (40, 35), (0, 25), (27, 7), (30, 36), (3, 10), (1, 39), (22, 14), (21, 29), (32, 32), (31, 15), (12, 34), (46, 4), (26, 35), (11, 24), (11, 32), (10, 19), (32, 6), (10, 21), (13, 34), (42, 13), (20, 39), (18, 1), (36, 0), (34, 16), (26, 32), (1, 18), (6, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 14), (24, 13), (6, 34), (29, 21), (15, 7), (12, 45), (19, 12), (8, 0), (29, 15), (2, 14), (34, 27), (33, 38), (1, 38), (7, 31), (32, 47), (10, 39), (18, 11), (23, 42), (0, 46), (11, 15), (7, 33), (24, 22), (39, 41), (5, 35), (29, 31), (14, 34), (18, 12), (8, 19), (12, 37), (27, 8), (37, 3), (13, 46), (30, 36), (8, 39), (19, 42), (28, 47), (39, 23), (37, 30), (31, 0), (19, 6), (36, 46), (40, 40), (9, 44), (8, 22), (37, 8), (10, 13), (22, 47), (35, 23), (36, 40), (39, 33), (19, 29), (19, 11), (20, 13), (18, 34), (37, 7), (32, 27), (14, 28), (32, 21), (8, 34), (6, 36), (9, 32), (36, 15), (14, 16), (36, 39), (1, 26), (7, 43), (20, 2), (21, 47), (21, 29), (26, 10), (2, 18), (32, 42), (2, 40), (14, 7), (4, 40), (4, 36), (39, 44), (14, 31), (4, 17), (25, 5), (26, 17), (26, 46), (30, 10), (6, 27), (17, 47), (7, 46), (9, 1), (20, 23), (13, 21), (4, 43), (19, 19), (34, 33), (29, 26), (29, 43), (20, 5), (22, 12), (32, 38), (24, 48), (29, 9), (21, 40), (25, 10), (10, 42), (27, 27), (2, 36), (20, 34), (40, 47), (37, 39), (24, 34), (15, 6), (26, 37), (19, 39), (34, 48), (1, 8), (13, 30), (35, 34), (23, 23), (15, 10), (17, 0), (16, 15), (40, 41), (7, 12), (27, 30), (31, 12), (30, 20), (3, 34), (33, 39), (25, 6), (3, 16), (26, 20), (0, 38), (21, 41), (28, 4), (9, 4), (19, 17), (24, 26), (15, 2), (7, 15), (11, 1), (15, 13), (40, 23), (12, 20), (24, 3), (32, 31), (28, 36), (20, 36), (34, 30), (2, 20), (12, 27), (2, 5), (13, 23), (5, 17), (10, 21), (11, 16), (14, 6), (6, 10), (27, 42), (37, 12), (35, 47), (36, 16), (22, 16), (6, 5), (20, 32), (12, 24), (12, 31), (27, 13), (39, 42), (12, 3), (37, 13), (8, 17), (38, 9), (10, 47), (3, 29), (3, 13), (21, 8), (29, 47), (16, 4), (26, 42), (34, 1), (8, 12), (4, 9), (19, 3), (15, 28), (31, 25), (21, 32), (16, 26), (40, 46), (0, 2), (10, 46), (5, 20), (22, 19), (17, 16), (39, 15), (0, 9), (35, 35), (37, 18), (13, 29), (37, 41), (29, 0), (6, 45), (7, 29), (10, 23), (22, 8), (8, 29), (17, 7), (18, 5), (25, 48), (13, 3), (31, 22), (9, 21), (26, 19), (0, 32), (31, 32), (26, 30), (38, 25), (3, 4), (1, 13), (8, 28), (22, 38), (1, 18), (18, 0), (36, 25), (8, 15), (8, 18), (14, 43), (25, 27), (0, 20), (33, 37), (8, 27), (7, 6), (21, 36), (40, 1), (9, 38), (24, 8), (33, 18), (1, 30), (0, 11), (21, 35), (18, 14), (15, 22), (30, 24), (24, 14), (2, 47), (18, 39), (6, 42), (16, 31), (30, 18), (3, 39), (7, 2), (32, 28), (28, 9), (32, 48), (7, 17), (1, 0), (5, 5), (6, 37), (26, 12), (5, 25), (3, 18), (0, 4), (16, 40), (14, 27), (11, 31), (17, 22), (13, 17), (33, 23), (38, 23), (28, 28), (32, 16), (3, 45), (18, 3), (18, 32), (18, 35), (0, 25), (33, 33), (19, 30), (12, 25), (30, 6), (37, 2), (9, 41), (22, 45), (8, 35), (1, 42), (0, 3), (27, 11), (1, 21), (21, 31), (39, 45), (9, 36), (36, 22), (3, 28), (19, 32), (37, 6), (28, 7), (10, 37), (16, 23), (4, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 41), (24, 25), (30, 38), (11, 18), (44, 0), (34, 23), (32, 27), (2, 32), (28, 20), (39, 26), (29, 4), (42, 36), (10, 40), (29, 16), (19, 40), (40, 6), (19, 16), (43, 20), (7, 20), (30, 37), (32, 11), (35, 5), (20, 3), (21, 20), (11, 27), (3, 7), (12, 6), (20, 19), (22, 3), (17, 33), (44, 28), (13, 21), (43, 10), (35, 14), (31, 8), (3, 9), (25, 36), (9, 6), (20, 6), (40, 34), (12, 37), (21, 35), (4, 40), (2, 2), (21, 11), (24, 28), (32, 38), (41, 36), (37, 17), (33, 20), (21, 6), (29, 17), (0, 40), (41, 11), (27, 17), (0, 34), (42, 24), (4, 5), (35, 39), (31, 37), (34, 11), (11, 34), (17, 9), (17, 20), (27, 23), (1, 13), (6, 29), (18, 2), (21, 15), (5, 32), (34, 28), (27, 28), (1, 19), (12, 3), (7, 28), (10, 1), (28, 40), (15, 31), (15, 14), (40, 13), (0, 8), (21, 4), (27, 13), (34, 1), (34, 22), (6, 32), (31, 22), (43, 28), (30, 19), (9, 4), (31, 28), (20, 12), (39, 31), (25, 28), (21, 2), (16, 24), (0, 16), (28, 25), (37, 24), (23, 11), (20, 34), (43, 31), (25, 29), (20, 35), (39, 20), (19, 17), (18, 5), (42, 23), (9, 22), (18, 35), (27, 5), (22, 30), (37, 41), (23, 41), (20, 31), (34, 29), (16, 16), (44, 7), (35, 30), (24, 18), (7, 2), (26, 18), (16, 7), (44, 10), (28, 41), (28, 36), (44, 23), (15, 25), (18, 37), (31, 35), (17, 38), (10, 16), (1, 18), (23, 28), (42, 11), (10, 27), (43, 9), (14, 19), (39, 12), (26, 20), (12, 27), (7, 30), (45, 15), (8, 17), (8, 9), (33, 12), (4, 2), (11, 36), (3, 13), (16, 25), (17, 4), (25, 2), (10, 34), (31, 15), (31, 30), (31, 6), (45, 28), (9, 34), (31, 12), (24, 26), (33, 4), (35, 17), (16, 1), (19, 3), (31, 38), (12, 32), (25, 5), (3, 14), (8, 26), (10, 20), (24, 16), (23, 32), (24, 2), (43, 37), (35, 15), (34, 9), (2, 41), (34, 13), (13, 19), (35, 20), (8, 27), (23, 16), (3, 19), (8, 3), (7, 5), (3, 16), (42, 10), (33, 38), (33, 11), (11, 4), (4, 18), (44, 24), (41, 27), (6, 22), (4, 24), (4, 12), (29, 33), (2, 39), (44, 8), (22, 23), (5, 14), (13, 16), (42, 39), (35, 16), (5, 16), (27, 29), (34, 0), (23, 21), (0, 39), (38, 19), (17, 5), (13, 27), (19, 7), (23, 6), (43, 7), (18, 31), (16, 27), (40, 27), (0, 5), (18, 16), (10, 18), (1, 33), (38, 8), (42, 34), (23, 17), (16, 28), (30, 2), (19, 31), (25, 7), (17, 14), (20, 4), (15, 21), (45, 17), (39, 34), (12, 10), (38, 20), (38, 10), (39, 38), (27, 39), (14, 0), (16, 29), (44, 26), (40, 0), (19, 10), (42, 15), (35, 12), (32, 7), (44, 27), (34, 25), (24, 23), (40, 19), (1, 12), (39, 3), (33, 10), (40, 7), (42, 17), (21, 14), (7, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (45, 21), (13, 15), (13, 1), (30, 33), (38, 41), (39, 8), (42, 18), (36, 24), (4, 25), (20, 5), (42, 37), (30, 15), (44, 20), (40, 39), (16, 17), (46, 26), (36, 36), (18, 8), (44, 22), (38, 38), (9, 22), (32, 41), (17, 23), (39, 13), (0, 22), (36, 10), (21, 25), (28, 25), (40, 23), (24, 32), (0, 1), (16, 31), (33, 15), (21, 33), (32, 34), (29, 32), (28, 36), (19, 10), (7, 35), (38, 29), (5, 32), (25, 30), (22, 23), (21, 18), (46, 6), (46, 11), (9, 6), (34, 20), (24, 7), (28, 29), (41, 26), (35, 41), (10, 14), (25, 9), (44, 35), (18, 23), (38, 39), (40, 10), (19, 11), (17, 4), (13, 41), (3, 17), (0, 33), (25, 15), (37, 4), (34, 9), (5, 12), (3, 9), (15, 23), (7, 26), (0, 18), (3, 41), (20, 28), (23, 21), (34, 31), (48, 13), (9, 3), (16, 16), (6, 4), (44, 21), (21, 32), (41, 14), (31, 1), (31, 8), (34, 21), (15, 2), (20, 4), (20, 13), (0, 31), (8, 11), (15, 27), (36, 9), (7, 3), (43, 7), (23, 28), (19, 14), (7, 25), (1, 40), (38, 1), (35, 12), (29, 27), (29, 24), (34, 19), (38, 21), (8, 28), (6, 9), (34, 35), (32, 12), (2, 0), (39, 28), (24, 37), (4, 33), (46, 35), (27, 0), (46, 23), (10, 0), (15, 39), (40, 20), (3, 37), (12, 13), (32, 8), (39, 27), (25, 10), (23, 13), (3, 22), (4, 14), (30, 10), (39, 36), (23, 8), (19, 26), (9, 41), (12, 21), (8, 22), (34, 14), (20, 17), (43, 11), (18, 39), (13, 28), (28, 4), (23, 23), (33, 29), (30, 18), (8, 34), (47, 29), (39, 32), (5, 14), (47, 14), (43, 41), (28, 8), (4, 6), (15, 6), (35, 26), (29, 6), (47, 22), (27, 36), (10, 4), (11, 40), (41, 5), (3, 12), (17, 38), (40, 6), (3, 21), (39, 31), (30, 17), (39, 24), (7, 32), (47, 8), (33, 18), (26, 33), (25, 0), (45, 13), (34, 38), (36, 20), (6, 31), (28, 37), (35, 5), (32, 38), (30, 24), (45, 10), (28, 12), (48, 19), (45, 14), (34, 10), (31, 17), (31, 23), (36, 15), (19, 32), (24, 0), (1, 22), (27, 22), (10, 41), (47, 7), (31, 34), (4, 3), (7, 15), (16, 40), (8, 39), (35, 36), (7, 27), (2, 10), (2, 14), (26, 12), (40, 0), (22, 12), (10, 20), (24, 23), (15, 1), (37, 7), (6, 36), (1, 31), (39, 15), (33, 38), (19, 2), (45, 16), (29, 33), (26, 2), (35, 3), (21, 3), (5, 28), (41, 16), (30, 6), (45, 19), (10, 16), (23, 11), (5, 31), (5, 11), (45, 15), (23, 18), (0, 15), (40, 11), (35, 35), (36, 18), (33, 9), (33, 25), (7, 30), (40, 21), (32, 17), (6, 33), (20, 31), (24, 27), (25, 36), (16, 15), (41, 19), (27, 3), (24, 35), (36, 32), (9, 33), (4, 13), (40, 14), (24, 10), (35, 25), (46, 22), (35, 11), (17, 21), (43, 12), (13, 34), (46, 15), (13, 22), (40, 17), (8, 19), (31, 0), (30, 36), (3, 11), (7, 9), (27, 5), (28, 15), (41, 7), (32, 25), (1, 23), (46, 25), (41, 12), (27, 23), (47, 39), (4, 7), (20, 22), (8, 25), (23, 34), (46, 24), (27, 31), (36, 17), (38, 32), (48, 10), (17, 22), (23, 7), (46, 32), (14, 13), (47, 27), (11, 12), (39, 20), (21, 34), (1, 7), (9, 34), (24, 28), (1, 20), (30, 12), (13, 5), (46, 41), (27, 21), (10, 39), (21, 40), (39, 12), (3, 14), (34, 7), (8, 29), (1, 10), (7, 36), (11, 4), (31, 27), (46, 3), (21, 37), (24, 34), (13, 37), (31, 2), (35, 29), (31, 26), (30, 40), (10, 37), (1, 39), (48, 17), (37, 5), (48, 35), (4, 38), (19, 41), (22, 34), (1, 3), (0, 36), (20, 1), (11, 19), (12, 31), (31, 18), (34, 39), (35, 15), (16, 2), (47, 31), (46, 1), (18, 18), (31, 20), (1, 5), (9, 7), (3, 32), (3, 8), (0, 40), (31, 29), (34, 5), (41, 4), (47, 28), (22, 38), (38, 10), (24, 39), (48, 34), (34, 1), (31, 31), (32, 11), (35, 21), (17, 6), (12, 0), (35, 37), (13, 2), (23, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 19), (35, 30), (11, 25), (17, 8), (6, 25), (41, 13), (17, 2), (43, 13), (1, 11), (15, 15), (19, 27), (26, 29), (12, 29), (10, 11), (12, 0), (37, 4), (13, 30), (38, 20), (44, 9), (37, 6), (8, 36), (43, 8), (42, 17), (27, 18), (22, 33), (2, 24), (3, 0), (0, 23), (11, 7), (3, 9), (17, 33), (32, 23), (38, 33), (36, 35), (25, 13), (27, 25), (35, 33), (31, 36), (12, 30), (21, 21), (40, 27), (10, 16), (3, 37), (1, 36), (26, 2), (14, 36), (15, 4), (9, 24), (29, 3), (18, 29), (2, 16), (18, 13), (10, 20), (29, 21), (21, 20), (6, 9), (8, 24), (36, 20), (39, 31), (31, 16), (22, 5), (28, 21), (38, 34), (41, 26), (41, 34), (35, 16), (10, 5), (23, 5), (8, 27), (39, 30), (34, 27), (0, 6), (16, 36), (33, 37), (0, 36), (30, 27), (23, 0), (10, 27), (29, 20), (19, 14), (24, 38), (1, 25), (11, 36), (19, 9), (40, 35), (37, 2), (11, 28), (44, 33), (5, 28), (0, 17), (41, 21), (0, 32), (38, 26), (37, 24), (12, 24), (27, 19), (22, 22), (7, 1), (43, 18), (0, 35), (14, 12), (27, 22), (30, 12), (10, 24), (6, 17), (8, 39), (23, 27), (10, 38), (4, 20), (39, 14), (28, 9), (6, 39), (5, 25), (40, 24), (19, 29), (44, 21), (32, 18), (39, 24), (14, 29), (6, 16), (38, 9), (13, 31), (10, 32), (18, 5), (29, 4), (21, 32), (27, 5), (42, 24), (2, 1), (42, 31), (3, 2), (7, 33), (2, 28), (4, 6), (0, 15), (10, 3), (28, 33), (20, 12), (40, 39), (21, 34), (2, 36), (3, 8), (5, 16), (19, 24), (35, 31), (3, 29), (19, 22), (28, 4), (2, 8), (3, 16), (38, 5), (5, 22), (5, 20), (32, 11), (43, 32), (34, 28), (0, 29), (24, 0), (4, 1), (40, 21), (37, 25), (1, 7), (16, 38), (36, 19), (44, 28), (34, 22), (16, 9), (27, 6), (37, 22), (29, 19), (38, 28), (40, 9), (15, 3), (38, 23), (13, 23), (34, 1), (9, 31), (40, 14), (32, 29), (3, 10), (10, 13), (4, 21), (13, 14), (31, 4), (32, 32), (0, 27), (43, 28), (24, 21), (15, 16), (4, 26), (9, 34), (25, 26), (20, 37), (42, 29), (7, 8), (36, 36), (41, 30), (22, 38), (37, 0), (41, 15), (11, 21), (3, 25), (39, 19), (33, 0), (14, 27), (37, 36), (11, 0), (8, 18), (33, 9), (14, 28), (34, 30), (18, 0), (30, 11), (12, 1), (36, 26), (33, 3), (28, 3), (22, 1), (4, 17), (28, 5), (3, 21), (17, 39), (35, 9), (23, 19), (12, 7), (26, 24), (18, 33), (30, 21), (24, 5), (40, 28), (2, 35), (28, 29), (36, 11), (30, 10), (39, 32), (15, 24), (41, 39), (31, 20), (28, 38), (27, 38), (26, 32), (34, 8), (12, 34), (40, 26), (30, 19), (24, 16), (4, 32), (40, 10), (24, 12), (29, 16), (7, 4), (12, 11), (41, 0), (41, 7), (43, 10), (8, 12), (32, 3), (37, 7), (9, 25), (8, 31), (17, 3), (30, 28), (11, 26), (40, 5), (9, 29), (8, 34), (28, 26), (1, 19), (28, 23), (37, 26), (2, 23), (12, 13), (7, 19), (35, 28), (13, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 7), (25, 10), (27, 34), (4, 8), (38, 45), (26, 11), (29, 0), (31, 17), (27, 26), (40, 38), (19, 34), (4, 4), (37, 31), (6, 25), (30, 19), (30, 16), (9, 45), (37, 3), (15, 10), (35, 44), (23, 5), (33, 30), (25, 23), (41, 29), (2, 41), (39, 35), (38, 16), (15, 27), (39, 27), (38, 4), (42, 11), (31, 24), (39, 23), (8, 8), (17, 3), (0, 27), (43, 31), (24, 39), (6, 34), (31, 44), (32, 2), (0, 35), (2, 11), (42, 36), (26, 29), (42, 34), (40, 31), (11, 5), (7, 27), (20, 4), (23, 17), (43, 5), (30, 10), (40, 8), (42, 5), (7, 9), (33, 15), (27, 40), (14, 11), (15, 20), (11, 26), (34, 10), (37, 6), (22, 34), (35, 4), (32, 31), (30, 2), (25, 46), (31, 35), (6, 28), (26, 17), (30, 24), (29, 19), (8, 9), (42, 46), (3, 32), (28, 17), (25, 14), (11, 39), (24, 17), (25, 5), (22, 32), (6, 13), (38, 31), (35, 42), (2, 36), (2, 10), (4, 46), (23, 36), (18, 46), (27, 10), (37, 10), (24, 26), (2, 15), (23, 3), (12, 24), (31, 8), (5, 1), (18, 35), (33, 24), (36, 22), (32, 34), (20, 37), (8, 2), (30, 30), (29, 13), (13, 20), (25, 3), (38, 8), (18, 9), (0, 43), (23, 13), (15, 46), (23, 10), (20, 42), (13, 13), (44, 16), (24, 12), (21, 39), (32, 35), (35, 7), (22, 11), (11, 2), (22, 38), (11, 36), (34, 11), (20, 0), (19, 35), (31, 23), (32, 28), (41, 6), (3, 20), (5, 29), (40, 3), (27, 45), (6, 8), (34, 34), (13, 0), (17, 42), (41, 20), (29, 10), (23, 8), (11, 22), (28, 34), (3, 33), (11, 19), (16, 23), (26, 6), (25, 13), (38, 41), (20, 21), (40, 41), (44, 19), (19, 15), (32, 30), (11, 38), (13, 11), (5, 20), (17, 24), (10, 9), (22, 14), (32, 38), (37, 15), (40, 37), (4, 37), (22, 0), (19, 1), (12, 9), (36, 24), (1, 18), (30, 28), (37, 23), (20, 22), (4, 45), (41, 43), (11, 7), (41, 11), (42, 19), (9, 21), (21, 5), (32, 13), (9, 20), (11, 18), (40, 33), (42, 39), (9, 31), (22, 43), (23, 0), (3, 11), (41, 16), (34, 3), (31, 1), (12, 31), (15, 16), (27, 9), (41, 13), (44, 30), (34, 7), (39, 31), (36, 33), (38, 32), (10, 6), (4, 28), (32, 29), (15, 8), (0, 37), (9, 14), (44, 37), (42, 45), (34, 29), (43, 17), (26, 32), (8, 40), (23, 27), (39, 1), (7, 32), (10, 19), (3, 42), (17, 19), (29, 32), (21, 29), (1, 36), (42, 7), (25, 29), (4, 17), (36, 38), (30, 42), (21, 36), (8, 23), (5, 21), (33, 31), (16, 33), (7, 34), (24, 28), (0, 6), (31, 12), (14, 17), (4, 41), (21, 17), (40, 7), (12, 12), (18, 18), (16, 41), (18, 21), (2, 32), (42, 30), (15, 3), (41, 9), (4, 44), (9, 30), (5, 3), (0, 28), (30, 39), (30, 21), (19, 26), (35, 8), (39, 18), (16, 39), (17, 32), (15, 21), (44, 9), (20, 26), (20, 32), (40, 19), (9, 8), (24, 21), (25, 31), (10, 38), (1, 39), (26, 13), (14, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 10), (32, 20), (6, 2), (25, 17), (31, 38), (27, 21), (29, 21), (26, 30), (5, 3), (3, 34), (34, 14), (4, 34), (12, 33), (21, 1), (40, 24), (29, 31), (35, 27), (11, 15), (39, 27), (32, 17), (6, 28), (29, 13), (34, 13), (29, 1), (3, 21), (29, 18), (33, 8), (13, 11), (8, 16), (25, 36), (7, 6), (26, 35), (18, 29), (33, 2), (39, 5), (23, 22), (29, 14), (16, 10), (26, 21), (35, 24), (23, 26), (2, 11), (16, 6), (18, 6), (26, 25), (22, 3), (12, 22), (31, 8), (17, 18), (28, 12), (29, 35), (22, 17), (37, 4), (10, 9), (27, 30), (33, 6), (5, 4), (36, 30), (2, 33), (26, 37), (13, 19), (19, 13), (1, 35), (38, 7), (28, 22), (14, 22), (23, 37), (23, 35), (7, 21), (29, 37), (7, 17), (31, 3), (30, 21), (18, 8), (21, 10), (38, 16), (11, 30), (0, 5), (40, 23), (27, 23), (7, 18), (11, 16), (13, 37), (23, 25), (37, 9), (32, 16), (8, 15), (26, 23), (24, 3), (36, 2), (4, 22), (19, 0), (35, 29), (22, 6), (21, 21), (28, 10), (14, 7), (37, 37), (35, 31), (17, 14), (21, 35), (32, 23), (12, 29), (33, 30), (26, 33), (36, 15), (15, 36), (8, 7), (26, 31), (29, 16), (17, 6), (15, 8), (37, 6), (1, 33), (8, 9), (40, 33), (8, 24), (16, 1), (39, 40), (13, 18), (27, 2), (11, 11), (39, 33), (1, 1), (2, 29), (32, 31), (38, 17), (1, 7), (24, 2), (25, 19), (16, 15), (35, 7), (28, 25), (20, 22), (8, 33), (8, 21), (25, 40), (32, 29), (23, 29), (14, 36), (36, 16), (18, 12), (34, 12), (2, 32), (12, 13), (18, 19), (12, 0), (20, 37), (9, 21), (3, 32), (7, 0), (22, 30), (1, 3), (0, 24), (11, 19), (1, 16), (9, 31), (15, 40), (19, 16), (21, 15), (18, 39), (0, 8), (20, 6), (13, 27), (24, 36), (36, 25), (15, 12), (21, 18), (30, 15), (33, 17), (5, 0), (39, 34), (15, 33), (9, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 13), (12, 1), (34, 32), (20, 34), (29, 6), (8, 6), (9, 19), (10, 34), (1, 24), (1, 10), (19, 28), (10, 32), (19, 16), (39, 4), (27, 37), (20, 9), (18, 34), (11, 36), (13, 37), (18, 17), (22, 17), (33, 23), (41, 20), (23, 17), (27, 29), (0, 8), (28, 4), (32, 20), (32, 34), (19, 17), (17, 32), (9, 20), (24, 0), (14, 9), (27, 28), (8, 13), (20, 3), (22, 40), (14, 40), (2, 9), (0, 32), (7, 0), (37, 25), (1, 16), (0, 39), (30, 36), (25, 39), (15, 25), (12, 24), (0, 3), (16, 20), (20, 7), (32, 21), (13, 25), (27, 18), (29, 27), (15, 20), (22, 16), (7, 20), (31, 24), (41, 10), (19, 35), (8, 4), (41, 19), (37, 32), (30, 39), (6, 37), (3, 14), (34, 3), (8, 10), (31, 21), (22, 37), (1, 20), (6, 21), (40, 25), (15, 6), (3, 25), (11, 15), (19, 13), (28, 9), (0, 28), (22, 18), (25, 14), (30, 15), (35, 15), (31, 30), (1, 39), (20, 23), (24, 3), (13, 38), (20, 33), (33, 19), (26, 2), (6, 19), (6, 40), (15, 11), (31, 12), (23, 13), (36, 39), (39, 22), (38, 37), (28, 40), (39, 31), (5, 27), (29, 30), (36, 0), (15, 0), (13, 14), (21, 0), (38, 27), (28, 16), (14, 27), (9, 31), (19, 19), (21, 39), (2, 31), (6, 22), (19, 23), (16, 2), (29, 24), (32, 5), (33, 27), (16, 35), (25, 34), (32, 40), (5, 35), (41, 24), (26, 10), (35, 23), (30, 14), (19, 29), (7, 18), (6, 39), (33, 0), (4, 18), (27, 36), (4, 27), (19, 32), (22, 27), (29, 34), (23, 34), (15, 9), (13, 26), (29, 20), (12, 22), (21, 24), (28, 21), (36, 26), (17, 4), (7, 1), (39, 26), (7, 12), (8, 18), (9, 16), (35, 18), (17, 40), (31, 1), (6, 34), (23, 2), (6, 13), (1, 36), (3, 16), (14, 19), (38, 17), (4, 9), (30, 2), (40, 40), (11, 32), (25, 2), (0, 29), (32, 22), (7, 9), (29, 29), (26, 7), (5, 25), (14, 39), (36, 25), (8, 3), (28, 25), (5, 4), (26, 20), (22, 14), (28, 38), (30, 35), (0, 4), (36, 32), (9, 24), (37, 23), (36, 28), (2, 3), (18, 5), (11, 3), (17, 2), (38, 10), (28, 2), (40, 22), (27, 24), (23, 26), (34, 4), (17, 17), (25, 25), (11, 23), (18, 21), (24, 9), (0, 19), (7, 7), (22, 6), (30, 24), (14, 4), (29, 11), (10, 26), (4, 26), (27, 39), (7, 23), (23, 15), (15, 17), (36, 3), (1, 13), (7, 40), (14, 37), (16, 27), (1, 6), (2, 32), (9, 8), (38, 19), (41, 2), (6, 31), (33, 24), (21, 34), (7, 38), (3, 36), (33, 5), (5, 15), (28, 39), (19, 10), (23, 1), (23, 10), (27, 5), (26, 15), (12, 7), (24, 20), (11, 9), (16, 14), (4, 13), (37, 38), (31, 13), (11, 40), (32, 9), (37, 31), (40, 34), (41, 37), (11, 27), (34, 18), (2, 20), (22, 2), (12, 11), (3, 33), (25, 16), (23, 3), (10, 16), (19, 38), (33, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 31), (5, 21), (24, 32), (26, 12), (0, 31), (24, 23), (14, 28), (14, 4), (12, 26), (23, 5), (29, 40), (16, 35), (29, 21), (42, 10), (37, 42), (19, 0), (4, 6), (37, 6), (28, 6), (31, 20), (6, 12), (32, 18), (30, 11), (8, 42), (29, 24), (34, 19), (17, 8), (22, 5), (39, 15), (6, 10), (38, 20), (26, 11), (32, 11), (7, 2), (11, 18), (28, 42), (4, 12), (23, 21), (38, 38), (21, 7), (29, 19), (42, 39), (28, 13), (25, 40), (42, 12), (13, 0), (29, 17), (5, 5), (8, 41), (42, 26), (34, 39), (38, 42), (20, 20), (31, 42), (21, 36), (6, 11), (15, 23), (12, 22), (39, 4), (11, 36), (9, 43), (22, 34), (24, 22), (7, 16), (19, 44), (30, 7), (32, 9), (14, 41), (24, 40), (5, 6), (37, 12), (11, 42), (39, 22), (34, 1), (13, 14), (0, 26), (41, 11), (13, 7), (36, 4), (41, 33), (36, 5), (37, 21), (25, 36), (32, 38), (21, 6), (29, 6), (21, 0), (33, 41), (34, 42), (13, 35), (29, 38), (30, 9), (20, 12), (15, 0), (9, 38), (12, 15), (13, 31), (21, 5), (36, 20), (10, 11), (8, 10), (42, 16), (13, 25), (22, 40), (38, 14), (31, 31), (35, 41), (39, 3), (10, 4), (27, 24), (25, 10), (19, 31), (35, 21), (0, 19), (26, 39), (26, 10), (5, 11), (12, 5), (16, 27), (10, 19), (33, 9), (28, 10), (33, 3), (42, 27), (4, 3), (1, 10), (18, 12), (2, 4), (32, 24), (6, 37), (11, 19), (16, 8), (22, 10), (13, 27), (8, 8), (16, 32), (18, 5), (27, 26), (5, 14), (42, 15), (19, 27), (25, 19), (20, 8), (39, 16), (7, 5), (1, 30), (8, 5), (37, 18), (30, 38), (26, 44), (37, 9), (21, 35), (33, 35), (27, 6), (2, 14), (42, 2), (6, 32), (42, 25), (3, 5), (0, 3), (3, 39), (2, 0), (13, 34), (0, 8), (34, 8), (10, 33), (13, 3), (21, 26), (23, 8), (18, 37), (26, 36), (28, 22), (39, 25), (12, 16), (13, 19), (14, 9), (32, 34), (7, 20), (19, 10), (2, 26), (7, 8), (20, 42), (26, 27), (14, 20), (12, 37), (39, 37), (30, 29), (2, 25), (35, 13), (2, 44), (9, 37), (34, 20), (31, 37), (18, 34), (21, 40), (15, 25), (37, 40), (1, 38), (34, 28), (22, 38), (31, 26), (41, 42), (24, 12), (16, 31), (32, 44), (40, 15), (41, 28), (41, 14), (3, 9), (7, 15), (34, 9), (10, 27), (21, 42), (17, 34), (40, 44), (15, 2), (0, 29), (32, 2), (21, 37), (32, 6), (41, 34), (1, 31), (27, 36), (9, 42), (29, 8), (21, 4), (34, 10), (34, 3), (31, 13), (39, 7), (13, 32), (39, 9), (27, 31), (22, 31), (33, 0), (34, 5), (30, 12), (16, 12), (5, 23), (19, 18), (28, 31), (31, 23), (11, 39), (23, 0), (37, 41), (5, 17), (21, 20), (36, 32), (17, 38), (0, 22), (42, 19), (0, 33), (12, 7), (15, 6), (22, 15), (37, 31), (20, 13), (25, 29), (22, 3), (5, 34), (37, 35), (0, 18), (6, 29), (41, 0), (27, 5), (35, 24), (34, 15), (29, 7), (16, 29), (36, 31), (6, 23), (37, 37), (30, 23), (17, 26), (14, 22), (15, 34), (26, 28), (4, 24), (0, 5), (24, 41), (34, 37), (18, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 10), (36, 23), (34, 30), (25, 10), (13, 42), (39, 4), (1, 18), (6, 14), (27, 17), (6, 18), (39, 36), (39, 5), (12, 17), (30, 31), (24, 4), (38, 15), (34, 35), (3, 34), (21, 4), (26, 3), (38, 4), (34, 27), (33, 13), (25, 14), (5, 29), (35, 34), (17, 40), (30, 39), (3, 3), (22, 9), (13, 21), (24, 7), (26, 39), (4, 22), (31, 1), (10, 30), (12, 39), (4, 36), (27, 12), (2, 8), (39, 2), (19, 35), (34, 24), (22, 41), (10, 21), (9, 34), (22, 15), (24, 13), (36, 42), (21, 33), (24, 11), (14, 39), (5, 4), (4, 6), (38, 8), (1, 7), (17, 23), (39, 39), (27, 25), (25, 13), (23, 38), (37, 11), (22, 28), (23, 10), (5, 36), (16, 21), (20, 25), (12, 9), (0, 36), (19, 26), (5, 32), (39, 25), (2, 6), (35, 42), (6, 19), (16, 2), (16, 40), (6, 8), (16, 24), (25, 28), (29, 30), (35, 17), (31, 13), (5, 33), (29, 24), (29, 3), (0, 27), (13, 11), (23, 20), (4, 2), (26, 29), (18, 14), (0, 20), (22, 16), (25, 16), (39, 6), (39, 8), (25, 6), (27, 30), (38, 35), (18, 37), (8, 7), (4, 15), (33, 16), (27, 21), (31, 10), (30, 23), (21, 8), (22, 17), (10, 31), (36, 41), (5, 42), (22, 25), (37, 31), (21, 38), (23, 37), (3, 36), (31, 0), (2, 7), (1, 15), (20, 33), (12, 38), (18, 18), (15, 9), (31, 6), (36, 34), (22, 34), (3, 39), (10, 1), (2, 42), (33, 10), (13, 12), (22, 2), (8, 25), (37, 14), (11, 27), (16, 15), (39, 41), (4, 27), (6, 6), (18, 5), (18, 15), (27, 34), (7, 35), (0, 42), (8, 0), (35, 6), (25, 23), (8, 21), (10, 39), (20, 9), (20, 7), (17, 14), (17, 33), (18, 1), (0, 2), (13, 8), (29, 42), (27, 5), (12, 5), (26, 10), (1, 13), (6, 41), (4, 25), (23, 26), (39, 12), (38, 20), (5, 37), (16, 16), (34, 32), (16, 41), (33, 31), (35, 29), (20, 37), (9, 42), (12, 23), (32, 32), (30, 38), (0, 9), (17, 2), (9, 41), (39, 11), (20, 4), (20, 29), (37, 38), (11, 7), (31, 42), (13, 26), (30, 15), (0, 21), (12, 28), (33, 30), (10, 27), (12, 37), (20, 26), (0, 22), (19, 18), (25, 8), (38, 40), (15, 19), (27, 37), (39, 24), (24, 42), (22, 13), (34, 12), (1, 19), (2, 14), (37, 20), (5, 24), (7, 38), (30, 12), (3, 30), (34, 31), (21, 0), (28, 2), (35, 40), (35, 3), (26, 15), (9, 19), (18, 23), (16, 27), (21, 40), (0, 18), (37, 16), (17, 27), (26, 22), (27, 33), (29, 19), (21, 30), (6, 16), (24, 22), (4, 26), (7, 39), (18, 12), (3, 15), (26, 14), (32, 17), (37, 3), (4, 20), (2, 36), (36, 10), (17, 19), (10, 35), (29, 33), (12, 21), (1, 5), (6, 25), (8, 11), (8, 40), (24, 30), (36, 3), (28, 0), (36, 40), (19, 22), (16, 37), (36, 27), (34, 10), (38, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 27), (47, 20), (3, 18), (12, 1), (0, 4), (47, 10), (5, 0), (31, 21), (3, 31), (32, 23), (47, 24), (29, 11), (2, 11), (14, 15), (0, 7), (16, 44), (45, 33), (32, 1), (14, 33), (19, 30), (37, 37), (2, 1), (27, 7), (21, 42), (43, 26), (16, 32), (1, 34), (32, 43), (16, 9), (4, 3), (4, 27), (13, 33), (11, 40), (18, 34), (30, 32), (34, 39), (3, 40), (38, 22), (28, 35), (8, 40), (16, 20), (42, 24), (9, 23), (7, 44), (26, 9), (19, 38), (26, 20), (36, 11), (17, 40), (21, 5), (27, 12), (40, 30), (1, 14), (29, 25), (13, 25), (35, 11), (31, 11), (26, 10), (5, 36), (38, 2), (10, 34), (35, 10), (10, 23), (33, 30), (47, 12), (32, 21), (46, 23), (28, 32), (27, 20), (10, 3), (27, 11), (0, 19), (46, 25), (47, 26), (27, 25), (37, 30), (29, 39), (32, 14), (18, 21), (28, 8), (20, 10), (13, 15), (37, 32), (22, 22), (21, 27), (38, 40), (1, 42), (17, 25), (4, 19), (28, 18), (10, 36), (43, 27), (30, 2), (46, 29), (16, 3), (11, 29), (0, 33), (29, 2), (3, 38), (1, 17), (46, 5), (7, 23), (0, 1), (20, 7), (23, 3), (19, 42), (47, 6), (32, 19), (44, 22), (27, 32), (0, 11), (21, 41), (47, 29), (11, 19), (3, 33), (24, 29), (3, 5), (21, 2), (36, 34), (43, 30), (27, 33), (18, 33), (14, 29), (42, 32), (31, 43), (19, 39), (23, 23), (30, 10), (47, 13), (0, 36), (13, 2), (18, 7), (9, 35), (37, 18), (36, 15), (7, 21), (28, 10), (35, 33), (4, 41), (5, 5), (12, 8), (4, 29), (0, 13), (18, 1), (0, 22), (16, 24), (6, 32), (26, 43), (28, 37), (34, 10), (3, 7), (41, 18), (41, 36), (36, 29), (24, 24), (8, 15), (43, 2), (42, 33), (37, 13), (33, 14), (44, 12), (8, 3), (33, 42), (33, 15), (4, 42), (18, 41), (46, 18), (12, 35), (11, 18), (15, 23), (24, 7), (46, 21), (14, 22), (3, 19), (0, 27), (16, 25), (44, 24), (17, 18), (20, 2), (2, 20), (39, 25), (24, 15), (4, 5), (5, 7), (13, 31), (21, 26), (21, 31), (16, 26), (22, 38), (13, 30), (24, 16), (44, 13), (11, 2), (3, 25), (34, 36), (37, 29), (22, 16), (31, 42), (36, 35), (18, 11), (7, 29), (46, 15), (12, 10), (47, 22), (14, 25), (40, 25), (38, 26), (11, 36), (2, 34), (38, 17), (29, 18), (43, 8), (28, 15), (20, 41), (20, 25), (41, 30), (8, 30), (38, 0), (32, 26), (34, 17), (15, 35), (26, 2), (17, 1), (14, 28), (23, 12), (15, 17), (31, 24), (42, 43), (27, 19), (41, 7), (2, 41), (35, 16), (25, 28), (3, 41), (22, 9), (28, 21), (13, 44), (31, 8), (20, 22), (40, 18), (7, 9), (7, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 7), (4, 24), (37, 5), (7, 38), (39, 37), (34, 20), (19, 38), (41, 18), (40, 5), (34, 10), (7, 7), (1, 5), (40, 34), (30, 24), (19, 0), (12, 18), (1, 2), (17, 2), (24, 3), (26, 9), (22, 1), (25, 15), (33, 28), (31, 30), (25, 3), (13, 35), (9, 35), (35, 11), (37, 31), (12, 12), (21, 16), (38, 19), (32, 8), (1, 22), (39, 18), (40, 31), (17, 18), (37, 2), (5, 15), (26, 6), (28, 33), (38, 32), (38, 10), (29, 0), (19, 14), (27, 22), (4, 35), (12, 30), (17, 10), (2, 34), (26, 1), (27, 18), (10, 34), (5, 7), (7, 40), (33, 12), (38, 35), (3, 9), (5, 17), (30, 37), (14, 35), (9, 5), (0, 26), (1, 25), (0, 18), (6, 29), (14, 19), (34, 23), (15, 27), (22, 22), (7, 32), (9, 6), (4, 39), (31, 27), (8, 24), (5, 23), (10, 1), (23, 29), (13, 6), (41, 35), (7, 26), (14, 6), (31, 0), (39, 36), (33, 8), (35, 33), (6, 24), (9, 9), (32, 13), (14, 12), (26, 0), (20, 11), (10, 28), (12, 17), (38, 17), (37, 3), (27, 38), (36, 6), (9, 10), (24, 32), (12, 7), (33, 16), (10, 12), (1, 28), (31, 39), (23, 33), (37, 8), (35, 23), (23, 22), (25, 20), (29, 20), (25, 7), (1, 16), (7, 11), (10, 2), (37, 6), (31, 33), (15, 38), (34, 1), (21, 25), (22, 9), (35, 21), (31, 19), (18, 23), (25, 9), (27, 31), (28, 18), (8, 10), (0, 23), (26, 15), (33, 14), (16, 29), (0, 6), (13, 3), (16, 39), (26, 12), (31, 11), (17, 14), (4, 32), (21, 36), (27, 2), (11, 24), (2, 2), (13, 28), (36, 9), (27, 8), (19, 15), (27, 24), (23, 20), (4, 33), (19, 5), (17, 11), (17, 6), (30, 4), (13, 33), (16, 17), (13, 11), (26, 21), (27, 4), (16, 23), (3, 6), (17, 5), (3, 5), (21, 40), (26, 8), (14, 8), (29, 18), (15, 36), (5, 27), (35, 29), (35, 18), (36, 29), (21, 29), (27, 21), (25, 16), (39, 22), (24, 9), (7, 3), (12, 37), (9, 26), (31, 40), (32, 7), (3, 36), (34, 30), (41, 24), (39, 5), (0, 25), (41, 8), (5, 30), (26, 32), (31, 4), (38, 40), (0, 9), (6, 13), (35, 15), (1, 24), (41, 39), (21, 11), (19, 32), (33, 10), (1, 6), (23, 17), (39, 23), (38, 30), (28, 15), (3, 40), (21, 35), (8, 8), (9, 20), (24, 7), (8, 27), (3, 21), (41, 30), (22, 11), (30, 25), (10, 20), (21, 33), (19, 3), (7, 14), (1, 13), (25, 26), (1, 31), (22, 35), (39, 0), (7, 29), (35, 4), (27, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 7), (18, 32), (28, 15), (11, 41), (4, 22), (10, 31), (20, 16), (8, 42), (0, 36), (20, 43), (37, 19), (28, 23), (14, 28), (35, 18), (39, 1), (35, 17), (26, 20), (25, 6), (35, 22), (23, 28), (12, 28), (28, 26), (26, 22), (23, 13), (18, 12), (5, 43), (12, 6), (18, 18), (39, 40), (26, 6), (14, 6), (32, 0), (32, 8), (35, 25), (6, 41), (31, 16), (28, 41), (27, 22), (14, 37), (6, 32), (19, 4), (25, 31), (6, 15), (17, 8), (30, 20), (30, 17), (1, 8), (9, 0), (13, 20), (15, 35), (18, 17), (38, 21), (19, 15), (30, 19), (4, 39), (7, 45), (31, 40), (35, 2), (13, 29), (5, 41), (34, 11), (39, 16), (35, 27), (36, 7), (11, 40), (0, 26), (14, 44), (33, 21), (35, 13), (37, 38), (13, 3), (31, 38), (38, 29), (38, 31), (4, 38), (30, 22), (6, 6), (8, 40), (23, 40), (36, 37), (18, 43), (27, 35), (17, 6), (37, 4), (29, 19), (19, 26), (39, 43), (18, 15), (1, 25), (31, 34), (33, 19), (13, 19), (28, 38), (9, 34), (2, 15), (32, 38), (0, 15), (7, 32), (34, 34), (5, 27), (5, 6), (38, 23), (13, 6), (29, 36), (8, 27), (36, 0), (21, 24), (12, 26), (15, 45), (37, 10), (27, 21), (22, 42), (11, 20), (11, 42), (2, 42), (6, 5), (1, 6), (38, 4), (3, 28), (15, 29), (4, 2), (7, 24), (13, 13), (13, 25), (20, 44), (33, 33), (36, 32), (14, 11), (4, 9), (6, 17), (39, 6), (23, 29), (27, 38), (20, 22), (36, 36), (19, 14), (3, 41), (32, 10), (24, 26), (17, 10), (20, 8), (2, 13), (10, 11), (0, 33), (23, 17), (8, 4), (11, 25), (28, 29), (12, 14), (33, 28), (3, 43), (29, 25), (18, 29), (13, 32), (17, 41), (30, 25), (22, 23), (24, 12), (2, 19), (34, 20), (2, 20), (12, 17), (15, 21), (4, 12), (4, 6), (30, 30), (23, 43), (28, 27), (31, 11), (38, 25), (34, 40), (11, 23), (19, 20), (23, 9), (12, 21), (25, 42), (25, 15), (35, 38), (21, 6), (28, 6), (34, 45), (15, 6), (36, 43), (4, 37), (37, 30), (29, 9), (9, 23), (7, 42), (8, 22), (14, 22), (2, 32), (24, 27), (24, 0), (33, 17), (12, 8), (24, 33), (5, 7), (27, 15), (25, 26), (12, 22), (28, 25), (25, 30), (7, 15), (27, 42), (36, 17), (1, 33), (12, 42), (12, 27), (20, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 13), (33, 37), (31, 40), (9, 45), (22, 22), (16, 21), (22, 25), (40, 46), (28, 35), (40, 1), (33, 43), (9, 43), (19, 42), (41, 7), (27, 13), (17, 46), (25, 2), (28, 34), (4, 8), (39, 35), (24, 25), (30, 41), (11, 20), (1, 35), (2, 43), (33, 4), (27, 9), (41, 46), (15, 2), (35, 25), (29, 29), (15, 28), (22, 23), (31, 12), (30, 33), (31, 2), (11, 28), (41, 35), (0, 48), (39, 19), (20, 44), (4, 45), (4, 16), (26, 27), (25, 17), (35, 33), (2, 14), (5, 34), (14, 45), (27, 42), (25, 24), (8, 20), (23, 12), (28, 21), (18, 3), (32, 29), (11, 11), (9, 24), (19, 20), (41, 2), (36, 3), (11, 30), (17, 1), (8, 31), (10, 22), (29, 12), (10, 46), (18, 23), (21, 48), (7, 28), (21, 31), (35, 30), (11, 41), (13, 4), (28, 28), (39, 16), (6, 28), (9, 28), (23, 11), (1, 16), (40, 47), (28, 40), (35, 26), (28, 13), (14, 34), (5, 11), (30, 0), (35, 44), (28, 38), (0, 15), (18, 25), (2, 44), (12, 12), (26, 0), (9, 39), (15, 15), (24, 48), (5, 17), (11, 6), (2, 17), (30, 39), (17, 13), (0, 9), (34, 5), (6, 31), (18, 2), (33, 35), (2, 27), (33, 9), (35, 16), (17, 35), (10, 47), (40, 40), (2, 0), (7, 9), (35, 8), (4, 20), (19, 37), (32, 4), (13, 32), (31, 37), (25, 18), (21, 41), (10, 44), (15, 5), (2, 45), (36, 7), (19, 28), (5, 30), (38, 12), (18, 19), (11, 12), (35, 41), (29, 43), (27, 44), (40, 30), (30, 35), (35, 15), (21, 36), (36, 47), (15, 43), (27, 38), (34, 32), (12, 10), (1, 23), (2, 9), (16, 9), (39, 21), (37, 41), (32, 14), (2, 16), (19, 23), (7, 39), (31, 4), (10, 10), (41, 45), (25, 20), (5, 41), (7, 37), (27, 25), (21, 28), (36, 38), (7, 40), (34, 22), (26, 35), (35, 38), (4, 14), (19, 29), (23, 27), (17, 11), (0, 42), (37, 15), (35, 32), (12, 26), (25, 41), (13, 30), (37, 46), (25, 12), (2, 18), (19, 2), (31, 29), (33, 27), (14, 11), (31, 24), (41, 40), (39, 12), (29, 8), (23, 41), (15, 23), (13, 33), (2, 32), (2, 37), (27, 39), (21, 12), (2, 46), (23, 5), (7, 43), (3, 7), (25, 34), (29, 22), (23, 31), (5, 32), (6, 1), (0, 43), (20, 40), (26, 47), (36, 32), (12, 28), (12, 41), (19, 36), (4, 24), (31, 7), (34, 7), (13, 42), (7, 44), (39, 37), (4, 40), (4, 37), (19, 10), (34, 6), (6, 48), (0, 35), (24, 41), (16, 16), (11, 43), (23, 15), (3, 30), (26, 12), (32, 6), (23, 24), (25, 13), (27, 11), (10, 11), (4, 47), (37, 36), (37, 19), (0, 2), (24, 29), (13, 1), (26, 46), (23, 7), (8, 1), (21, 18), (19, 31), (23, 18), (10, 20), (8, 9), (8, 7), (15, 41), (28, 14), (23, 20), (30, 31), (9, 14), (34, 24), (36, 36), (6, 18), (13, 7), (29, 17), (33, 17), (21, 33), (39, 46), (4, 4), (17, 25), (21, 43), (16, 6), (22, 14), (12, 25), (32, 32), (34, 23), (0, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 27), (30, 20), (34, 39), (8, 38), (20, 45), (16, 37), (22, 1), (14, 29), (11, 36), (7, 45), (27, 4), (28, 10), (30, 15), (3, 27), (7, 1), (31, 33), (11, 23), (21, 22), (11, 15), (19, 9), (30, 0), (23, 28), (19, 33), (31, 36), (13, 9), (11, 43), (8, 13), (18, 7), (1, 6), (29, 30), (15, 40), (4, 7), (4, 3), (35, 9), (37, 22), (9, 46), (8, 6), (1, 15), (2, 32), (16, 43), (31, 18), (35, 13), (24, 23), (1, 40), (13, 3), (21, 37), (29, 18), (27, 42), (9, 17), (7, 26), (6, 42), (9, 4), (17, 37), (9, 2), (26, 22), (33, 40), (33, 22), (31, 37), (39, 0), (20, 27), (13, 24), (16, 6), (34, 36), (3, 26), (1, 36), (2, 35), (8, 23), (21, 40), (13, 46), (32, 13), (36, 24), (28, 35), (37, 15), (37, 30), (14, 10), (15, 33), (21, 34), (18, 24), (17, 6), (22, 36), (7, 11), (18, 28), (36, 25), (32, 5), (39, 4), (33, 38), (4, 47), (6, 8), (38, 43), (28, 47), (20, 8), (22, 17), (6, 2), (30, 33), (10, 17), (3, 45), (4, 30), (36, 36), (26, 29), (11, 31), (32, 41), (0, 18), (8, 3), (38, 23), (13, 45), (20, 42), (18, 32), (28, 26), (37, 5), (21, 14), (0, 43), (38, 6), (12, 25), (35, 10), (25, 44), (27, 39), (37, 13), (0, 30), (11, 47), (39, 23), (15, 24), (15, 13), (32, 12), (38, 46), (29, 22), (27, 20), (20, 1), (20, 39), (31, 39), (22, 12), (19, 21), (27, 36), (0, 13), (12, 26), (25, 4), (16, 5), (14, 3), (30, 16), (28, 15), (22, 31), (30, 19), (3, 38), (18, 29), (12, 23), (0, 45), (13, 32), (17, 21), (29, 28), (10, 13), (11, 1), (10, 24), (0, 34), (4, 38), (39, 39), (16, 23), (2, 26), (27, 23), (20, 3), (26, 2), (9, 40), (34, 11), (28, 21), (4, 12), (6, 24), (23, 33), (11, 40), (9, 12), (10, 46), (4, 35), (30, 12), (19, 38), (9, 11), (17, 26), (6, 20), (36, 18), (11, 9), (14, 23), (35, 35), (27, 14), (30, 29), (33, 10), (14, 40), (18, 38), (33, 14), (4, 33), (3, 41), (10, 45), (34, 29), (36, 34), (38, 37), (16, 16), (27, 5), (24, 25), (36, 9), (20, 4), (24, 24), (24, 30), (12, 11), (1, 23), (10, 22), (14, 16), (35, 47), (19, 7), (8, 25), (11, 26), (8, 20), (3, 35), (38, 11), (2, 42), (6, 43), (21, 33), (21, 26), (21, 5), (18, 4), (29, 14), (29, 10), (12, 38), (22, 41), (22, 34), (29, 13), (0, 16), (28, 14), (29, 7), (38, 18), (20, 17), (33, 27), (23, 4), (32, 33), (10, 10), (3, 7), (35, 39), (23, 44), (20, 40), (32, 22), (13, 13), (5, 38), (23, 32), (32, 17), (32, 6), (33, 29), (4, 14), (23, 46), (10, 20), (16, 7), (28, 20), (22, 7), (33, 26), (37, 32), (28, 22), (17, 46), (34, 22), (5, 25), (8, 2), (16, 26), (27, 30), (30, 3), (16, 21), (0, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 26), (11, 33), (28, 27), (7, 20), (30, 21), (45, 21), (35, 18), (21, 6), (0, 9), (23, 7), (45, 12), (8, 4), (27, 0), (26, 30), (10, 4), (42, 17), (39, 6), (39, 36), (45, 8), (32, 24), (24, 29), (7, 32), (39, 37), (10, 1), (8, 16), (9, 28), (5, 32), (18, 37), (9, 8), (31, 2), (5, 38), (23, 34), (42, 36), (3, 31), (2, 30), (29, 31), (3, 4), (23, 5), (26, 0), (0, 38), (2, 34), (19, 33), (1, 27), (0, 34), (25, 20), (40, 2), (33, 7), (36, 14), (12, 29), (40, 21), (46, 34), (9, 16), (23, 37), (9, 13), (45, 27), (29, 9), (42, 19), (3, 14), (19, 18), (15, 7), (9, 22), (46, 16), (21, 23), (28, 34), (12, 12), (12, 35), (39, 4), (24, 5), (32, 35), (2, 1), (21, 16), (5, 20), (17, 37), (22, 20), (20, 13), (10, 30), (12, 7), (44, 14), (33, 12), (24, 19), (41, 22), (45, 0), (18, 9), (40, 3), (9, 3), (41, 28), (39, 12), (17, 34), (30, 1), (19, 25), (44, 27), (8, 38), (29, 35), (39, 29), (23, 18), (26, 14), (44, 23), (10, 3), (8, 5), (43, 26), (46, 28), (45, 37), (24, 31), (9, 33), (0, 10), (28, 16), (30, 27), (37, 8), (36, 33), (1, 8), (25, 21), (37, 0), (43, 8), (27, 16), (22, 15), (37, 9), (46, 22), (43, 29), (38, 9), (37, 18), (6, 34), (43, 36), (7, 33), (23, 23), (34, 7), (41, 17), (11, 10), (1, 23), (41, 31), (39, 19), (16, 29), (5, 31), (27, 17), (10, 25), (25, 29), (38, 3), (25, 4), (2, 16), (8, 32), (39, 33), (31, 3), (17, 9), (44, 24), (44, 4), (21, 39), (42, 8), (21, 18), (6, 25), (34, 23), (3, 29), (17, 21), (33, 36), (38, 27), (20, 6), (21, 25), (28, 21), (37, 26), (18, 3), (10, 16), (35, 8), (42, 32), (27, 24), (11, 39), (18, 17), (14, 6), (27, 33), (36, 21), (8, 14), (42, 28), (21, 31), (36, 28), (27, 30), (1, 0), (1, 15), (10, 29), (41, 0), (42, 9), (4, 32), (6, 1), (17, 27), (33, 34), (14, 1), (35, 33), (40, 28), (6, 15), (24, 4), (3, 27), (34, 25), (44, 37), (13, 14), (25, 24), (25, 16), (10, 32), (35, 9), (12, 21), (17, 7), (11, 16), (37, 32), (5, 8), (13, 20), (32, 17), (44, 22), (0, 32), (9, 29), (40, 7), (41, 24), (21, 30), (37, 15), (46, 13), (0, 24), (0, 17), (26, 5), (46, 18), (42, 29), (16, 30), (15, 27), (36, 39), (39, 9), (27, 13), (2, 29), (4, 10), (42, 22), (14, 0), (36, 38), (15, 34), (31, 6), (4, 0), (37, 34), (28, 18), (2, 26), (2, 24), (28, 10), (22, 39), (13, 10), (16, 32), (2, 35), (5, 39), (1, 6), (38, 26), (32, 31), (27, 36), (9, 39), (24, 30), (9, 34), (13, 11), (23, 30), (42, 31), (27, 11), (36, 34), (16, 16), (45, 20), (23, 21), (0, 7), (29, 11), (17, 23), (40, 10), (11, 36), (6, 8), (30, 15), (30, 5), (14, 4), (18, 16), (11, 4), (15, 3), (10, 35), (46, 4), (5, 33), (35, 10), (5, 5), (30, 39), (33, 25), (0, 3), (0, 13), (20, 24), (33, 4), (40, 35), (27, 7), (29, 25), (44, 2), (4, 13), (24, 37), (18, 39), (29, 23), (15, 9), (29, 2), (45, 30), (38, 25), (38, 39), (2, 39), (21, 1), (25, 11), (25, 28), (13, 2), (18, 21), (17, 25), (22, 12), (42, 7), (46, 36), (44, 6), (4, 38), (2, 22), (32, 38), (13, 12), (32, 8), (21, 17), (12, 6), (13, 36), (3, 33), (23, 27), (10, 7), (22, 33), (18, 33), (46, 3), (8, 11), (41, 20), (13, 24), (2, 10), (22, 5), (35, 17), (27, 38)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 8), (4, 22), (22, 4), (35, 13), (41, 18), (43, 20), (44, 12), (15, 26), (35, 23), (16, 21), (33, 10), (37, 28), (28, 3), (41, 38), (43, 26), (40, 34), (27, 6), (31, 13), (30, 20), (0, 32), (23, 2), (10, 11), (42, 5), (27, 33), (38, 11), (34, 27), (7, 1), (39, 1), (33, 34), (17, 27), (45, 0), (19, 29), (7, 36), (21, 39), (9, 17), (13, 37), (25, 12), (9, 7), (36, 28), (3, 20), (16, 22), (29, 1), (38, 23), (38, 16), (3, 34), (11, 6), (20, 18), (30, 6), (41, 20), (18, 10), (44, 7), (22, 36), (19, 23), (43, 10), (13, 5), (4, 33), (5, 37), (12, 4), (40, 13), (14, 23), (5, 31), (0, 22), (16, 14), (35, 32), (22, 21), (21, 1), (42, 18), (17, 5), (24, 35), (35, 27), (37, 2), (18, 33), (23, 28), (37, 27), (17, 25), (28, 0), (13, 24), (12, 20), (41, 1), (41, 23), (25, 28), (39, 6), (5, 25), (27, 2), (42, 33), (29, 13), (18, 21), (44, 20), (42, 19), (25, 7), (40, 14), (22, 16), (31, 15), (2, 23), (2, 12), (7, 29), (40, 33), (9, 33), (22, 33), (42, 1), (38, 29), (15, 21), (35, 12), (42, 22), (44, 33), (4, 14), (44, 9), (16, 32), (33, 20), (11, 15), (43, 37), (26, 18), (43, 14), (45, 8), (45, 11), (18, 39), (26, 36), (6, 23), (6, 8), (5, 2), (28, 19), (30, 24), (14, 29), (15, 25), (9, 36), (15, 34), (1, 24), (39, 35), (10, 31), (7, 25), (24, 21), (12, 7), (21, 24), (19, 22), (9, 15), (33, 24), (8, 19), (11, 5), (34, 7), (16, 19), (19, 0), (21, 4), (32, 6), (8, 18), (5, 0), (31, 30), (6, 28), (0, 24), (26, 7), (15, 37), (43, 34), (43, 33), (24, 20), (0, 30), (34, 13), (10, 14), (42, 35), (7, 19), (32, 10), (16, 10), (9, 22), (32, 36), (28, 20), (2, 34), (2, 22), (40, 8), (3, 21), (20, 10), (30, 39), (19, 31), (41, 35), (22, 11), (37, 25), (23, 15), (33, 29), (13, 36), (22, 1), (43, 35), (25, 37), (14, 34), (26, 4), (2, 4), (33, 33), (32, 30), (8, 0), (3, 0), (19, 6), (20, 21), (31, 6), (1, 11), (19, 32), (23, 35), (25, 0), (8, 7), (17, 34), (39, 18), (36, 11), (8, 6), (4, 4), (25, 36), (40, 0), (45, 20), (45, 18), (16, 12), (19, 26), (45, 29), (15, 1), (37, 13), (28, 16), (36, 34), (12, 38), (14, 35), (3, 9), (38, 30), (12, 35), (11, 31), (27, 36), (30, 30), (38, 35), (34, 33), (3, 13), (5, 8), (38, 22), (40, 38), (31, 39), (10, 35), (1, 33), (31, 11), (0, 5), (0, 17), (3, 3), (8, 5), (10, 32), (28, 26), (18, 7), (21, 13), (35, 8), (18, 11), (3, 11), (24, 31), (10, 8), (25, 32), (6, 1), (2, 28), (21, 19), (42, 28), (23, 0), (3, 23), (0, 27), (7, 39), (40, 6), (5, 28), (15, 23), (30, 32), (7, 20), (10, 37), (23, 29), (4, 17), (41, 5), (32, 20), (33, 6), (4, 26), (29, 27), (4, 5), (11, 10), (42, 16), (33, 23), (43, 16), (22, 12), (27, 28), (6, 9), (25, 23), (43, 13), (39, 0), (38, 38), (36, 23), (4, 24), (43, 12), (2, 27), (29, 16), (20, 32), (31, 2), (4, 37), (24, 1), (7, 3), (39, 36), (45, 1), (11, 27), (43, 39), (41, 22), (37, 3), (12, 25), (42, 31), (24, 10), (6, 25), (39, 7), (31, 8), (25, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 39), (25, 20), (11, 7), (27, 27), (39, 23), (2, 11), (8, 33), (5, 29), (27, 36), (13, 16), (5, 3), (25, 34), (29, 11), (13, 3), (7, 30), (33, 4), (20, 13), (24, 40), (37, 34), (11, 29), (6, 14), (3, 32), (36, 42), (29, 28), (36, 28), (34, 28), (4, 40), (4, 12), (37, 15), (9, 40), (12, 2), (40, 20), (4, 1), (16, 36), (19, 17), (21, 35), (32, 40), (13, 38), (4, 4), (28, 11), (18, 21), (44, 37), (24, 35), (35, 39), (6, 24), (34, 1), (18, 41), (28, 21), (20, 21), (23, 31), (21, 8), (36, 20), (11, 27), (25, 23), (40, 11), (0, 1), (40, 16), (25, 29), (35, 1), (34, 2), (40, 31), (43, 9), (39, 19), (11, 19), (8, 25), (13, 27), (8, 35), (21, 39), (23, 40), (35, 17), (41, 17), (7, 10), (37, 20), (30, 14), (22, 18), (34, 16), (5, 23), (33, 30), (15, 21), (3, 41), (11, 14), (23, 29), (8, 19), (35, 20), (0, 6), (22, 1), (2, 3), (11, 6), (21, 13), (20, 10), (13, 6), (39, 13), (3, 24), (20, 9), (41, 31), (1, 21), (14, 20), (10, 7), (12, 26), (8, 12), (10, 17), (9, 26), (44, 34), (34, 21), (33, 15), (35, 5), (23, 33), (15, 5), (8, 18), (42, 30), (40, 27), (43, 23), (2, 6), (29, 27), (27, 6), (5, 15), (28, 19), (19, 20), (6, 34), (5, 33), (1, 5), (36, 27), (17, 15), (3, 19), (37, 32), (7, 35), (32, 2), (42, 36), (4, 18), (33, 14), (7, 25), (35, 27), (11, 12), (44, 21), (9, 42), (15, 24), (0, 12), (38, 4), (30, 0), (14, 40), (17, 16), (35, 9), (20, 8), (12, 13), (12, 21), (14, 1), (39, 31), (21, 36), (3, 33), (11, 31), (6, 12), (33, 40), (27, 42), (8, 2), (19, 41), (41, 34), (35, 12), (19, 32), (29, 31), (19, 12), (3, 14), (13, 36), (40, 34), (18, 11), (32, 11), (31, 36), (22, 34), (30, 32), (38, 22), (1, 19), (12, 31), (12, 37), (21, 2), (1, 31), (4, 33), (30, 11), (37, 38), (24, 34), (31, 21), (33, 0), (9, 6), (34, 13), (29, 1), (19, 27), (13, 9), (41, 33), (41, 9), (36, 40), (7, 23), (8, 0), (39, 11), (35, 4), (29, 12), (15, 32), (37, 35), (23, 32), (0, 35), (18, 32), (42, 8), (32, 19), (13, 15), (22, 32), (42, 39), (33, 2), (29, 39), (17, 28), (16, 25), (43, 6), (43, 18), (39, 34), (11, 34), (42, 28), (9, 27), (36, 13), (35, 15), (2, 13), (26, 21), (19, 40), (17, 23), (2, 19), (1, 7), (38, 31), (21, 6), (38, 21), (11, 38), (12, 5), (5, 28), (2, 42), (21, 17), (38, 40), (38, 25), (1, 33), (4, 26), (17, 12), (9, 0), (37, 4), (11, 30), (15, 15), (26, 1), (28, 18), (39, 26), (2, 39), (43, 1), (30, 26), (5, 18), (39, 25), (21, 4), (42, 1), (15, 33), (0, 9), (9, 29), (35, 37), (34, 29), (14, 13), (17, 21), (31, 30), (0, 36), (9, 20), (10, 20), (43, 31), (38, 8), (30, 38), (43, 4), (28, 39), (37, 23), (22, 29), (34, 23), (4, 9), (35, 38), (4, 31), (44, 29), (34, 6), (20, 36), (19, 33), (14, 5), (38, 2), (25, 7), (18, 30), (36, 10), (4, 37), (44, 5), (40, 13), (25, 21), (0, 10), (16, 42), (4, 41), (20, 29), (8, 26), (10, 41), (39, 7), (34, 33), (1, 18), (17, 36), (35, 22), (21, 33), (29, 16), (16, 28), (6, 31), (14, 4), (17, 10), (4, 15), (28, 9), (14, 38), (5, 24), (7, 21), (25, 30), (24, 29), (14, 23), (34, 42), (9, 3), (36, 1), (44, 33), (21, 41), (39, 27), (25, 37), (40, 36), (15, 17), (37, 19), (4, 25), (32, 34), (18, 38), (10, 16), (21, 7), (37, 9), (34, 0), (5, 10), (37, 31), (23, 7), (42, 24), (24, 10), (0, 22), (16, 12), (31, 10), (42, 15), (15, 2), (7, 3), (33, 13), (10, 30), (39, 18), (22, 28), (43, 39), (15, 8), (1, 25), (5, 36), (37, 17), (24, 39), (27, 4), (20, 24), (10, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 29), (33, 0), (6, 20), (27, 40), (3, 12), (27, 4), (0, 10), (19, 37), (40, 16), (37, 39), (27, 22), (24, 23), (3, 19), (3, 31), (39, 31), (37, 37), (8, 0), (33, 29), (18, 32), (33, 18), (9, 13), (8, 31), (17, 10), (35, 2), (20, 18), (40, 15), (34, 34), (18, 36), (30, 6), (7, 28), (32, 33), (13, 20), (8, 39), (14, 18), (39, 15), (22, 0), (13, 9), (26, 33), (24, 35), (34, 21), (39, 24), (23, 6), (40, 4), (9, 21), (0, 24), (34, 6), (31, 19), (0, 5), (36, 20), (35, 32), (29, 27), (26, 29), (29, 22), (25, 15), (7, 24), (23, 33), (28, 37), (11, 27), (40, 22), (23, 20), (14, 32), (32, 2), (14, 1), (6, 5), (19, 30), (18, 30), (27, 32), (19, 33), (17, 8), (6, 8), (40, 3), (3, 8), (17, 25), (3, 39), (22, 25), (21, 19), (21, 30), (11, 28), (10, 21), (33, 2), (30, 28), (21, 9), (27, 29), (4, 26), (32, 20), (13, 24), (36, 26), (26, 24), (40, 37), (27, 7), (18, 7), (16, 5), (20, 37), (32, 9), (16, 21), (20, 30), (26, 26), (30, 26), (19, 13), (28, 33), (11, 15), (19, 31), (25, 34), (5, 21), (19, 9), (34, 38), (4, 38), (22, 4), (13, 2), (13, 7), (11, 1), (20, 16), (7, 35), (2, 32), (6, 27), (14, 30), (38, 7), (32, 39), (4, 39), (38, 26), (28, 24), (18, 29), (40, 14), (6, 28), (15, 30), (25, 16), (16, 18), (24, 37), (38, 6), (39, 28), (20, 33), (18, 2), (34, 3), (22, 26), (10, 28), (23, 10), (1, 17), (16, 4), (16, 27), (35, 3), (12, 22), (9, 32), (20, 12), (30, 34), (8, 21), (23, 11), (18, 27), (36, 25), (37, 40), (17, 39), (2, 16), (28, 18), (5, 27), (14, 26), (24, 6), (27, 3), (13, 8), (19, 7), (34, 13), (1, 23), (24, 3), (31, 22), (3, 14), (16, 37), (34, 8), (36, 40), (7, 2), (2, 10), (35, 1), (16, 17), (5, 26), (27, 39), (25, 6), (19, 21), (8, 15), (33, 32), (10, 5), (0, 14), (31, 39), (10, 25), (16, 12), (1, 22), (13, 21), (40, 30), (36, 5), (0, 9), (32, 8), (19, 25), (2, 30), (11, 24), (10, 38), (23, 28), (25, 24), (26, 17), (6, 40), (4, 6), (38, 12), (32, 25), (3, 9), (11, 33), (35, 38), (36, 27), (10, 37), (2, 38), (2, 4), (28, 19), (35, 22), (18, 10), (10, 9), (28, 16), (12, 6), (26, 27), (19, 2), (40, 34), (4, 37), (1, 15), (38, 23), (36, 17), (7, 9), (30, 19), (24, 12), (9, 40), (15, 14), (11, 40), (7, 3), (37, 0), (39, 9), (29, 39), (29, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 38), (16, 5), (31, 5), (2, 27), (22, 4), (6, 36), (13, 14), (41, 40), (17, 45), (23, 18), (41, 15), (33, 32), (14, 14), (39, 1), (21, 47), (5, 10), (22, 33), (28, 44), (35, 41), (18, 40), (16, 2), (31, 19), (38, 29), (26, 39), (41, 34), (27, 8), (4, 34), (16, 4), (43, 2), (36, 18), (26, 6), (28, 13), (4, 32), (32, 9), (43, 22), (18, 44), (3, 20), (42, 37), (11, 5), (3, 28), (12, 36), (40, 9), (27, 19), (2, 29), (46, 23), (14, 23), (32, 1), (19, 18), (46, 20), (11, 42), (27, 29), (5, 6), (2, 47), (10, 30), (21, 44), (4, 26), (11, 28), (17, 21), (36, 35), (13, 12), (3, 18), (18, 25), (18, 24), (33, 5), (39, 18), (4, 6), (42, 16), (30, 4), (29, 41), (46, 13), (31, 23), (9, 0), (24, 39), (27, 11), (29, 30), (31, 34), (25, 8), (46, 10), (17, 9), (27, 6), (11, 4), (24, 9), (36, 21), (7, 7), (37, 18), (24, 3), (40, 30), (24, 5), (11, 13), (10, 47), (35, 39), (6, 0), (25, 38), (5, 37), (26, 44), (42, 28), (24, 32), (3, 26), (44, 46), (37, 4), (35, 43), (23, 33), (46, 5), (34, 47), (0, 12), (25, 14), (26, 13), (4, 40), (5, 0), (10, 10), (9, 46), (10, 2), (23, 20), (27, 33), (39, 40), (37, 38), (15, 42), (29, 31), (43, 35), (44, 9), (24, 6), (15, 41), (43, 40), (9, 38), (37, 8), (37, 6), (22, 7), (41, 5), (31, 29), (11, 26), (33, 14), (40, 3), (19, 47), (20, 45), (32, 20), (5, 9), (21, 14), (42, 39), (25, 1), (2, 40), (24, 28), (28, 17), (22, 30), (36, 9), (34, 41), (37, 14), (1, 14), (34, 22), (30, 26), (2, 7), (3, 31), (45, 17), (42, 22), (4, 22), (26, 8), (42, 36), (4, 42), (38, 20), (39, 25), (20, 36), (46, 46), (3, 42), (0, 28), (46, 9), (41, 24), (31, 15), (15, 5), (2, 5), (23, 25), (26, 33), (23, 28), (24, 36), (8, 7), (10, 36), (34, 38), (0, 43), (7, 10), (9, 7), (0, 14), (35, 14), (1, 45), (25, 25), (5, 5), (34, 33), (43, 45), (43, 42), (23, 5), (24, 16), (43, 7), (11, 47), (32, 28), (17, 25), (23, 27), (7, 41), (19, 5), (40, 29), (15, 44), (24, 31), (35, 9), (20, 5), (28, 30), (28, 22), (32, 3), (39, 14), (45, 32), (16, 44), (4, 7), (2, 10), (6, 35), (27, 16), (37, 7), (28, 28), (22, 26), (7, 31), (0, 47), (32, 10), (38, 37), (18, 34), (39, 20), (8, 9), (6, 30), (40, 25), (9, 1), (4, 10), (16, 8), (6, 45), (27, 3), (46, 36), (9, 4), (23, 2), (13, 0), (44, 47), (14, 12), (31, 33), (37, 5), (27, 25), (22, 32), (20, 3), (39, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 13), (13, 41), (17, 39), (17, 22), (10, 37), (22, 28), (31, 10), (13, 14), (31, 38), (27, 10), (37, 41), (38, 24), (10, 4), (2, 15), (9, 7), (20, 33), (26, 29), (33, 29), (12, 18), (27, 42), (30, 35), (20, 30), (14, 1), (17, 21), (21, 8), (19, 29), (23, 15), (6, 15), (14, 31), (2, 32), (38, 42), (24, 21), (17, 40), (6, 31), (37, 24), (27, 6), (27, 22), (12, 0), (11, 28), (25, 27), (29, 6), (27, 17), (15, 31), (16, 37), (21, 39), (18, 37), (0, 8), (25, 21), (10, 3), (27, 9), (23, 16), (5, 6), (22, 3), (31, 40), (0, 19), (20, 27), (35, 28), (29, 12), (7, 36), (27, 15), (7, 4), (18, 7), (37, 0), (21, 27), (14, 25), (16, 22), (34, 13), (26, 14), (31, 15), (24, 28), (10, 20), (39, 21), (20, 26), (6, 17), (39, 34), (19, 33), (7, 40), (8, 3), (1, 34), (30, 1), (35, 25), (33, 12), (31, 37), (1, 39), (1, 0), (38, 18), (1, 10), (39, 8), (30, 42), (28, 22), (25, 18), (17, 12), (24, 20), (38, 41), (40, 30), (19, 30), (36, 38), (20, 11), (1, 14), (26, 22), (6, 34), (38, 13), (29, 37), (0, 18), (23, 37), (30, 19), (25, 10), (28, 41), (29, 8), (13, 0), (15, 42), (22, 37), (21, 10), (9, 18), (24, 9), (39, 12), (6, 32), (39, 25), (23, 5), (30, 2), (34, 31), (19, 1), (17, 31), (11, 16), (3, 42), (15, 40), (17, 41), (23, 38), (28, 19), (15, 5), (14, 18), (12, 26), (25, 23), (39, 38), (27, 4), (31, 18), (27, 38), (17, 13), (24, 36), (6, 40), (6, 24), (16, 1), (13, 13), (33, 27), (11, 36), (29, 13), (13, 9), (19, 14), (2, 8), (17, 33), (0, 13), (37, 20), (24, 2), (17, 30), (15, 10), (18, 25), (40, 17), (21, 28), (24, 5), (15, 14), (40, 14), (5, 4), (24, 34), (5, 31), (38, 35), (28, 33), (35, 15), (19, 22), (11, 23), (28, 6), (1, 26), (23, 19), (12, 39), (32, 9), (19, 42), (28, 37), (3, 33), (4, 28), (4, 2), (7, 16), (22, 8), (33, 26), (34, 19), (31, 23), (24, 42), (7, 20), (29, 29), (37, 25), (18, 15), (3, 41), (1, 36), (34, 0), (1, 29), (29, 39), (33, 13), (6, 20), (26, 2), (23, 28), (29, 16), (17, 19), (32, 3), (35, 40), (34, 32), (29, 23), (11, 12), (22, 14), (9, 13), (10, 7), (35, 39), (6, 0), (32, 17), (34, 36), (37, 4), (11, 40), (5, 2), (7, 10), (21, 22), (23, 8), (27, 41), (37, 5), (24, 6), (20, 1), (14, 3), (8, 30), (4, 34), (7, 17), (4, 30), (32, 32), (18, 32), (22, 26), (1, 4), (35, 8), (8, 35), (33, 30), (37, 28), (39, 30), (35, 24), (25, 20), (18, 24), (40, 34), (15, 2), (24, 13), (14, 21), (28, 18), (19, 21), (4, 11), (1, 13), (13, 22), (23, 14), (36, 3), (23, 10), (2, 38), (1, 30), (14, 15), (33, 23), (8, 15), (0, 36), (2, 21), (35, 31), (21, 31), (11, 5), (31, 35), (38, 27), (33, 32), (10, 19), (31, 4), (25, 41), (27, 27), (20, 20), (21, 12), (18, 19), (25, 6), (22, 2), (22, 36), (0, 10), (4, 24), (26, 32), (16, 4), (6, 41), (34, 28), (30, 41), (33, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 32), (3, 19), (7, 35), (19, 26), (0, 11), (33, 25), (29, 24), (34, 5), (24, 13), (29, 6), (16, 10), (13, 10), (11, 6), (23, 18), (25, 38), (3, 10), (21, 17), (39, 11), (22, 1), (42, 2), (40, 5), (38, 31), (3, 15), (42, 39), (14, 16), (9, 7), (5, 12), (29, 9), (27, 6), (29, 32), (24, 33), (14, 20), (2, 19), (4, 19), (36, 8), (21, 4), (35, 28), (41, 18), (19, 9), (27, 35), (20, 14), (3, 0), (3, 26), (31, 35), (17, 25), (18, 17), (11, 32), (4, 16), (18, 16), (18, 20), (31, 40), (36, 30), (15, 7), (23, 12), (15, 40), (8, 32), (9, 12), (17, 12), (27, 14), (37, 23), (7, 38), (25, 27), (13, 0), (19, 6), (19, 18), (3, 36), (14, 27), (24, 37), (36, 19), (27, 15), (39, 33), (0, 37), (34, 22), (21, 21), (28, 25), (7, 12), (15, 36), (6, 22), (18, 18), (31, 36), (40, 14), (33, 38), (2, 36), (5, 10), (11, 16), (9, 3), (4, 15), (5, 16), (3, 22), (16, 39), (7, 16), (21, 30), (9, 33), (6, 25), (13, 26), (39, 5), (33, 2), (20, 37), (17, 38), (44, 12), (24, 23), (31, 34), (41, 6), (14, 15), (24, 26), (44, 37), (1, 4), (15, 38), (12, 23), (38, 16), (19, 7), (19, 11), (0, 27), (42, 36), (20, 22), (14, 35), (33, 40), (6, 38), (27, 28), (44, 9), (36, 3), (22, 11), (15, 34), (12, 7), (29, 0), (3, 35), (31, 17), (30, 11), (8, 37), (40, 38), (34, 32), (2, 39), (36, 23), (16, 9), (31, 25), (6, 7), (24, 10), (26, 16), (6, 8), (42, 1), (1, 3), (2, 11), (43, 16), (44, 23), (40, 10), (17, 6), (4, 30), (35, 17), (23, 24), (21, 36), (23, 40), (20, 25), (11, 20), (19, 17), (9, 29), (36, 21), (14, 40), (3, 32), (3, 37), (13, 25), (26, 23), (21, 19), (3, 23), (34, 40), (1, 13), (38, 20), (42, 40), (40, 27), (3, 2), (2, 8), (40, 18), (0, 34), (37, 10), (44, 5), (20, 39), (7, 2), (42, 28), (20, 7), (21, 9), (4, 13), (10, 9), (17, 24), (10, 0), (7, 9), (44, 36), (31, 4), (31, 37), (2, 7), (14, 11), (30, 10), (0, 10), (15, 16), (6, 17), (12, 14), (17, 28), (25, 19), (43, 10), (11, 2), (15, 27), (7, 28), (37, 16), (33, 16), (36, 6), (38, 12), (4, 37), (6, 36), (44, 10), (19, 1), (24, 16), (13, 9), (18, 12), (12, 25), (30, 21), (29, 28), (22, 7), (8, 7), (24, 22), (1, 2), (30, 36), (3, 5), (4, 4), (11, 1), (2, 23), (44, 15), (37, 13), (22, 12), (4, 38), (4, 9), (38, 17), (7, 37), (9, 31), (11, 23), (43, 39), (32, 16), (12, 36), (16, 13), (10, 11), (28, 17), (32, 25), (12, 17), (24, 8), (12, 4), (38, 7), (34, 37), (34, 28), (13, 12), (2, 12), (6, 37), (37, 21), (28, 2), (17, 1), (12, 34), (4, 12), (25, 33), (5, 30), (26, 13), (22, 32), (32, 23), (17, 16), (42, 8), (21, 1), (38, 21), (21, 37), (10, 10), (15, 35), (22, 5), (0, 31), (31, 31), (6, 13), (20, 13), (6, 32), (18, 1), (24, 1), (37, 29), (38, 14), (33, 17), (1, 37), (11, 31), (18, 36), (30, 16), (20, 34), (5, 15), (33, 22), (40, 4), (18, 32), (22, 20), (14, 17), (37, 5), (23, 31), (16, 40), (20, 38), (10, 16), (43, 34), (13, 15), (30, 37), (22, 3), (14, 14), (1, 39), (19, 10), (5, 5), (39, 35), (23, 32), (42, 4), (33, 39), (38, 26), (44, 25), (23, 36), (15, 11), (23, 26), (19, 33), (27, 30), (21, 39), (1, 36), (0, 17), (18, 10), (7, 15), (38, 23), (29, 31), (29, 33), (25, 20), (16, 35), (6, 14), (1, 38), (30, 7), (7, 22), (6, 2), (28, 29), (0, 18), (2, 25), (29, 35), (20, 28), (10, 39), (10, 35), (40, 3), (40, 7), (44, 14), (22, 15), (27, 16), (32, 17), (21, 3), (18, 14), (41, 1), (20, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 25), (9, 13), (3, 21), (23, 4), (35, 10), (35, 8), (9, 21), (26, 1), (32, 21), (10, 3), (23, 14), (27, 27), (18, 14), (9, 23), (33, 32), (11, 24), (13, 29), (19, 33), (22, 26), (21, 37), (26, 8), (30, 37), (18, 12), (18, 25), (21, 25), (31, 30), (19, 20), (5, 8), (14, 13), (16, 24), (0, 7), (18, 5), (1, 25), (18, 11), (5, 9), (1, 15), (39, 3), (29, 14), (1, 19), (27, 4), (6, 6), (0, 30), (3, 23), (6, 14), (10, 38), (0, 39), (32, 1), (24, 35), (5, 5), (13, 18), (25, 21), (10, 8), (15, 16), (25, 28), (35, 21), (30, 39), (31, 24), (34, 25), (24, 33), (16, 38), (31, 1), (22, 31), (32, 13), (18, 36), (28, 29), (29, 0), (34, 6), (3, 0), (20, 35), (36, 38), (15, 11), (22, 22), (1, 30), (8, 30), (34, 39), (21, 5), (22, 11), (31, 3), (20, 25), (20, 26), (36, 34), (23, 15), (21, 10), (10, 21), (8, 8), (22, 38), (18, 39), (11, 5), (33, 29), (16, 39), (4, 30), (36, 4), (1, 35), (12, 7), (38, 13), (0, 2), (24, 14), (2, 2), (23, 21), (33, 21), (14, 5), (19, 22), (11, 34), (17, 18), (10, 28), (19, 8), (17, 15), (1, 13), (0, 37), (28, 18), (22, 20), (24, 8), (28, 7), (7, 24), (15, 29), (28, 25), (20, 28), (35, 35), (19, 15), (24, 4), (35, 37), (14, 12), (18, 17), (32, 34), (2, 13), (39, 28), (19, 10), (8, 11), (17, 13), (23, 24), (16, 1), (34, 21), (20, 17), (13, 5), (4, 39), (6, 13), (32, 23), (14, 1), (11, 32), (24, 12), (1, 29), (38, 4), (29, 3), (34, 8), (38, 26), (39, 22), (19, 38), (26, 3), (2, 34), (33, 8), (19, 36), (13, 16), (6, 3), (35, 14), (18, 26), (7, 14), (3, 8), (15, 5), (22, 39), (32, 2), (10, 16), (25, 13), (13, 9), (34, 11), (0, 8), (27, 24), (21, 6), (7, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 4), (44, 23), (2, 24), (4, 15), (14, 38), (23, 23), (20, 7), (20, 10), (39, 26), (10, 21), (12, 7), (17, 37), (6, 39), (41, 33), (42, 1), (6, 17), (11, 20), (16, 3), (43, 33), (39, 33), (43, 14), (25, 11), (4, 12), (36, 30), (24, 14), (25, 28), (44, 0), (25, 5), (9, 13), (24, 34), (41, 19), (13, 34), (28, 10), (10, 28), (23, 11), (30, 22), (11, 15), (31, 18), (15, 23), (25, 29), (29, 7), (32, 32), (22, 3), (10, 12), (15, 2), (32, 19), (37, 27), (25, 10), (5, 19), (32, 5), (3, 39), (22, 32), (30, 14), (42, 26), (35, 20), (2, 35), (0, 13), (8, 22), (37, 18), (27, 27), (15, 9), (0, 34), (30, 19), (27, 4), (11, 36), (41, 9), (10, 23), (27, 29), (7, 10), (13, 22), (12, 11), (12, 6), (15, 40), (1, 37), (35, 15), (25, 38), (34, 25), (10, 33), (7, 26), (1, 41), (40, 21), (2, 39), (1, 10), (21, 21), (7, 7), (33, 5), (2, 34), (4, 14), (44, 13), (37, 30), (28, 17), (1, 35), (20, 34), (16, 29), (11, 18), (34, 34), (23, 35), (23, 17), (44, 35), (34, 12), (16, 27), (16, 37), (13, 37), (22, 15), (37, 26), (11, 28), (14, 28), (3, 33), (21, 2), (22, 27), (38, 14), (7, 22), (13, 3), (39, 32), (37, 31), (30, 35), (43, 22), (6, 4), (40, 18), (21, 34), (5, 27), (33, 2), (40, 7), (3, 25), (12, 25), (44, 21), (28, 32), (25, 15), (25, 13), (43, 2), (22, 23), (32, 28), (2, 3), (6, 6), (9, 31), (31, 24), (41, 26), (21, 41), (28, 37), (33, 29), (15, 28), (43, 26), (35, 39), (25, 27), (24, 15), (21, 23), (7, 0), (37, 20), (4, 23), (34, 6), (22, 35), (27, 14), (19, 40), (4, 9), (30, 15), (40, 31), (2, 26), (15, 33), (40, 29), (12, 38), (43, 0), (11, 31), (10, 19), (4, 7), (9, 38), (26, 9), (20, 32), (1, 7), (18, 6), (37, 36), (21, 7), (21, 37), (28, 21), (36, 20), (24, 35), (15, 3), (30, 38), (32, 11), (0, 28), (21, 22), (43, 32), (34, 4), (0, 33), (14, 7), (41, 2), (12, 28), (27, 33), (32, 1), (39, 34), (17, 19), (6, 28), (39, 38), (43, 30), (24, 2), (21, 16), (19, 0), (32, 24), (5, 0), (23, 41), (26, 13), (19, 32), (24, 23), (14, 24), (37, 6), (42, 31), (32, 17), (13, 15), (35, 40), (42, 20), (1, 0), (36, 27), (13, 41), (0, 36), (39, 24), (12, 34), (23, 12), (1, 5), (44, 37), (26, 2), (3, 13), (43, 16), (20, 15), (12, 0), (34, 22), (31, 11), (38, 35), (40, 13), (17, 15), (42, 40), (18, 20), (2, 38), (3, 15), (41, 29), (5, 8), (2, 33), (39, 31), (39, 29), (28, 6), (35, 1), (9, 12), (26, 10), (9, 25), (14, 19), (22, 38), (29, 4), (38, 38), (17, 29), (5, 32), (22, 39), (27, 5), (44, 31), (13, 17), (36, 32), (0, 5), (2, 16), (40, 41), (14, 34), (19, 23), (8, 11), (14, 32), (27, 36), (26, 0), (15, 25), (36, 3), (18, 18), (24, 21), (40, 0), (39, 0), (3, 2), (20, 40), (14, 39), (8, 27), (18, 3), (11, 14), (32, 39), (23, 0), (14, 12), (41, 38), (44, 15), (24, 28), (17, 10), (1, 11), (27, 6), (43, 23), (30, 12), (36, 28), (23, 2), (6, 31), (17, 39), (36, 19), (43, 28), (8, 19), (3, 19), (7, 30), (17, 27), (30, 5), (19, 2), (41, 7), (5, 33), (13, 18), (41, 12), (0, 12), (26, 25), (38, 34), (21, 33), (30, 23), (29, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 6), (33, 41), (37, 33), (12, 9), (38, 30), (39, 35), (8, 41), (11, 37), (26, 38), (4, 27), (45, 31), (32, 19), (8, 1), (8, 34), (4, 38), (36, 21), (42, 9), (38, 41), (33, 2), (3, 24), (25, 33), (17, 17), (1, 41), (22, 43), (24, 41), (34, 15), (18, 28), (10, 17), (1, 13), (37, 15), (3, 0), (29, 46), (39, 42), (44, 0), (10, 14), (29, 40), (20, 13), (34, 24), (28, 1), (10, 23), (3, 5), (6, 21), (13, 27), (14, 39), (9, 23), (1, 44), (4, 10), (25, 29), (23, 10), (4, 34), (16, 16), (0, 35), (13, 3), (35, 27), (24, 13), (9, 27), (13, 21), (2, 10), (46, 43), (21, 18), (23, 22), (2, 37), (20, 46), (18, 17), (30, 45), (8, 9), (19, 45), (26, 33), (35, 29), (35, 46), (23, 23), (46, 11), (2, 41), (31, 28), (17, 35), (19, 44), (10, 41), (0, 28), (45, 28), (46, 41), (41, 11), (45, 18), (31, 13), (33, 43), (16, 6), (38, 38), (17, 33), (21, 32), (39, 11), (23, 28), (18, 40), (18, 35), (19, 24), (37, 21), (40, 36), (5, 5), (20, 45), (46, 36), (13, 43), (1, 42), (35, 33), (44, 28), (7, 15), (40, 31), (24, 17), (16, 12), (12, 26), (37, 27), (32, 0), (40, 33), (2, 34), (36, 23), (30, 42), (46, 8), (23, 15), (28, 12), (12, 18), (8, 2), (6, 40), (11, 43), (38, 10), (38, 25), (37, 19), (8, 10), (31, 43), (10, 3), (4, 40), (13, 15), (15, 19), (18, 36), (46, 13), (26, 20), (18, 41), (43, 42), (41, 12), (26, 43), (15, 29), (30, 17), (41, 14), (15, 1), (11, 16), (36, 9), (4, 9), (41, 6), (38, 24), (5, 16), (17, 18), (20, 12), (10, 32), (15, 4), (43, 14), (40, 34), (36, 5), (38, 20), (27, 39), (2, 16), (33, 37), (17, 10), (21, 23), (22, 35), (8, 8), (45, 2), (10, 38), (44, 7), (38, 39), (31, 38), (43, 20), (7, 13), (21, 46), (14, 22), (19, 4), (26, 4), (1, 28), (46, 32), (38, 29), (42, 6), (11, 4), (7, 5), (26, 32), (32, 27), (0, 7), (5, 12), (38, 37), (20, 24), (6, 35), (21, 9), (43, 3), (13, 24), (24, 4), (32, 32), (43, 17), (46, 5), (16, 0), (9, 6), (30, 30), (2, 28), (4, 41), (10, 12), (44, 5), (14, 21), (27, 0), (26, 17), (44, 34), (38, 32), (21, 22), (29, 6), (31, 42), (46, 10), (28, 30), (15, 11), (6, 25), (7, 46), (28, 11), (44, 38), (8, 45), (5, 10), (15, 12), (21, 19), (40, 28), (36, 36), (27, 25), (11, 17), (32, 35), (4, 17), (24, 9), (41, 13), (21, 41), (20, 38), (37, 0), (7, 26), (14, 5), (11, 14), (13, 39), (45, 27), (46, 16), (9, 25), (9, 38), (23, 34), (34, 29), (31, 36), (22, 23), (41, 0), (37, 1), (34, 8), (34, 20), (45, 1), (3, 6), (41, 28), (4, 24), (4, 18), (11, 1), (15, 31), (42, 0), (20, 0), (27, 11), (29, 35), (26, 30), (23, 25), (20, 16), (40, 3), (14, 42), (29, 41), (13, 45), (1, 10), (20, 2), (40, 45), (34, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 33), (0, 40), (47, 32), (47, 29), (43, 36), (30, 27), (45, 37), (24, 12), (4, 5), (32, 33), (37, 41), (3, 26), (31, 16), (42, 9), (32, 29), (48, 11), (19, 32), (37, 38), (45, 29), (23, 40), (21, 27), (4, 39), (44, 21), (21, 32), (19, 8), (26, 8), (32, 12), (48, 36), (9, 2), (36, 8), (13, 30), (29, 7), (37, 5), (27, 0), (35, 19), (28, 31), (10, 36), (31, 33), (19, 22), (3, 7), (41, 3), (16, 4), (24, 11), (42, 20), (13, 27), (19, 41), (12, 25), (32, 40), (34, 29), (22, 14), (44, 8), (29, 15), (18, 26), (41, 13), (27, 36), (33, 13), (23, 17), (21, 29), (14, 7), (9, 23), (6, 34), (41, 12), (47, 1), (18, 31), (6, 6), (46, 13), (1, 3), (5, 22), (9, 6), (22, 27), (22, 22), (46, 30), (10, 9), (17, 11), (48, 24), (14, 28), (22, 13), (23, 0), (43, 7), (13, 37), (31, 24), (9, 10), (14, 33), (41, 14), (10, 34), (35, 9), (18, 29), (18, 32), (11, 1), (39, 40), (6, 37), (6, 7), (4, 7), (29, 3), (22, 32), (7, 32), (32, 32), (2, 26), (24, 3), (44, 4), (44, 27), (13, 36), (42, 33), (7, 28), (44, 40), (0, 29), (43, 34), (26, 10), (30, 11), (40, 41), (47, 13), (36, 19), (4, 27), (30, 37), (31, 8), (13, 15), (16, 5), (26, 12), (0, 9), (14, 23), (38, 27), (3, 31), (26, 6), (24, 33), (44, 11), (8, 22), (3, 3), (20, 15), (31, 7), (4, 13), (4, 4), (8, 33), (23, 4), (25, 32), (36, 17), (26, 13), (21, 26), (41, 8), (17, 3), (32, 34), (20, 14), (31, 13), (40, 26), (18, 36), (47, 41), (28, 5), (40, 15), (45, 12), (39, 33), (4, 40), (23, 36), (47, 25), (8, 32), (41, 2), (21, 19), (46, 7), (37, 12), (41, 17), (4, 23), (25, 19), (13, 28), (36, 14), (37, 28), (47, 39), (25, 0), (17, 18), (15, 21), (17, 40), (20, 27), (2, 6), (20, 1), (24, 6), (21, 22), (29, 31), (41, 26), (48, 27), (21, 36), (45, 39), (32, 17), (6, 19), (7, 13), (32, 35), (3, 25), (6, 30), (22, 8), (35, 12), (19, 21), (25, 29), (42, 19), (34, 38), (17, 27), (7, 4), (5, 39), (34, 17), (31, 41), (19, 14), (24, 1), (43, 12), (46, 16), (0, 12), (3, 38), (1, 36), (26, 14), (14, 16), (48, 34), (36, 40), (41, 21), (33, 19), (39, 16), (3, 9), (41, 22), (22, 1), (20, 24), (22, 6), (32, 0), (37, 11), (8, 38), (16, 41), (7, 12), (44, 32), (30, 2), (40, 32), (31, 25), (28, 23), (47, 24), (15, 2), (4, 3), (21, 14), (0, 24), (7, 20), (22, 28), (25, 16), (46, 10), (31, 37), (35, 35), (31, 0), (47, 3), (9, 40), (18, 37), (46, 28), (32, 31), (2, 12), (15, 29), (20, 13), (27, 31), (8, 19), (34, 12), (33, 0), (43, 23), (17, 12), (20, 8), (1, 24), (5, 0), (44, 37), (8, 14), (21, 18), (30, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 46x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 24), (33, 38), (45, 45), (35, 6), (33, 24), (9, 11), (26, 8), (32, 33), (26, 32), (12, 10), (43, 12), (25, 8), (2, 32), (17, 14), (17, 29), (39, 19), (40, 3), (28, 0), (20, 26), (31, 36), (5, 24), (4, 24), (4, 27), (23, 46), (31, 5), (1, 23), (1, 6), (3, 12), (32, 39), (4, 26), (4, 34), (25, 22), (6, 41), (22, 19), (10, 35), (2, 22), (30, 24), (5, 47), (6, 15), (7, 35), (18, 21), (5, 7), (28, 4), (9, 27), (32, 4), (11, 40), (8, 5), (19, 6), (9, 1), (15, 26), (41, 28), (38, 35), (39, 33), (11, 25), (38, 5), (38, 33), (0, 41), (4, 1), (12, 6), (36, 19), (27, 0), (22, 38), (14, 35), (42, 17), (29, 27), (12, 46), (26, 19), (13, 19), (21, 13), (11, 0), (38, 19), (34, 1), (3, 2), (38, 12), (38, 44), (36, 11), (9, 14), (25, 23), (18, 30), (42, 15), (41, 44), (31, 30), (17, 46), (42, 32), (15, 35), (31, 19), (38, 30), (5, 11), (6, 2), (24, 5), (22, 25), (3, 20), (35, 28), (14, 30), (21, 20), (16, 29), (25, 18), (17, 20), (17, 28), (31, 9), (6, 17), (9, 18), (15, 6), (36, 39), (15, 18), (6, 31), (23, 43), (1, 3), (10, 45), (37, 27), (41, 12), (30, 3), (7, 28), (1, 42), (16, 47), (11, 26), (19, 34), (26, 21), (7, 2), (35, 12), (12, 28), (8, 31), (44, 14), (20, 35), (16, 41), (17, 19), (23, 32), (25, 6), (15, 30), (37, 2), (33, 29), (35, 24), (11, 23), (35, 18), (42, 4), (20, 31), (18, 25), (37, 12), (32, 24), (38, 25), (4, 46), (27, 19), (36, 34), (20, 18), (39, 24), (24, 21), (11, 15), (27, 12), (39, 42), (13, 3), (10, 31), (41, 31), (36, 6), (25, 37), (38, 6), (27, 24), (9, 23), (4, 16), (30, 10), (12, 12), (13, 1), (6, 36), (8, 35), (26, 35), (18, 33), (23, 20), (40, 19), (1, 44), (35, 3), (21, 5), (17, 34), (3, 39), (25, 25), (16, 39), (38, 14), (29, 44), (39, 12), (3, 35), (23, 34), (0, 25), (2, 15), (41, 16), (33, 11), (36, 12), (0, 38), (22, 24), (10, 3), (27, 8), (28, 23), (10, 13), (7, 34), (29, 47), (45, 43), (32, 19), (33, 23), (9, 30), (24, 38), (19, 8), (44, 9), (11, 18), (36, 17), (19, 45), (31, 15), (31, 3), (12, 37), (42, 3), (34, 35), (32, 16), (14, 7), (3, 26), (24, 47), (10, 20), (30, 5), (25, 19), (24, 31), (23, 35), (11, 47), (6, 13), (6, 8), (33, 3), (39, 28), (26, 27), (40, 20), (23, 42), (1, 41), (5, 29), (20, 37), (42, 6), (43, 7), (28, 28), (34, 39), (33, 2), (38, 3), (5, 28), (1, 2), (3, 23), (37, 5), (4, 33), (10, 34), (5, 31), (16, 25), (30, 38), (3, 22), (13, 18), (39, 1), (35, 41), (2, 31), (19, 27), (41, 21), (44, 6), (8, 29), (32, 28), (39, 31), (0, 27), (36, 32), (10, 0), (15, 36), (30, 22), (12, 15), (4, 23), (42, 37), (18, 1), (21, 2), (40, 30), (22, 45), (39, 41), (45, 38), (4, 42), (33, 43), (15, 29), (12, 7), (2, 42), (22, 39), (26, 12), (29, 14), (35, 34), (16, 14), (20, 23), (23, 36), (44, 11), (4, 17), (32, 6), (11, 12), (8, 25), (29, 0), (15, 34), (44, 1), (14, 26), (40, 33), (9, 31), (9, 40), (35, 23), (19, 16), (44, 2), (17, 47), (3, 33), (28, 5), (39, 6), (2, 4), (37, 17), (43, 21), (31, 20), (34, 26), (9, 39), (16, 26), (22, 12), (35, 47), (37, 33), (13, 12), (37, 3), (7, 22), (11, 36), (13, 41), (39, 4), (45, 31), (12, 4), (12, 30), (17, 0), (20, 38), (8, 22), (34, 7), (2, 46), (20, 4), (30, 32), (41, 29), (23, 29), (19, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 14), (9, 11), (18, 20), (33, 24), (35, 19), (32, 4), (5, 2), (36, 8), (38, 23), (21, 25), (41, 2), (16, 34), (25, 18), (31, 1), (33, 4), (14, 25), (17, 4), (22, 16), (23, 13), (36, 34), (22, 40), (33, 20), (0, 37), (25, 12), (40, 14), (10, 8), (25, 10), (17, 20), (26, 17), (29, 23), (33, 36), (29, 7), (7, 30), (18, 27), (24, 28), (13, 35), (27, 13), (16, 21), (1, 38), (11, 12), (18, 38), (15, 26), (28, 19), (8, 19), (6, 30), (5, 37), (30, 29), (11, 34), (18, 18), (2, 16), (25, 20), (35, 9), (21, 16), (11, 28), (38, 24), (22, 15), (15, 30), (1, 30), (18, 0), (2, 24), (41, 8), (22, 6), (38, 30), (15, 9), (27, 0), (2, 34), (5, 23), (8, 17), (17, 37), (14, 24), (1, 6), (30, 24), (42, 8), (27, 40), (3, 31), (37, 14), (26, 7), (31, 23), (23, 16), (11, 16), (25, 11), (12, 23), (2, 33), (10, 6), (18, 40), (1, 36), (23, 3), (15, 1), (2, 4), (29, 15), (13, 38), (11, 38), (6, 5), (7, 19), (8, 10), (21, 7), (6, 37), (5, 5), (5, 3), (17, 34), (6, 16), (17, 26), (14, 8), (30, 15), (8, 0), (27, 21), (29, 3), (21, 32), (16, 18), (8, 38), (32, 14), (35, 24), (7, 16), (18, 10), (12, 37), (25, 5), (26, 6), (38, 38), (17, 38), (34, 10), (26, 39), (21, 12), (32, 19), (21, 39), (5, 21), (21, 13), (40, 9), (36, 12), (12, 25), (28, 37), (14, 22), (16, 2), (27, 39), (15, 39), (32, 40), (15, 0), (40, 3), (29, 1), (4, 29), (34, 33), (30, 35), (34, 35), (29, 14), (32, 5), (41, 15), (37, 40), (32, 11), (38, 12), (6, 15), (36, 19), (12, 6), (33, 21), (12, 1), (3, 11), (25, 2), (17, 31), (36, 7), (12, 4), (8, 20), (30, 12), (23, 30), (7, 10), (35, 5), (10, 30), (42, 34), (18, 39), (17, 33), (27, 26), (3, 30), (2, 0), (22, 19), (37, 5), (2, 18), (34, 21), (2, 14), (14, 32), (8, 30), (34, 3), (10, 28), (19, 14), (31, 16), (38, 26), (0, 35), (32, 8), (7, 11), (25, 8), (6, 3), (2, 5), (34, 40), (28, 1), (13, 21), (34, 25), (27, 1), (1, 27), (28, 11), (34, 7), (22, 22), (40, 28), (9, 35), (3, 34), (34, 11), (27, 25), (10, 32), (21, 31), (1, 22), (2, 26), (14, 30), (6, 28), (26, 34), (15, 8), (2, 35), (39, 31), (23, 15), (5, 15), (33, 11), (37, 16), (0, 15), (37, 19), (36, 35), (24, 18), (38, 20), (40, 5), (20, 23), (36, 1), (4, 10), (18, 28), (41, 32), (30, 28), (7, 23), (23, 19), (24, 39), (41, 33), (16, 17), (25, 30), (29, 38), (0, 40), (7, 28), (6, 36), (24, 9), (32, 16), (19, 29), (22, 29), (15, 11), (23, 33), (15, 36), (14, 5), (35, 29), (21, 5), (32, 27), (20, 8), (33, 2), (3, 22), (24, 2), (20, 2), (40, 11), (23, 36), (13, 24), (22, 1), (1, 13), (14, 10), (39, 4), (39, 32), (19, 7), (13, 32), (22, 39), (9, 27), (9, 34), (18, 9), (30, 5), (23, 23), (24, 32), (16, 27), (12, 28), (41, 7), (6, 1), (1, 21), (35, 4), (6, 11), (2, 31), (0, 39), (14, 18), (9, 36), (0, 30), (2, 23), (23, 27), (42, 29), (0, 22), (42, 21), (23, 5), (27, 12), (6, 29), (19, 33), (39, 25), (30, 30), (17, 27), (13, 20), (17, 2), (38, 27), (33, 1), (12, 10), (3, 18), (8, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 30), (45, 46), (38, 24), (14, 8), (0, 26), (43, 5), (38, 16), (45, 16), (11, 42), (4, 37), (14, 20), (9, 39), (4, 16), (0, 39), (38, 39), (31, 14), (14, 21), (31, 10), (29, 14), (16, 18), (38, 45), (28, 35), (14, 47), (37, 17), (20, 24), (39, 44), (16, 10), (14, 23), (28, 36), (28, 14), (17, 34), (20, 45), (6, 30), (17, 41), (44, 18), (33, 25), (47, 24), (45, 11), (19, 37), (29, 43), (22, 30), (18, 16), (0, 34), (35, 17), (37, 1), (30, 29), (46, 7), (10, 34), (39, 2), (21, 44), (35, 45), (18, 34), (22, 7), (1, 40), (29, 24), (13, 22), (47, 43), (30, 1), (35, 26), (30, 38), (37, 39), (29, 9), (26, 42), (20, 14), (6, 32), (20, 13), (47, 2), (2, 38), (21, 1), (11, 7), (35, 12), (24, 32), (13, 12), (8, 24), (32, 41), (27, 31), (14, 36), (1, 44), (26, 22), (2, 28), (36, 46), (21, 38), (45, 21), (0, 24), (19, 27), (35, 25), (42, 11), (14, 40), (47, 0), (38, 38), (36, 5), (31, 31), (45, 9), (30, 22), (45, 6), (7, 26), (6, 10), (10, 12), (40, 14), (3, 18), (36, 32), (42, 25), (7, 24), (10, 43), (17, 18), (23, 13), (10, 14), (27, 28), (19, 20), (39, 11), (42, 19), (20, 10), (31, 4), (25, 7), (1, 3), (41, 31), (27, 4), (6, 5), (4, 8), (7, 22), (47, 6), (46, 38), (42, 16), (43, 44), (25, 42), (39, 22), (22, 41), (30, 39), (3, 34), (33, 11), (0, 16), (28, 37), (20, 18), (1, 25), (4, 46), (22, 19), (29, 5), (19, 19), (40, 26), (41, 23), (14, 24), (0, 7), (10, 31), (9, 19), (34, 42), (9, 21), (5, 7), (42, 6), (1, 32), (1, 8), (6, 37), (40, 41), (34, 28), (12, 43), (41, 41), (13, 14), (20, 39), (31, 30), (16, 31), (23, 43), (17, 40), (45, 31), (19, 11), (46, 1), (17, 42), (0, 2), (2, 19), (10, 15), (29, 20), (34, 44), (46, 22), (38, 26), (11, 30), (40, 30), (8, 39), (13, 21), (18, 30), (12, 17), (16, 2), (46, 24), (11, 31), (42, 29), (15, 1), (24, 20), (41, 45), (6, 17), (40, 10), (5, 17), (15, 13), (2, 37), (46, 41), (35, 4), (10, 23), (12, 20), (45, 45), (7, 9), (36, 34), (24, 47), (33, 29), (2, 29), (43, 7), (29, 41), (10, 17), (44, 28), (10, 21), (11, 11), (22, 17), (34, 7), (16, 44), (12, 23), (25, 8), (39, 4), (7, 5), (33, 10), (14, 31), (42, 5), (23, 0), (20, 21), (31, 8), (6, 33), (25, 43), (21, 37), (20, 29), (40, 34), (38, 6), (20, 32), (31, 5), (0, 40), (9, 36), (12, 45), (13, 36), (40, 40), (43, 6), (28, 17), (23, 12), (1, 13), (22, 29), (10, 40), (38, 41), (5, 31), (23, 17), (5, 20), (26, 46), (32, 26), (36, 47), (19, 22), (23, 18), (30, 4), (43, 18), (41, 1), (42, 42), (31, 24), (42, 39), (30, 36), (35, 31), (21, 18), (21, 25), (27, 3), (30, 37), (10, 28), (27, 9), (18, 20), (41, 46), (41, 0), (43, 26), (21, 24), (37, 37), (37, 9), (7, 30), (44, 27), (33, 24), (12, 28), (35, 30), (7, 15), (40, 5), (21, 43), (4, 18), (43, 0), (14, 46), (6, 42), (47, 4), (18, 11), (37, 2), (37, 33), (23, 45), (6, 11), (16, 14), (20, 8), (36, 35), (24, 9), (22, 33), (26, 36), (12, 10), (45, 3), (3, 27), (37, 46), (2, 24), (22, 37), (20, 4), (1, 22), (30, 13), (29, 29), (35, 28), (1, 37), (16, 21), (9, 0), (31, 22), (46, 23), (32, 0), (2, 7), (16, 29), (27, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 13), (30, 28), (26, 14), (12, 40), (37, 34), (38, 10), (20, 25), (0, 22), (25, 10), (26, 34), (20, 21), (40, 21), (18, 23), (31, 9), (37, 3), (42, 37), (1, 37), (30, 4), (41, 38), (40, 5), (42, 10), (2, 34), (8, 15), (1, 38), (13, 9), (32, 2), (41, 29), (34, 30), (26, 36), (13, 14), (10, 18), (18, 16), (6, 7), (40, 38), (26, 11), (4, 17), (36, 8), (13, 29), (30, 25), (18, 39), (41, 19), (19, 40), (11, 15), (27, 33), (25, 17), (35, 4), (40, 24), (13, 16), (9, 4), (10, 8), (33, 8), (33, 22), (14, 37), (7, 29), (28, 5), (32, 21), (38, 4), (11, 37), (17, 35), (24, 34), (24, 31), (19, 23), (37, 10), (4, 5), (27, 25), (10, 28), (11, 14), (4, 32), (34, 18), (9, 40), (13, 23), (14, 38), (9, 39), (41, 37), (0, 33), (3, 32), (40, 3), (12, 18), (10, 7), (11, 4), (17, 25), (25, 3), (37, 32), (1, 28), (37, 16), (26, 25), (8, 34), (18, 19), (42, 39), (34, 3), (20, 17), (26, 39), (9, 0), (41, 41), (16, 14), (20, 31), (10, 4), (40, 17), (4, 1), (8, 31), (34, 19), (7, 2), (33, 4), (32, 12), (38, 8), (41, 12), (27, 41), (29, 5), (10, 1), (1, 7), (26, 26), (3, 17), (6, 6), (27, 8), (3, 14), (27, 10), (18, 12), (18, 38), (37, 2), (30, 12), (32, 11), (39, 5), (1, 21), (21, 35), (28, 7), (15, 14), (23, 18), (10, 11), (35, 30), (3, 2), (33, 2), (26, 16), (38, 29), (16, 11), (22, 30), (4, 24), (23, 29), (18, 14), (30, 9), (40, 2), (24, 17), (26, 22), (38, 37), (13, 21), (29, 18), (7, 33), (5, 26), (28, 13), (26, 37), (3, 15), (40, 22), (34, 25), (36, 41), (18, 27), (6, 1), (33, 13), (30, 36), (33, 9), (25, 1), (14, 39), (40, 11), (4, 15), (29, 9), (35, 3), (2, 17), (37, 14), (4, 13), (12, 34), (31, 32), (38, 1), (11, 1), (15, 31), (14, 0), (15, 8), (22, 38), (12, 17), (39, 36), (32, 38), (28, 12), (3, 8), (19, 11), (17, 23), (42, 5), (7, 12), (2, 22), (18, 13), (7, 32), (8, 6), (15, 24), (36, 37), (25, 41), (41, 11), (12, 22), (20, 1), (29, 34), (21, 31), (7, 0), (35, 33), (34, 28), (9, 10), (29, 28), (4, 41), (7, 21), (28, 40), (23, 26), (17, 5), (21, 14), (4, 30), (13, 5), (19, 28), (37, 27), (22, 41), (13, 7), (12, 15), (23, 35), (15, 22), (23, 8), (10, 34), (38, 21), (8, 33), (26, 7), (8, 38), (29, 3), (21, 8), (5, 16), (7, 41), (34, 14), (9, 8), (37, 19), (23, 4), (12, 7), (18, 26), (39, 11), (17, 29), (21, 10), (23, 20), (13, 38), (19, 10), (38, 40), (6, 38), (2, 13), (23, 23), (12, 19), (30, 31), (18, 22), (13, 34), (3, 18), (1, 15), (40, 13), (14, 9), (6, 15), (15, 23), (22, 19), (37, 22), (22, 4), (34, 20), (25, 14), (22, 25), (20, 0), (15, 32), (31, 24), (6, 30), (36, 11), (27, 15), (4, 2), (0, 13), (7, 7), (26, 1), (12, 31), (7, 25), (18, 28), (30, 20), (27, 13), (4, 39), (21, 19), (5, 4), (36, 0), (9, 9), (34, 34), (8, 41), (19, 32), (38, 15), (15, 5), (2, 10), (1, 32), (14, 7), (11, 29), (33, 32), (8, 27), (25, 15), (3, 33), (15, 25), (13, 25), (10, 2), (22, 34), (29, 22), (31, 11), (10, 3), (31, 26), (37, 36), (41, 10), (13, 19), (9, 37), (21, 20), (17, 27), (0, 3), (17, 0), (0, 6), (10, 17), (17, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 49x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 43), (36, 32), (22, 2), (35, 36), (22, 27), (14, 9), (24, 29), (18, 4), (31, 35), (29, 27), (44, 33), (40, 28), (37, 35), (6, 15), (31, 27), (48, 44), (0, 28), (42, 10), (42, 23), (42, 33), (8, 24), (31, 8), (43, 10), (27, 8), (44, 14), (9, 16), (35, 15), (5, 10), (15, 1), (13, 12), (34, 24), (22, 16), (28, 25), (17, 30), (31, 11), (3, 42), (48, 23), (4, 9), (9, 20), (6, 42), (11, 20), (42, 8), (19, 30), (7, 28), (8, 21), (24, 23), (2, 12), (39, 26), (48, 28), (48, 43), (5, 19), (4, 0), (8, 1), (16, 24), (30, 12), (30, 34), (17, 44), (18, 2), (22, 0), (40, 46), (3, 29), (1, 37), (48, 41), (14, 7), (26, 21), (1, 29), (37, 2), (21, 12), (15, 21), (12, 32), (46, 21), (18, 18), (29, 31), (9, 15), (18, 9), (41, 43), (3, 20), (27, 36), (19, 8), (12, 36), (16, 13), (38, 6), (3, 37), (45, 6), (8, 15), (27, 23), (14, 45), (47, 33), (45, 27), (4, 7), (27, 2), (42, 28), (24, 26), (34, 39), (47, 27), (37, 27), (18, 38), (20, 37), (33, 5), (16, 8), (29, 21), (44, 30), (23, 26), (17, 40), (13, 2), (36, 2), (47, 23), (20, 0), (48, 9), (48, 38), (38, 8), (45, 24), (4, 41), (18, 36), (29, 15), (3, 8), (9, 23), (41, 29), (45, 19), (7, 1), (32, 39), (10, 44), (31, 9), (48, 4), (48, 21), (18, 46), (23, 17), (6, 28), (7, 19), (47, 37), (36, 23), (25, 29), (13, 43), (5, 29), (8, 22), (24, 42), (9, 19), (23, 37), (33, 17), (38, 21), (26, 37), (34, 6), (38, 13), (30, 38), (11, 38), (23, 25), (32, 35), (11, 9), (10, 26), (25, 37), (26, 19), (3, 0), (35, 31), (45, 23), (25, 25), (28, 7), (46, 23), (38, 12), (31, 15), (14, 46), (24, 43), (35, 40), (12, 42), (7, 10), (20, 25), (47, 31), (6, 12), (7, 14), (10, 28), (39, 11), (33, 20), (24, 11), (39, 27), (36, 46), (17, 29), (1, 20), (33, 30), (8, 26), (22, 43), (4, 24), (25, 45), (21, 24), (45, 29), (35, 30), (14, 4), (12, 44), (1, 38), (18, 6), (11, 10), (15, 27), (20, 8), (42, 45), (28, 28), (29, 16), (8, 25), (35, 22), (39, 6), (31, 18), (37, 32), (12, 39), (3, 40), (1, 5), (14, 37), (48, 10), (6, 39), (36, 30), (48, 19), (7, 0), (5, 41), (42, 22), (30, 32), (4, 32), (28, 0), (41, 24), (39, 36), (45, 35), (32, 45), (42, 31), (22, 24), (5, 3), (16, 37), (3, 19), (14, 17), (1, 45), (2, 9), (35, 46), (23, 44), (1, 34), (36, 41), (6, 11), (36, 21), (43, 33), (16, 27), (40, 15), (48, 8), (7, 2), (44, 22), (25, 33), (40, 0), (45, 41), (11, 26), (16, 26), (28, 6), (41, 10), (7, 26), (10, 38), (47, 40), (33, 44), (12, 27), (3, 38), (4, 12), (15, 26), (22, 20), (12, 4), (3, 33), (14, 13), (26, 46), (6, 32), (11, 35), (28, 5), (14, 28), (26, 2), (19, 17), (18, 24), (32, 23), (3, 28), (44, 23), (10, 25), (34, 14), (36, 24), (10, 46), (34, 36), (29, 14), (10, 10), (0, 19), (21, 13), (20, 10), (28, 13), (3, 35), (16, 36), (15, 37), (15, 35), (7, 3), (25, 3), (31, 38), (23, 27), (20, 19), (47, 18), (19, 3), (45, 43), (14, 41), (11, 40), (8, 45), (10, 24), (39, 17), (43, 8), (0, 32), (15, 6), (22, 1), (39, 45), (34, 2), (21, 3), (41, 40), (36, 5), (10, 6), (8, 29), (35, 12), (41, 30), (8, 37), (27, 37), (13, 3), (36, 22), (41, 46), (46, 30), (21, 4), (21, 2), (47, 29), (9, 39), (36, 45), (19, 35), (27, 12), (37, 8), (31, 25), (3, 2), (11, 1), (1, 6), (1, 28), (10, 43), (36, 27), (30, 10), (25, 17), (42, 43), (23, 4), (11, 2), (32, 28), (13, 42), (25, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 16), (19, 41), (25, 0), (23, 5), (2, 4), (21, 36), (1, 27), (45, 9), (11, 2), (13, 27), (41, 13), (13, 43), (37, 13), (8, 9), (4, 22), (19, 42), (32, 5), (3, 26), (17, 24), (13, 1), (28, 16), (25, 27), (37, 6), (5, 1), (19, 12), (6, 5), (13, 42), (37, 31), (4, 15), (2, 21), (1, 5), (39, 46), (7, 24), (15, 31), (11, 3), (15, 0), (20, 39), (28, 4), (45, 31), (36, 7), (11, 8), (20, 32), (24, 44), (37, 41), (13, 12), (11, 37), (16, 31), (0, 17), (39, 17), (43, 16), (8, 18), (30, 8), (13, 15), (41, 41), (0, 22), (30, 0), (44, 24), (2, 35), (33, 31), (22, 15), (19, 14), (33, 27), (33, 28), (5, 4), (17, 3), (12, 12), (10, 33), (35, 26), (3, 6), (12, 41), (33, 30), (36, 2), (7, 42), (16, 42), (13, 6), (19, 26), (13, 26), (13, 2), (38, 22), (28, 43), (11, 44), (41, 21), (38, 27), (35, 42), (38, 1), (19, 9), (5, 25), (42, 15), (16, 28), (43, 44), (24, 9), (42, 19), (34, 20), (34, 25), (21, 29), (18, 35), (45, 7), (3, 17), (19, 5), (26, 34), (34, 39), (21, 10), (35, 22), (27, 7), (37, 34), (10, 43), (23, 18), (23, 31), (14, 33), (14, 39), (15, 26), (39, 12), (23, 46), (7, 26), (11, 9), (16, 4), (4, 23), (9, 35), (24, 11), (32, 30), (36, 10), (32, 15), (26, 14), (24, 12), (36, 8), (30, 12), (30, 18), (13, 40), (34, 27), (15, 35), (45, 25), (0, 45), (7, 7), (23, 42), (20, 46), (9, 45), (22, 12), (7, 37), (31, 15), (9, 19), (45, 12), (42, 43), (1, 43), (32, 32), (13, 18), (14, 26), (41, 37), (1, 8), (23, 44), (42, 29), (36, 3), (31, 23), (27, 16), (0, 29), (23, 20), (25, 39), (34, 43), (6, 32), (1, 20), (16, 5), (10, 14), (10, 4), (12, 35), (4, 21), (2, 6), (27, 13), (31, 8), (31, 34), (6, 8), (43, 5), (1, 34), (28, 45), (5, 46), (26, 20), (8, 42), (22, 8), (32, 17), (38, 23), (14, 42), (32, 20), (15, 32), (30, 29), (27, 8), (30, 42), (22, 39), (11, 40), (23, 0), (44, 14), (32, 25), (37, 16), (33, 5), (44, 45), (5, 9), (30, 27), (25, 20), (18, 34), (13, 38), (3, 29), (39, 31), (31, 45), (8, 30), (34, 41), (13, 0), (24, 13), (12, 16), (38, 43), (25, 14), (18, 25), (34, 46), (14, 40), (3, 37), (17, 9), (25, 32), (2, 46), (45, 35), (28, 46), (21, 11), (45, 24), (2, 16), (14, 31), (31, 29), (16, 37), (7, 41), (27, 5), (1, 24), (24, 6), (43, 29), (1, 44), (7, 30), (25, 33), (5, 14), (33, 29), (11, 6), (28, 34), (9, 31), (41, 3), (2, 45), (44, 10), (18, 7), (22, 18), (24, 17), (6, 11), (42, 1), (13, 4), (13, 20), (33, 7), (37, 18), (17, 6), (39, 42), (30, 31), (17, 27), (14, 8), (11, 34), (30, 3), (24, 34), (29, 45), (13, 11), (31, 27), (22, 35), (39, 36), (33, 20), (17, 34), (6, 34), (28, 35), (27, 11), (24, 29), (23, 14), (15, 29), (25, 41), (11, 46), (35, 24), (22, 5), (28, 12), (42, 9), (18, 15), (9, 5), (4, 5), (5, 21), (24, 15), (4, 43), (1, 33), (31, 1), (18, 38), (17, 25), (25, 4), (1, 38), (10, 8), (22, 9), (13, 41), (19, 3), (24, 42), (12, 31), (5, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 1), (24, 7), (6, 16), (4, 9), (40, 21), (24, 43), (23, 40), (34, 27), (12, 37), (6, 34), (38, 11), (15, 8), (35, 11), (38, 23), (28, 25), (25, 11), (8, 14), (27, 2), (14, 31), (12, 31), (38, 5), (24, 26), (37, 26), (10, 13), (8, 15), (0, 21), (19, 6), (10, 16), (7, 30), (1, 6), (22, 27), (7, 24), (26, 37), (14, 34), (14, 11), (4, 13), (24, 2), (0, 16), (6, 26), (21, 21), (13, 17), (29, 8), (18, 27), (6, 17), (0, 44), (31, 7), (2, 9), (13, 12), (36, 10), (27, 3), (21, 14), (3, 18), (12, 4), (38, 37), (32, 1), (17, 21), (32, 3), (26, 2), (26, 17), (24, 42), (27, 44), (17, 40), (23, 31), (32, 19), (0, 26), (26, 1), (7, 23), (16, 39), (40, 2), (22, 42), (15, 11), (18, 19), (38, 25), (20, 9), (22, 20), (12, 23), (37, 23), (25, 34), (36, 30), (13, 13), (30, 14), (20, 5), (14, 16), (35, 23), (8, 7), (4, 39), (25, 30), (14, 25), (25, 40), (22, 9), (40, 39), (28, 36), (26, 25), (18, 5), (0, 40), (23, 13), (11, 39), (16, 35), (36, 40), (16, 9), (1, 38), (30, 22), (7, 31), (0, 6), (13, 34), (32, 4), (3, 3), (5, 7), (18, 30), (28, 30), (23, 34), (21, 11), (27, 28), (28, 13), (27, 30), (31, 33), (18, 1), (15, 28), (24, 4), (4, 22), (16, 37), (37, 29), (17, 4), (34, 17), (1, 23), (5, 15), (17, 34), (11, 11), (34, 26), (21, 6), (15, 17), (33, 27), (16, 5), (17, 1), (19, 12), (13, 32), (32, 7), (24, 33), (11, 40), (25, 20), (15, 7), (10, 19), (13, 4), (8, 24), (24, 39), (23, 24), (8, 12), (10, 36), (12, 13), (20, 1), (30, 25), (40, 33), (25, 22), (3, 37), (19, 15), (18, 2), (5, 16), (0, 11), (26, 23), (16, 32), (19, 22), (39, 43), (27, 31), (31, 19), (9, 0), (40, 29), (30, 8), (4, 15), (11, 0), (22, 31), (4, 2), (3, 43), (27, 16), (33, 1), (15, 44), (35, 24), (21, 7), (27, 13), (21, 1), (27, 18), (37, 19), (18, 21), (16, 10), (6, 23), (9, 22), (28, 4), (39, 25), (26, 39), (9, 20), (28, 17), (31, 3), (4, 0), (16, 24), (8, 10), (2, 7), (6, 25), (21, 29), (8, 19), (40, 10), (8, 42), (25, 0), (5, 6), (19, 21), (11, 2), (33, 2), (32, 35), (30, 42), (12, 34), (28, 40), (5, 44), (28, 33), (14, 26), (14, 18), (25, 6), (2, 29), (6, 27), (20, 8), (27, 41), (40, 11), (40, 26), (39, 29), (37, 2), (27, 37), (7, 11), (31, 2), (0, 10), (6, 2), (28, 23), (36, 37), (32, 26), (31, 35), (13, 42), (18, 18), (31, 1), (37, 20), (17, 28), (36, 17), (5, 28), (11, 41), (36, 4), (39, 22), (3, 40), (12, 12), (15, 5), (14, 12), (21, 17), (2, 41), (13, 39), (34, 20), (35, 22), (35, 29), (32, 9), (17, 23), (10, 29), (15, 15), (19, 14), (0, 38), (3, 12), (9, 33), (30, 21), (11, 1), (31, 9), (32, 12), (9, 26), (33, 41), (15, 40), (8, 2), (10, 9), (16, 16), (20, 16), (19, 23), (23, 17), (26, 13), (24, 29), (19, 4), (25, 21), (37, 21), (31, 5), (3, 16), (9, 38), (25, 25), (22, 13), (10, 12), (40, 1), (25, 8), (20, 11), (8, 30), (13, 24), (31, 28), (39, 39), (28, 10), (30, 7), (31, 12), (3, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 42), (13, 1), (25, 7), (34, 7), (0, 11), (25, 13), (12, 36), (4, 10), (41, 7), (38, 44), (28, 8), (24, 15), (21, 31), (42, 26), (12, 37), (40, 36), (37, 1), (33, 23), (6, 37), (8, 6), (3, 12), (38, 37), (42, 16), (32, 41), (11, 17), (37, 41), (40, 21), (13, 21), (16, 40), (12, 41), (7, 7), (11, 9), (30, 14), (28, 29), (11, 42), (12, 22), (38, 11), (5, 7), (35, 31), (16, 0), (20, 15), (18, 20), (18, 16), (36, 12), (38, 27), (42, 17), (10, 30), (21, 28), (31, 43), (21, 17), (36, 25), (34, 13), (4, 20), (11, 7), (34, 39), (37, 9), (4, 34), (14, 14), (10, 21), (18, 9), (27, 17), (20, 43), (28, 26), (23, 13), (14, 11), (7, 6), (13, 41), (7, 42), (27, 9), (37, 2), (31, 6), (39, 32), (18, 40), (40, 28), (9, 43), (22, 37), (10, 28), (40, 25), (21, 45), (35, 7), (43, 18), (10, 29), (41, 36), (5, 28), (7, 27), (10, 5), (8, 41), (30, 34), (24, 24), (0, 45), (12, 32), (4, 7), (27, 43), (15, 11), (14, 6), (37, 27), (17, 11), (24, 44), (19, 20), (5, 38), (35, 23), (13, 26), (7, 23), (14, 43), (37, 0), (32, 21), (4, 42), (40, 38), (35, 35), (1, 33), (42, 14), (29, 8), (42, 33), (12, 19), (43, 22), (12, 18), (9, 35), (22, 20), (13, 23), (37, 40), (22, 11), (16, 43), (10, 8), (43, 10), (8, 28), (41, 26), (3, 43), (22, 43), (40, 8), (40, 29), (32, 9), (16, 36), (43, 5), (19, 11), (39, 1), (8, 3), (11, 36), (24, 3), (40, 33), (31, 3), (34, 14), (41, 37), (22, 10), (43, 30), (0, 39), (3, 13), (37, 12), (32, 43), (22, 32), (27, 33), (25, 27), (26, 0), (26, 11), (24, 32), (4, 24), (24, 41), (2, 30), (14, 34), (40, 20), (10, 25), (26, 38), (12, 35), (34, 8), (26, 23), (13, 38), (23, 32), (11, 16), (41, 41), (42, 36), (2, 45), (22, 1), (5, 35), (17, 45), (43, 44), (24, 28), (30, 9), (1, 44), (9, 27), (38, 38), (36, 18), (24, 18), (5, 37), (18, 33), (42, 8), (19, 28), (27, 44), (28, 20), (6, 20), (29, 16), (25, 3), (6, 11), (32, 19), (14, 37), (29, 35), (11, 5), (0, 34), (39, 6), (8, 4), (9, 8), (16, 44), (16, 14), (11, 30), (38, 6), (17, 34), (0, 1), (19, 0), (21, 11), (42, 27), (38, 17), (12, 12), (19, 30), (28, 39), (18, 27), (29, 36), (24, 0), (1, 29), (23, 31), (33, 16), (41, 21), (26, 2), (27, 38), (37, 36), (40, 35), (10, 11), (11, 38), (3, 16), (13, 24), (9, 6), (21, 2), (2, 24), (9, 5), (23, 38), (34, 40), (3, 24), (23, 1), (2, 40), (7, 32), (8, 42), (11, 18), (27, 32), (30, 11), (25, 10), (38, 19), (26, 25), (43, 41), (15, 34), (29, 1), (41, 9), (43, 25), (2, 17), (18, 36), (14, 9), (22, 27), (0, 2), (35, 30), (5, 21), (20, 26), (2, 32), (4, 14), (16, 9), (30, 36), (10, 24), (23, 2), (17, 1), (4, 27), (8, 2), (11, 1), (19, 8), (11, 24), (18, 22), (35, 13), (41, 8), (22, 14), (24, 45), (29, 6), (1, 40), (10, 12), (13, 0), (22, 44), (20, 19), (12, 6), (38, 12), (40, 17), (38, 35), (23, 6), (9, 18), (29, 38), (40, 40), (42, 11), (42, 1), (3, 45), (25, 40), (1, 38), (30, 22), (24, 26), (37, 42), (5, 23), (40, 41), (36, 40), (11, 41), (13, 8), (9, 17), (9, 36), (0, 3), (33, 20), (10, 35), (8, 30), (19, 10), (25, 17), (1, 6), (25, 14), (3, 32), (13, 9), (16, 10), (25, 32), (35, 21), (38, 2), (42, 25), (9, 42), (5, 9), (3, 0), (7, 11), (8, 43), (1, 43), (38, 30), (23, 14), (36, 9), (29, 13), (24, 6), (33, 28), (28, 32), (6, 19), (7, 14), (31, 7), (43, 37), (22, 17), (40, 1), (28, 28), (0, 16), (26, 37), (42, 37), (20, 32), (37, 34), (36, 29), (22, 18), (2, 1), (3, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 7), (18, 10), (9, 8), (15, 35), (28, 35), (24, 18), (27, 39), (11, 1), (33, 6), (20, 15), (22, 44), (11, 31), (1, 6), (35, 25), (12, 13), (40, 16), (7, 12), (11, 17), (34, 43), (33, 16), (31, 0), (37, 37), (31, 8), (29, 43), (31, 11), (13, 41), (22, 4), (29, 8), (4, 25), (13, 6), (17, 31), (10, 29), (35, 17), (1, 0), (40, 19), (21, 24), (26, 44), (34, 12), (39, 39), (13, 43), (21, 12), (3, 42), (12, 9), (28, 11), (4, 41), (13, 11), (23, 33), (3, 37), (16, 41), (2, 22), (15, 2), (5, 18), (12, 36), (12, 23), (37, 29), (25, 7), (11, 8), (34, 1), (13, 27), (39, 11), (6, 6), (35, 39), (35, 13), (15, 7), (1, 5), (4, 21), (10, 19), (32, 37), (15, 31), (4, 6), (29, 29), (3, 6), (21, 42), (8, 11), (25, 10), (14, 39), (3, 41), (9, 12), (19, 33), (32, 27), (3, 30), (6, 5), (2, 43), (30, 10), (20, 7), (30, 40), (39, 38), (23, 26), (25, 32), (31, 21), (24, 23), (3, 18), (21, 35), (22, 43), (7, 39), (33, 20), (21, 1), (7, 9), (23, 25), (7, 0), (10, 4), (30, 18), (2, 1), (24, 25), (25, 26), (31, 42), (34, 22), (35, 18), (7, 33), (35, 43), (27, 8), (15, 27), (19, 18), (2, 6), (37, 8), (6, 35), (10, 25), (16, 14), (8, 40), (24, 36), (2, 27), (1, 34), (15, 23), (21, 26), (14, 32), (22, 35), (6, 44), (37, 9), (4, 33), (30, 34), (11, 11), (9, 2), (38, 19), (6, 30), (13, 12), (23, 32), (9, 40), (25, 33), (22, 6), (12, 37), (24, 12), (11, 19), (11, 41), (16, 38), (35, 4), (33, 4), (11, 14), (9, 33), (5, 25), (41, 25), (35, 35), (32, 13), (6, 2), (32, 2), (34, 13), (39, 20), (36, 27), (15, 38), (10, 9), (32, 39), (33, 11), (33, 10), (27, 14), (5, 36), (6, 13), (31, 44), (19, 0), (14, 20), (36, 26), (0, 24), (41, 35), (27, 6), (36, 20), (6, 41), (26, 24), (10, 34), (2, 8), (37, 24), (31, 6), (36, 38), (24, 41), (40, 38), (16, 7), (18, 33), (21, 2), (31, 20), (34, 41), (33, 9), (11, 23), (21, 13), (29, 5), (16, 40), (31, 35), (18, 15), (5, 31), (3, 14), (27, 22), (13, 37), (27, 0), (21, 8), (0, 22), (9, 44), (1, 36), (15, 14), (8, 34), (7, 16), (19, 25), (9, 27), (27, 17), (14, 5), (14, 42), (38, 22), (20, 11), (28, 30), (29, 42), (13, 21), (7, 37), (37, 7), (38, 6), (14, 4), (21, 25), (0, 44), (8, 4), (13, 9), (39, 28), (26, 10), (34, 32), (24, 27), (4, 38), (17, 3), (18, 3), (18, 2), (19, 14), (32, 6), (20, 40), (15, 12), (22, 41), (20, 18), (39, 5), (12, 29), (35, 16), (33, 15), (8, 10), (22, 2), (13, 2), (19, 6), (38, 44), (31, 15), (28, 5), (19, 32), (26, 28), (1, 28), (1, 42), (22, 0), (20, 21), (0, 20), (17, 29), (11, 44), (27, 15), (11, 25), (37, 33), (9, 30), (19, 5), (13, 38), (18, 28), (6, 23), (26, 30), (40, 11), (40, 27), (35, 42), (36, 28), (30, 5), (2, 44), (37, 41), (27, 13), (22, 22), (0, 13), (28, 33), (13, 13), (37, 42), (33, 35), (16, 25), (10, 17), (5, 8), (18, 6), (10, 28), (31, 27), (26, 22), (0, 19), (24, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 9), (8, 28), (23, 47), (20, 43), (18, 17), (34, 48), (12, 9), (34, 17), (8, 30), (11, 0), (17, 47), (19, 43), (33, 42), (44, 13), (43, 8), (41, 15), (15, 2), (4, 19), (44, 16), (14, 30), (23, 28), (31, 17), (28, 14), (37, 12), (22, 25), (30, 19), (19, 36), (10, 36), (29, 27), (0, 42), (19, 7), (37, 9), (7, 22), (43, 42), (4, 41), (17, 25), (30, 42), (13, 9), (17, 41), (3, 34), (25, 9), (8, 27), (27, 36), (14, 0), (38, 40), (43, 3), (27, 44), (11, 5), (25, 36), (18, 25), (25, 27), (20, 8), (27, 41), (10, 22), (41, 43), (20, 23), (36, 34), (34, 20), (14, 48), (0, 12), (7, 29), (16, 2), (19, 3), (5, 17), (36, 19), (8, 15), (32, 5), (18, 39), (15, 25), (35, 16), (3, 31), (41, 44), (23, 13), (37, 5), (5, 19), (24, 18), (23, 37), (8, 6), (40, 39), (19, 26), (7, 30), (10, 6), (30, 33), (15, 6), (27, 10), (14, 32), (8, 9), (1, 36), (34, 13), (28, 42), (18, 37), (16, 48), (19, 9), (32, 7), (27, 2), (7, 41), (16, 27), (34, 27), (22, 30), (43, 2), (38, 25), (3, 15), (32, 4), (32, 28), (41, 33), (37, 3), (33, 26), (22, 3), (13, 2), (22, 48), (22, 24), (29, 17), (38, 5), (32, 46), (14, 26), (33, 28), (36, 43), (0, 46), (35, 30), (38, 36), (10, 34), (38, 14), (23, 33), (13, 35), (4, 2), (10, 31), (31, 3), (37, 43), (33, 1), (44, 3), (20, 48), (26, 26), (22, 44), (36, 40), (15, 47), (14, 24), (41, 13), (27, 8), (35, 25), (37, 31), (18, 6), (17, 34), (40, 30), (21, 44), (22, 27), (6, 9), (43, 11), (33, 35), (40, 17), (34, 30), (20, 33), (2, 13), (24, 7), (36, 41), (37, 17), (28, 30), (41, 26), (24, 48), (6, 0), (3, 1), (17, 27), (43, 37), (32, 40), (14, 34), (38, 8), (9, 40), (25, 17), (18, 13), (5, 11), (16, 46), (32, 0), (37, 39), (37, 26), (38, 46), (28, 45), (30, 18), (20, 13), (41, 36), (24, 8), (6, 32), (7, 20), (1, 21), (38, 38), (39, 22), (17, 20), (31, 10), (42, 12), (35, 17), (30, 16), (36, 32), (32, 20), (6, 29), (43, 0), (28, 24), (10, 10), (1, 40), (38, 39), (22, 32), (16, 15), (43, 35), (21, 4), (25, 41), (31, 4), (12, 43), (18, 28), (34, 16), (7, 43), (20, 6), (25, 10), (1, 9), (27, 43), (13, 29), (9, 24), (36, 27), (33, 20), (13, 1), (41, 31), (18, 44), (41, 32), (11, 25), (23, 1), (9, 4), (17, 19), (1, 33), (30, 5), (36, 8), (26, 41), (4, 39), (37, 33), (1, 46), (11, 8), (19, 28), (17, 14), (4, 48), (22, 22), (18, 16), (26, 18), (13, 20), (30, 25), (7, 32), (3, 24), (6, 33), (17, 9), (15, 18), (37, 34), (19, 17), (39, 25), (13, 37), (36, 24), (4, 10), (27, 26), (13, 28), (33, 36), (29, 44), (43, 15), (41, 28), (4, 11), (43, 23), (21, 22), (26, 43), (15, 44), (39, 2), (19, 0), (41, 11), (27, 6), (37, 35), (31, 45), (44, 25), (9, 15), (23, 16), (41, 39), (36, 1), (20, 7), (44, 22), (31, 13), (12, 39), (43, 13), (10, 29), (10, 5), (15, 46), (19, 12), (0, 45), (27, 3), (0, 18), (6, 7), (6, 16), (15, 8), (18, 8), (8, 31), (11, 26), (12, 46), (38, 48), (38, 20), (7, 25), (35, 37), (2, 42), (29, 9), (11, 19), (15, 26), (9, 42), (34, 34), (4, 12), (37, 2), (6, 48), (22, 15), (24, 16), (44, 0), (29, 39), (9, 23), (12, 8), (40, 26), (36, 7), (38, 42), (21, 13), (33, 3), (4, 34), (36, 35), (4, 32), (9, 6), (10, 7), (21, 30), (29, 33), (4, 31), (32, 11), (27, 29), (41, 27), (42, 18), (10, 18), (28, 38), (24, 29), (35, 24), (33, 2), (34, 47), (29, 47), (19, 22), (39, 45), (9, 14), (22, 21), (25, 44), (6, 2), (14, 40), (13, 15), (24, 30), (40, 2), (14, 17), (15, 37), (22, 43), (17, 26), (7, 27), (18, 40), (31, 40), (30, 3), (13, 10), (16, 22), (37, 14), (6, 21), (21, 46), (39, 37), (39, 3), (12, 0), (40, 13), (39, 15), (30, 32), (41, 29), (42, 2), (34, 37), (38, 12), (9, 45), (2, 45), (21, 16), (2, 28), (14, 37), (5, 5), (4, 25), (1, 11), (30, 22), (8, 0), (24, 20), (4, 18), (33, 47), (29, 46), (31, 22), (20, 18), (11, 42), (5, 32), (38, 28), (25, 40), (44, 12), (32, 24), (9, 36), (21, 39), (2, 34), (3, 27), (39, 33), (17, 48), (15, 13), (43, 22), (4, 13), (13, 44), (34, 3), (29, 3), (39, 46), (28, 31), (35, 43), (39, 14), (22, 5), (37, 6), (27, 11), (11, 3), (36, 25), (42, 8), (30, 31), (11, 37), (16, 44), (34, 15), (3, 20), (36, 44), (44, 43), (24, 24), (39, 13), (23, 34), (24, 46), (40, 18), (19, 4), (10, 9), (11, 29), (28, 23), (4, 40), (16, 24), (30, 7), (29, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 17), (25, 15), (17, 5), (40, 15), (12, 1), (4, 13), (9, 39), (23, 37), (35, 33), (17, 21), (31, 14), (25, 39), (34, 32), (29, 22), (18, 20), (4, 29), (17, 7), (40, 2), (33, 0), (28, 34), (26, 2), (33, 18), (21, 30), (27, 19), (11, 11), (30, 35), (2, 34), (39, 11), (1, 21), (35, 4), (26, 8), (4, 32), (34, 0), (30, 24), (27, 8), (10, 0), (38, 11), (31, 39), (37, 14), (34, 2), (28, 16), (2, 16), (11, 10), (13, 35), (19, 17), (6, 34), (40, 30), (0, 25), (8, 7), (4, 30), (39, 24), (39, 9), (36, 37), (18, 15), (22, 25), (24, 5), (32, 11), (21, 34), (3, 24), (0, 34), (15, 6), (15, 2), (39, 5), (24, 18), (20, 6), (16, 4), (24, 0), (23, 5), (26, 30), (15, 18), (19, 33), (39, 29), (15, 7), (14, 38), (20, 2), (26, 37), (23, 15), (18, 1), (18, 17), (35, 0), (38, 12), (35, 34), (5, 31), (12, 6), (5, 19), (25, 27), (23, 31), (24, 16), (11, 4), (16, 39), (27, 31), (27, 27), (34, 23), (6, 7), (16, 18), (8, 38), (29, 13), (5, 24), (13, 21), (0, 16), (4, 15), (30, 32), (21, 23), (2, 35), (36, 16), (24, 19), (39, 25), (3, 29), (6, 5), (5, 1), (25, 34), (29, 38), (3, 16), (19, 26), (34, 14), (39, 28), (26, 12), (39, 23), (35, 26), (7, 11), (14, 26), (39, 14), (12, 24), (5, 21), (30, 4), (10, 2), (23, 19), (10, 9), (39, 39), (15, 15), (18, 23), (20, 38), (21, 28), (16, 0), (39, 36), (27, 39), (38, 18), (4, 25), (23, 10), (30, 0), (40, 14), (12, 14), (2, 32), (15, 28), (7, 17), (10, 24), (9, 21), (3, 31), (24, 8), (23, 26), (26, 33), (38, 2), (22, 7), (20, 19), (26, 19), (17, 12), (0, 18), (36, 0), (2, 30), (8, 30), (5, 25), (21, 29), (35, 20), (3, 34), (11, 33), (40, 10), (13, 10), (16, 31), (33, 8), (31, 26), (38, 20), (20, 8), (35, 13), (19, 13), (5, 13), (31, 19), (3, 12), (13, 8), (4, 14), (17, 36), (2, 24), (38, 35), (23, 0), (11, 7), (34, 28), (12, 0), (27, 13), (36, 28), (10, 30), (33, 1), (35, 23), (28, 7), (35, 10), (40, 34), (13, 28), (20, 7), (9, 19), (34, 10), (23, 11), (1, 28), (33, 35), (5, 39), (14, 39), (37, 18), (12, 13), (14, 8), (11, 15), (7, 28), (34, 7), (26, 1), (31, 9), (25, 9), (35, 9), (20, 10), (19, 1), (20, 17), (33, 36), (5, 12), (30, 37), (29, 0), (4, 26), (37, 21), (34, 24), (39, 12), (16, 29), (29, 35), (26, 27), (27, 9), (20, 32), (22, 31), (14, 9), (33, 9), (20, 4), (40, 23), (26, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 30), (15, 41), (44, 3), (40, 46), (3, 40), (23, 46), (40, 26), (3, 45), (0, 38), (46, 8), (42, 2), (16, 15), (40, 44), (6, 3), (28, 6), (21, 28), (15, 21), (16, 19), (10, 10), (18, 7), (24, 32), (33, 11), (40, 8), (18, 12), (27, 18), (25, 30), (0, 9), (24, 0), (18, 25), (31, 29), (37, 45), (34, 18), (42, 16), (21, 42), (43, 42), (32, 34), (37, 9), (43, 45), (12, 37), (8, 8), (15, 33), (25, 21), (42, 18), (41, 6), (21, 3), (12, 11), (27, 36), (16, 5), (19, 5), (9, 25), (30, 24), (21, 12), (18, 23), (8, 7), (31, 40), (36, 38), (16, 11), (27, 9), (40, 35), (12, 26), (30, 36), (41, 41), (26, 15), (34, 7), (5, 34), (13, 23), (34, 42), (41, 34), (42, 3), (22, 27), (40, 3), (13, 18), (1, 27), (11, 45), (45, 1), (10, 39), (40, 37), (40, 30), (29, 29), (36, 42), (39, 35), (29, 10), (29, 7), (24, 15), (2, 44), (15, 2), (24, 13), (26, 4), (11, 18), (38, 2), (9, 29), (22, 12), (33, 1), (29, 17), (13, 27), (3, 27), (35, 3), (16, 36), (18, 8), (36, 40), (30, 4), (11, 26), (3, 23), (37, 43), (15, 31), (27, 42), (46, 16), (33, 14), (6, 24), (22, 9), (9, 14), (31, 42), (44, 11), (44, 0), (8, 31), (46, 27), (28, 12), (21, 22), (6, 27), (29, 32), (33, 6), (25, 23), (44, 27), (38, 16), (4, 10), (25, 9), (26, 44), (12, 32), (35, 6), (27, 21), (18, 15), (12, 25), (28, 46), (13, 34), (5, 36), (10, 9), (32, 42), (27, 0), (10, 43), (26, 29), (6, 2), (38, 1), (5, 1), (18, 4), (23, 40), (6, 12), (36, 39), (37, 10), (6, 5), (10, 14), (8, 6), (11, 10), (4, 45), (15, 27), (3, 21), (15, 45), (5, 18), (31, 13), (24, 38), (5, 5), (41, 39), (34, 46), (16, 44), (15, 9), (19, 6), (12, 40), (3, 43), (29, 15), (27, 41), (8, 37), (15, 25), (40, 40), (27, 29), (20, 23), (22, 24), (37, 21), (10, 38), (6, 11), (20, 9), (19, 46), (2, 45), (1, 5), (36, 44), (15, 6), (25, 44), (2, 28), (0, 6), (19, 12), (34, 30), (11, 34), (33, 28), (25, 0), (33, 39), (23, 8), (22, 14), (26, 3), (44, 28), (2, 8), (36, 6), (21, 18), (26, 16), (11, 42), (44, 20), (13, 13), (34, 36), (26, 34), (29, 26), (5, 28), (17, 30), (42, 29), (29, 6), (36, 32), (19, 32), (45, 24), (6, 38), (35, 10), (9, 24), (24, 41), (37, 13), (24, 12), (30, 30), (8, 44), (8, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 36), (27, 42), (32, 19), (5, 17), (37, 0), (34, 38), (26, 34), (3, 10), (22, 20), (7, 17), (23, 36), (25, 20), (11, 40), (11, 2), (11, 16), (12, 10), (26, 20), (20, 40), (36, 23), (25, 33), (15, 8), (13, 31), (19, 4), (11, 5), (13, 13), (35, 38), (8, 24), (36, 13), (19, 37), (29, 29), (16, 2), (38, 27), (34, 37), (18, 0), (27, 4), (12, 34), (23, 37), (36, 34), (5, 24), (18, 41), (15, 43), (2, 32), (10, 5), (14, 23), (18, 12), (12, 17), (24, 6), (31, 37), (29, 12), (4, 36), (28, 28), (4, 27), (23, 43), (2, 7), (23, 30), (8, 3), (36, 5), (2, 14), (0, 20), (2, 28), (26, 36), (34, 2), (12, 41), (19, 29), (6, 25), (14, 13), (5, 7), (17, 29), (1, 25), (13, 10), (24, 24), (37, 15), (13, 15), (11, 20), (27, 16), (31, 11), (23, 0), (6, 22), (0, 25), (32, 34), (31, 1), (1, 38), (8, 38), (16, 8), (1, 40), (11, 33), (29, 35), (30, 3), (36, 40), (35, 32), (11, 25), (4, 15), (31, 35), (21, 2), (27, 35), (30, 35), (28, 0), (7, 23), (16, 12), (10, 42), (3, 6), (17, 1), (17, 6), (24, 23), (36, 3), (16, 38), (15, 2), (14, 33), (13, 17), (32, 8), (4, 1), (15, 1), (14, 15), (29, 18), (37, 35), (16, 43), (33, 30), (35, 13), (11, 37), (30, 27), (21, 20), (29, 43), (7, 15), (37, 42), (20, 3), (18, 31), (22, 9), (3, 19), (7, 12), (10, 13), (6, 40), (30, 22), (27, 37), (9, 27), (34, 21), (37, 40), (3, 32), (0, 18), (6, 20), (28, 41), (19, 15), (30, 16), (25, 27), (5, 16), (28, 23), (18, 42), (29, 11), (2, 18), (19, 28), (32, 6), (39, 9), (30, 6), (19, 32), (22, 6), (13, 30), (32, 7), (35, 23), (17, 42), (12, 7), (14, 30), (24, 2), (9, 12), (17, 33), (26, 0), (10, 34), (31, 8), (22, 41), (14, 7), (30, 14), (15, 42), (28, 9), (14, 31), (1, 36), (16, 36), (32, 11), (27, 41), (7, 24), (8, 39), (29, 36), (18, 40), (3, 34), (35, 9), (27, 22), (24, 41), (18, 8), (5, 12), (27, 8), (34, 12), (21, 43), (19, 38), (31, 12), (31, 36), (3, 4), (14, 8), (4, 0), (38, 39), (31, 38), (38, 16), (8, 17), (17, 28), (29, 31), (37, 23), (27, 20), (21, 23), (9, 14), (26, 27), (15, 34), (29, 42), (28, 5), (11, 36), (17, 11), (31, 39), (9, 1), (16, 18), (24, 26), (18, 36), (15, 9), (12, 22), (39, 42), (13, 2), (37, 12), (29, 33), (20, 5), (15, 35), (6, 1), (29, 25), (36, 1), (35, 5), (37, 3), (39, 18), (16, 39), (10, 25), (13, 32), (28, 37), (37, 6), (21, 31), (2, 25), (23, 27), (3, 30), (31, 26), (10, 21), (23, 39), (23, 8), (32, 10), (21, 34), (36, 32), (10, 18), (28, 17), (4, 21), (35, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 48), (26, 4), (44, 31), (35, 20), (21, 30), (26, 17), (30, 22), (7, 44), (28, 34), (1, 5), (10, 10), (12, 7), (9, 15), (32, 37), (10, 35), (44, 5), (29, 46), (22, 8), (20, 44), (42, 25), (20, 38), (36, 32), (20, 42), (44, 1), (41, 24), (35, 7), (30, 4), (25, 40), (43, 27), (13, 15), (45, 13), (16, 42), (40, 34), (42, 44), (6, 16), (41, 40), (13, 27), (39, 11), (20, 20), (13, 48), (27, 39), (25, 16), (24, 15), (3, 42), (26, 41), (25, 21), (22, 5), (9, 43), (7, 28), (45, 28), (37, 43), (15, 24), (39, 45), (15, 27), (41, 45), (11, 43), (9, 7), (22, 10), (13, 23), (31, 5), (27, 13), (39, 20), (8, 24), (4, 37), (15, 35), (43, 20), (19, 16), (9, 47), (1, 42), (38, 43), (29, 14), (10, 14), (16, 12), (43, 16), (39, 30), (29, 23), (28, 22), (39, 0), (39, 6), (43, 28), (25, 34), (10, 0), (2, 36), (37, 10), (34, 39), (32, 22), (34, 23), (23, 0), (26, 31), (9, 21), (21, 14), (31, 36), (31, 28), (41, 4), (7, 23), (26, 39), (10, 19), (5, 1), (0, 2), (38, 47), (43, 42), (14, 5), (21, 25), (15, 5), (12, 30), (3, 10), (30, 31), (40, 37), (33, 38), (22, 14), (11, 13), (28, 7), (0, 32), (11, 15), (42, 45), (20, 34), (14, 12), (41, 10), (29, 1), (45, 40), (40, 6), (44, 0), (3, 46), (35, 12), (21, 33), (29, 4), (28, 29), (6, 26), (19, 15), (12, 22), (0, 20), (9, 48), (30, 29), (17, 26), (22, 30), (26, 0), (39, 4), (29, 17), (4, 17), (39, 28), (3, 17), (23, 45), (38, 9), (18, 12), (1, 25), (34, 10), (22, 45), (9, 1), (23, 12), (6, 8), (31, 11), (19, 43), (14, 16), (38, 37), (30, 32), (19, 38), (30, 16), (37, 45), (5, 25), (21, 21), (8, 14), (34, 47), (2, 17), (18, 32), (45, 11), (17, 30), (13, 19), (19, 40), (42, 12), (22, 2), (4, 36), (25, 3), (3, 14), (33, 46), (21, 31), (9, 3), (9, 36), (20, 1), (6, 32), (14, 47), (3, 15), (31, 6), (35, 4), (17, 34), (44, 24), (34, 4), (4, 21), (33, 24), (25, 37), (24, 37), (38, 41), (12, 35), (21, 6), (35, 40), (8, 19), (19, 23), (34, 22), (33, 27), (28, 3), (24, 21), (43, 36), (7, 41), (3, 41), (13, 9), (30, 7), (4, 22), (32, 13), (32, 2), (10, 23), (31, 34), (21, 23), (7, 9), (22, 44), (9, 27), (38, 30), (40, 9), (41, 41), (40, 22), (37, 4), (1, 40), (9, 17), (32, 30), (10, 37), (12, 14), (23, 6), (8, 35), (5, 42), (3, 1), (41, 48), (18, 41), (39, 38), (21, 44), (38, 5), (32, 3), (27, 11), (41, 7), (23, 46), (23, 15), (32, 38), (30, 37), (44, 7), (36, 2), (23, 29), (5, 31), (26, 24), (27, 27), (12, 42), (28, 46), (12, 31), (44, 21), (21, 24), (18, 15), (4, 47), (37, 18), (19, 41), (21, 5), (35, 46), (32, 17), (33, 7), (4, 1), (14, 44), (4, 30), (19, 11), (15, 17), (35, 14), (13, 16), (26, 35), (5, 12), (31, 9), (13, 42), (26, 13), (29, 10), (32, 24), (39, 25), (38, 22), (6, 25), (24, 47), (21, 36), (42, 46), (12, 29), (1, 44), (30, 21), (3, 36), (31, 47), (16, 20), (2, 33), (41, 14), (17, 12), (43, 9), (24, 35), (40, 45), (37, 44), (33, 34), (22, 1), (20, 24), (29, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 9), (41, 44), (39, 28), (25, 5), (17, 36), (22, 30), (14, 29), (31, 20), (40, 41), (5, 25), (20, 14), (30, 14), (14, 13), (39, 46), (37, 21), (30, 39), (28, 28), (20, 1), (37, 33), (8, 13), (12, 18), (24, 8), (22, 15), (26, 25), (39, 21), (12, 30), (3, 29), (41, 9), (12, 14), (28, 36), (15, 4), (5, 44), (1, 26), (12, 22), (28, 37), (22, 6), (29, 32), (27, 24), (5, 11), (24, 5), (39, 4), (15, 46), (6, 41), (41, 22), (3, 19), (33, 12), (33, 2), (24, 27), (38, 13), (10, 33), (26, 8), (36, 20), (3, 8), (39, 23), (1, 41), (24, 15), (2, 28), (12, 31), (28, 7), (38, 41), (28, 12), (23, 2), (10, 27), (36, 13), (38, 40), (9, 42), (22, 7), (31, 26), (6, 22), (29, 39), (0, 8), (4, 16), (6, 45), (29, 9), (28, 4), (41, 42), (40, 20), (6, 27), (17, 23), (23, 32), (37, 34), (27, 7), (12, 13), (4, 11), (24, 33), (40, 2), (11, 25), (32, 2), (7, 31), (29, 3), (10, 1), (41, 0), (1, 40), (25, 13), (27, 22), (7, 4), (34, 6), (31, 4), (18, 1), (2, 33), (22, 19), (25, 34), (18, 21), (30, 28), (27, 28), (30, 0), (40, 32), (6, 32), (1, 27), (27, 17), (14, 39), (12, 0), (23, 27), (42, 0), (10, 12), (33, 17), (27, 11), (22, 35), (39, 5), (20, 9), (31, 47), (24, 9), (11, 45), (5, 38), (1, 29), (10, 42), (6, 14), (4, 45), (24, 45), (21, 22), (12, 41), (37, 4), (12, 15), (11, 44), (15, 32), (12, 33), (28, 41), (8, 23), (0, 4), (20, 41), (18, 26), (21, 14), (0, 38), (24, 39), (40, 5), (41, 24), (31, 34), (29, 47), (24, 0), (22, 41), (9, 31), (26, 6), (0, 9), (23, 39), (34, 18), (25, 41), (11, 42), (42, 13), (23, 3), (5, 31), (29, 24), (27, 44), (17, 30), (38, 39), (36, 28), (16, 42), (17, 25), (21, 19), (31, 24), (12, 23), (3, 37), (38, 31), (9, 24), (31, 14), (19, 5), (24, 6), (3, 10), (19, 6), (39, 33), (14, 28), (7, 36), (5, 32), (31, 2), (42, 15), (3, 26), (28, 27), (32, 3), (4, 32), (7, 16), (15, 43), (40, 19), (5, 40), (29, 19), (32, 39), (40, 1), (24, 30), (19, 31), (17, 31), (28, 24), (36, 44), (27, 27), (27, 32), (29, 4), (31, 40), (7, 12), (16, 39), (18, 33), (39, 36), (31, 39), (35, 17), (11, 46), (34, 9), (30, 41), (11, 18), (6, 1), (14, 30), (41, 4), (12, 46), (20, 27), (22, 3), (19, 4), (0, 3), (6, 29), (39, 3), (27, 3), (38, 47), (13, 44), (5, 6), (28, 23), (29, 30), (38, 35), (20, 17), (39, 44), (42, 11), (5, 0), (13, 9), (27, 30), (16, 0), (5, 3), (32, 42), (9, 18), (18, 43), (20, 21), (35, 42), (41, 14), (42, 38), (26, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 30), (37, 8), (26, 35), (1, 11), (23, 16), (17, 10), (25, 18), (9, 5), (38, 23), (13, 10), (38, 0), (3, 27), (1, 47), (4, 31), (17, 25), (0, 35), (29, 17), (12, 29), (26, 45), (27, 2), (6, 3), (6, 17), (34, 46), (26, 34), (27, 22), (39, 44), (35, 23), (3, 18), (16, 29), (1, 39), (13, 44), (27, 38), (40, 29), (12, 7), (17, 28), (28, 1), (3, 25), (35, 13), (0, 6), (21, 25), (12, 5), (29, 46), (10, 22), (5, 12), (9, 4), (30, 23), (14, 6), (34, 38), (37, 22), (4, 4), (12, 31), (17, 18), (8, 43), (0, 37), (33, 48), (5, 10), (16, 23), (10, 23), (34, 37), (21, 47), (30, 30), (11, 22), (29, 14), (25, 24), (2, 4), (26, 40), (12, 33), (31, 18), (30, 36), (4, 42), (25, 47), (36, 18), (27, 16), (33, 11), (17, 14), (3, 6), (30, 13), (7, 46), (5, 6), (34, 24), (21, 30), (10, 16), (10, 28), (15, 19), (8, 40), (19, 26), (18, 38), (30, 17), (37, 38), (8, 19), (5, 30), (26, 31), (35, 16), (26, 21), (40, 9), (11, 24), (26, 39), (5, 22), (5, 46), (24, 9), (12, 47), (41, 42), (25, 0), (9, 9), (30, 40), (6, 9), (35, 42), (15, 34), (7, 33), (24, 38), (7, 38), (27, 25), (15, 47), (24, 42), (36, 45), (19, 29), (12, 39), (19, 48), (33, 24), (2, 0), (23, 34), (23, 30), (16, 3), (8, 6), (36, 21), (23, 39), (39, 10), (30, 43), (31, 9), (33, 46), (23, 12), (14, 27), (26, 46), (7, 44), (19, 5), (9, 19), (5, 44), (4, 47), (0, 38), (1, 22), (17, 27), (30, 38), (38, 30), (32, 31), (18, 47), (27, 6), (26, 44), (34, 25), (8, 28), (33, 47), (0, 44), (27, 46), (18, 29), (14, 13), (4, 45), (22, 32), (19, 32), (20, 33), (41, 41), (1, 48), (23, 9), (7, 27), (2, 22), (8, 41), (31, 41), (2, 45), (23, 37), (25, 28), (35, 3), (32, 18), (9, 35), (14, 5), (19, 21), (35, 9), (33, 43), (29, 37), (18, 41), (21, 14), (15, 14), (28, 36), (11, 13), (36, 29), (39, 30), (0, 21), (27, 28), (21, 3), (12, 42), (38, 9), (22, 13), (21, 5), (5, 45), (5, 47), (8, 0), (25, 46), (35, 46), (23, 2), (40, 3), (10, 48), (35, 4), (19, 36), (23, 44), (32, 9), (41, 29), (41, 37), (33, 1), (25, 10), (29, 43), (32, 23), (24, 39), (14, 4), (29, 27), (23, 42), (18, 12), (40, 23), (23, 13), (16, 37), (13, 6), (2, 36), (40, 31), (13, 4), (3, 36), (19, 33), (10, 40), (30, 39), (16, 35), (24, 7), (6, 37), (11, 5), (28, 13), (33, 3), (29, 42), (34, 5), (31, 15), (39, 39), (34, 47), (22, 38), (17, 45), (13, 20), (7, 24), (8, 31), (1, 2), (18, 31), (29, 40), (29, 13), (25, 35), (29, 16), (20, 14), (27, 40), (41, 4), (41, 17), (16, 1), (28, 29), (30, 16), (40, 48), (31, 2), (17, 5), (19, 9), (38, 31), (12, 43), (4, 39), (22, 45), (3, 26), (40, 17), (35, 20), (33, 45), (19, 46), (20, 28), (6, 29), (17, 47), (33, 7), (5, 5), (36, 47), (41, 10), (11, 8), (37, 45), (29, 45), (26, 33), (10, 36), (3, 1), (34, 34), (24, 36), (12, 30), (25, 30), (21, 41), (16, 40), (1, 1), (6, 34), (36, 6), (26, 13), (17, 23), (2, 26), (30, 32), (28, 35), (30, 48), (0, 32), (25, 31), (21, 31), (30, 33), (28, 33), (0, 11), (28, 42), (11, 19), (20, 23), (37, 25), (39, 4), (34, 10), (40, 35), (16, 41), (10, 47), (28, 23), (7, 1), (19, 28), (7, 29), (36, 22), (28, 45), (40, 11), (18, 42), (11, 26), (21, 8), (28, 43), (34, 45), (32, 46), (6, 22), (15, 12), (41, 20), (31, 1), (19, 13), (22, 18), (32, 1), (21, 39), (19, 8), (4, 2), (32, 20), (0, 30), (19, 18), (28, 41), (35, 27), (25, 6), (40, 41), (25, 7), (26, 27), (15, 26), (2, 15), (25, 34), (1, 7), (32, 4), (8, 8), (37, 15), (12, 17), (9, 10), (31, 20), (30, 11), (30, 41), (10, 19), (22, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 40x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 29), (34, 44), (21, 35), (13, 43), (11, 14), (38, 21), (30, 22), (37, 22), (30, 12), (37, 37), (2, 36), (11, 13), (0, 10), (19, 2), (21, 2), (14, 40), (34, 35), (35, 41), (38, 22), (31, 3), (22, 32), (12, 31), (11, 11), (32, 27), (30, 1), (33, 23), (35, 17), (5, 16), (6, 35), (28, 40), (12, 18), (17, 18), (1, 15), (0, 37), (39, 27), (6, 3), (1, 41), (28, 2), (20, 31), (19, 42), (9, 18), (21, 3), (6, 43), (23, 29), (23, 30), (1, 0), (5, 42), (10, 45), (38, 25), (1, 27), (7, 17), (7, 13), (37, 40), (3, 28), (8, 30), (29, 3), (33, 27), (9, 13), (22, 39), (21, 18), (29, 32), (17, 17), (10, 36), (17, 29), (30, 3), (37, 12), (19, 43), (32, 33), (5, 33), (17, 31), (22, 34), (16, 0), (23, 13), (11, 22), (7, 12), (33, 43), (17, 33), (27, 36), (39, 13), (24, 28), (20, 34), (28, 1), (10, 2), (23, 20), (24, 36), (7, 39), (31, 34), (27, 21), (10, 34), (24, 34), (2, 16), (24, 5), (33, 6), (11, 20), (9, 42), (34, 33), (32, 9), (31, 12), (35, 34), (5, 27), (3, 1), (13, 22), (14, 35), (27, 31), (6, 20), (19, 39), (8, 19), (19, 16), (36, 13), (22, 8), (39, 16), (39, 14), (35, 38), (27, 8), (30, 19), (13, 13), (16, 16), (20, 27), (39, 18), (13, 6), (12, 25), (25, 14), (0, 30), (39, 25), (21, 36), (14, 44), (16, 11), (8, 21), (2, 6), (31, 6), (30, 30), (17, 28), (17, 6), (5, 39), (16, 4), (19, 1), (39, 44), (26, 0), (7, 43), (0, 12), (31, 32), (13, 45), (5, 2), (22, 22), (9, 31), (34, 41), (4, 43), (29, 43), (15, 18), (5, 23), (28, 33), (36, 32), (26, 37), (16, 3), (25, 0), (11, 28), (5, 21), (25, 44), (24, 2), (32, 39), (18, 33), (35, 15), (3, 37), (3, 9), (30, 16), (37, 33), (21, 7), (33, 13), (24, 19), (4, 9), (23, 31), (34, 26), (34, 3), (9, 40), (11, 43), (22, 28), (25, 41), (0, 42), (38, 28), (28, 36), (36, 33), (2, 9), (29, 1), (19, 9), (30, 31), (17, 7), (30, 28), (18, 13), (35, 12), (31, 36), (29, 31), (30, 24), (5, 9), (19, 44), (37, 42), (26, 43), (15, 1), (3, 8), (30, 4), (0, 28), (16, 20), (13, 39), (25, 32), (24, 40), (29, 19), (12, 24), (25, 36), (17, 14), (14, 16), (37, 34), (36, 0), (39, 26), (13, 24), (16, 14), (34, 29), (37, 3), (2, 43), (28, 31), (16, 45), (19, 13), (17, 30), (18, 20), (8, 42), (25, 35), (34, 11), (8, 13), (29, 28), (14, 18), (2, 21), (39, 22), (20, 3), (14, 11), (37, 0), (0, 33), (11, 3), (8, 5), (27, 37), (19, 41), (8, 45), (30, 43), (15, 21), (33, 25), (10, 43), (5, 35), (2, 20), (22, 43), (23, 11), (34, 40), (31, 17), (8, 24), (38, 39), (36, 28), (38, 8), (29, 4), (2, 42), (31, 31), (21, 39), (29, 30), (28, 14), (32, 29), (16, 43), (38, 30), (15, 2), (33, 44), (4, 45), (34, 14), (22, 38), (23, 24), (37, 19), (30, 11), (38, 15), (25, 21), (0, 45), (32, 5), (8, 17), (30, 32), (20, 24), (1, 33), (15, 22), (19, 21), (37, 45), (1, 11), (8, 33), (9, 19), (11, 45), (28, 3), (29, 10), (4, 13), (32, 11), (23, 1), (3, 6), (26, 45), (32, 20), (3, 20), (24, 20), (1, 16), (6, 28), (5, 41), (24, 8), (37, 17), (14, 28), (32, 31), (19, 30), (3, 43), (13, 12), (38, 37), (10, 11), (0, 38), (16, 28), (6, 1), (20, 13), (3, 3), (19, 10), (3, 5), (28, 42), (17, 43), (15, 39), (35, 45), (29, 14), (22, 36), (38, 14), (7, 2), (37, 13), (13, 25), (25, 43), (37, 35), (0, 22), (35, 11), (37, 14), (21, 37), (34, 42), (15, 43), (34, 19), (32, 21), (34, 36), (8, 0), (17, 0), (38, 16), (35, 6), (29, 29), (2, 41), (2, 10), (39, 38), (13, 38), (11, 39), (39, 32), (17, 44), (10, 3), (14, 19), (1, 28), (32, 2), (20, 9), (9, 29), (3, 26), (13, 2), (12, 45), (27, 15), (22, 30), (16, 30), (4, 0), (21, 16), (22, 17), (8, 1), (12, 3), (17, 12), (10, 31), (12, 2), (26, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 37), (14, 16), (23, 25), (17, 20), (40, 27), (40, 8), (12, 10), (12, 19), (3, 19), (17, 35), (24, 25), (23, 5), (18, 9), (12, 12), (16, 18), (26, 40), (20, 15), (13, 13), (6, 34), (20, 38), (16, 39), (22, 37), (27, 14), (11, 26), (1, 32), (3, 6), (31, 37), (37, 27), (14, 2), (17, 39), (18, 2), (20, 0), (6, 25), (10, 11), (36, 8), (40, 17), (0, 2), (27, 39), (38, 16), (37, 21), (36, 24), (8, 13), (30, 13), (8, 31), (14, 26), (4, 11), (39, 28), (22, 7), (26, 27), (31, 25), (9, 26), (36, 2), (15, 18), (34, 33), (39, 0), (13, 34), (4, 32), (5, 27), (32, 16), (39, 23), (4, 2), (6, 39), (5, 11), (9, 10), (18, 33), (6, 23), (37, 5), (28, 9), (10, 7), (34, 10), (18, 20), (26, 35), (23, 0), (30, 6), (13, 2), (36, 9), (18, 25), (28, 0), (38, 36), (24, 32), (31, 6), (11, 28), (4, 5), (6, 37), (35, 1), (28, 23), (4, 14), (40, 4), (19, 38), (9, 11), (1, 8), (7, 10), (9, 18), (23, 29), (23, 14), (35, 18), (26, 34), (30, 33), (34, 9), (8, 37), (5, 17), (39, 13), (1, 22), (25, 22), (29, 28), (8, 8), (28, 18), (15, 0), (19, 11), (29, 40), (19, 16), (17, 24), (15, 39), (25, 37), (10, 16), (11, 0), (4, 0), (22, 16), (16, 35), (35, 2), (23, 9), (40, 28), (12, 35), (36, 35), (5, 14), (35, 32), (20, 23), (26, 25), (39, 33), (40, 39), (25, 15), (27, 12), (29, 12), (20, 16), (21, 16), (21, 11), (36, 1), (21, 28), (39, 25), (40, 16), (2, 3), (39, 31), (12, 7), (14, 11), (11, 21), (37, 39), (14, 27), (29, 9), (16, 31), (24, 16), (16, 7), (6, 33), (23, 37), (10, 6), (19, 15), (38, 24), (22, 35), (9, 33), (16, 3), (33, 25), (9, 2), (5, 2), (7, 30), (13, 39), (33, 26), (4, 1), (38, 17), (1, 38), (13, 38), (10, 17), (34, 24), (35, 5), (33, 34), (12, 9), (6, 16), (32, 21), (33, 23), (39, 27), (30, 34), (13, 35), (7, 29), (2, 36), (35, 31), (4, 35), (29, 20), (33, 1), (39, 2), (38, 7), (8, 40), (36, 17), (38, 2), (38, 39), (7, 1), (11, 36), (3, 2), (38, 22), (1, 29), (40, 13), (40, 26), (7, 0), (13, 32), (3, 32), (32, 40), (21, 29), (33, 15), (32, 11), (36, 21), (31, 19), (12, 8), (13, 20), (0, 8), (4, 30), (22, 0), (33, 18), (40, 7), (7, 32), (18, 8), (25, 25), (22, 8), (6, 0), (28, 38), (29, 27), (24, 28), (3, 5), (14, 36), (37, 6), (3, 22), (20, 35), (5, 0), (22, 18), (16, 0), (9, 22), (5, 6), (38, 4), (36, 26), (23, 39), (3, 10), (1, 13), (30, 8), (26, 1), (8, 22), (8, 25), (26, 28), (4, 38), (18, 17), (27, 30), (24, 15), (30, 10), (26, 33), (17, 21), (32, 25), (31, 24), (2, 21), (10, 23), (21, 2), (1, 7), (35, 15), (40, 20), (1, 6), (1, 37), (9, 21), (30, 23), (25, 6), (15, 36), (35, 27), (3, 23), (2, 29), (19, 25), (9, 20), (28, 37), (31, 36), (10, 22), (2, 7), (7, 23), (36, 4), (12, 17), (0, 16), (23, 3), (0, 21), (0, 38), (0, 40), (31, 20), (32, 4), (5, 15), (11, 24), (30, 5), (37, 4), (35, 11), (0, 1), (17, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 42), (15, 34), (17, 13), (5, 27), (29, 11), (16, 8), (16, 21), (28, 45), (32, 22), (23, 2), (10, 8), (39, 24), (2, 20), (30, 9), (3, 13), (20, 29), (36, 28), (23, 27), (14, 36), (43, 29), (13, 30), (36, 6), (19, 5), (27, 14), (38, 22), (15, 0), (34, 7), (1, 39), (31, 7), (33, 29), (14, 41), (39, 1), (31, 32), (22, 35), (9, 2), (4, 4), (11, 41), (15, 9), (33, 8), (39, 28), (34, 10), (18, 41), (16, 36), (6, 25), (3, 44), (1, 31), (19, 17), (7, 6), (15, 17), (1, 4), (8, 30), (28, 17), (33, 39), (2, 45), (41, 30), (42, 15), (18, 16), (20, 24), (24, 33), (10, 11), (29, 18), (3, 30), (32, 31), (27, 3), (29, 23), (26, 9), (17, 45), (17, 10), (7, 43), (39, 33), (42, 42), (23, 33), (4, 14), (25, 0), (43, 39), (30, 1), (12, 4), (20, 31), (43, 38), (16, 1), (3, 37), (30, 20), (10, 23), (35, 25), (18, 36), (39, 31), (7, 8), (36, 39), (27, 23), (16, 10), (2, 35), (32, 42), (24, 32), (36, 16), (1, 44), (14, 37), (42, 28), (42, 39), (6, 39), (27, 28), (1, 20), (42, 20), (5, 44), (14, 21), (22, 0), (24, 13), (0, 43), (31, 10), (7, 44), (36, 44), (2, 15), (35, 2), (4, 12), (10, 24), (13, 12), (40, 30), (29, 31), (10, 39), (4, 44), (26, 32), (2, 11), (33, 10), (14, 32), (4, 29), (13, 43), (28, 25), (23, 16), (0, 44), (1, 1), (3, 6), (25, 24), (43, 3), (2, 40), (43, 18), (3, 40), (19, 44), (14, 27), (34, 24), (18, 3), (33, 45), (2, 27), (6, 35), (15, 11), (6, 14), (31, 35), (20, 20), (26, 43), (8, 32), (28, 7), (6, 29), (8, 2), (19, 38), (10, 42), (27, 17), (10, 22), (33, 31), (23, 26), (30, 17), (32, 4), (33, 37), (43, 20), (42, 44), (37, 42), (40, 11), (12, 20), (40, 24), (15, 18), (21, 39), (2, 1), (26, 35), (21, 37), (39, 9), (12, 44), (14, 19), (26, 31), (20, 27), (5, 0), (12, 29), (41, 1), (18, 42), (5, 21), (36, 7), (43, 21), (12, 35), (40, 44), (17, 42), (20, 21), (22, 24), (8, 31), (34, 29), (15, 2), (36, 17), (13, 14), (14, 0), (1, 37), (21, 5), (20, 15), (18, 43), (27, 5), (28, 43), (9, 25), (9, 39), (29, 41), (6, 19), (30, 37), (23, 43), (4, 43), (7, 21), (27, 21), (38, 2), (1, 8), (38, 7), (29, 17), (8, 28), (26, 6), (31, 20), (32, 34), (27, 19), (30, 26), (8, 5), (31, 23), (9, 20), (16, 43), (24, 34), (7, 34), (11, 28), (41, 8), (12, 14), (8, 13), (26, 5), (3, 3), (19, 6), (20, 32), (40, 43), (9, 5), (41, 37), (37, 28), (19, 45), (15, 30), (36, 33), (9, 26), (14, 30), (11, 19), (30, 41), (31, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (7, 25), (12, 41), (25, 16), (5, 20), (13, 35), (15, 34), (1, 41), (29, 36), (12, 30), (4, 11), (13, 28), (16, 33), (31, 1), (20, 26), (35, 41), (28, 15), (21, 9), (20, 48), (6, 31), (18, 28), (39, 7), (1, 33), (10, 2), (32, 42), (9, 6), (9, 25), (36, 24), (5, 4), (4, 32), (18, 2), (14, 43), (24, 1), (7, 37), (30, 21), (14, 48), (25, 38), (37, 1), (19, 18), (26, 17), (10, 24), (16, 18), (37, 37), (12, 23), (41, 34), (5, 25), (39, 40), (1, 39), (38, 45), (20, 1), (3, 13), (32, 35), (8, 47), (21, 29), (23, 31), (32, 39), (2, 7), (9, 43), (17, 30), (11, 15), (41, 43), (20, 24), (17, 0), (4, 37), (18, 7), (36, 8), (16, 38), (4, 33), (9, 20), (15, 42), (33, 21), (8, 3), (20, 34), (26, 8), (29, 45), (5, 40), (3, 1), (17, 19), (30, 31), (18, 20), (7, 26), (37, 36), (20, 5), (22, 28), (6, 23), (23, 35), (35, 20), (29, 26), (38, 42), (28, 46), (8, 29), (5, 43), (0, 19), (35, 0), (40, 17), (39, 39), (33, 14), (21, 18), (28, 34), (39, 4), (29, 6), (22, 16), (19, 47), (16, 21), (28, 39), (30, 44), (10, 11), (1, 9), (14, 46), (8, 36), (15, 12), (22, 11), (35, 21), (13, 4), (20, 36), (39, 0), (16, 32), (24, 8), (36, 41), (30, 12), (0, 34), (9, 12), (20, 8), (24, 47), (4, 19), (37, 40), (39, 28), (20, 29), (32, 1), (18, 34), (3, 8), (39, 16), (38, 26), (24, 42), (12, 47), (29, 27), (5, 41), (32, 30), (22, 20), (25, 12), (22, 33), (21, 28), (0, 14), (20, 40), (24, 25), (6, 17), (32, 3), (0, 24), (8, 27), (15, 27), (6, 45), (1, 20), (28, 35), (30, 22), (2, 34), (0, 3), (13, 39), (5, 45), (11, 36), (7, 23), (29, 32), (15, 19), (31, 45), (18, 33), (17, 21), (29, 19), (22, 12), (35, 16), (21, 41), (10, 1), (19, 32), (8, 5), (5, 37), (23, 22), (3, 21), (11, 33), (41, 18), (36, 7), (25, 13), (34, 30), (24, 40), (3, 43), (12, 26), (24, 29), (15, 25), (7, 48), (37, 30), (17, 37), (31, 7), (39, 12), (35, 32), (13, 44), (36, 27), (16, 28), (31, 22), (10, 13), (16, 47), (33, 48), (7, 14), (13, 47), (11, 2), (34, 15), (13, 20), (17, 16), (31, 18), (33, 13), (5, 47), (15, 10), (4, 2), (38, 35), (28, 37), (8, 1), (12, 1), (31, 40), (8, 14), (0, 7), (39, 3), (35, 29), (31, 44), (22, 42), (16, 14), (23, 39), (16, 6), (1, 7), (6, 40), (40, 26), (16, 8), (18, 36), (5, 8), (13, 22), (27, 42), (23, 16), (9, 41), (23, 25), (23, 24), (11, 14), (34, 6), (27, 13), (5, 30), (17, 24), (28, 16), (30, 42), (31, 9), (7, 0), (30, 9), (3, 26), (22, 36), (31, 34), (22, 32), (4, 25), (3, 45), (32, 20), (6, 21), (38, 40), (34, 3), (23, 38), (34, 35), (35, 14), (23, 15), (17, 46), (16, 26), (21, 17), (15, 30), (40, 43), (11, 9), (35, 18), (14, 41), (10, 36), (32, 17), (6, 33), (29, 34), (22, 38), (39, 26), (6, 39), (0, 45), (14, 10), (9, 40), (4, 26), (37, 43), (31, 28), (31, 30), (33, 41), (21, 42), (29, 11), (7, 35), (38, 27), (5, 26), (24, 30), (39, 5), (40, 41), (36, 40), (31, 17), (28, 40), (23, 44), (14, 12), (1, 36), (21, 34), (21, 30), (14, 1), (23, 37), (5, 13), (13, 41), (15, 23), (2, 17), (22, 37), (25, 46), (23, 42), (13, 43), (14, 26), (15, 35), (7, 8), (41, 44), (19, 16), (18, 10), (5, 17), (16, 36), (22, 13), (41, 22), (36, 47), (4, 17), (16, 37), (14, 20), (5, 48), (18, 6), (2, 23), (7, 1), (38, 39), (4, 7), (27, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 32), (14, 29), (4, 14), (28, 25), (36, 10), (19, 10), (37, 8), (19, 1), (20, 14), (42, 20), (16, 22), (39, 40), (31, 4), (8, 5), (23, 34), (22, 33), (2, 31), (40, 45), (26, 34), (36, 25), (35, 5), (25, 0), (7, 9), (24, 16), (8, 40), (19, 46), (33, 32), (42, 32), (39, 13), (35, 34), (23, 41), (9, 28), (19, 45), (33, 29), (17, 36), (6, 1), (24, 18), (24, 10), (3, 14), (38, 16), (2, 8), (29, 9), (32, 20), (40, 33), (4, 2), (40, 11), (6, 28), (18, 23), (1, 48), (39, 12), (26, 24), (10, 18), (30, 21), (16, 2), (30, 30), (34, 9), (11, 28), (24, 44), (15, 27), (41, 3), (11, 47), (23, 42), (40, 12), (14, 8), (17, 37), (35, 40), (33, 34), (38, 6), (23, 11), (13, 22), (36, 19), (3, 41), (36, 40), (38, 22), (18, 13), (14, 24), (4, 10), (24, 25), (18, 0), (39, 20), (8, 20), (12, 37), (41, 42), (26, 19), (29, 29), (32, 11), (41, 23), (26, 48), (20, 5), (26, 18), (39, 45), (19, 15), (5, 7), (36, 44), (27, 10), (26, 27), (3, 18), (31, 44), (10, 16), (42, 37), (20, 42), (8, 22), (19, 47), (15, 18), (13, 34), (14, 20), (22, 10), (29, 15), (37, 31), (2, 4), (4, 24), (37, 1), (23, 38), (14, 14), (29, 17), (29, 26), (21, 11), (34, 34), (34, 15), (0, 23), (41, 4), (8, 9), (32, 27), (32, 28), (10, 12), (1, 1), (1, 34), (3, 4), (39, 18), (35, 35), (41, 7), (15, 6), (23, 23), (16, 9), (14, 12), (33, 45), (3, 32), (25, 30), (4, 46), (12, 19), (4, 25), (11, 23), (25, 28), (11, 44), (12, 16), (20, 0), (3, 24), (42, 1), (15, 42), (7, 45), (42, 16), (21, 47), (6, 9), (26, 21), (9, 25), (14, 33), (15, 21), (3, 44), (40, 24), (1, 42), (21, 25), (14, 28), (12, 3), (31, 36), (32, 30), (24, 40), (27, 30), (2, 20), (24, 12), (21, 1), (21, 39), (6, 42), (39, 11), (17, 18), (6, 41), (32, 44), (36, 24), (42, 4), (31, 12), (1, 5), (39, 27), (37, 44), (13, 31), (39, 46), (5, 29), (32, 42), (10, 1), (7, 24), (18, 21), (12, 11), (42, 46), (18, 12), (37, 47), (20, 20), (34, 42), (30, 32), (19, 6), (30, 9), (7, 21), (29, 46), (33, 26), (5, 5), (13, 5), (20, 33), (22, 42), (35, 27), (35, 18), (25, 37), (37, 30), (0, 20), (40, 31), (2, 1), (2, 10), (38, 18), (21, 23), (27, 40), (41, 36), (32, 47), (9, 24), (12, 21), (11, 24), (32, 26), (10, 8), (3, 28), (4, 44), (0, 41), (42, 47), (20, 19), (25, 2), (6, 47), (19, 29), (8, 4), (18, 41), (30, 33), (35, 16), (35, 22), (29, 38), (18, 32), (20, 18), (15, 35), (29, 32), (9, 45), (32, 1), (17, 14), (7, 16), (11, 42), (28, 10), (0, 3), (25, 4), (8, 47), (15, 11), (0, 26), (3, 42), (1, 14), (15, 39), (34, 17), (18, 45), (42, 40), (0, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 17), (2, 7), (8, 43), (22, 12), (19, 39), (40, 5), (6, 15), (1, 17), (22, 28), (12, 33), (16, 41), (7, 27), (17, 29), (16, 4), (21, 32), (30, 14), (39, 23), (17, 38), (10, 6), (40, 31), (31, 5), (39, 12), (18, 28), (28, 17), (23, 31), (26, 0), (40, 25), (31, 28), (14, 42), (38, 1), (25, 13), (0, 22), (24, 20), (35, 21), (28, 30), (42, 35), (4, 6), (30, 38), (41, 35), (24, 28), (25, 26), (7, 34), (14, 32), (37, 17), (14, 21), (39, 14), (8, 39), (29, 31), (12, 20), (10, 1), (41, 16), (28, 21), (18, 23), (39, 30), (17, 15), (27, 14), (34, 32), (7, 6), (42, 12), (13, 2), (35, 35), (13, 21), (21, 15), (37, 29), (36, 14), (10, 31), (30, 40), (32, 31), (32, 40), (0, 30), (24, 12), (32, 9), (34, 41), (27, 3), (2, 28), (4, 28), (6, 27), (39, 34), (17, 19), (7, 42), (14, 40), (15, 42), (35, 15), (39, 8), (4, 13), (10, 12), (40, 3), (21, 27), (21, 40), (38, 5), (18, 6), (42, 23), (20, 26), (3, 15), (29, 41), (23, 7), (8, 4), (7, 18), (31, 32), (14, 24), (41, 43), (7, 19), (36, 24), (31, 35), (31, 42), (36, 5), (37, 27), (11, 37), (3, 9), (2, 2), (23, 39), (21, 36), (34, 22), (5, 16), (1, 34), (21, 12), (33, 10), (11, 16), (25, 14), (38, 20), (0, 32), (13, 37), (20, 28), (17, 32), (3, 36), (22, 8), (11, 42), (17, 6), (13, 22), (31, 36), (3, 7), (32, 23), (33, 25), (6, 4), (15, 36), (0, 8), (36, 4), (7, 39), (25, 4), (19, 29), (21, 16), (22, 35), (11, 14), (30, 28), (42, 4), (2, 9), (21, 21), (17, 8), (35, 26), (37, 14), (21, 10), (23, 0), (40, 1), (42, 20), (20, 2), (21, 8), (35, 19), (22, 33), (35, 32), (15, 6), (22, 1), (3, 19), (35, 2), (6, 8), (42, 7), (32, 30), (32, 1), (6, 24), (4, 27), (0, 21), (32, 8), (8, 35), (37, 2), (37, 19), (34, 10), (6, 11), (41, 19), (28, 27), (6, 32), (26, 34), (21, 3), (17, 5), (9, 3), (21, 43), (0, 33), (33, 22), (1, 24), (32, 20), (23, 5), (19, 14), (22, 0), (13, 13), (27, 24), (5, 31), (32, 17), (22, 31), (23, 20), (1, 19), (22, 37), (19, 7), (11, 2), (3, 39), (33, 34), (35, 10), (5, 37), (5, 5), (32, 12), (20, 9), (7, 15), (4, 23), (42, 39), (13, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 36), (32, 4), (27, 17), (25, 23), (28, 22), (37, 39), (26, 15), (16, 33), (26, 32), (7, 13), (18, 4), (0, 34), (35, 22), (2, 26), (36, 1), (6, 34), (22, 32), (25, 35), (7, 12), (13, 40), (37, 6), (32, 41), (41, 37), (35, 40), (21, 25), (35, 18), (19, 36), (31, 35), (7, 34), (19, 22), (10, 42), (37, 32), (25, 11), (0, 40), (29, 15), (12, 9), (24, 24), (21, 35), (12, 21), (14, 41), (46, 5), (5, 40), (27, 23), (30, 40), (21, 15), (39, 19), (22, 36), (23, 39), (0, 28), (18, 26), (39, 21), (3, 22), (32, 2), (31, 31), (2, 10), (6, 18), (34, 28), (21, 19), (45, 39), (34, 2), (38, 31), (13, 21), (29, 11), (9, 15), (1, 32), (1, 34), (30, 5), (44, 36), (43, 21), (25, 34), (43, 10), (23, 40), (35, 36), (39, 28), (31, 19), (36, 15), (10, 23), (32, 40), (43, 37), (41, 6), (22, 38), (14, 25), (26, 24), (7, 42), (30, 17), (24, 23), (26, 28), (10, 35), (18, 6), (25, 13), (6, 26), (34, 21), (42, 41), (27, 20), (43, 13), (3, 8), (29, 18), (24, 25), (16, 15), (21, 5), (38, 0), (35, 19), (41, 42), (37, 25), (34, 6), (43, 35), (44, 12), (45, 27), (11, 25), (22, 18), (12, 23), (15, 13), (26, 14), (37, 30), (9, 1), (42, 20), (20, 30), (20, 42), (32, 27), (22, 24), (39, 39), (39, 1), (8, 11), (16, 27), (2, 14), (13, 9), (38, 2), (11, 23), (25, 27), (37, 23), (46, 41), (42, 2), (7, 38), (37, 36), (0, 5), (15, 20), (22, 5), (30, 41), (45, 25), (25, 41), (41, 10), (41, 24), (23, 38), (8, 23), (2, 40), (8, 17), (38, 29), (32, 32), (19, 31), (35, 10), (26, 29), (33, 28), (41, 1), (29, 34), (32, 10), (5, 28), (4, 4), (6, 29), (11, 3), (44, 33), (22, 16), (4, 24), (25, 28), (24, 2), (16, 39), (4, 42), (38, 8), (33, 22), (39, 18), (45, 11), (41, 20), (28, 30), (45, 0), (7, 8), (7, 27), (29, 29), (40, 9), (12, 7), (6, 14), (2, 19), (43, 17), (34, 25), (9, 11), (2, 35), (46, 29), (2, 8), (12, 27), (29, 36), (9, 31), (43, 40), (20, 37), (39, 35), (12, 32), (21, 11), (40, 36), (45, 22), (46, 34), (40, 41), (46, 24), (22, 22), (5, 17), (23, 32), (39, 33), (45, 41), (5, 24), (20, 15), (10, 36), (36, 23), (6, 13), (42, 15), (4, 11), (5, 22), (4, 21), (4, 37), (44, 15), (38, 26), (28, 36), (10, 8), (20, 7), (44, 16), (35, 1), (31, 29), (4, 39), (10, 24), (10, 20), (6, 41), (38, 14), (17, 0), (24, 11), (13, 15), (25, 7), (23, 42), (30, 3), (20, 31), (34, 36), (23, 15), (38, 12), (18, 10), (2, 31), (1, 35), (14, 32), (14, 31), (36, 17), (1, 14), (11, 19), (32, 18), (36, 21), (19, 40), (42, 10), (30, 24), (8, 4), (26, 38), (19, 2), (1, 9), (15, 22), (18, 13), (24, 19), (27, 28), (21, 27), (46, 40), (7, 10), (15, 4), (9, 12), (2, 30), (40, 10), (42, 31), (1, 17), (29, 0), (44, 26), (24, 6), (26, 27), (18, 31), (14, 42), (3, 33), (19, 33), (36, 39), (11, 16), (21, 34), (19, 21), (7, 29), (43, 8), (14, 17), (26, 18), (0, 11), (16, 32), (16, 29), (13, 24), (1, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 44), (30, 34), (25, 23), (36, 42), (18, 32), (6, 26), (43, 20), (35, 43), (23, 43), (28, 43), (21, 1), (13, 23), (3, 18), (31, 5), (40, 28), (43, 9), (44, 7), (2, 33), (1, 33), (29, 42), (14, 19), (38, 13), (25, 18), (37, 41), (31, 9), (18, 3), (7, 30), (11, 28), (15, 19), (26, 40), (17, 14), (16, 34), (27, 37), (28, 1), (0, 45), (3, 46), (18, 6), (28, 40), (18, 12), (6, 10), (14, 16), (19, 40), (39, 45), (30, 45), (43, 3), (12, 42), (11, 23), (42, 9), (17, 31), (19, 32), (12, 5), (37, 23), (15, 20), (5, 11), (3, 0), (24, 25), (42, 11), (26, 30), (15, 43), (28, 2), (4, 43), (34, 0), (37, 43), (22, 8), (11, 40), (13, 32), (29, 37), (15, 17), (21, 36), (14, 30), (20, 26), (35, 12), (17, 12), (34, 36), (40, 21), (12, 31), (1, 46), (3, 36), (29, 0), (38, 4), (17, 1), (1, 10), (15, 25), (28, 24), (12, 14), (35, 4), (0, 15), (41, 25), (27, 35), (32, 1), (6, 17), (19, 36), (25, 40), (41, 16), (19, 0), (14, 44), (0, 28), (30, 27), (34, 30), (39, 8), (29, 16), (42, 5), (7, 35), (42, 35), (41, 28), (1, 19), (43, 32), (9, 44), (23, 5), (6, 28), (12, 20), (19, 10), (1, 26), (25, 33), (25, 19), (15, 40), (43, 1), (11, 32), (12, 4), (37, 13), (27, 19), (24, 22), (39, 28), (37, 40), (4, 0), (43, 44), (32, 25), (0, 20), (32, 19), (32, 35), (2, 9), (30, 4), (18, 28), (38, 46), (7, 10), (44, 12), (24, 13), (23, 46), (40, 7), (0, 32), (18, 46), (36, 19), (21, 21), (11, 29), (38, 14), (37, 24), (5, 18), (26, 16), (33, 32), (16, 15), (20, 29), (44, 36), (41, 24), (33, 0), (25, 26), (37, 39), (13, 30), (29, 3), (28, 29), (36, 18), (40, 44), (6, 43), (33, 3), (14, 34), (43, 39), (18, 36), (7, 11), (1, 7), (6, 12), (19, 30), (25, 35), (21, 13), (4, 37), (2, 31), (8, 16), (38, 31), (14, 29), (41, 8), (44, 6), (40, 36), (18, 10), (10, 29), (23, 10), (30, 42), (27, 10), (9, 2), (14, 45), (40, 25), (27, 13), (20, 1), (3, 20), (39, 10), (41, 2), (12, 24), (7, 39), (29, 43), (44, 30), (34, 27), (16, 35), (38, 0), (17, 15), (13, 26), (11, 46), (0, 18), (18, 8), (40, 19), (40, 41), (11, 19), (40, 15), (20, 8), (19, 11), (38, 35), (5, 4), (43, 15), (41, 21), (0, 34), (2, 28), (10, 37), (11, 44), (24, 34), (12, 23), (22, 21), (18, 11), (36, 2), (37, 18), (42, 37), (40, 12), (6, 20), (41, 32), (9, 8), (26, 15), (13, 13), (38, 3), (23, 28), (8, 31), (14, 46), (12, 40), (40, 13), (21, 5), (40, 22), (36, 6), (33, 20), (10, 11), (30, 44), (21, 43), (41, 22), (42, 25), (33, 22), (15, 39), (16, 1), (23, 21), (23, 38), (28, 16), (42, 1), (12, 0), (25, 27), (0, 11), (16, 41), (30, 2), (25, 14), (40, 34), (37, 11), (9, 39), (13, 44), (18, 35), (5, 24), (33, 17), (14, 6), (34, 22), (32, 11), (43, 28), (6, 22), (22, 0), (7, 0), (24, 44), (12, 46), (8, 26), (10, 45), (21, 28), (37, 44), (37, 1), (0, 33), (12, 1), (2, 32), (19, 28), (21, 42), (41, 19), (38, 44), (18, 31), (8, 24), (21, 30), (44, 16), (29, 36), (16, 7), (15, 29), (26, 14), (27, 27), (15, 22), (7, 32), (3, 28), (14, 4), (42, 17), (9, 17), (11, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 31), (15, 37), (2, 35), (6, 1), (27, 15), (33, 15), (16, 0), (22, 0), (17, 35), (26, 4), (2, 31), (34, 18), (13, 26), (39, 11), (39, 18), (37, 33), (17, 1), (37, 12), (21, 21), (5, 0), (32, 36), (14, 24), (2, 33), (21, 16), (2, 23), (10, 1), (8, 17), (25, 33), (17, 12), (9, 30), (23, 28), (15, 7), (8, 23), (22, 26), (10, 23), (39, 28), (0, 7), (5, 35), (34, 24), (13, 19), (17, 6), (38, 19), (10, 27), (7, 34), (34, 23), (25, 9), (17, 25), (24, 36), (33, 34), (22, 27), (33, 8), (16, 11), (35, 12), (5, 13), (2, 12), (29, 20), (18, 21), (33, 23), (31, 32), (13, 1), (37, 2), (39, 24), (4, 26), (8, 32), (1, 4), (18, 34), (31, 19), (35, 33), (1, 38), (26, 21), (27, 8), (33, 37), (26, 5), (23, 15), (20, 26), (38, 20), (5, 21), (8, 37), (36, 3), (35, 18), (36, 2), (16, 37), (34, 13), (30, 18), (6, 39), (20, 37), (12, 24), (14, 9), (25, 39), (37, 23), (26, 38), (13, 13), (24, 7), (21, 6), (22, 38), (18, 29), (27, 39), (16, 23), (32, 7), (12, 1), (15, 39), (26, 9), (3, 7), (19, 39), (10, 10), (17, 30), (26, 35), (38, 11), (26, 33), (5, 8), (34, 33), (0, 5), (29, 11), (22, 20), (10, 21), (37, 35), (32, 31), (21, 12), (20, 17), (21, 26), (13, 29), (36, 30), (10, 29), (7, 2), (1, 11), (38, 16), (16, 29), (5, 4), (19, 7), (3, 2), (7, 30), (8, 4), (12, 33), (29, 1), (21, 9), (35, 20), (35, 39), (19, 0), (9, 23), (25, 29), (36, 28), (12, 38), (37, 24), (24, 5), (27, 21), (16, 17), (9, 19), (9, 17), (21, 10), (0, 29), (4, 11), (37, 20), (6, 20), (4, 24), (22, 24), (5, 17), (16, 10), (8, 13), (10, 3), (8, 9), (0, 33), (28, 24), (33, 1), (11, 39), (16, 30), (20, 7), (14, 20), (11, 30), (15, 38), (10, 19), (25, 32), (10, 33), (7, 14), (29, 26), (28, 2), (35, 11), (13, 38), (9, 21), (36, 21), (1, 0), (21, 34), (39, 29), (16, 26), (14, 6), (25, 21), (36, 37), (30, 21), (0, 36), (8, 19), (19, 28), (28, 35), (8, 31), (4, 16), (39, 7), (0, 12), (28, 5), (7, 17), (9, 9), (10, 36), (33, 10), (39, 21), (4, 27), (29, 28), (28, 0), (8, 11), (22, 7), (8, 3), (0, 11), (19, 2), (37, 6), (30, 25), (31, 8), (6, 10), (11, 16), (37, 18), (6, 8), (5, 32), (9, 24), (15, 35), (36, 5), (0, 4), (36, 36), (16, 15), (16, 22), (6, 0), (13, 16), (1, 35), (36, 11), (1, 7), (7, 39), (38, 7), (16, 32), (10, 26), (4, 13), (14, 11), (8, 33), (35, 16), (29, 18), (1, 37), (25, 34), (16, 34), (10, 39), (6, 7), (21, 36), (16, 31), (16, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 30), (45, 22), (0, 25), (7, 28), (22, 26), (21, 34), (37, 10), (23, 37), (38, 35), (18, 6), (45, 10), (43, 1), (37, 25), (22, 9), (29, 26), (34, 19), (3, 25), (43, 37), (2, 21), (32, 18), (45, 2), (18, 32), (31, 18), (11, 13), (19, 32), (37, 16), (29, 2), (14, 19), (45, 28), (20, 14), (23, 31), (42, 18), (30, 19), (24, 7), (30, 32), (15, 30), (33, 1), (44, 21), (29, 22), (8, 24), (18, 33), (9, 23), (43, 6), (43, 14), (20, 19), (3, 24), (43, 23), (27, 16), (26, 11), (13, 18), (35, 11), (36, 18), (10, 2), (29, 7), (9, 9), (39, 39), (45, 14), (21, 18), (37, 39), (11, 1), (33, 6), (5, 38), (34, 33), (22, 0), (12, 33), (40, 31), (14, 13), (22, 34), (7, 11), (27, 19), (41, 27), (4, 3), (32, 25), (5, 14), (13, 16), (27, 20), (15, 4), (37, 4), (5, 29), (27, 17), (8, 16), (40, 20), (28, 23), (7, 6), (30, 37), (23, 14), (24, 32), (14, 14), (41, 35), (23, 26), (25, 14), (32, 38), (23, 11), (5, 18), (39, 6), (7, 16), (10, 28), (23, 15), (33, 16), (40, 8), (26, 19), (14, 32), (16, 13), (36, 21), (31, 32), (25, 22), (13, 4), (9, 20), (35, 37), (34, 34), (43, 22), (13, 23), (33, 13), (19, 31), (20, 35), (0, 13), (9, 2), (1, 8), (9, 18), (13, 39), (26, 33), (37, 1), (38, 17), (22, 17), (36, 17), (5, 32), (26, 37), (40, 18), (34, 38), (44, 30), (4, 33), (30, 25), (17, 29), (36, 25), (18, 34), (3, 28), (5, 10), (12, 15), (12, 32), (19, 14), (7, 5), (5, 33), (9, 31), (2, 9), (14, 27), (8, 32), (1, 21), (26, 0), (12, 36), (18, 9), (27, 21), (25, 19), (11, 5), (27, 5), (42, 33), (38, 33), (8, 33), (34, 15), (12, 9), (35, 18), (36, 3), (2, 37), (39, 9), (32, 12), (9, 34), (17, 27), (10, 13), (26, 30), (18, 28), (6, 4), (44, 5), (1, 1), (11, 30), (20, 21), (44, 19), (16, 16), (19, 3), (28, 25), (27, 10), (42, 9), (10, 30), (10, 7), (8, 14), (9, 33), (17, 16), (21, 39), (4, 4), (12, 26), (5, 35), (37, 15), (3, 12), (13, 0), (27, 3), (25, 18), (28, 5), (15, 20), (13, 10), (2, 4), (4, 32), (22, 20), (0, 2), (25, 12), (10, 31), (27, 1), (38, 12), (7, 30), (24, 26), (35, 35), (1, 15), (16, 25), (0, 33), (5, 16), (30, 26), (1, 4), (41, 30), (33, 26), (20, 22), (8, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 5), (11, 18), (24, 0), (27, 37), (2, 34), (33, 13), (14, 35), (14, 16), (20, 0), (29, 23), (29, 16), (27, 1), (7, 11), (15, 25), (27, 15), (11, 14), (0, 13), (32, 38), (25, 23), (5, 36), (13, 1), (6, 31), (6, 20), (9, 26), (17, 34), (39, 7), (22, 32), (12, 30), (4, 13), (4, 7), (14, 39), (12, 29), (35, 25), (10, 2), (24, 23), (33, 3), (25, 25), (35, 33), (4, 0), (3, 16), (8, 7), (18, 1), (9, 30), (16, 20), (26, 26), (38, 33), (39, 33), (25, 14), (39, 22), (21, 19), (3, 0), (1, 3), (15, 0), (3, 14), (31, 35), (16, 22), (24, 2), (17, 33), (7, 16), (17, 37), (39, 12), (37, 3), (23, 22), (5, 14), (3, 6), (33, 8), (40, 16), (25, 27), (10, 32), (38, 8), (40, 11), (39, 24), (10, 8), (3, 37), (10, 28), (34, 32), (6, 30), (21, 22), (18, 3), (14, 15), (25, 32), (37, 14), (2, 26), (31, 20), (7, 12), (3, 34), (18, 14), (8, 21), (39, 21), (0, 8), (0, 17), (8, 26), (27, 38), (3, 3), (29, 0), (7, 30), (39, 18), (0, 24), (15, 21), (23, 35), (9, 22), (17, 32), (7, 28), (33, 10), (27, 0), (24, 13), (38, 5), (6, 11), (35, 17), (22, 35), (33, 29), (22, 19), (20, 5), (3, 12), (30, 17), (22, 33), (21, 16), (17, 22), (12, 21), (0, 39), (6, 37), (17, 17), (10, 3), (23, 25), (6, 16), (26, 10), (1, 29), (28, 8), (28, 23), (11, 32), (34, 31), (25, 0), (27, 25), (35, 19), (25, 18), (13, 17), (18, 13), (7, 34), (9, 21), (4, 38), (15, 4), (2, 8), (19, 1), (0, 16), (6, 25), (3, 5), (11, 26), (38, 6), (11, 20), (10, 18), (2, 15), (10, 31), (8, 36), (19, 30), (2, 21), (9, 39), (35, 22), (30, 29), (5, 19), (26, 30), (29, 32), (3, 33), (13, 13), (26, 33), (38, 35), (5, 27), (38, 34), (13, 2), (9, 32), (1, 32), (17, 4), (39, 37), (34, 11), (17, 8), (9, 1), (34, 29), (18, 10), (19, 34), (25, 13), (32, 27), (37, 26), (2, 22), (31, 6), (19, 19), (40, 9), (37, 38), (6, 33), (39, 23), (7, 7), (15, 20), (2, 16), (39, 13), (28, 2), (1, 18), (28, 10), (33, 9), (36, 13), (25, 17), (18, 25), (18, 12), (29, 11), (3, 32), (31, 17), (21, 25), (10, 19), (16, 38), (2, 17), (4, 2), (16, 21), (15, 5), (27, 2), (36, 26), (14, 23), (6, 4), (12, 6), (22, 3), (29, 29), (33, 11), (2, 36), (8, 0), (18, 18), (18, 26), (18, 16), (7, 39), (11, 4), (25, 11), (7, 29), (36, 28), (31, 21), (13, 6), (6, 12), (21, 10), (19, 27), (6, 23), (35, 37), (11, 2), (34, 26), (24, 28), (14, 37), (25, 30), (17, 24), (16, 32), (39, 27), (15, 7), (21, 11), (23, 4), (38, 9), (6, 5), (4, 34), (19, 31), (24, 26), (2, 1), (40, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 22), (4, 30), (28, 8), (10, 20), (9, 22), (23, 0), (22, 30), (30, 22), (27, 23), (27, 13), (10, 35), (13, 23), (24, 0), (5, 1), (1, 13), (16, 6), (29, 26), (8, 36), (3, 13), (33, 12), (24, 4), (24, 38), (14, 7), (34, 4), (17, 17), (17, 40), (35, 32), (13, 1), (23, 34), (3, 38), (36, 4), (2, 20), (2, 2), (33, 35), (17, 37), (24, 14), (14, 16), (17, 30), (28, 16), (23, 29), (6, 15), (28, 32), (14, 31), (1, 27), (23, 5), (39, 13), (36, 7), (37, 23), (9, 36), (31, 9), (9, 7), (38, 22), (32, 7), (13, 33), (3, 4), (24, 25), (38, 16), (9, 33), (5, 29), (35, 13), (19, 35), (15, 15), (18, 18), (32, 40), (28, 6), (6, 37), (11, 23), (1, 2), (39, 22), (4, 2), (7, 39), (0, 38), (40, 24), (35, 35), (6, 30), (27, 19), (36, 20), (33, 38), (34, 7), (5, 31), (1, 28), (21, 26), (14, 29), (11, 14), (39, 33), (13, 29), (27, 8), (4, 24), (7, 13), (36, 23), (8, 2), (4, 0), (10, 2), (36, 12), (2, 16), (22, 14), (3, 8), (2, 7), (23, 25), (7, 38), (24, 10), (35, 8), (26, 39), (38, 20), (20, 7), (7, 14), (25, 23), (15, 36), (35, 16), (24, 11), (33, 40), (25, 7), (25, 39), (21, 29), (15, 37), (8, 8), (11, 24), (15, 25), (10, 5), (31, 8), (38, 36), (33, 4), (26, 14), (9, 27), (4, 23), (10, 34), (12, 12), (31, 40), (12, 34), (1, 40), (29, 16), (18, 19), (21, 16), (7, 26), (2, 24), (30, 30), (30, 18), (4, 21), (26, 7), (11, 15), (22, 24), (18, 30), (3, 11), (15, 0), (4, 6), (3, 40), (8, 16), (39, 35), (39, 19), (17, 9), (27, 36), (9, 35), (19, 16), (25, 6), (8, 24), (28, 5), (40, 15), (6, 18), (29, 32), (17, 21), (24, 17), (28, 35), (13, 21), (30, 10), (15, 21), (10, 12), (2, 1), (21, 14), (39, 9), (31, 35), (25, 1), (29, 0), (13, 31), (35, 12), (8, 27), (5, 38), (25, 11), (9, 30), (23, 35), (33, 28), (17, 14), (0, 23), (22, 19), (25, 19), (15, 26), (8, 20), (29, 2), (39, 14), (32, 28), (23, 19), (34, 12), (8, 32), (32, 4), (9, 8), (22, 15), (18, 24), (30, 15), (4, 1), (20, 19), (36, 29), (31, 14), (15, 8), (7, 28), (3, 30), (2, 39), (2, 21), (30, 21), (17, 25), (16, 7), (26, 25), (7, 22), (21, 13), (28, 37), (39, 18), (1, 24), (14, 2), (37, 38), (27, 2), (5, 18), (5, 21), (33, 32), (6, 33), (7, 31), (16, 0), (16, 34), (22, 27), (23, 3), (24, 34), (40, 9), (10, 1), (17, 11), (3, 35), (27, 4), (9, 4), (3, 12), (7, 8), (34, 39), (15, 1), (33, 3), (3, 26), (15, 34), (34, 22), (4, 37), (9, 29), (39, 34), (32, 12), (39, 37), (37, 30), (13, 35), (37, 4), (39, 6), (2, 10), (14, 14), (19, 30), (21, 12), (31, 36), (2, 36), (27, 40), (28, 33), (2, 40), (23, 4), (25, 18), (38, 17), (33, 16), (23, 27), (35, 30), (29, 14), (8, 5), (24, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 33), (40, 0), (17, 9), (1, 12), (7, 1), (23, 11), (24, 21), (0, 40), (33, 10), (26, 18), (36, 15), (26, 4), (14, 19), (6, 5), (31, 29), (32, 0), (20, 12), (20, 22), (27, 37), (23, 15), (7, 8), (21, 30), (16, 35), (19, 5), (36, 27), (20, 23), (32, 21), (13, 40), (15, 20), (27, 31), (14, 38), (35, 24), (38, 28), (32, 19), (17, 28), (27, 3), (37, 20), (12, 33), (4, 5), (4, 17), (39, 25), (33, 34), (15, 3), (8, 3), (21, 37), (24, 22), (23, 28), (26, 6), (17, 33), (14, 24), (23, 34), (25, 17), (29, 1), (13, 22), (1, 20), (40, 23), (15, 33), (21, 0), (30, 26), (23, 29), (11, 35), (6, 3), (7, 24), (25, 27), (16, 13), (5, 7), (15, 16), (32, 9), (5, 8), (21, 10), (22, 4), (17, 22), (36, 13), (11, 4), (12, 32), (10, 20), (12, 27), (10, 2), (28, 21), (39, 13), (18, 13), (20, 18), (26, 26), (12, 37), (19, 26), (27, 34), (34, 20), (2, 18), (39, 33), (4, 13), (28, 19), (28, 36), (5, 37), (37, 32), (12, 30), (31, 7), (18, 16), (13, 29), (28, 1), (18, 6), (27, 8), (13, 3), (6, 27), (40, 31), (37, 6), (26, 15), (34, 40), (0, 31), (4, 15), (32, 23), (28, 12), (33, 9), (36, 25), (33, 14), (28, 20), (18, 4), (18, 31), (16, 34), (28, 31), (8, 22), (23, 14), (16, 15), (26, 10), (32, 26), (3, 2), (34, 24), (22, 23), (31, 23), (15, 15), (19, 25), (19, 29), (22, 14), (38, 12), (6, 4), (30, 8), (1, 9), (15, 12), (1, 22), (9, 9), (26, 24), (37, 33), (29, 3), (26, 38), (34, 28), (20, 27), (37, 25), (17, 32), (31, 0), (40, 6), (38, 26), (14, 18), (10, 12), (2, 2), (4, 1), (14, 35), (15, 18), (25, 8), (4, 7), (38, 10), (13, 12), (3, 18), (14, 29), (30, 3), (36, 37), (24, 36), (19, 2), (28, 24), (12, 4), (36, 7), (5, 12), (2, 25), (13, 28), (20, 17), (6, 24), (35, 26), (6, 7), (31, 2), (13, 13), (3, 24), (7, 29), (17, 7), (18, 25), (38, 3), (13, 2), (16, 39), (27, 7), (4, 28), (34, 0), (3, 40), (0, 33), (15, 1), (4, 12), (35, 38), (40, 2), (9, 35), (31, 33), (27, 0), (31, 21), (19, 15), (11, 18), (12, 38), (29, 25), (12, 40), (31, 19), (36, 20), (4, 35), (1, 30), (25, 4), (23, 3), (7, 12), (8, 20), (32, 1), (34, 8), (34, 32), (29, 11), (20, 33), (23, 40), (33, 0), (5, 10), (13, 32), (32, 28), (23, 35), (29, 38), (2, 20), (29, 26), (17, 34), (31, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 23), (21, 23), (32, 13), (9, 13), (34, 19), (16, 37), (45, 6), (13, 21), (42, 37), (8, 0), (48, 11), (48, 39), (45, 33), (27, 3), (14, 26), (41, 6), (36, 26), (19, 23), (3, 23), (10, 39), (25, 14), (27, 6), (5, 32), (23, 10), (37, 5), (26, 14), (21, 29), (22, 32), (20, 17), (8, 35), (11, 34), (15, 13), (35, 30), (33, 34), (22, 35), (29, 35), (12, 1), (35, 23), (6, 16), (24, 8), (28, 37), (5, 30), (1, 10), (23, 31), (27, 18), (41, 33), (20, 19), (2, 24), (38, 32), (11, 35), (42, 22), (47, 14), (47, 31), (32, 24), (29, 18), (5, 35), (1, 17), (22, 7), (17, 37), (5, 5), (7, 15), (1, 34), (8, 4), (9, 7), (24, 39), (32, 36), (19, 20), (45, 29), (23, 32), (7, 38), (24, 29), (35, 22), (39, 27), (19, 26), (15, 7), (39, 14), (15, 1), (16, 12), (29, 14), (14, 13), (28, 27), (33, 32), (37, 35), (18, 8), (34, 27), (43, 19), (0, 39), (35, 31), (21, 17), (21, 18), (35, 15), (22, 30), (32, 40), (18, 31), (46, 7), (1, 24), (43, 24), (14, 37), (9, 18), (43, 36), (26, 26), (3, 25), (47, 30), (11, 10), (25, 36), (16, 28), (5, 3), (5, 28), (19, 37), (23, 18), (30, 17), (9, 1), (23, 12), (10, 20), (24, 1), (20, 26), (40, 6), (2, 35), (46, 26), (33, 20), (33, 7), (34, 22), (33, 19), (41, 28), (9, 15), (47, 26), (18, 22), (31, 2), (40, 16), (15, 33), (25, 30), (44, 33), (10, 23), (37, 22), (36, 30), (42, 4), (46, 21), (15, 10), (13, 5), (12, 7), (44, 1), (21, 35), (6, 39), (36, 25), (14, 25), (34, 21), (21, 24), (36, 22), (17, 13), (26, 29), (10, 6), (17, 21), (18, 37), (3, 32), (10, 26), (33, 11), (33, 38), (20, 20), (41, 19), (6, 36), (7, 3), (6, 35), (26, 10), (24, 38), (4, 24), (10, 28), (5, 23), (13, 26), (3, 28), (47, 5), (45, 19), (17, 36), (34, 28), (32, 2), (34, 33), (6, 19), (43, 33), (26, 6), (15, 29), (14, 6), (0, 28), (18, 36), (3, 8), (13, 14), (1, 21), (4, 7), (15, 23), (5, 29), (10, 24), (42, 0), (44, 28), (26, 27), (4, 33), (17, 16), (34, 25), (35, 10), (34, 15), (17, 14), (48, 9), (27, 4), (20, 8), (3, 0), (23, 17), (36, 29), (35, 39), (14, 20), (29, 21), (4, 13), (17, 29), (18, 15), (15, 40), (42, 5), (17, 10), (25, 27), (40, 31), (20, 34), (45, 5), (12, 25), (20, 18), (8, 19), (38, 3), (35, 0), (36, 19), (24, 5), (43, 25), (43, 27), (23, 13), (3, 1), (16, 34), (32, 29), (14, 19), (46, 22), (11, 8), (22, 15), (14, 39), (44, 27), (29, 28), (41, 40), (44, 37), (26, 16), (41, 3), (1, 25), (38, 10), (11, 36), (37, 36), (4, 38), (46, 15), (46, 18), (28, 29), (9, 2), (33, 28), (2, 32), (42, 16), (35, 4), (42, 14), (41, 22), (12, 3), (3, 29), (11, 0), (23, 7), (29, 11), (1, 22), (28, 39), (7, 7), (42, 39), (42, 17), (31, 35), (17, 30), (38, 36), (36, 37), (15, 35), (26, 32), (29, 27), (17, 12), (12, 26), (37, 30), (16, 13), (33, 16), (18, 7), (19, 32), (25, 39), (26, 38), (2, 12), (17, 32), (22, 14), (21, 39), (25, 9), (33, 36), (48, 35), (39, 0), (27, 8), (47, 37), (22, 22), (13, 3), (22, 4), (41, 30), (34, 10), (42, 26), (17, 27), (40, 17), (5, 20), (36, 8), (38, 35), (22, 36), (9, 11), (46, 5), (8, 3), (38, 14), (44, 19), (19, 8), (24, 7), (13, 10), (22, 5), (18, 32), (4, 9), (16, 0), (26, 22), (5, 11), (28, 5), (3, 14), (31, 24), (38, 15), (45, 37), (34, 7), (36, 39), (15, 12), (19, 2), (45, 24), (36, 9), (2, 1), (5, 14), (9, 40), (34, 32), (33, 22), (40, 35), (23, 3), (43, 14), (9, 25), (21, 15), (46, 23), (26, 12), (34, 8), (20, 4), (16, 33), (27, 27), (18, 11), (4, 12), (35, 27), (26, 28), (39, 17), (0, 21), (40, 36), (43, 34), (12, 14), (39, 37), (11, 37), (39, 19), (7, 5), (32, 19), (2, 40), (41, 14), (20, 3), (36, 11), (12, 11), (9, 28), (1, 19), (46, 29), (18, 29), (35, 37), (45, 23), (3, 9), (14, 32), (2, 8), (28, 32), (48, 23), (35, 21), (28, 6), (36, 34), (43, 15), (40, 27), (13, 23), (4, 5), (0, 14), (4, 37), (47, 0), (0, 27), (26, 5), (6, 34), (28, 20), (32, 32), (33, 39), (44, 16), (36, 0), (43, 6), (45, 13), (39, 18), (18, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 6), (24, 38), (4, 40), (14, 18), (6, 15), (17, 22), (17, 8), (18, 17), (9, 7), (44, 14), (0, 40), (25, 1), (21, 14), (27, 39), (33, 24), (43, 37), (8, 15), (31, 2), (5, 11), (23, 8), (16, 20), (27, 32), (32, 16), (42, 0), (3, 15), (0, 9), (29, 3), (2, 21), (21, 18), (29, 31), (44, 33), (20, 18), (37, 5), (15, 4), (33, 27), (8, 32), (24, 17), (18, 33), (1, 6), (0, 22), (17, 30), (24, 10), (34, 24), (27, 35), (24, 32), (13, 32), (40, 7), (3, 29), (6, 9), (27, 14), (36, 29), (26, 20), (22, 19), (10, 4), (22, 3), (33, 32), (31, 33), (25, 11), (24, 1), (24, 25), (11, 27), (14, 9), (36, 30), (29, 8), (4, 2), (9, 2), (27, 38), (34, 9), (36, 3), (37, 14), (30, 32), (9, 40), (43, 11), (30, 35), (31, 19), (39, 30), (18, 22), (6, 8), (24, 20), (44, 0), (0, 34), (26, 33), (6, 22), (25, 28), (36, 4), (9, 25), (15, 27), (20, 5), (31, 27), (31, 34), (11, 17), (22, 25), (40, 32), (20, 21), (2, 18), (37, 26), (26, 39), (20, 13), (19, 29), (0, 30), (43, 23), (16, 3), (24, 5), (6, 36), (42, 19), (42, 10), (33, 31), (28, 24), (9, 23), (24, 16), (36, 37), (8, 11), (14, 22), (43, 29), (28, 26), (8, 34), (35, 11), (17, 11), (26, 28), (7, 24), (17, 1), (23, 23), (13, 31), (28, 11), (12, 19), (14, 30), (13, 3), (16, 16), (18, 36), (16, 19), (15, 23), (5, 23), (14, 7), (25, 5), (17, 21), (33, 28), (7, 36), (19, 28), (41, 20), (1, 4), (20, 19), (28, 38), (10, 26), (12, 21), (28, 35), (17, 36), (27, 23), (21, 26), (12, 32), (0, 11), (18, 10), (37, 21), (24, 9), (33, 9), (5, 19), (6, 13), (11, 7), (34, 18), (16, 1), (11, 32), (12, 11), (30, 27), (38, 1), (30, 8), (7, 13), (16, 32), (33, 13), (44, 39), (20, 32), (40, 6), (39, 19), (10, 40), (33, 8), (11, 13), (40, 38), (30, 39), (21, 0), (8, 36), (11, 33), (11, 2), (17, 39), (40, 30), (1, 3), (26, 36), (1, 38), (35, 3), (38, 20), (36, 8), (23, 5), (6, 25), (6, 1), (20, 27), (18, 8), (2, 24), (30, 40), (31, 37), (24, 36), (15, 29), (34, 38), (20, 37), (26, 3), (43, 30), (14, 19), (23, 21), (30, 23), (24, 19), (8, 18), (25, 4), (38, 35), (38, 8), (9, 13), (32, 35), (31, 11), (30, 21), (14, 21), (22, 33), (19, 25), (17, 33), (40, 21), (42, 5), (8, 8), (18, 3), (40, 10), (10, 23), (17, 23), (8, 31), (43, 2), (43, 38), (10, 27), (35, 25), (28, 13), (13, 40), (4, 20), (2, 20), (38, 19), (8, 9), (8, 23), (40, 34), (29, 29), (19, 17), (3, 0), (32, 7), (39, 13), (35, 15), (10, 13), (35, 27), (24, 28), (2, 7), (31, 35), (25, 27), (11, 1), (44, 13), (2, 33), (24, 6), (42, 16), (7, 21), (0, 4), (5, 26), (8, 13), (19, 0), (14, 4), (12, 14), (22, 18), (20, 16), (39, 26), (43, 27), (40, 13), (34, 31), (8, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 19), (25, 40), (38, 8), (33, 12), (14, 7), (22, 21), (4, 21), (23, 30), (8, 27), (9, 32), (20, 34), (10, 5), (26, 29), (7, 25), (27, 45), (40, 26), (0, 8), (18, 40), (6, 0), (42, 20), (11, 27), (24, 35), (27, 20), (35, 45), (41, 1), (23, 45), (40, 45), (8, 9), (8, 14), (31, 2), (30, 39), (0, 12), (28, 34), (0, 28), (11, 24), (40, 24), (15, 40), (16, 45), (0, 1), (23, 7), (37, 2), (4, 17), (34, 19), (18, 37), (9, 6), (5, 33), (20, 33), (14, 33), (27, 24), (38, 34), (5, 29), (35, 11), (29, 21), (37, 41), (37, 10), (34, 33), (3, 24), (39, 45), (40, 10), (33, 29), (26, 19), (0, 35), (30, 17), (34, 43), (1, 33), (38, 11), (6, 34), (30, 38), (39, 24), (21, 34), (12, 24), (41, 3), (24, 21), (26, 21), (41, 33), (11, 23), (37, 18), (32, 6), (40, 41), (33, 28), (36, 42), (3, 23), (36, 37), (30, 37), (12, 2), (23, 13), (15, 25), (15, 9), (3, 5), (22, 35), (15, 10), (24, 7), (9, 42), (22, 4), (3, 0), (11, 17), (16, 44), (16, 0), (5, 1), (12, 18), (30, 4), (40, 43), (33, 16), (10, 4), (14, 34), (32, 11), (16, 3), (14, 28), (10, 0), (24, 11), (31, 35), (22, 20), (27, 43), (20, 3), (2, 7), (12, 40), (37, 29), (19, 2), (5, 22), (35, 20), (39, 1), (4, 19), (22, 25), (11, 42), (26, 28), (36, 41), (3, 17), (41, 25), (41, 17), (34, 40), (14, 20), (40, 31), (21, 17), (31, 19), (35, 2), (26, 5), (34, 3), (6, 23), (16, 43), (15, 33), (14, 38), (36, 23), (32, 21), (37, 22), (28, 45), (27, 22), (13, 4), (14, 31), (33, 45), (4, 45), (36, 3), (21, 40), (0, 22), (5, 39), (16, 16), (13, 9), (40, 20), (3, 41), (15, 27), (37, 39), (9, 36), (0, 34), (17, 34), (12, 30), (38, 16), (23, 24), (8, 20), (0, 39), (27, 15), (28, 8), (22, 40), (10, 36), (26, 38), (23, 36), (17, 30), (11, 4), (27, 40), (25, 25), (0, 32), (26, 4), (30, 11), (31, 34), (12, 27), (2, 17), (35, 29), (24, 43), (35, 10), (18, 11), (38, 14), (42, 34), (23, 18), (6, 21), (10, 27), (26, 41), (35, 19), (38, 20), (4, 12), (10, 26), (13, 19), (33, 18), (13, 28), (35, 38), (0, 11), (25, 31), (14, 16), (37, 5), (18, 19), (2, 4), (37, 38), (37, 3), (18, 27), (23, 22), (17, 9), (35, 34), (10, 32), (2, 28), (22, 8), (18, 7), (21, 1), (4, 42), (32, 23), (7, 21), (31, 8), (28, 13), (18, 21), (20, 12), (17, 5), (5, 42), (10, 22), (22, 12), (31, 14), (12, 45), (11, 26), (1, 22), (22, 5), (21, 5), (40, 2), (38, 32), (19, 35), (14, 14), (28, 26), (31, 1), (34, 35), (8, 45), (31, 29), (34, 41), (13, 10), (29, 37), (20, 9), (17, 25), (29, 33), (4, 20), (41, 11), (29, 4), (29, 45), (32, 24), (13, 14), (38, 44), (26, 34), (14, 2), (42, 21), (5, 44), (12, 39), (38, 25), (4, 33), (41, 38), (38, 5), (37, 31), (39, 10), (12, 26), (5, 32), (36, 43), (19, 45), (32, 40), (19, 33), (16, 14), (1, 13), (2, 26), (2, 42), (11, 38), (27, 36), (18, 13), (16, 31), (26, 31), (28, 14), (3, 34), (23, 33), (26, 37), (33, 25), (35, 3), (4, 44), (15, 7), (8, 17), (12, 15), (31, 45), (9, 29), (36, 16), (27, 38), (29, 27), (16, 9), (26, 7), (34, 8), (41, 0), (8, 43), (42, 12), (41, 34), (2, 29), (29, 8), (22, 42), (35, 35), (34, 32), (31, 40), (32, 16), (14, 9), (14, 0), (22, 7), (18, 20), (28, 32), (12, 20), (25, 16), (3, 19), (12, 14), (11, 13), (20, 36), (32, 29), (2, 3), (3, 29), (27, 3), (18, 4), (0, 7), (19, 10), (30, 31), (20, 32), (20, 44), (3, 38), (18, 15), (6, 32), (8, 21), (15, 8), (39, 30), (6, 40), (36, 38), (28, 41), (27, 31), (1, 8), (3, 2), (6, 27), (31, 39), (41, 40), (19, 14), (27, 12), (22, 38), (41, 2), (13, 17), (22, 24), (26, 6), (11, 30), (2, 22), (19, 6), (31, 26), (38, 33), (29, 5), (36, 12), (37, 34), (18, 5), (9, 43), (10, 40), (17, 40), (36, 29), (36, 34), (35, 17), (12, 9), (7, 16), (15, 12), (23, 29), (1, 9), (28, 37), (4, 6), (28, 39), (8, 36), (26, 43), (9, 0), (31, 33), (17, 33), (34, 21), (39, 0), (26, 2), (25, 8), (22, 37), (42, 1), (9, 1), (15, 23), (19, 20), (8, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 40x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 6), (12, 2), (35, 34), (13, 38), (31, 3), (28, 42), (20, 21), (38, 4), (5, 17), (22, 33), (18, 10), (0, 7), (29, 36), (36, 42), (6, 9), (34, 39), (29, 15), (1, 20), (22, 21), (10, 20), (8, 23), (25, 39), (6, 22), (22, 18), (24, 34), (39, 43), (12, 0), (33, 42), (6, 19), (27, 11), (19, 41), (28, 11), (19, 15), (33, 13), (16, 1), (36, 28), (8, 3), (20, 0), (29, 21), (35, 26), (1, 37), (11, 2), (7, 28), (13, 23), (1, 0), (8, 26), (26, 11), (14, 35), (30, 29), (10, 19), (13, 22), (24, 23), (35, 16), (37, 12), (39, 35), (39, 16), (9, 38), (38, 37), (35, 5), (21, 29), (30, 41), (27, 43), (26, 16), (35, 2), (15, 27), (27, 12), (10, 39), (37, 19), (3, 10), (34, 30), (11, 18), (38, 28), (11, 36), (9, 23), (33, 19), (12, 20), (29, 24), (9, 22), (28, 1), (2, 38), (7, 1), (30, 23), (25, 33), (33, 29), (8, 27), (1, 25), (15, 12), (0, 17), (18, 23), (9, 41), (29, 42), (31, 28), (38, 26), (26, 15), (29, 31), (17, 24), (19, 7), (17, 44), (4, 25), (24, 32), (8, 44), (39, 7), (13, 43), (29, 17), (23, 22), (11, 32), (0, 9), (2, 44), (19, 13), (0, 29), (13, 0), (16, 28), (23, 11), (9, 40), (9, 43), (23, 35), (4, 44), (24, 5), (16, 35), (12, 1), (18, 33), (11, 10), (1, 44), (10, 31), (28, 12), (22, 37), (10, 21), (28, 38), (27, 21), (36, 27), (39, 29), (8, 42), (13, 18), (36, 9), (35, 35), (7, 7), (31, 31), (36, 31), (1, 43), (17, 15), (16, 43), (1, 23), (14, 20), (33, 23), (16, 11), (26, 2), (27, 29), (5, 26), (17, 5), (22, 3), (25, 32), (1, 3), (32, 4), (19, 40), (17, 9), (2, 39), (3, 9), (25, 35), (0, 16), (20, 42), (28, 15), (3, 35), (21, 3), (25, 37), (38, 33), (25, 6), (0, 42), (33, 9), (27, 8), (10, 33), (4, 5), (8, 7), (11, 37), (8, 37), (22, 41), (17, 16), (3, 42), (11, 34), (24, 0), (17, 40), (6, 10), (30, 10), (26, 1), (5, 40), (38, 6), (6, 34), (21, 39), (31, 12), (18, 14), (6, 4), (20, 22), (22, 40), (36, 26), (20, 35), (33, 8), (12, 12), (26, 20), (36, 2), (16, 44), (16, 40), (33, 39), (14, 40), (28, 31), (22, 8), (23, 44), (14, 5), (34, 31), (29, 34), (13, 31), (30, 5), (17, 37), (32, 13), (36, 18), (20, 28), (14, 39), (31, 21), (22, 31), (10, 9), (19, 20), (28, 19), (29, 40), (32, 28), (12, 22), (1, 10), (5, 1), (10, 10), (31, 25), (29, 37), (22, 30), (39, 40), (32, 2), (7, 19), (29, 6), (33, 10), (39, 5), (9, 31), (22, 14), (12, 26), (37, 25), (10, 26), (3, 6), (28, 3), (30, 43), (21, 28), (26, 29), (1, 16), (7, 30), (18, 15), (36, 32), (23, 7), (34, 26), (2, 41), (30, 6), (2, 26), (31, 26), (15, 30), (15, 38), (13, 27), (4, 13), (24, 17), (36, 14), (1, 1), (37, 5), (29, 26), (30, 22), (6, 27), (2, 20), (1, 21), (31, 5), (21, 42), (30, 37), (35, 1), (3, 12), (0, 18), (5, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 29), (25, 12), (9, 30), (25, 33), (39, 19), (35, 4), (8, 0), (6, 30), (16, 10), (40, 11), (27, 39), (31, 3), (26, 13), (23, 35), (10, 40), (35, 21), (23, 37), (35, 2), (38, 13), (32, 0), (8, 10), (7, 18), (19, 17), (12, 24), (35, 19), (33, 26), (18, 21), (1, 24), (42, 23), (8, 6), (5, 1), (12, 26), (6, 7), (0, 10), (23, 12), (11, 18), (14, 12), (37, 33), (22, 26), (4, 6), (29, 18), (7, 1), (42, 20), (20, 28), (11, 41), (44, 11), (3, 38), (1, 7), (27, 16), (32, 24), (31, 12), (42, 27), (33, 21), (6, 8), (0, 30), (8, 40), (44, 6), (8, 16), (36, 7), (4, 28), (21, 6), (30, 37), (22, 34), (28, 30), (32, 28), (8, 23), (1, 1), (5, 19), (0, 11), (38, 28), (21, 41), (6, 1), (24, 1), (29, 8), (27, 32), (38, 18), (32, 30), (9, 32), (25, 36), (37, 25), (20, 33), (32, 18), (3, 14), (0, 27), (23, 3), (38, 12), (33, 9), (13, 38), (31, 34), (28, 38), (44, 28), (24, 23), (34, 3), (7, 16), (4, 3), (35, 17), (35, 37), (10, 29), (34, 28), (2, 5), (1, 38), (41, 17), (5, 28), (26, 15), (1, 2), (24, 0), (20, 5), (3, 17), (21, 21), (7, 23), (20, 18), (35, 32), (13, 26), (10, 38), (43, 10), (3, 22), (24, 9), (20, 30), (31, 27), (38, 24), (25, 32), (10, 2), (17, 21), (5, 39), (3, 13), (38, 34), (9, 39), (42, 30), (25, 35), (9, 7), (34, 30), (33, 14), (44, 8), (19, 9), (33, 3), (4, 22), (16, 9), (15, 1), (11, 32), (19, 18), (34, 7), (20, 21), (10, 20), (6, 27), (31, 7), (1, 34), (9, 24), (39, 40), (26, 40), (25, 38), (38, 8), (20, 14), (4, 9), (44, 35), (16, 35), (10, 23), (37, 0), (42, 9), (17, 20), (37, 15), (41, 0), (9, 10), (24, 36), (21, 36), (31, 31), (34, 16), (10, 11), (15, 25), (30, 10), (28, 21), (0, 12), (18, 8), (29, 19), (11, 19), (5, 3), (2, 3), (8, 17), (38, 40), (32, 25), (9, 17), (29, 38), (31, 18), (43, 20), (10, 35), (14, 22), (39, 2), (20, 13), (0, 7), (35, 22), (30, 16), (29, 12), (34, 10), (29, 35), (27, 25), (24, 16), (39, 9), (16, 4), (38, 6), (4, 32), (11, 16), (36, 6), (30, 7), (30, 5), (33, 23), (25, 26), (2, 31), (28, 17), (0, 18), (39, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (16, 38), (38, 3), (14, 32), (20, 15), (7, 16), (12, 31), (15, 25), (10, 14), (15, 10), (0, 29), (23, 25), (23, 33), (14, 4), (19, 25), (3, 22), (31, 22), (6, 42), (30, 39), (21, 37), (23, 38), (12, 20), (14, 18), (45, 42), (21, 4), (14, 20), (21, 27), (18, 26), (20, 36), (28, 37), (40, 10), (6, 36), (45, 20), (43, 40), (27, 24), (0, 22), (42, 12), (10, 11), (26, 20), (39, 24), (4, 39), (45, 40), (9, 15), (30, 17), (34, 8), (30, 2), (23, 8), (39, 12), (9, 24), (32, 36), (17, 0), (5, 27), (35, 19), (48, 9), (30, 18), (9, 4), (44, 2), (30, 33), (34, 21), (24, 15), (2, 25), (25, 28), (10, 24), (21, 44), (19, 31), (2, 27), (38, 2), (10, 39), (43, 5), (25, 32), (28, 42), (37, 20), (21, 18), (19, 8), (1, 39), (43, 1), (29, 4), (5, 39), (27, 9), (1, 8), (19, 10), (7, 32), (28, 31), (38, 16), (40, 14), (0, 12), (27, 31), (8, 22), (29, 6), (40, 21), (11, 2), (29, 43), (1, 21), (46, 7), (16, 12), (42, 36), (8, 42), (4, 35), (4, 14), (46, 4), (3, 11), (24, 40), (8, 26), (28, 3), (15, 38), (43, 28), (40, 34), (30, 35), (41, 19), (25, 3), (10, 19), (37, 44), (5, 34), (16, 20), (12, 38), (26, 32), (35, 10), (31, 0), (15, 12), (30, 40), (46, 30), (41, 15), (39, 9), (16, 40), (40, 13), (34, 0), (8, 8), (3, 16), (22, 20), (3, 20), (33, 43), (20, 11), (47, 30), (31, 15), (41, 37), (44, 0), (47, 32), (29, 13), (39, 15), (47, 39), (42, 10), (22, 7), (39, 20), (11, 40), (41, 14), (48, 35), (34, 33), (16, 3), (18, 23), (10, 34), (34, 10), (16, 34), (41, 36), (7, 4), (5, 44), (32, 40), (5, 0), (43, 33), (42, 11), (3, 2), (26, 22), (33, 3), (11, 30), (32, 2), (29, 0), (44, 40), (13, 32), (4, 17), (24, 9), (3, 24), (9, 29), (3, 0), (15, 34), (32, 17), (39, 36), (12, 2), (27, 19), (7, 9), (16, 26), (19, 26), (24, 26), (20, 26), (25, 15), (45, 27), (42, 13), (30, 43), (3, 32), (29, 22), (4, 33), (46, 16), (24, 27), (47, 29), (6, 12), (31, 10), (7, 31), (4, 22), (18, 27), (7, 41), (17, 6), (28, 44), (26, 33), (39, 7), (26, 30), (40, 31), (44, 25), (32, 44), (30, 24), (34, 20), (23, 40), (33, 25), (3, 30), (27, 13), (47, 23), (17, 27), (37, 25), (24, 11), (12, 30), (22, 22), (35, 23), (23, 28), (3, 40), (0, 36), (0, 5), (36, 9), (3, 3), (27, 25), (0, 37), (35, 12), (6, 25), (29, 21), (25, 35), (4, 24), (44, 38), (1, 1), (25, 40), (48, 30), (32, 8), (10, 0), (5, 7), (40, 30), (43, 41), (39, 27), (13, 18), (45, 32), (3, 43), (46, 17), (26, 36), (7, 28), (12, 42), (28, 34), (23, 15), (10, 7), (33, 6), (5, 28), (46, 2), (15, 16), (5, 33), (2, 43), (39, 8), (39, 37), (3, 7), (26, 16), (24, 39), (2, 12), (25, 12), (33, 41), (47, 44), (45, 22), (15, 8), (25, 30), (32, 7), (38, 31), (3, 9), (19, 24), (48, 25), (3, 37), (21, 5), (9, 10), (13, 3), (40, 6), (29, 33), (24, 29), (22, 19), (40, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 0), (2, 23), (37, 44), (1, 23), (5, 45), (34, 5), (19, 23), (33, 41), (47, 12), (14, 38), (15, 10), (17, 26), (35, 28), (31, 42), (14, 3), (31, 38), (4, 5), (33, 29), (30, 11), (25, 32), (17, 5), (46, 23), (11, 42), (30, 5), (24, 18), (0, 45), (9, 11), (36, 21), (40, 30), (4, 3), (3, 33), (40, 0), (25, 40), (37, 30), (42, 41), (4, 19), (10, 6), (35, 33), (22, 12), (36, 5), (10, 28), (38, 35), (11, 21), (5, 28), (15, 2), (37, 6), (12, 39), (13, 1), (0, 26), (40, 43), (14, 44), (26, 0), (4, 42), (29, 37), (28, 5), (5, 13), (21, 4), (21, 5), (10, 22), (37, 16), (5, 35), (43, 16), (31, 2), (25, 17), (9, 15), (9, 10), (36, 43), (8, 8), (44, 31), (36, 3), (37, 3), (6, 42), (8, 1), (31, 20), (39, 36), (47, 30), (20, 15), (11, 4), (34, 6), (5, 44), (36, 2), (3, 15), (34, 17), (29, 7), (29, 39), (25, 16), (13, 44), (10, 5), (28, 6), (16, 17), (21, 11), (3, 12), (12, 45), (45, 31), (8, 39), (0, 20), (26, 7), (3, 10), (28, 8), (17, 12), (25, 44), (41, 15), (16, 22), (38, 22), (29, 3), (24, 30), (35, 12), (38, 37), (31, 0), (32, 37), (17, 19), (20, 43), (46, 27), (27, 19), (40, 45), (40, 37), (43, 18), (22, 7), (18, 28), (37, 34), (11, 31), (27, 44), (6, 8), (47, 31), (44, 42), (46, 14), (21, 40), (26, 27), (30, 42), (28, 32), (2, 10), (24, 35), (16, 21), (7, 23), (20, 5), (43, 15), (32, 21), (7, 11), (6, 27), (21, 34), (42, 6), (18, 25), (43, 4), (12, 41), (42, 7), (20, 29), (45, 40), (31, 27), (9, 41), (46, 6), (38, 36), (3, 8), (35, 39), (42, 27), (36, 20), (31, 30), (35, 15), (40, 14), (8, 7), (43, 23), (43, 6), (37, 23), (24, 37), (3, 43), (28, 1), (2, 12), (28, 22), (22, 40), (16, 16), (31, 37), (44, 9), (7, 2), (13, 2), (3, 7), (9, 30), (11, 16), (37, 20), (38, 29), (41, 1), (35, 29), (25, 1), (8, 14), (43, 9), (40, 26), (22, 44), (20, 18), (13, 25), (47, 13), (6, 32), (18, 39), (34, 1), (35, 31), (40, 16), (46, 22), (3, 14), (3, 9), (38, 14), (40, 23), (2, 38), (38, 45), (22, 32), (43, 0), (25, 25), (7, 18), (5, 17), (10, 26), (12, 11), (31, 45), (45, 24), (28, 44), (0, 4), (10, 7), (31, 7), (4, 18), (38, 31), (11, 9), (41, 22), (45, 20), (1, 44), (17, 2), (5, 7), (35, 37), (42, 38), (43, 26), (31, 19), (41, 30), (47, 14), (30, 14), (25, 37), (44, 39), (8, 42), (8, 10), (41, 3), (0, 37), (3, 26), (1, 39), (19, 26), (46, 15), (11, 11), (5, 32), (29, 31), (9, 40), (1, 4), (14, 14), (15, 39), (22, 42), (19, 30), (6, 10), (35, 44), (15, 5), (1, 38), (1, 43), (27, 6), (24, 24), (36, 12), (33, 24), (29, 26), (29, 11), (45, 21), (0, 39), (46, 20), (46, 25), (32, 41), (31, 9), (14, 1), (24, 5), (26, 1), (6, 43), (12, 31), (30, 41), (34, 39), (13, 23), (29, 10), (46, 19), (35, 19), (14, 5), (2, 35), (23, 24), (44, 44), (35, 26), (20, 35), (18, 19), (42, 10), (38, 10), (29, 8), (37, 4), (9, 7), (28, 0), (45, 28), (9, 1), (38, 38), (0, 11), (34, 8), (9, 21), (33, 26), (1, 17), (8, 37), (17, 45), (39, 22), (14, 24), (44, 43), (17, 38), (30, 18), (3, 5), (38, 39), (1, 12), (4, 35), (1, 5), (11, 41), (22, 27), (37, 42), (10, 27), (1, 36), (43, 22), (43, 20), (38, 3), (3, 3), (12, 5), (12, 32), (40, 38), (28, 33), (39, 31), (47, 9), (11, 20), (42, 36), (32, 9), (42, 29), (24, 41), (46, 44), (2, 28), (25, 28), (29, 29), (37, 37), (38, 19), (38, 30), (13, 32), (1, 22), (25, 6), (11, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 39), (17, 9), (1, 35), (17, 47), (25, 25), (1, 37), (11, 18), (37, 24), (9, 26), (21, 19), (1, 27), (10, 23), (7, 37), (27, 40), (4, 15), (19, 40), (11, 36), (6, 32), (0, 6), (36, 22), (36, 18), (32, 32), (16, 27), (37, 40), (11, 11), (14, 8), (28, 39), (5, 36), (35, 45), (15, 40), (36, 2), (33, 47), (40, 46), (29, 6), (0, 16), (9, 20), (18, 43), (29, 41), (12, 30), (32, 44), (15, 28), (5, 27), (33, 10), (40, 43), (24, 36), (22, 6), (16, 10), (26, 17), (24, 17), (41, 20), (37, 15), (19, 47), (20, 44), (2, 14), (1, 11), (33, 0), (1, 1), (14, 4), (42, 43), (5, 39), (2, 45), (26, 46), (12, 12), (2, 16), (18, 1), (12, 48), (0, 18), (23, 33), (11, 3), (8, 34), (34, 30), (1, 18), (7, 47), (10, 11), (26, 43), (17, 1), (0, 3), (28, 31), (33, 29), (23, 16), (38, 43), (13, 41), (9, 29), (19, 11), (4, 31), (13, 14), (8, 17), (24, 40), (16, 26), (23, 20), (30, 40), (41, 31), (18, 26), (9, 31), (22, 39), (31, 46), (24, 9), (11, 4), (6, 40), (2, 33), (8, 40), (30, 43), (3, 10), (37, 48), (28, 20), (11, 46), (23, 23), (18, 2), (12, 2), (21, 21), (23, 41), (19, 38), (22, 25), (38, 26), (13, 38), (17, 2), (28, 11), (1, 17), (14, 9), (17, 28), (33, 42), (8, 35), (2, 17), (14, 37), (22, 48), (23, 8), (34, 10), (40, 36), (8, 4), (2, 47), (4, 4), (19, 3), (11, 6), (30, 16), (29, 8), (2, 0), (15, 30), (7, 27), (0, 10), (23, 0), (31, 30), (13, 1), (40, 5), (20, 1), (12, 25), (19, 25), (37, 9), (11, 22), (40, 12), (37, 28), (22, 3), (39, 46), (34, 24), (5, 4), (24, 30), (2, 44), (16, 9), (17, 14), (20, 21), (4, 29), (30, 20), (40, 25), (24, 34), (34, 28), (20, 2), (6, 12), (27, 30), (33, 18), (35, 33), (30, 19), (17, 11), (2, 8), (32, 16), (36, 30), (37, 43), (12, 45), (39, 3), (14, 12), (7, 32), (21, 39), (3, 21), (25, 36), (23, 18), (9, 32), (23, 11), (42, 41), (1, 16), (28, 47), (14, 15), (17, 0), (26, 25), (33, 25), (17, 23), (22, 11), (21, 12), (2, 35), (32, 42), (15, 43), (24, 42), (36, 6), (21, 36), (6, 46), (34, 43), (19, 10), (42, 30), (5, 33), (27, 28), (39, 10), (14, 23), (38, 37), (20, 35), (31, 29), (34, 29), (30, 15), (1, 30), (33, 5), (24, 39), (5, 2), (26, 19), (27, 47), (17, 42), (30, 26), (38, 45), (26, 42), (17, 33), (39, 22), (18, 22), (23, 21), (17, 16), (1, 5), (3, 35), (16, 0), (9, 18), (20, 33), (40, 18), (30, 48), (31, 3), (41, 22), (20, 29), (11, 13), (5, 9), (27, 25), (10, 32), (29, 32), (2, 22), (4, 39), (23, 6), (41, 44), (23, 3), (20, 28), (42, 9), (24, 13), (39, 40), (39, 35), (32, 37), (30, 28), (31, 6), (29, 12), (41, 5), (42, 34), (7, 39), (18, 30), (3, 37), (19, 9), (20, 45), (3, 43), (36, 5), (3, 17), (36, 21), (27, 38), (27, 23), (39, 8), (28, 38), (29, 40), (13, 9), (7, 35), (19, 15), (7, 2), (5, 45), (12, 44), (40, 14), (26, 36), (40, 11), (5, 1), (5, 19), (36, 9), (4, 47), (22, 28), (14, 31), (7, 30), (22, 7), (8, 29), (26, 28), (28, 45), (11, 43)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 13), (31, 22), (43, 31), (6, 9), (12, 24), (22, 39), (1, 27), (31, 39), (32, 22), (14, 21), (22, 40), (25, 16), (31, 31), (10, 15), (35, 23), (17, 40), (31, 7), (43, 21), (10, 9), (22, 9), (13, 8), (16, 17), (41, 11), (40, 4), (38, 15), (35, 16), (12, 21), (14, 40), (39, 21), (34, 31), (29, 44), (16, 15), (41, 42), (1, 25), (19, 45), (36, 33), (1, 10), (16, 45), (40, 12), (23, 44), (16, 38), (10, 12), (3, 11), (24, 4), (19, 35), (23, 31), (0, 12), (11, 29), (18, 19), (23, 12), (32, 37), (24, 8), (9, 25), (33, 5), (9, 6), (25, 5), (41, 12), (29, 38), (12, 10), (9, 5), (34, 1), (25, 0), (7, 12), (18, 39), (26, 37), (6, 40), (4, 42), (21, 37), (38, 10), (39, 1), (44, 11), (41, 1), (22, 25), (30, 12), (27, 21), (22, 34), (32, 27), (14, 23), (7, 2), (23, 17), (35, 17), (25, 23), (4, 18), (38, 35), (41, 38), (14, 14), (25, 44), (5, 35), (8, 28), (44, 37), (25, 37), (35, 27), (30, 3), (7, 35), (18, 29), (13, 13), (14, 29), (42, 37), (11, 40), (0, 34), (30, 45), (0, 26), (11, 45), (6, 37), (38, 37), (16, 34), (40, 37), (27, 32), (8, 25), (23, 1), (42, 26), (22, 31), (1, 14), (32, 38), (34, 24), (20, 2), (16, 19), (16, 23), (32, 7), (33, 29), (41, 22), (22, 42), (0, 25), (44, 28), (22, 44), (10, 31), (44, 26), (10, 1), (31, 16), (19, 32), (42, 4), (0, 33), (12, 13), (13, 18), (38, 9), (9, 41), (40, 28), (30, 2), (6, 22), (20, 37), (43, 8), (14, 37), (42, 13), (10, 36), (38, 16), (17, 39), (16, 1), (38, 5), (25, 28), (29, 41), (43, 25), (37, 42), (8, 35), (31, 29), (41, 23), (40, 31), (8, 16), (3, 14), (16, 8), (7, 8), (17, 12), (18, 23), (0, 10), (12, 44), (19, 38), (25, 27), (0, 13), (8, 18), (17, 5), (22, 11), (31, 5), (21, 11), (32, 12), (36, 4), (9, 18), (18, 35), (33, 24), (26, 14), (41, 4), (41, 18), (41, 15), (41, 28), (13, 22), (37, 36), (7, 19), (19, 11), (33, 20), (38, 28), (14, 9), (38, 32), (42, 19), (15, 0), (21, 6), (26, 0), (28, 36), (8, 17), (26, 7), (21, 5), (4, 24), (18, 22), (38, 0), (23, 4), (12, 3), (20, 32), (2, 4), (25, 43), (4, 7), (34, 43), (41, 33), (32, 42), (29, 1), (29, 17), (22, 27), (7, 13), (0, 6), (21, 36), (0, 21), (10, 33), (26, 5), (11, 37), (34, 39), (42, 41), (13, 44), (22, 22), (18, 25), (42, 6), (43, 13), (13, 4), (28, 30), (13, 17), (3, 25), (2, 29), (20, 43), (10, 27), (27, 24), (1, 28), (28, 13), (11, 10), (3, 1), (16, 30), (27, 23), (26, 29), (1, 31), (44, 15), (15, 28), (43, 23), (25, 42), (19, 26), (12, 15), (25, 19), (9, 14), (31, 25), (31, 9), (7, 6), (0, 27), (12, 36), (34, 25), (36, 7), (4, 29), (39, 10), (20, 14), (44, 31), (0, 3), (26, 10), (25, 38), (8, 13), (8, 27), (21, 45), (39, 30), (35, 36), (35, 3), (9, 15), (32, 31), (3, 41), (27, 38), (7, 44), (16, 40), (36, 34), (42, 28), (1, 33), (26, 28), (28, 23), (19, 42), (12, 19), (34, 13), (13, 9), (6, 31), (27, 45), (4, 16), (2, 38), (43, 28), (27, 15), (32, 33), (5, 39), (44, 24), (7, 7), (29, 24), (33, 19), (1, 29), (43, 17), (26, 21), (1, 3), (31, 10), (16, 28), (23, 34), (23, 41), (15, 42), (43, 6), (34, 14), (32, 16), (31, 1), (44, 18), (24, 12), (3, 29), (2, 28), (26, 27), (26, 25), (42, 18), (34, 27), (35, 1), (3, 5), (28, 42), (16, 29), (18, 3), (15, 37), (12, 39), (41, 2), (41, 21), (7, 21), (32, 9), (24, 11), (13, 36), (10, 16), (12, 26), (33, 25), (40, 35), (27, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 0), (28, 35), (17, 22), (24, 15), (20, 11), (3, 8), (43, 20), (41, 0), (14, 39), (27, 40), (2, 35), (4, 27), (1, 40), (10, 38), (31, 6), (37, 36), (23, 4), (37, 18), (31, 33), (20, 15), (32, 5), (31, 41), (20, 13), (26, 19), (13, 9), (38, 24), (39, 12), (12, 40), (12, 18), (27, 17), (30, 22), (12, 6), (44, 6), (1, 26), (32, 16), (41, 26), (13, 35), (5, 41), (1, 23), (22, 13), (34, 35), (43, 23), (14, 23), (36, 32), (6, 31), (24, 16), (18, 35), (28, 32), (37, 13), (21, 5), (18, 30), (40, 30), (8, 27), (43, 4), (25, 31), (13, 19), (36, 20), (17, 27), (39, 27), (16, 28), (17, 6), (41, 41), (33, 29), (13, 2), (21, 36), (36, 40), (10, 35), (3, 10), (17, 3), (23, 18), (4, 17), (25, 17), (27, 24), (22, 41), (18, 21), (26, 20), (45, 37), (9, 17), (11, 27), (37, 34), (6, 35), (38, 8), (6, 40), (35, 19), (21, 7), (44, 2), (9, 39), (25, 27), (11, 24), (43, 26), (4, 15), (17, 35), (44, 40), (28, 19), (3, 11), (21, 31), (16, 5), (28, 27), (34, 34), (18, 19), (31, 27), (29, 24), (36, 11), (0, 5), (37, 15), (39, 16), (12, 41), (38, 20), (0, 17), (3, 6), (23, 7), (7, 8), (23, 27), (4, 25), (24, 21), (16, 18), (14, 22), (39, 32), (22, 0), (18, 20), (7, 23), (37, 27), (28, 15), (42, 1), (29, 41), (16, 11), (31, 22), (25, 22), (41, 17), (33, 8), (2, 30), (6, 13), (0, 3), (32, 4), (39, 33), (23, 28), (4, 3), (30, 20), (17, 13), (31, 15), (29, 28), (17, 19), (7, 20), (7, 35), (22, 11), (21, 26), (38, 35), (31, 3), (32, 40), (30, 2), (25, 15), (36, 27), (5, 39), (36, 33), (26, 38), (38, 7), (33, 22), (10, 2), (37, 0), (6, 36), (19, 20), (29, 22), (20, 3), (10, 29), (15, 27), (40, 15), (18, 41), (26, 15), (21, 11), (8, 11), (11, 21), (29, 40), (6, 16), (28, 1), (43, 33), (42, 11), (14, 11), (11, 11), (26, 37), (24, 19), (42, 34), (11, 16), (9, 20), (38, 41), (9, 35), (17, 12), (3, 25), (18, 16), (39, 22), (43, 5), (38, 32), (37, 39), (43, 0), (16, 0), (45, 15), (27, 26), (30, 34), (36, 8), (35, 41), (25, 1), (9, 41), (3, 7), (26, 9), (40, 3), (18, 12), (35, 0), (14, 32), (28, 33), (33, 11), (19, 10), (43, 3), (0, 20), (5, 25), (30, 14), (31, 10), (5, 6), (21, 4), (10, 25), (6, 18), (36, 39), (2, 1), (5, 30), (13, 39), (0, 41), (44, 36), (22, 39), (18, 38), (45, 23), (18, 1), (1, 8), (14, 5), (12, 34), (0, 25), (9, 0), (27, 13), (23, 33), (13, 5), (20, 34), (40, 7), (0, 39), (42, 33), (15, 36), (44, 18), (44, 16), (3, 34), (42, 16), (13, 37), (6, 30), (22, 37), (19, 11), (41, 34), (45, 6), (35, 40), (19, 26), (3, 15), (35, 8), (26, 12), (33, 0), (29, 27), (38, 4), (21, 32), (22, 6), (7, 4), (4, 22), (41, 14), (16, 15), (13, 7), (5, 40), (10, 8), (32, 10), (41, 18), (10, 17), (42, 18), (0, 35), (34, 20), (12, 10), (2, 39), (14, 33), (26, 27), (23, 10), (4, 11), (18, 7), (32, 23), (17, 29), (13, 22), (24, 37), (3, 4), (19, 8), (37, 31), (39, 14), (11, 32), (34, 5), (0, 7), (1, 17), (25, 0), (10, 22), (34, 7), (17, 0), (25, 9), (4, 21), (26, 0), (0, 40), (20, 37), (34, 6), (33, 24), (20, 24), (21, 23), (13, 26), (0, 33), (28, 29), (36, 13), (22, 36), (36, 3), (15, 32), (15, 7), (26, 8), (35, 33), (5, 2), (35, 14), (42, 40), (34, 32), (9, 8), (7, 2), (4, 20), (42, 2), (15, 38), (9, 14), (14, 29), (12, 9), (27, 41), (43, 31), (22, 35), (24, 35), (11, 3), (35, 38), (13, 31), (25, 11), (23, 22), (9, 15), (32, 1), (23, 21), (6, 26), (42, 0), (5, 8), (24, 33), (18, 39), (10, 18), (26, 14), (5, 28), (44, 5), (11, 10), (30, 26), (24, 28), (41, 35), (24, 39), (17, 15), (11, 5), (29, 2), (32, 13), (44, 38), (21, 38), (8, 24), (35, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 36), (37, 11), (17, 37), (10, 5), (23, 29), (47, 6), (48, 35), (18, 0), (22, 5), (15, 41), (7, 45), (22, 25), (5, 42), (7, 26), (26, 8), (30, 28), (8, 14), (28, 22), (41, 27), (9, 38), (30, 22), (38, 40), (31, 46), (0, 18), (47, 38), (18, 39), (19, 46), (11, 27), (2, 40), (32, 24), (25, 12), (25, 41), (37, 32), (34, 47), (34, 45), (26, 36), (45, 11), (23, 5), (6, 23), (43, 3), (41, 14), (9, 46), (46, 42), (0, 12), (23, 40), (3, 28), (39, 10), (7, 2), (19, 9), (31, 44), (46, 8), (20, 19), (41, 44), (30, 36), (24, 32), (6, 20), (5, 9), (39, 47), (48, 10), (19, 38), (29, 8), (12, 33), (31, 39), (21, 28), (24, 45), (47, 11), (11, 21), (26, 25), (0, 41), (29, 44), (22, 37), (6, 4), (9, 42), (33, 31), (11, 30), (13, 35), (20, 21), (32, 26), (24, 25), (30, 1), (36, 26), (35, 28), (17, 28), (47, 7), (20, 42), (30, 13), (32, 43), (18, 34), (30, 31), (18, 16), (36, 48), (11, 17), (17, 5), (41, 39), (5, 18), (27, 24), (13, 0), (40, 16), (6, 36), (22, 2), (22, 48), (11, 13), (10, 38), (42, 25), (45, 38), (39, 8), (40, 32), (22, 27), (23, 47), (25, 0), (20, 27), (16, 0), (39, 16), (18, 10), (29, 42), (30, 6), (46, 0), (25, 10), (17, 30), (36, 7), (7, 46), (0, 27), (48, 37), (13, 33), (25, 22), (41, 8), (7, 33), (34, 31), (18, 14), (20, 22), (26, 1), (45, 4), (2, 36), (3, 47), (10, 3), (35, 48), (25, 46), (36, 19), (40, 6), (44, 33), (21, 48), (30, 10), (35, 41), (20, 32), (0, 7), (39, 39), (20, 29), (0, 16), (47, 23), (9, 44), (31, 31), (24, 15), (26, 37), (11, 41), (41, 35), (3, 39), (17, 43), (18, 3), (27, 47), (42, 5), (14, 1), (41, 28), (30, 42), (39, 9), (29, 37), (20, 3), (48, 42), (2, 37), (46, 35), (16, 18), (21, 20), (4, 7), (40, 2), (4, 34), (45, 3), (21, 1), (36, 40), (32, 10), (19, 21), (29, 18), (25, 34), (23, 8), (14, 13), (32, 23), (19, 45), (35, 0), (5, 22), (30, 14), (28, 44), (23, 48), (26, 32), (25, 28), (41, 37), (33, 14), (1, 46), (12, 13), (16, 25), (22, 47), (6, 5), (8, 22), (18, 23), (20, 38), (30, 7), (28, 8), (17, 6), (22, 20), (37, 47), (47, 31), (38, 9), (4, 25), (10, 39), (17, 44), (2, 30), (8, 16), (20, 15), (19, 33), (1, 41), (47, 8), (6, 25), (0, 29), (44, 30), (14, 8), (45, 48), (37, 18), (46, 2), (41, 47), (27, 14), (25, 27), (22, 16), (7, 12), (14, 30), (28, 41), (35, 9), (46, 20), (17, 1), (35, 45), (23, 18), (35, 24), (33, 44), (33, 26), (7, 32), (43, 7), (9, 40), (29, 34), (28, 9), (9, 7), (35, 8), (32, 32), (20, 40), (44, 39), (9, 22), (3, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 30), (23, 20), (7, 8), (18, 28), (14, 27), (7, 5), (25, 36), (14, 13), (41, 10), (21, 41), (15, 22), (36, 6), (42, 29), (21, 2), (7, 13), (27, 41), (40, 16), (3, 41), (28, 32), (28, 12), (26, 34), (6, 4), (10, 10), (9, 37), (25, 2), (4, 11), (34, 19), (6, 29), (2, 16), (29, 29), (18, 17), (38, 7), (17, 30), (28, 20), (13, 6), (31, 28), (13, 27), (21, 18), (21, 0), (5, 34), (28, 22), (5, 37), (0, 5), (28, 10), (40, 25), (34, 22), (16, 40), (22, 13), (42, 30), (19, 19), (27, 19), (42, 3), (10, 16), (9, 35), (18, 19), (31, 3), (17, 12), (33, 0), (16, 1), (32, 19), (24, 41), (23, 5), (13, 12), (30, 24), (42, 8), (38, 32), (33, 42), (3, 0), (35, 32), (35, 39), (18, 25), (37, 37), (22, 40), (1, 33), (11, 0), (27, 32), (7, 14), (12, 10), (39, 38), (5, 14), (37, 21), (35, 8), (27, 18), (32, 32), (36, 14), (40, 40), (34, 11), (3, 36), (7, 0), (6, 37), (29, 8), (32, 10), (12, 20), (26, 22), (20, 38), (27, 6), (23, 8), (18, 38), (12, 24), (0, 21), (22, 39), (11, 38), (23, 40), (17, 11), (15, 18), (20, 18), (28, 28), (29, 16), (11, 35), (12, 29), (8, 32), (32, 23), (11, 29), (17, 4), (4, 14), (1, 7), (21, 34), (41, 33), (15, 11), (29, 22), (8, 42), (13, 38), (34, 7), (5, 30), (17, 18), (8, 1), (4, 7), (20, 7), (22, 38), (26, 40), (5, 24), (42, 20), (0, 1), (35, 28), (4, 20), (9, 5), (28, 27), (26, 11), (7, 1), (28, 34), (29, 41), (5, 21), (0, 39), (1, 3), (31, 24), (39, 29), (22, 15), (28, 41), (23, 33), (2, 32), (11, 6), (19, 31), (3, 1), (14, 14), (20, 11), (1, 6), (24, 5), (7, 15), (14, 11), (6, 7), (35, 1), (38, 13), (10, 35), (16, 24), (16, 2), (36, 42), (42, 35), (23, 17), (7, 6), (40, 24), (33, 4), (6, 21), (3, 5), (31, 5), (18, 27), (17, 7), (2, 19), (9, 11), (19, 20), (30, 9), (2, 40), (34, 30), (21, 28), (15, 17), (11, 15), (29, 21), (17, 8), (10, 28), (37, 10), (21, 36), (42, 12), (27, 25), (30, 5), (34, 9), (11, 1), (29, 15), (39, 13), (19, 3), (29, 30), (6, 42), (18, 10), (7, 10), (36, 40), (23, 1), (42, 14), (35, 24), (20, 27), (17, 1), (10, 21), (25, 7), (1, 38), (29, 7), (17, 38), (17, 17), (21, 7), (3, 42), (36, 37), (6, 17), (18, 36), (7, 30), (6, 3), (42, 37), (0, 22), (10, 25), (15, 34), (40, 0), (21, 32), (39, 17), (18, 34), (4, 36), (16, 26), (16, 33), (27, 23), (23, 27), (18, 41), (33, 13), (32, 16), (9, 4), (22, 4), (22, 1), (40, 19), (9, 28), (8, 19), (20, 42), (29, 32), (24, 23), (15, 8), (40, 23), (38, 0), (30, 30), (13, 26), (22, 37), (17, 42), (19, 23), (28, 36), (25, 0), (11, 9), (34, 4), (8, 25), (26, 38), (7, 26), (16, 27), (20, 26), (6, 0), (10, 15), (1, 28), (33, 27), (8, 12), (30, 37), (9, 22), (12, 26), (38, 22), (3, 4), (18, 22), (23, 35), (34, 36), (11, 26), (32, 36), (33, 8), (22, 41), (33, 1), (9, 38), (30, 0), (24, 1), (14, 3), (22, 14), (38, 15), (13, 18), (32, 33), (27, 7), (18, 2), (38, 30), (3, 32), (3, 11), (5, 18), (30, 36), (20, 30), (7, 12), (40, 32), (1, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 20), (28, 39), (16, 21), (39, 4), (13, 15), (31, 12), (25, 9), (30, 39), (27, 7), (43, 15), (23, 35), (38, 34), (14, 14), (35, 42), (20, 32), (20, 26), (30, 40), (30, 18), (41, 37), (37, 16), (9, 36), (6, 28), (27, 20), (41, 13), (43, 4), (7, 23), (38, 38), (25, 28), (16, 20), (39, 32), (29, 30), (42, 42), (0, 16), (16, 17), (14, 30), (31, 36), (23, 41), (30, 24), (8, 39), (36, 30), (21, 40), (8, 3), (10, 36), (6, 7), (20, 15), (8, 11), (3, 12), (11, 38), (27, 15), (10, 29), (16, 8), (10, 31), (35, 22), (32, 1), (13, 19), (41, 10), (19, 2), (25, 25), (32, 26), (2, 8), (25, 1), (12, 39), (2, 16), (2, 6), (1, 8), (3, 9), (4, 28), (31, 8), (10, 42), (9, 23), (6, 17), (0, 33), (14, 4), (28, 13), (20, 34), (32, 23), (13, 12), (36, 19), (26, 12), (7, 38), (0, 41), (36, 43), (15, 4), (22, 6), (19, 38), (7, 24), (8, 28), (26, 33), (3, 24), (15, 33), (35, 18), (20, 10), (25, 41), (23, 23), (3, 30), (34, 42), (4, 22), (26, 31), (36, 2), (10, 32), (0, 35), (27, 32), (4, 10), (24, 9), (5, 18), (28, 12), (26, 1), (5, 35), (30, 22), (1, 12), (38, 33), (31, 29), (28, 5), (16, 7), (28, 7), (37, 35), (37, 33), (17, 18), (10, 23), (28, 9), (37, 13), (29, 32), (36, 22), (23, 4), (6, 15), (29, 27), (42, 8), (18, 27), (1, 43), (11, 26), (3, 25), (22, 11), (39, 9), (25, 3), (35, 1), (24, 36), (1, 40), (14, 15), (13, 37), (27, 25), (30, 14), (24, 30), (0, 42), (1, 13), (7, 0), (31, 21), (33, 29), (24, 0), (13, 1), (13, 22), (20, 11), (21, 37), (40, 42), (20, 33), (3, 14), (33, 12), (37, 34), (42, 39), (31, 30), (31, 38), (27, 17), (33, 38), (3, 43), (39, 40), (21, 35), (20, 4), (16, 41), (41, 17), (4, 43), (34, 30), (9, 8), (17, 43), (19, 13), (42, 7), (26, 40), (39, 12), (39, 1), (34, 5), (21, 14), (33, 11), (15, 26), (3, 42), (22, 1), (19, 11), (21, 31), (7, 43), (10, 1), (43, 18), (11, 18), (33, 37), (25, 37), (26, 35), (19, 25), (10, 40), (19, 23), (23, 25), (43, 6), (30, 11), (12, 12), (31, 16), (17, 19), (19, 6), (38, 15), (13, 2), (40, 31), (40, 14), (7, 32), (39, 35), (11, 19), (32, 0), (8, 42), (32, 36), (10, 30), (39, 27), (26, 42), (13, 11), (9, 6), (35, 30), (37, 40), (29, 16), (3, 21), (16, 12), (29, 29), (2, 2), (37, 15), (5, 16), (4, 12), (15, 15), (31, 28), (29, 12), (17, 4), (23, 6), (25, 10), (5, 21), (5, 1), (12, 15), (39, 37), (37, 17), (18, 12), (10, 3), (42, 1), (32, 30), (4, 25), (27, 5), (40, 32), (25, 11), (39, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (15, 45), (14, 9), (7, 18), (33, 45), (1, 26), (1, 1), (35, 3), (5, 6), (23, 40), (27, 19), (25, 47), (38, 14), (34, 13), (37, 37), (38, 1), (11, 24), (5, 32), (17, 17), (9, 1), (19, 2), (19, 27), (30, 34), (31, 47), (19, 17), (36, 1), (5, 3), (15, 47), (6, 37), (23, 37), (0, 16), (22, 31), (35, 45), (32, 37), (3, 29), (16, 12), (35, 2), (31, 1), (16, 34), (19, 12), (14, 4), (16, 8), (0, 34), (26, 36), (27, 8), (13, 22), (31, 19), (5, 18), (12, 46), (34, 35), (27, 33), (13, 4), (39, 13), (13, 24), (23, 29), (12, 15), (0, 22), (10, 8), (30, 38), (24, 9), (14, 2), (8, 33), (3, 46), (4, 1), (8, 5), (38, 31), (25, 42), (29, 33), (7, 11), (38, 34), (6, 14), (36, 42), (36, 35), (8, 15), (4, 8), (35, 37), (4, 16), (7, 13), (13, 8), (5, 10), (11, 30), (22, 6), (8, 20), (20, 37), (29, 16), (13, 9), (4, 7), (6, 21), (22, 38), (17, 38), (19, 40), (39, 39), (37, 32), (26, 1), (18, 8), (8, 22), (4, 37), (16, 23), (28, 15), (27, 37), (10, 22), (19, 0), (13, 42), (26, 41), (16, 28), (5, 43), (8, 9), (18, 21), (12, 23), (19, 11), (30, 44), (36, 5), (30, 17), (15, 9), (18, 9), (21, 45), (19, 4), (2, 20), (6, 8), (21, 25), (16, 19), (26, 3), (33, 8), (3, 36), (25, 25), (38, 16), (1, 46), (24, 36), (32, 41), (0, 14), (19, 28), (33, 25), (5, 20), (38, 28), (0, 19), (23, 45), (15, 0), (6, 4), (22, 24), (35, 44), (2, 41), (31, 43), (23, 33), (33, 1), (25, 18), (35, 18), (32, 24), (0, 18), (31, 3), (19, 41), (23, 10), (32, 4), (18, 36), (35, 16), (9, 31), (1, 0), (11, 20), (2, 33), (11, 9), (30, 10), (28, 4), (17, 23), (12, 24), (27, 40), (29, 19), (39, 33), (28, 8), (9, 2), (30, 16), (3, 2), (36, 47), (19, 20), (39, 5), (17, 1), (16, 17), (2, 23), (29, 22), (16, 24), (32, 14), (29, 35), (1, 4), (30, 40), (39, 4), (18, 11), (18, 17), (1, 19), (22, 23), (24, 6), (19, 34), (35, 35), (4, 47), (38, 36), (18, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 21), (16, 9), (11, 31), (33, 4), (5, 0), (9, 2), (36, 6), (19, 17), (18, 1), (20, 23), (8, 40), (26, 9), (7, 21), (11, 40), (32, 9), (17, 37), (41, 25), (19, 10), (7, 9), (15, 36), (3, 38), (13, 35), (29, 26), (28, 9), (32, 2), (2, 0), (37, 10), (29, 36), (30, 2), (33, 31), (34, 12), (25, 15), (26, 38), (22, 20), (40, 37), (26, 17), (35, 34), (2, 36), (23, 16), (25, 16), (34, 26), (25, 29), (30, 30), (26, 10), (8, 30), (22, 17), (5, 39), (27, 28), (22, 35), (17, 8), (5, 35), (35, 36), (12, 7), (19, 22), (38, 24), (30, 39), (39, 32), (30, 29), (39, 6), (39, 8), (5, 7), (26, 2), (40, 19), (27, 1), (25, 1), (13, 17), (15, 37), (30, 37), (23, 3), (12, 2), (10, 16), (6, 18), (8, 9), (8, 3), (37, 23), (11, 12), (13, 16), (18, 38), (34, 7), (36, 13), (39, 17), (0, 28), (10, 22), (9, 13), (36, 35), (14, 12), (24, 30), (40, 21), (21, 4), (36, 23), (31, 31), (0, 32), (2, 24), (41, 8), (15, 22), (34, 35), (35, 8), (15, 4), (6, 5), (29, 5), (28, 1), (37, 22), (10, 17), (31, 30), (38, 17), (41, 24), (1, 20), (19, 11), (27, 4), (33, 0), (28, 25), (15, 24), (22, 26), (9, 11), (39, 7), (28, 14), (1, 35), (14, 15), (24, 17), (11, 16), (16, 24), (32, 40), (21, 12), (38, 15), (16, 11), (19, 1), (1, 0), (12, 31), (8, 12), (16, 19), (30, 3), (10, 9), (21, 23), (40, 32), (9, 22), (16, 31), (7, 33), (18, 16), (28, 27), (3, 40), (0, 18), (22, 30), (19, 32), (34, 27), (24, 2), (40, 16), (31, 11), (13, 6), (38, 5), (31, 26), (20, 6), (17, 12), (29, 6), (40, 39), (18, 40), (0, 15), (6, 13), (1, 27), (4, 24), (39, 28), (31, 13), (31, 16), (13, 0), (30, 32), (40, 30), (39, 39), (14, 2), (4, 16), (11, 28), (41, 36), (35, 35), (29, 1), (39, 31), (25, 35), (34, 30), (7, 24), (40, 29), (25, 24), (4, 4), (28, 28), (11, 22), (13, 9), (38, 0), (23, 32), (8, 38), (18, 33), (36, 9), (1, 1), (25, 17), (9, 4), (32, 20), (24, 35), (33, 32), (23, 21), (39, 9), (11, 19), (17, 23), (41, 19), (39, 21), (20, 15), (10, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 8), (23, 20), (34, 41), (13, 34), (33, 2), (24, 26), (17, 2), (14, 16), (22, 31), (13, 9), (0, 41), (32, 23), (38, 39), (13, 4), (15, 26), (14, 28), (8, 42), (38, 18), (30, 40), (16, 29), (5, 26), (23, 5), (0, 6), (28, 6), (6, 4), (37, 22), (39, 29), (27, 33), (18, 46), (22, 15), (17, 7), (4, 17), (2, 39), (14, 44), (39, 33), (15, 40), (12, 39), (24, 8), (24, 15), (0, 28), (1, 34), (15, 45), (11, 9), (8, 20), (16, 14), (26, 29), (14, 41), (8, 31), (21, 2), (18, 41), (1, 21), (14, 0), (11, 43), (4, 31), (22, 14), (17, 0), (9, 11), (26, 25), (35, 25), (0, 39), (28, 20), (22, 12), (31, 34), (36, 16), (13, 32), (21, 42), (21, 45), (30, 21), (8, 29), (13, 22), (19, 3), (3, 45), (7, 42), (20, 17), (11, 27), (16, 30), (37, 31), (2, 19), (10, 39), (36, 6), (35, 39), (14, 4), (3, 15), (12, 5), (23, 44), (2, 7), (0, 19), (9, 37), (11, 29), (36, 22), (32, 10), (15, 42), (19, 5), (9, 35), (6, 8), (5, 14), (23, 12), (29, 3), (29, 34), (38, 36), (32, 14), (16, 2), (24, 31), (7, 20), (32, 45), (17, 21), (34, 40), (14, 45), (32, 6), (24, 27), (18, 22), (27, 24), (20, 18), (16, 27), (12, 2), (11, 39), (20, 45), (27, 37), (11, 17), (33, 42), (37, 41), (13, 0), (16, 43), (18, 44), (13, 14), (25, 12), (18, 28), (22, 8), (1, 19), (30, 16), (9, 41), (13, 39), (38, 19), (0, 35), (22, 33), (19, 38), (22, 24), (25, 1), (8, 14), (4, 15), (22, 43), (20, 44), (26, 10), (10, 32), (29, 15), (10, 6), (7, 23), (29, 19), (37, 19), (20, 22), (31, 33), (22, 23), (13, 6), (1, 9), (22, 9), (30, 30), (38, 21), (5, 27), (6, 19), (37, 14), (8, 15), (38, 28), (25, 27), (1, 25), (1, 0), (18, 23), (34, 14), (3, 16), (30, 38), (3, 17), (3, 9), (7, 37), (18, 30), (36, 11), (36, 41), (5, 43), (38, 34), (26, 22), (21, 12), (35, 24), (9, 36), (24, 19), (38, 2), (39, 26), (32, 12), (2, 20), (35, 42), (37, 38), (17, 16), (3, 4), (21, 21), (1, 31), (9, 27), (15, 16), (21, 10), (29, 4), (18, 32), (26, 15), (8, 22), (4, 30), (6, 27), (10, 16), (15, 28), (11, 0), (2, 11), (5, 33), (23, 6), (4, 28), (16, 16), (30, 0), (2, 45), (27, 0), (39, 32), (35, 28), (10, 12), (12, 45), (36, 42), (34, 38), (30, 26), (7, 36), (5, 20), (30, 46), (16, 5), (28, 41), (37, 21), (10, 45), (33, 26), (33, 7), (3, 30), (11, 16), (2, 28), (34, 46), (28, 24), (17, 10), (37, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 29), (35, 36), (24, 4), (33, 2), (23, 28), (2, 0), (36, 35), (14, 37), (28, 19), (19, 17), (8, 15), (41, 33), (32, 1), (31, 37), (41, 24), (11, 18), (30, 10), (16, 24), (43, 34), (25, 19), (22, 27), (35, 16), (17, 32), (44, 37), (6, 23), (3, 4), (46, 24), (35, 30), (27, 14), (9, 36), (25, 24), (23, 3), (39, 0), (26, 30), (22, 36), (23, 29), (40, 0), (40, 32), (0, 2), (36, 13), (40, 26), (20, 37), (23, 18), (28, 25), (14, 31), (43, 7), (12, 8), (11, 36), (25, 6), (34, 17), (38, 29), (29, 19), (5, 25), (23, 22), (6, 4), (22, 32), (45, 30), (9, 2), (5, 18), (28, 32), (41, 37), (26, 7), (16, 33), (40, 9), (3, 9), (7, 11), (23, 19), (37, 1), (20, 31), (18, 7), (46, 11), (43, 28), (32, 18), (47, 16), (3, 5), (29, 10), (4, 6), (21, 12), (41, 32), (26, 12), (21, 7), (42, 14), (5, 39), (33, 14), (38, 14), (4, 5), (11, 27), (47, 22), (9, 30), (38, 30), (6, 38), (34, 28), (30, 19), (11, 16), (9, 0), (16, 10), (24, 18), (20, 14), (17, 27), (7, 1), (2, 14), (15, 35), (19, 13), (28, 33), (36, 25), (8, 2), (1, 0), (16, 13), (16, 25), (33, 13), (14, 14), (6, 21), (24, 22), (22, 15), (6, 27), (38, 26), (18, 25), (39, 17), (17, 23), (45, 12), (25, 34), (13, 23), (38, 8), (7, 31), (7, 21), (16, 37), (42, 28), (37, 9), (41, 23), (6, 18), (44, 30), (31, 2), (18, 5), (11, 0), (18, 21), (41, 22), (4, 13), (4, 11), (17, 12), (32, 28), (17, 1), (17, 20), (29, 30), (0, 31), (46, 39), (37, 6), (21, 26), (7, 33), (24, 0), (22, 3), (45, 23), (21, 37), (32, 17), (30, 14), (44, 4), (34, 9), (34, 1), (31, 27), (23, 38), (34, 33), (14, 16), (8, 38), (24, 23), (18, 34), (31, 34), (21, 2), (15, 38), (32, 32), (8, 35), (29, 26), (6, 7), (15, 26), (4, 18), (46, 16), (1, 30), (43, 15), (43, 31), (8, 16), (5, 4), (16, 9), (44, 19), (33, 32), (37, 12), (39, 8), (3, 12), (21, 23), (1, 23), (10, 11), (21, 27), (18, 1), (12, 38), (16, 20), (39, 25), (6, 16), (10, 17), (32, 37), (5, 6), (7, 39), (38, 5), (24, 3), (18, 2), (5, 3), (17, 38), (25, 16), (28, 29), (19, 15), (2, 12), (28, 28), (22, 2), (33, 21), (27, 32), (40, 15), (12, 4), (0, 17), (30, 6), (41, 0), (44, 11), (38, 24), (6, 9), (27, 26), (7, 9), (39, 16), (7, 5), (5, 30), (22, 25), (3, 36), (39, 19), (13, 28), (1, 20), (36, 22), (34, 39), (30, 33), (20, 20), (26, 6), (17, 3), (8, 25), (30, 8), (22, 22), (47, 28), (26, 21), (12, 17), (23, 36), (28, 13), (34, 2), (38, 13), (2, 7), (46, 32), (8, 8), (8, 20), (20, 16), (15, 29), (43, 32), (19, 36), (6, 10), (33, 3), (28, 26), (47, 19), (47, 3), (19, 11), (42, 18), (15, 12), (28, 18), (45, 19), (28, 5), (10, 22), (31, 29), (1, 3), (10, 16), (26, 27), (8, 37), (12, 34), (25, 38), (13, 21), (15, 23), (37, 28), (42, 7), (43, 5), (39, 10), (9, 14), (4, 31), (41, 2), (20, 33), (44, 34), (47, 11), (11, 17), (47, 10), (35, 9), (4, 35), (32, 7), (31, 9), (13, 29), (0, 13), (16, 39), (40, 3), (11, 22), (4, 26), (7, 25), (9, 18), (46, 29), (6, 20), (36, 15), (8, 1), (44, 0), (8, 36), (25, 28), (25, 3), (36, 33), (14, 17), (42, 12), (30, 5), (32, 19), (6, 6), (40, 17), (33, 23), (10, 26), (6, 22), (43, 37), (46, 22), (2, 19), (43, 38), (14, 34), (45, 29), (21, 19), (26, 22), (21, 32), (32, 12), (18, 16), (14, 29), (23, 9), (11, 21), (18, 39), (11, 35), (34, 23), (41, 34), (17, 36), (39, 23), (20, 2), (3, 17), (16, 18), (15, 15), (26, 23), (33, 19), (44, 21), (25, 27), (3, 26), (13, 38), (40, 31), (1, 27), (35, 11), (19, 27), (18, 3), (20, 15), (4, 16), (21, 25), (22, 26), (0, 23), (8, 28), (5, 5), (43, 11), (2, 20), (45, 10), (9, 26), (30, 20), (29, 39), (16, 27), (18, 27), (19, 24), (10, 18), (36, 28), (14, 18), (7, 34), (0, 25), (24, 34), (24, 9), (32, 5), (6, 24), (36, 29), (42, 26), (4, 1), (15, 20), (43, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 15), (45, 26), (18, 36), (44, 19), (14, 20), (24, 44), (29, 3), (16, 23), (18, 3), (30, 7), (19, 28), (7, 25), (13, 11), (15, 12), (34, 37), (42, 23), (15, 37), (41, 22), (23, 22), (24, 21), (16, 44), (23, 7), (10, 4), (24, 9), (39, 23), (2, 1), (32, 7), (43, 0), (41, 47), (46, 11), (7, 22), (6, 32), (20, 18), (31, 0), (22, 38), (27, 25), (46, 6), (41, 14), (2, 28), (31, 37), (41, 48), (16, 2), (32, 34), (30, 26), (30, 23), (27, 37), (13, 1), (4, 21), (16, 22), (12, 33), (33, 21), (24, 4), (27, 4), (0, 12), (39, 36), (33, 3), (17, 0), (30, 2), (3, 10), (11, 44), (40, 15), (29, 28), (46, 5), (12, 9), (29, 33), (2, 26), (16, 40), (29, 24), (47, 8), (19, 39), (34, 22), (30, 17), (35, 12), (21, 18), (43, 41), (27, 28), (6, 3), (42, 4), (30, 9), (22, 15), (4, 37), (21, 48), (30, 13), (2, 37), (26, 16), (31, 29), (35, 6), (11, 25), (10, 1), (3, 36), (15, 33), (25, 45), (29, 38), (5, 8), (31, 36), (9, 0), (39, 29), (21, 8), (17, 27), (2, 13), (1, 25), (40, 22), (3, 11), (23, 16), (42, 11), (40, 3), (45, 5), (18, 4), (44, 3), (40, 0), (5, 12), (27, 27), (18, 25), (31, 42), (20, 40), (6, 20), (21, 6), (19, 5), (26, 28), (43, 13), (16, 30), (1, 43), (19, 25), (37, 23), (24, 47), (45, 8), (5, 34), (24, 0), (42, 31), (33, 20), (29, 31), (27, 12), (32, 26), (41, 46), (33, 5), (9, 7), (2, 35), (22, 9), (35, 14), (20, 7), (46, 31), (39, 41), (19, 42), (22, 27), (27, 7), (21, 46), (14, 15), (42, 29), (24, 31), (15, 35), (34, 47), (45, 40), (8, 0), (6, 19), (24, 43), (40, 48), (18, 31), (45, 45), (30, 47), (8, 32), (41, 25), (19, 29), (21, 27), (18, 22), (47, 30), (37, 35), (38, 24), (29, 35), (42, 20), (27, 23), (44, 11), (21, 16), (41, 8), (16, 13), (27, 31), (26, 0), (1, 33), (34, 29), (23, 9), (13, 2), (38, 48), (44, 9), (34, 15), (17, 17), (5, 45), (22, 24), (2, 29), (4, 20), (34, 2), (18, 17), (3, 3), (24, 6), (3, 13), (38, 36), (14, 32), (30, 18), (26, 4), (20, 14), (2, 23), (26, 31), (25, 44), (34, 35), (10, 13), (3, 22), (17, 33), (14, 41), (22, 44), (27, 39), (47, 24), (20, 17), (28, 14), (46, 8), (23, 36), (25, 15), (19, 16), (23, 27), (47, 42), (21, 7), (21, 47), (1, 18), (17, 46), (18, 40), (4, 38), (20, 22), (0, 47), (23, 30), (18, 34), (21, 14), (31, 35), (22, 19), (28, 36), (14, 28), (2, 14), (21, 32), (17, 2), (32, 16), (44, 48), (16, 25), (43, 14), (26, 10), (0, 20), (12, 26), (11, 10), (36, 29), (25, 10), (32, 46), (5, 2), (20, 2), (30, 8), (14, 14), (26, 44), (28, 46), (44, 12), (44, 26), (41, 16), (28, 34), (8, 4), (32, 15), (3, 9), (39, 6), (1, 17), (16, 20), (16, 0), (1, 20), (47, 47), (12, 48), (13, 9), (7, 44), (15, 16), (12, 11), (35, 24), (9, 11), (17, 48), (18, 26), (3, 43), (9, 23), (31, 41), (20, 0), (32, 6), (35, 22), (16, 5), (19, 8), (28, 40), (15, 15), (18, 44), (37, 40), (9, 35), (15, 4), (0, 3), (30, 32), (3, 28), (5, 41), (16, 48), (41, 31), (34, 5), (2, 25), (21, 3), (12, 43), (22, 16), (39, 48), (1, 36), (32, 24), (41, 37), (12, 15), (27, 36), (16, 4), (24, 30), (4, 30), (44, 35), (46, 36), (23, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 41), (30, 34), (13, 1), (24, 13), (37, 0), (19, 15), (13, 15), (36, 33), (17, 21), (31, 21), (0, 23), (36, 45), (36, 31), (23, 14), (32, 35), (3, 15), (0, 39), (28, 17), (13, 14), (3, 6), (33, 28), (29, 43), (2, 20), (25, 44), (17, 2), (35, 18), (7, 43), (4, 43), (14, 34), (25, 11), (18, 6), (10, 30), (11, 24), (41, 30), (1, 5), (40, 12), (29, 12), (44, 5), (11, 18), (40, 4), (21, 20), (16, 32), (42, 13), (22, 41), (14, 42), (25, 21), (0, 2), (40, 37), (36, 2), (9, 17), (9, 42), (26, 7), (8, 30), (34, 15), (24, 0), (21, 18), (27, 10), (36, 1), (24, 2), (20, 42), (37, 6), (32, 38), (42, 11), (44, 6), (40, 15), (39, 9), (29, 34), (15, 22), (41, 14), (42, 9), (28, 39), (11, 3), (2, 33), (0, 25), (10, 3), (7, 42), (38, 10), (34, 14), (43, 9), (19, 31), (7, 9), (4, 3), (8, 2), (3, 26), (4, 30), (43, 15), (31, 25), (28, 13), (12, 20), (11, 38), (17, 13), (16, 34), (25, 16), (14, 45), (39, 20), (25, 32), (3, 42), (22, 1), (23, 36), (43, 33), (0, 38), (9, 37), (36, 35), (43, 36), (32, 21), (24, 42), (4, 19), (30, 11), (6, 16), (23, 42), (3, 21), (8, 37), (36, 44), (17, 11), (31, 18), (21, 27), (10, 34), (15, 43), (37, 44), (12, 30), (1, 39), (10, 32), (14, 7), (22, 25), (24, 3), (36, 5), (11, 12), (37, 14), (16, 9), (35, 45), (19, 29), (26, 37), (15, 14), (33, 30), (16, 11), (37, 21), (0, 10), (40, 0), (4, 31), (22, 43), (11, 26), (16, 33), (11, 39), (16, 30), (39, 23), (26, 13), (31, 41), (28, 44), (12, 34), (4, 10), (11, 4), (1, 28), (21, 42), (34, 20), (17, 37), (8, 17), (32, 18), (28, 9), (3, 37), (4, 2), (9, 29), (35, 38), (30, 4), (44, 15), (29, 5), (13, 28), (22, 32), (7, 40), (27, 21), (39, 14), (19, 32), (20, 10), (44, 32), (14, 33), (2, 34), (12, 33), (4, 35), (12, 18), (36, 18), (36, 15), (14, 20), (11, 13), (39, 8), (41, 34), (19, 43), (6, 44), (5, 11), (5, 44), (2, 8), (13, 13), (32, 11), (3, 43), (6, 32), (8, 5), (1, 17), (32, 23), (13, 25), (8, 29), (26, 11), (29, 33), (31, 33), (44, 33), (11, 41), (10, 2), (22, 10), (20, 41), (42, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 1), (6, 41), (39, 38), (6, 15), (44, 6), (34, 0), (10, 20), (33, 33), (31, 11), (11, 7), (41, 35), (18, 8), (9, 41), (14, 28), (5, 44), (38, 5), (33, 26), (40, 13), (40, 37), (27, 25), (4, 20), (14, 21), (44, 44), (41, 33), (3, 13), (26, 23), (20, 30), (37, 9), (26, 4), (4, 35), (21, 20), (23, 27), (12, 40), (21, 34), (16, 47), (12, 10), (44, 9), (0, 11), (9, 27), (3, 15), (31, 8), (6, 20), (2, 31), (15, 32), (41, 4), (13, 38), (32, 25), (38, 28), (40, 20), (25, 0), (9, 29), (19, 40), (0, 28), (33, 18), (27, 36), (5, 33), (31, 35), (13, 33), (35, 28), (39, 25), (29, 46), (28, 2), (2, 13), (15, 22), (6, 19), (36, 43), (41, 27), (17, 9), (20, 3), (1, 23), (11, 0), (19, 41), (14, 17), (31, 9), (20, 41), (0, 4), (4, 3), (41, 39), (5, 24), (24, 44), (2, 20), (1, 0), (13, 30), (11, 29), (3, 12), (22, 43), (13, 14), (42, 6), (1, 10), (12, 8), (24, 5), (16, 16), (8, 8), (32, 22), (26, 11), (34, 17), (4, 14), (18, 35), (14, 41), (43, 24), (43, 41), (5, 17), (20, 23), (21, 19), (6, 38), (8, 9), (10, 37), (23, 24), (33, 10), (31, 18), (36, 42), (39, 37), (36, 32), (21, 38), (25, 40), (17, 4), (31, 44), (7, 30), (27, 28), (13, 3), (8, 42), (2, 16), (13, 40), (30, 32), (23, 32), (4, 23), (10, 33), (3, 19), (21, 17), (29, 22), (37, 32), (32, 14), (39, 31), (25, 25), (25, 7), (18, 11), (8, 11), (18, 10), (20, 46), (10, 2), (20, 21), (9, 17), (21, 28), (35, 5), (9, 32), (36, 12), (29, 18), (40, 27), (38, 16), (24, 9), (23, 5), (16, 28), (30, 13), (20, 40), (11, 12), (10, 8), (3, 16), (7, 27), (15, 18), (8, 35), (41, 26), (23, 17), (33, 28), (27, 27), (32, 1), (12, 31), (10, 43), (29, 30), (2, 43), (43, 42), (38, 23), (10, 1), (12, 42), (19, 17), (13, 7), (36, 13), (22, 45), (10, 31), (33, 1), (18, 21), (25, 22), (18, 34), (21, 39), (43, 20), (37, 37), (6, 11), (2, 44), (10, 0), (32, 44), (0, 19), (31, 14), (22, 28), (26, 17), (15, 21), (24, 6), (12, 22), (11, 25), (41, 44), (32, 19), (23, 30), (4, 19), (37, 39), (40, 23), (4, 37), (44, 27), (8, 34), (34, 3), (1, 29), (3, 32), (0, 26), (40, 29), (10, 9), (29, 43), (8, 13), (38, 2), (21, 35), (38, 24), (13, 45), (14, 36), (44, 42), (14, 9), (5, 42), (11, 23), (43, 7), (44, 31), (7, 41), (44, 14), (38, 22), (39, 22), (21, 13), (38, 0), (14, 35), (29, 44), (5, 1), (36, 10), (4, 28), (29, 13), (12, 28), (5, 5), (12, 16), (12, 14), (39, 36), (18, 28), (19, 28)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 5), (16, 17), (20, 22), (19, 19), (32, 27), (9, 32), (20, 46), (16, 22), (8, 16), (15, 29), (42, 45), (38, 34), (41, 18), (28, 39), (29, 27), (41, 42), (27, 41), (17, 25), (8, 43), (8, 28), (10, 32), (10, 30), (1, 39), (0, 10), (19, 41), (15, 14), (0, 6), (41, 39), (13, 15), (38, 44), (32, 4), (2, 2), (42, 34), (30, 30), (26, 14), (31, 42), (19, 33), (38, 18), (35, 41), (29, 7), (28, 19), (29, 28), (32, 19), (13, 45), (31, 22), (28, 34), (2, 5), (31, 10), (5, 8), (40, 6), (41, 27), (9, 26), (23, 42), (6, 33), (34, 15), (9, 35), (20, 42), (10, 37), (20, 24), (11, 42), (16, 24), (1, 21), (33, 11), (11, 29), (2, 7), (27, 5), (45, 18), (16, 5), (35, 32), (39, 46), (12, 42), (44, 0), (41, 45), (3, 2), (30, 1), (32, 40), (13, 25), (18, 24), (43, 15), (14, 43), (23, 2), (14, 29), (31, 13), (30, 25), (40, 20), (22, 44), (11, 39), (8, 18), (16, 12), (23, 15), (44, 23), (21, 34), (30, 28), (13, 37), (45, 29), (31, 39), (43, 18), (36, 2), (36, 0), (4, 24), (13, 19), (1, 42), (3, 45), (44, 43), (27, 16), (4, 1), (12, 11), (27, 32), (23, 44), (15, 36), (14, 24), (11, 23), (1, 0), (25, 18), (0, 18), (34, 30), (37, 8), (25, 19), (22, 36), (42, 17), (6, 22), (3, 20), (41, 28), (44, 38), (12, 16), (3, 0), (0, 3), (24, 5), (37, 45), (4, 43), (34, 12), (1, 16), (35, 39), (12, 2), (42, 8), (33, 19), (16, 7), (12, 41), (23, 27), (9, 29), (14, 18), (1, 17), (18, 21), (23, 14), (4, 16), (45, 27), (36, 46), (1, 14), (39, 42), (45, 36), (30, 14), (17, 10), (12, 14), (23, 41), (10, 19), (26, 20), (28, 6), (21, 19), (17, 41), (3, 32), (22, 28), (27, 42), (42, 25), (7, 7), (14, 5), (28, 36), (44, 15), (19, 16), (41, 15), (8, 6), (22, 5), (40, 9), (28, 23), (30, 15), (40, 10), (43, 11), (12, 22), (8, 0), (45, 1), (28, 27), (3, 42), (30, 40), (19, 22), (11, 9), (14, 33), (45, 22), (28, 13), (16, 41), (6, 34), (35, 14), (41, 36), (3, 24), (43, 22), (15, 27), (35, 24), (19, 23), (0, 28), (27, 8), (10, 39), (24, 25), (26, 15), (34, 4), (25, 17), (4, 44), (39, 19), (34, 9), (40, 43), (7, 3), (26, 36), (38, 20), (9, 20), (34, 28), (44, 16), (40, 5), (6, 19), (39, 15), (45, 19), (16, 19), (33, 15), (27, 9), (29, 13), (45, 17), (20, 3), (40, 30), (5, 44), (4, 19), (20, 40), (26, 0), (24, 24), (30, 26), (38, 33), (40, 38), (35, 37), (21, 43), (27, 7), (27, 43), (24, 16), (32, 45), (23, 33), (7, 23), (8, 46)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 5), (8, 6), (4, 23), (3, 23), (14, 2), (23, 21), (45, 18), (42, 5), (22, 1), (21, 6), (38, 8), (18, 32), (32, 21), (22, 40), (27, 12), (2, 29), (15, 15), (5, 24), (11, 40), (15, 24), (45, 25), (26, 23), (24, 22), (0, 20), (7, 36), (4, 32), (15, 21), (28, 18), (35, 31), (19, 21), (4, 31), (41, 34), (0, 5), (13, 12), (8, 23), (33, 37), (33, 32), (5, 37), (30, 4), (1, 26), (9, 22), (44, 2), (13, 11), (11, 1), (23, 6), (22, 13), (7, 9), (3, 26), (40, 10), (33, 31), (35, 28), (18, 17), (5, 12), (17, 22), (3, 40), (8, 22), (21, 10), (29, 21), (30, 28), (45, 37), (40, 18), (16, 40), (39, 29), (6, 16), (30, 17), (7, 17), (12, 32), (1, 21), (28, 8), (33, 40), (29, 26), (7, 3), (6, 33), (15, 30), (20, 2), (7, 26), (3, 17), (7, 14), (41, 32), (26, 21), (38, 22), (21, 7), (15, 28), (26, 31), (17, 6), (24, 28), (2, 7), (7, 12), (37, 33), (4, 37), (2, 16), (5, 18), (41, 19), (41, 10), (5, 14), (20, 36), (11, 31), (7, 28), (16, 11), (37, 40), (2, 35), (37, 14), (15, 33), (22, 10), (2, 6), (43, 20), (37, 19), (31, 14), (28, 29), (11, 10), (36, 26), (31, 21), (15, 37), (10, 23), (37, 0), (20, 6), (37, 18), (34, 6), (31, 22), (25, 40), (9, 15), (2, 26), (39, 11), (22, 14), (39, 36), (11, 34), (1, 0), (39, 24), (21, 14), (29, 0), (42, 35), (13, 8), (13, 13), (22, 16), (7, 37), (9, 33), (36, 1), (27, 25), (45, 21), (2, 10), (29, 10), (27, 18), (19, 20), (26, 27), (25, 1), (44, 11), (29, 19), (22, 30), (36, 2), (11, 36), (43, 35), (17, 7), (17, 15), (42, 33), (23, 36), (18, 24), (21, 29), (22, 27), (6, 34), (13, 10), (28, 20), (13, 0), (20, 15), (8, 40), (7, 10), (45, 2), (11, 35), (5, 10), (35, 40), (39, 18), (19, 33), (31, 30), (12, 21), (4, 40), (32, 31), (35, 14), (22, 37), (2, 25), (27, 13), (19, 18), (31, 36), (2, 33), (37, 16), (26, 37), (13, 35), (25, 7), (24, 3), (29, 29), (24, 30), (44, 40), (23, 32), (32, 27), (10, 19), (28, 39), (41, 1), (20, 31), (16, 6), (43, 4), (19, 11), (2, 18), (12, 40), (0, 13), (31, 15), (28, 4), (14, 25), (40, 4), (32, 18), (41, 0), (30, 14), (40, 16), (5, 31), (18, 1), (25, 32), (4, 15), (30, 3), (8, 10), (20, 4), (6, 1), (31, 5), (44, 10), (20, 1), (39, 3), (38, 7), (34, 33), (30, 13), (27, 22), (7, 15), (9, 3), (3, 2), (25, 17), (16, 31), (37, 3), (11, 28), (2, 28), (45, 12), (39, 28), (25, 24), (19, 19), (20, 39), (39, 14), (2, 14), (43, 3), (10, 32), (0, 7), (5, 30), (34, 30), (30, 19), (22, 17), (40, 7), (21, 38), (40, 21), (9, 12), (9, 16), (16, 12), (21, 30), (20, 7), (31, 26), (4, 27), (33, 4), (7, 6), (37, 9), (6, 6), (45, 7), (16, 26), (40, 26), (16, 16), (14, 9), (24, 5), (10, 3), (38, 25), (32, 20), (31, 28), (16, 39), (33, 20), (24, 2), (21, 22), (31, 27), (19, 10), (9, 32), (6, 9), (12, 26), (43, 6), (8, 16), (39, 2), (36, 19), (12, 34), (28, 38), (31, 39), (22, 2), (20, 5), (15, 29), (39, 6), (26, 30), (20, 9), (2, 38), (41, 12), (28, 36), (39, 19), (8, 11), (45, 19), (4, 26), (32, 37), (35, 35), (34, 5), (39, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (24, 18), (19, 45), (17, 38), (3, 14), (0, 33), (26, 9), (34, 1), (41, 26), (32, 14), (22, 18), (5, 30), (32, 29), (26, 37), (28, 2), (12, 3), (31, 6), (19, 36), (41, 37), (18, 9), (35, 42), (6, 3), (28, 45), (37, 42), (18, 3), (24, 41), (40, 34), (28, 23), (33, 24), (6, 25), (45, 24), (0, 5), (7, 11), (36, 42), (47, 40), (10, 20), (20, 42), (5, 16), (27, 16), (3, 5), (38, 6), (19, 14), (30, 8), (25, 37), (43, 3), (8, 30), (45, 27), (2, 32), (13, 7), (41, 11), (0, 41), (19, 11), (39, 19), (7, 7), (41, 2), (18, 2), (7, 18), (8, 34), (27, 35), (2, 18), (1, 46), (45, 32), (11, 23), (32, 36), (30, 45), (11, 22), (11, 31), (36, 44), (41, 31), (16, 41), (9, 3), (22, 44), (23, 18), (47, 42), (28, 41), (9, 30), (0, 11), (41, 9), (46, 28), (16, 6), (25, 20), (19, 2), (42, 0), (42, 25), (4, 28), (46, 38), (12, 4), (20, 31), (15, 36), (10, 34), (47, 12), (19, 4), (12, 24), (28, 0), (20, 23), (5, 33), (4, 25), (29, 37), (44, 12), (2, 10), (18, 6), (20, 30), (13, 44), (45, 44), (43, 14), (1, 44), (2, 37), (15, 7), (40, 6), (3, 9), (12, 12), (25, 28), (22, 43), (2, 17), (42, 14), (12, 25), (6, 1), (24, 19), (0, 19), (6, 28), (3, 26), (16, 7), (5, 13), (39, 5), (31, 26), (31, 8), (35, 46), (25, 24), (8, 2), (18, 1), (21, 18), (26, 41), (42, 22), (33, 21), (1, 12), (27, 1), (39, 34), (6, 11), (19, 12), (20, 34), (43, 32), (19, 1), (23, 0), (11, 28), (16, 19), (4, 27), (46, 25), (20, 39), (19, 29), (25, 22), (42, 27), (14, 8), (31, 1), (29, 25), (47, 2), (4, 34), (12, 8), (26, 42), (2, 11), (26, 2), (31, 24), (29, 36), (1, 34), (1, 33), (42, 46), (18, 24), (27, 30), (44, 16), (37, 17), (16, 27), (45, 33), (30, 19), (3, 25), (8, 8), (37, 9), (45, 3), (10, 46), (29, 19), (34, 33), (28, 13), (22, 13), (9, 9), (37, 32), (3, 24), (28, 44), (3, 33), (46, 44), (24, 28), (43, 27), (21, 11), (2, 25), (20, 14), (15, 4), (25, 30), (4, 13), (42, 34), (30, 2), (31, 0), (25, 33), (38, 0), (42, 33), (20, 36), (4, 8), (47, 1), (37, 10), (45, 34), (29, 8), (15, 24), (12, 9), (1, 5), (46, 27), (22, 21), (44, 44), (47, 3), (26, 17), (14, 44), (40, 45), (17, 39), (5, 20), (40, 3), (31, 2), (37, 31), (6, 13), (37, 41), (33, 1), (25, 8), (38, 8), (21, 5), (17, 16), (42, 2), (5, 31), (28, 22), (24, 39), (13, 42), (26, 36), (44, 27), (37, 29), (46, 5), (27, 11), (4, 44), (46, 36), (39, 4), (5, 6), (26, 19), (18, 45), (12, 16), (22, 23), (31, 38), (10, 38), (30, 24), (11, 32), (32, 3), (13, 16), (1, 10), (12, 38), (32, 40), (38, 18), (29, 41), (46, 42), (28, 11), (22, 5), (35, 16), (35, 30), (24, 38), (36, 14), (24, 27), (29, 45), (42, 5), (4, 41), (5, 3), (0, 23), (1, 30), (23, 17), (25, 10), (17, 0), (11, 30), (0, 4), (32, 17), (14, 11), (40, 7), (0, 32), (4, 22), (14, 26), (47, 35), (27, 7), (23, 43), (17, 41), (29, 3), (1, 9), (47, 21), (21, 32), (6, 24), (22, 8), (12, 44), (44, 15), (10, 22), (39, 15), (19, 22), (7, 33), (9, 6), (41, 21), (21, 22), (42, 45), (45, 17), (26, 30), (9, 22), (1, 0), (31, 37), (16, 43), (28, 6), (14, 40), (20, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 48x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 31), (26, 11), (26, 13), (46, 1), (32, 30), (37, 29), (10, 11), (16, 24), (1, 10), (33, 28), (12, 34), (24, 47), (25, 11), (34, 9), (10, 10), (2, 16), (30, 14), (23, 2), (2, 24), (4, 15), (24, 12), (24, 25), (17, 24), (2, 4), (25, 15), (47, 18), (27, 39), (28, 43), (29, 6), (29, 8), (34, 39), (4, 34), (24, 34), (22, 33), (22, 0), (42, 42), (7, 40), (21, 1), (38, 22), (14, 18), (38, 25), (45, 44), (32, 24), (18, 4), (47, 12), (10, 1), (41, 4), (44, 27), (45, 36), (29, 20), (35, 25), (31, 18), (33, 39), (12, 37), (15, 3), (1, 6), (22, 19), (19, 22), (23, 23), (43, 24), (4, 11), (15, 29), (37, 35), (47, 28), (29, 31), (3, 20), (9, 7), (39, 5), (42, 31), (8, 21), (44, 48), (5, 21), (0, 37), (0, 5), (5, 45), (36, 21), (29, 41), (8, 18), (25, 42), (9, 46), (29, 1), (12, 20), (47, 42), (31, 16), (6, 3), (38, 46), (42, 46), (30, 2), (26, 23), (42, 35), (19, 37), (31, 36), (15, 44), (25, 47), (16, 3), (9, 47), (12, 38), (10, 48), (12, 46), (25, 28), (6, 37), (39, 31), (21, 15), (14, 37), (27, 28), (33, 20), (3, 6), (28, 15), (20, 8), (10, 35), (18, 44), (8, 29), (9, 14), (30, 20), (0, 3), (1, 34), (47, 32), (41, 18), (17, 5), (29, 17), (16, 18), (28, 41), (8, 22), (7, 3), (26, 12), (21, 21), (12, 36), (27, 22), (21, 40), (1, 40), (11, 12), (25, 7), (29, 22), (18, 16), (40, 0), (8, 1), (12, 21), (11, 29), (34, 26), (0, 8), (18, 8), (11, 21), (45, 0), (38, 39), (14, 14), (43, 42), (10, 17), (14, 44), (37, 47), (25, 44), (37, 26), (14, 27), (42, 19), (16, 15), (31, 1), (44, 6), (24, 23), (40, 33), (4, 40), (5, 7), (28, 48), (28, 10), (33, 36), (30, 16), (34, 32), (22, 17), (34, 17), (6, 18), (4, 16), (39, 24), (23, 44), (17, 18), (11, 33), (25, 14), (9, 40), (41, 14), (5, 32), (15, 26), (38, 47), (39, 16), (8, 13), (21, 6), (1, 11), (21, 29), (28, 40), (11, 40), (37, 41), (1, 42), (31, 28), (24, 5), (38, 16), (15, 30), (25, 8), (24, 27), (38, 15), (11, 23), (12, 5), (1, 22), (2, 48), (35, 23), (5, 12), (2, 43), (37, 38), (0, 19), (10, 9), (47, 37), (38, 8), (18, 26), (27, 8), (28, 14), (0, 12), (10, 13), (19, 36), (20, 9), (31, 6), (15, 19), (6, 6), (36, 48), (43, 46), (46, 12), (37, 9), (19, 18), (38, 48), (46, 31), (18, 13), (21, 47), (20, 1), (31, 29), (0, 13), (2, 44), (21, 44), (19, 4), (11, 31), (39, 0), (20, 7), (16, 8), (39, 47), (17, 46), (33, 17), (45, 11), (38, 7), (10, 12), (30, 47), (29, 39), (31, 2), (5, 27), (11, 34), (6, 44), (5, 19), (13, 41), (36, 38), (46, 33), (0, 6), (12, 4), (24, 45), (38, 40), (44, 42), (36, 3), (39, 19), (16, 7), (42, 13), (42, 23), (28, 44), (47, 10), (4, 2), (46, 39), (9, 3), (4, 6), (8, 43), (38, 10), (33, 1), (15, 37), (42, 36), (36, 46), (6, 34), (5, 41), (29, 47), (40, 37), (38, 36), (11, 43), (42, 37), (10, 20), (27, 10), (29, 37), (46, 20), (2, 18), (15, 7), (22, 4), (41, 5), (8, 2), (40, 5), (6, 23), (14, 30), (11, 41), (21, 20), (10, 46), (13, 35), (26, 6), (31, 39), (43, 38), (43, 11), (31, 12), (15, 10), (4, 26), (18, 2), (33, 18), (45, 16), (5, 13), (8, 15), (45, 26), (17, 28), (31, 15), (44, 34), (3, 15), (22, 30), (4, 41), (37, 34), (42, 1), (42, 12), (11, 44), (20, 10), (21, 9), (16, 6), (15, 1), (39, 46), (29, 35), (44, 37), (27, 0), (27, 32), (15, 42), (40, 8), (19, 39), (20, 44), (36, 29), (6, 38), (11, 47), (14, 38), (17, 26), (38, 21), (3, 17), (43, 5), (43, 14), (24, 16), (33, 2), (31, 47), (20, 18), (47, 33), (23, 48), (20, 21), (10, 27), (47, 14), (40, 41), (0, 17), (14, 15), (47, 22), (2, 11), (26, 22), (23, 41), (8, 44), (10, 29), (0, 39), (45, 31), (34, 16), (15, 43), (25, 18), (31, 44), (46, 13), (46, 34), (41, 44), (10, 41), (7, 9), (23, 19), (3, 33), (5, 44), (17, 3), (31, 43), (11, 10), (33, 29), (6, 46), (39, 40), (37, 37), (22, 20), (27, 21), (31, 34), (1, 44), (43, 31), (5, 0), (2, 27), (40, 34), (25, 48), (19, 12), (38, 24), (36, 43), (12, 9), (28, 29), (46, 32), (8, 20), (10, 18), (8, 40), (1, 15), (5, 10), (35, 28), (10, 14), (26, 5), (19, 11), (9, 38), (36, 5), (5, 1), (20, 27), (7, 37), (0, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 10), (13, 11), (36, 38), (24, 18), (2, 27), (13, 6), (40, 2), (26, 33), (32, 11), (14, 23), (11, 39), (15, 23), (9, 34), (12, 24), (18, 35), (34, 29), (12, 10), (5, 30), (29, 12), (8, 14), (1, 38), (34, 14), (26, 10), (1, 21), (22, 27), (27, 20), (16, 18), (0, 37), (41, 25), (11, 0), (14, 16), (41, 30), (20, 4), (13, 34), (16, 24), (20, 7), (10, 27), (26, 15), (36, 5), (14, 39), (39, 23), (1, 34), (4, 0), (0, 21), (19, 26), (26, 37), (6, 20), (21, 14), (24, 30), (13, 9), (22, 20), (4, 8), (6, 9), (26, 21), (18, 36), (23, 34), (7, 17), (17, 15), (17, 30), (2, 36), (0, 23), (17, 18), (37, 31), (41, 16), (22, 12), (17, 38), (6, 37), (10, 29), (1, 29), (20, 22), (22, 4), (7, 35), (10, 30), (20, 37), (22, 35), (42, 23), (35, 32), (5, 24), (29, 23), (33, 34), (31, 35), (39, 10), (20, 1), (17, 31), (13, 31), (25, 26), (3, 6), (4, 32), (5, 23), (20, 33), (25, 20), (0, 7), (10, 20), (40, 0), (42, 20), (12, 13), (42, 8), (34, 4), (15, 1), (31, 26), (21, 11), (35, 4), (27, 7), (9, 25), (25, 15), (20, 14), (3, 36), (41, 5), (19, 10), (1, 25), (19, 33), (14, 29), (39, 16), (32, 26), (32, 18), (0, 13), (35, 18), (23, 10), (26, 32), (17, 11), (26, 8), (39, 27), (5, 2), (23, 21), (17, 20), (37, 24), (15, 5), (17, 1), (6, 30), (30, 32), (30, 1), (35, 13), (4, 7), (4, 26), (29, 15), (38, 28), (29, 29), (7, 9), (13, 36), (29, 18), (15, 8), (11, 17), (3, 2), (37, 22), (17, 5), (8, 20), (27, 1), (30, 29), (11, 2), (26, 3), (25, 37), (14, 37), (40, 27), (42, 19), (19, 8), (35, 0), (28, 12), (24, 13), (27, 19), (36, 32), (28, 30), (5, 22), (38, 24), (28, 29), (1, 32), (27, 28), (8, 19), (21, 32), (41, 33), (40, 22), (1, 33), (38, 13), (8, 16), (15, 19), (7, 27), (37, 26), (16, 32), (42, 4), (14, 31), (26, 22), (6, 14), (13, 35), (24, 25), (40, 8), (2, 31), (28, 1), (29, 0), (3, 35), (4, 27), (10, 8), (37, 4), (13, 2), (4, 6), (21, 33), (18, 26), (14, 2), (31, 39), (31, 7), (32, 17), (22, 9), (2, 4), (0, 6), (24, 7), (5, 5), (39, 20), (31, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 42), (0, 24), (18, 27), (22, 32), (31, 9), (6, 6), (1, 9), (21, 20), (33, 38), (25, 24), (9, 11), (25, 16), (9, 29), (25, 15), (24, 0), (18, 38), (13, 34), (9, 14), (28, 39), (3, 17), (1, 43), (19, 25), (28, 26), (24, 13), (32, 44), (16, 44), (38, 34), (3, 47), (28, 13), (27, 41), (17, 38), (35, 23), (17, 29), (25, 45), (18, 9), (6, 47), (5, 18), (0, 22), (19, 12), (37, 1), (23, 0), (40, 39), (27, 19), (31, 25), (27, 26), (33, 10), (20, 1), (9, 1), (39, 12), (18, 4), (32, 45), (34, 38), (15, 32), (5, 44), (4, 10), (18, 17), (11, 33), (34, 3), (35, 14), (7, 9), (22, 15), (3, 48), (2, 25), (22, 40), (34, 11), (3, 0), (27, 28), (22, 20), (23, 42), (0, 35), (34, 9), (21, 32), (26, 1), (1, 48), (1, 46), (23, 27), (0, 39), (29, 23), (37, 3), (23, 33), (38, 12), (5, 38), (29, 14), (4, 31), (34, 2), (23, 28), (38, 5), (1, 34), (37, 26), (1, 33), (21, 31), (4, 0), (27, 11), (19, 3), (1, 8), (20, 35), (24, 4), (30, 30), (26, 42), (28, 17), (8, 46), (3, 39), (5, 22), (34, 16), (10, 33), (20, 44), (21, 10), (28, 10), (27, 10), (17, 44), (4, 1), (10, 15), (7, 28), (27, 3), (6, 15), (33, 23), (5, 7), (12, 40), (39, 20), (31, 47), (20, 3), (12, 47), (40, 24), (8, 13), (34, 32), (24, 35), (6, 1), (9, 7), (25, 17), (33, 17), (37, 8), (22, 44), (40, 2), (11, 43), (4, 13), (18, 47), (3, 21), (22, 4), (8, 26), (3, 31), (24, 18), (7, 43), (3, 30), (22, 35), (12, 19), (32, 16), (7, 21), (35, 8), (15, 24), (18, 42), (35, 10), (0, 46), (27, 12), (28, 43), (20, 18), (37, 32), (35, 37), (35, 36), (8, 47), (15, 37), (28, 36), (20, 40), (30, 20), (36, 43), (36, 4), (34, 14), (19, 20), (19, 1), (27, 45), (37, 20), (16, 46), (16, 28), (38, 48), (37, 12), (38, 6), (38, 17), (24, 22), (7, 0), (24, 28), (38, 27), (38, 37), (14, 13), (11, 38), (26, 9), (9, 41), (29, 1), (18, 44), (23, 4), (6, 11), (29, 39), (22, 33), (0, 6), (28, 14), (1, 4), (6, 24), (26, 3), (33, 31), (3, 29), (21, 37), (32, 21), (29, 36), (35, 34), (2, 4), (23, 3), (23, 35), (17, 42), (36, 22), (39, 21), (4, 12), (28, 33), (7, 13), (10, 22), (19, 34), (6, 40), (33, 14), (14, 0), (22, 47), (10, 34), (15, 47), (11, 16), (34, 28), (39, 44), (7, 26), (9, 31), (33, 8), (36, 42), (32, 40), (12, 6), (25, 7), (11, 9), (39, 31), (20, 13), (39, 19), (30, 36), (5, 2), (8, 27), (24, 23), (16, 27), (37, 5), (5, 8), (10, 35), (35, 24), (26, 44), (21, 1), (4, 5), (3, 46), (13, 11), (7, 34), (5, 46), (25, 41), (34, 43), (19, 2), (35, 29), (15, 26), (7, 16), (11, 4), (38, 29), (15, 21), (13, 25), (22, 27), (20, 26), (23, 19), (17, 14), (12, 15), (19, 4), (30, 25), (14, 9), (21, 28), (12, 46), (5, 21), (27, 27), (38, 41), (22, 14), (26, 26), (17, 0), (15, 36), (11, 20), (26, 46), (16, 11), (26, 40), (9, 21), (7, 32), (24, 37), (14, 10), (5, 20), (35, 15), (38, 26), (33, 24), (35, 47), (26, 34), (18, 5), (0, 12), (1, 29), (23, 6), (24, 41), (22, 12), (24, 29), (21, 23), (28, 0), (24, 47), (28, 19), (20, 41), (32, 47), (35, 7), (28, 5), (15, 22), (21, 19), (31, 35), (29, 47), (20, 24), (22, 21), (12, 7), (39, 46), (39, 18), (17, 10), (30, 2), (3, 35), (18, 37), (25, 8), (31, 33), (28, 6), (11, 39), (8, 48), (3, 20), (9, 16), (0, 26), (2, 43), (36, 29), (39, 2), (21, 45), (20, 17), (16, 36), (34, 30), (5, 29), (38, 7), (25, 20), (40, 18), (12, 33), (39, 36), (40, 32), (23, 17), (16, 7), (2, 35), (21, 40), (37, 2), (7, 18), (24, 27), (17, 27), (13, 14), (22, 18), (7, 1), (12, 31), (3, 45), (6, 4), (37, 43), (22, 13), (27, 48), (4, 43), (18, 13), (8, 32), (36, 35), (40, 46), (15, 40), (32, 0), (14, 34), (24, 43), (16, 35), (20, 10), (3, 25), (36, 48), (29, 13), (23, 5), (11, 0), (34, 1), (1, 11), (27, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (3, 39), (41, 37), (1, 30), (9, 28), (16, 19), (25, 35), (20, 25), (6, 14), (18, 17), (16, 38), (31, 14), (19, 32), (11, 21), (26, 38), (6, 21), (1, 21), (38, 22), (40, 33), (0, 20), (30, 6), (40, 18), (23, 34), (32, 11), (16, 35), (4, 37), (6, 0), (4, 5), (34, 34), (19, 25), (44, 4), (25, 13), (27, 23), (34, 3), (39, 0), (24, 22), (23, 11), (44, 22), (22, 44), (25, 38), (40, 20), (42, 42), (41, 44), (7, 21), (17, 28), (41, 38), (32, 8), (43, 27), (33, 33), (33, 29), (3, 45), (36, 21), (22, 43), (44, 17), (21, 13), (26, 30), (18, 22), (15, 5), (27, 16), (3, 30), (42, 17), (17, 10), (23, 1), (3, 27), (5, 43), (38, 37), (41, 40), (2, 14), (38, 17), (1, 42), (10, 34), (24, 29), (42, 3), (2, 23), (15, 44), (40, 6), (30, 25), (40, 36), (37, 7), (0, 15), (23, 17), (31, 20), (13, 26), (19, 22), (21, 14), (22, 8), (32, 33), (29, 45), (30, 36), (19, 4), (15, 18), (3, 22), (16, 37), (18, 20), (1, 17), (30, 45), (41, 9), (44, 34), (32, 7), (7, 14), (44, 7), (1, 9), (40, 26), (43, 7), (7, 10), (9, 9), (38, 42), (22, 0), (43, 20), (34, 21), (3, 42), (27, 45), (6, 38), (33, 3), (17, 34), (25, 12), (38, 8), (35, 6), (34, 37), (37, 19), (37, 39), (23, 13), (42, 6), (1, 44), (5, 32), (26, 45), (38, 19), (37, 3), (30, 9), (23, 33), (34, 5), (5, 16), (42, 1), (17, 12), (18, 7), (28, 29), (23, 44), (17, 6), (24, 1), (38, 7), (41, 17), (20, 4), (19, 6), (9, 37), (16, 29), (34, 35), (13, 37), (42, 23), (13, 18), (1, 20), (39, 24), (44, 35), (21, 41), (21, 43), (6, 12), (19, 0), (33, 20), (16, 30), (40, 8), (39, 8), (25, 8), (23, 21), (32, 28), (1, 18), (35, 5), (15, 31), (15, 25), (11, 25), (10, 37), (43, 45), (4, 31), (34, 1), (8, 18), (43, 40), (39, 21), (26, 36), (34, 2), (35, 18), (17, 22), (22, 37), (17, 16), (26, 35), (3, 15), (9, 31), (43, 24), (35, 15), (22, 45), (41, 36), (18, 34), (42, 16), (24, 28), (33, 26), (18, 2), (32, 42), (13, 4), (36, 12), (28, 1), (28, 33), (42, 7), (17, 26), (11, 16), (39, 22), (26, 2), (12, 2), (13, 17), (42, 19), (26, 26), (11, 0), (3, 13), (23, 42), (4, 34), (43, 43), (8, 5), (39, 12), (30, 3), (18, 30), (24, 3), (6, 34), (44, 10), (20, 27), (33, 25), (8, 21), (6, 31), (34, 23), (27, 6), (28, 9), (32, 34), (28, 10), (17, 15), (27, 8), (37, 35), (35, 33), (35, 12), (22, 10), (22, 18), (12, 43), (25, 11), (38, 14), (1, 39), (17, 40), (29, 16), (7, 25), (15, 3), (4, 9), (32, 17), (44, 6), (31, 31), (21, 35), (3, 0), (3, 10), (42, 0), (16, 36), (43, 36), (34, 45), (17, 45), (0, 41), (37, 11), (41, 45), (24, 44), (21, 15), (30, 12), (6, 29), (20, 3), (13, 38), (19, 23), (31, 30), (22, 14), (5, 9), (26, 29), (37, 38), (25, 28), (14, 1), (44, 15), (37, 28), (37, 43), (36, 20), (44, 24), (1, 29), (4, 3), (0, 2), (11, 43), (9, 26), (25, 36), (7, 45), (23, 15), (19, 45), (42, 37), (26, 32), (6, 2), (6, 6), (37, 4), (7, 34), (32, 9), (33, 41), (4, 0), (4, 12), (9, 20), (35, 34), (26, 43), (9, 36), (29, 8), (6, 33), (31, 1), (39, 19), (22, 23), (39, 33), (42, 31), (26, 31), (22, 7), (9, 23), (31, 21), (11, 5), (8, 6), (0, 9), (39, 43), (30, 13), (19, 44), (2, 26), (24, 39), (28, 30), (13, 0), (33, 45), (40, 14), (0, 30), (33, 39), (44, 42), (17, 35), (38, 34), (23, 5), (3, 19), (16, 5), (26, 8), (37, 2), (12, 3), (11, 36), (7, 15), (27, 18), (5, 19), (17, 0), (5, 22), (38, 27), (0, 37), (2, 25), (23, 30), (11, 20), (18, 27), (29, 43), (42, 38), (19, 11), (25, 45), (39, 27), (35, 17), (0, 5), (30, 40), (29, 19), (7, 8), (40, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 48x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 30), (29, 25), (37, 31), (9, 33), (35, 12), (47, 31), (40, 9), (33, 39), (35, 39), (43, 1), (39, 12), (43, 33), (15, 40), (20, 16), (33, 29), (5, 27), (12, 21), (44, 8), (8, 27), (19, 40), (9, 9), (31, 25), (26, 18), (6, 7), (11, 5), (0, 12), (14, 30), (12, 39), (45, 39), (17, 28), (41, 30), (42, 35), (44, 22), (42, 29), (8, 33), (16, 31), (42, 7), (24, 16), (36, 24), (9, 14), (42, 23), (38, 35), (47, 18), (21, 2), (46, 13), (39, 8), (30, 22), (39, 17), (20, 22), (8, 11), (15, 13), (42, 17), (11, 10), (35, 9), (36, 1), (32, 11), (7, 22), (24, 21), (44, 18), (30, 14), (4, 34), (24, 23), (23, 36), (46, 24), (44, 20), (29, 36), (20, 39), (28, 36), (41, 37), (7, 8), (12, 0), (0, 31), (29, 10), (33, 1), (18, 23), (45, 33), (1, 11), (8, 3), (10, 29), (42, 16), (1, 20), (29, 35), (39, 2), (10, 36), (40, 34), (38, 13), (28, 33), (25, 6), (8, 22), (44, 12), (30, 20), (6, 2), (12, 37), (22, 16), (29, 5), (25, 3), (21, 15), (37, 7), (8, 26), (43, 30), (30, 27), (5, 40), (32, 15), (32, 27), (38, 22), (33, 7), (34, 7), (6, 19), (34, 25), (1, 31), (25, 28), (19, 30), (28, 9), (23, 38), (34, 31), (29, 16), (13, 23), (40, 5), (15, 39), (38, 0), (12, 35), (15, 27), (36, 29), (5, 26), (26, 28), (2, 2), (16, 1), (35, 0), (16, 7), (23, 37), (1, 3), (33, 36), (18, 3), (31, 4), (45, 35), (23, 35), (32, 35), (5, 20), (18, 22), (13, 20), (38, 32), (10, 20), (27, 10), (37, 32), (10, 34), (10, 5), (11, 17), (28, 3), (35, 24), (11, 37), (38, 37), (1, 10), (42, 37), (44, 9), (14, 28), (14, 36), (25, 26), (22, 25), (4, 39), (21, 23), (33, 22), (29, 30), (46, 3), (2, 22), (43, 2), (34, 21), (9, 40), (21, 40), (21, 5), (45, 1), (11, 19), (34, 29), (18, 5), (10, 16), (2, 25), (6, 32), (29, 33), (2, 14), (24, 9), (14, 7), (7, 14), (31, 37), (13, 4), (29, 18), (10, 6), (25, 21), (28, 38), (46, 39), (19, 19), (23, 15), (11, 29), (43, 34), (24, 27), (5, 28), (18, 20), (13, 34), (37, 22), (14, 6), (22, 12), (32, 8), (2, 18), (16, 27), (26, 5), (10, 19), (18, 17), (15, 31), (47, 12), (42, 34), (4, 12), (24, 33), (26, 24), (33, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 38), (7, 28), (18, 35), (8, 18), (6, 21), (34, 11), (21, 37), (11, 6), (5, 36), (14, 23), (27, 33), (28, 29), (33, 29), (18, 34), (3, 36), (22, 16), (12, 35), (28, 4), (47, 25), (8, 22), (20, 43), (35, 24), (6, 30), (14, 8), (19, 6), (6, 27), (10, 24), (8, 31), (29, 44), (34, 23), (13, 38), (41, 20), (27, 31), (17, 1), (18, 32), (2, 26), (25, 35), (33, 23), (43, 3), (31, 18), (17, 0), (1, 40), (13, 41), (5, 32), (27, 32), (15, 2), (28, 18), (10, 7), (1, 34), (27, 27), (30, 2), (2, 33), (18, 3), (13, 39), (39, 33), (16, 30), (13, 3), (41, 40), (18, 14), (15, 9), (17, 31), (27, 24), (0, 38), (27, 9), (48, 21), (2, 20), (46, 12), (17, 33), (7, 20), (10, 43), (46, 8), (18, 16), (0, 25), (29, 41), (40, 0), (30, 38), (43, 26), (2, 25), (37, 18), (44, 0), (11, 10), (20, 20), (21, 8), (10, 44), (32, 31), (39, 43), (45, 31), (37, 20), (3, 23), (1, 6), (0, 6), (9, 41), (4, 6), (14, 21), (2, 34), (15, 44), (7, 40), (0, 18), (32, 10), (5, 15), (47, 8), (9, 27), (24, 42), (20, 41), (8, 13), (12, 32), (47, 43), (12, 18), (26, 19), (21, 18), (8, 36), (11, 30), (44, 7), (6, 7), (30, 44), (11, 44), (27, 0), (15, 40), (30, 24), (8, 12), (0, 10), (0, 13), (1, 28), (42, 30), (22, 31), (17, 11), (30, 40), (4, 39), (35, 42), (47, 29), (39, 1), (42, 40), (10, 22), (18, 26), (22, 22), (34, 37), (40, 17), (48, 5), (25, 3), (10, 5), (35, 33), (43, 20), (37, 41), (1, 13), (30, 41), (34, 10), (17, 16), (48, 36), (31, 0), (46, 30), (15, 3), (0, 37), (8, 5), (0, 12), (1, 42), (6, 0), (5, 37), (33, 2), (7, 8), (47, 17), (26, 44), (33, 17), (10, 19), (20, 6), (41, 19), (28, 8), (8, 25), (47, 38), (18, 4), (7, 33), (12, 1), (21, 38), (39, 24), (7, 35), (25, 14), (15, 20), (47, 30), (42, 5), (30, 43), (28, 5), (2, 1), (48, 18), (31, 17), (23, 12), (18, 12), (9, 9), (16, 36), (39, 40), (29, 8), (14, 16), (2, 28), (5, 43), (42, 8), (30, 16), (23, 23), (4, 23), (18, 30), (24, 16), (26, 2), (15, 11), (32, 7), (5, 3), (44, 34), (36, 23), (20, 30), (48, 15), (18, 13), (37, 3), (8, 30), (40, 5), (44, 25), (40, 33), (19, 34), (8, 29), (5, 44), (33, 35), (29, 4), (4, 37), (27, 19), (15, 35), (18, 42), (42, 33), (20, 40), (11, 36), (33, 7), (6, 9), (38, 15), (22, 23), (37, 7), (22, 40), (25, 15), (34, 12), (13, 40), (41, 5), (15, 34), (16, 19), (33, 20), (1, 24), (17, 20), (39, 15), (11, 4), (13, 42), (4, 35), (13, 36), (41, 36), (33, 27), (7, 22), (17, 8), (6, 44), (10, 33), (12, 20), (35, 39), (9, 0), (9, 31), (12, 31), (25, 2), (37, 30), (30, 10), (37, 23), (23, 26), (41, 41), (36, 37), (39, 35), (44, 2), (16, 11), (20, 36), (22, 37), (40, 35), (4, 26), (21, 43), (1, 20), (27, 44), (7, 26), (47, 23), (47, 14), (0, 24), (20, 32), (28, 35), (8, 19), (13, 28), (20, 35), (29, 25), (8, 38), (16, 29), (22, 32), (22, 36), (30, 30), (34, 31), (23, 9), (35, 28), (44, 1), (19, 14), (0, 36), (22, 19), (17, 13), (14, 4), (5, 26), (2, 10), (34, 26), (19, 22), (12, 25), (16, 14), (37, 15), (24, 18), (46, 39), (14, 27), (46, 3), (29, 20), (44, 28), (35, 6), (0, 19), (24, 2), (32, 38), (44, 40), (47, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 21), (20, 38), (29, 4), (17, 14), (19, 27), (0, 28), (44, 38), (29, 30), (33, 29), (8, 18), (31, 19), (34, 19), (30, 42), (14, 7), (39, 32), (23, 21), (34, 17), (23, 40), (27, 13), (44, 7), (28, 11), (33, 0), (4, 1), (25, 30), (40, 37), (42, 5), (3, 12), (46, 0), (10, 40), (12, 5), (27, 15), (1, 19), (12, 35), (17, 42), (15, 5), (16, 26), (2, 22), (25, 42), (44, 41), (4, 29), (26, 11), (2, 15), (43, 37), (39, 19), (27, 27), (24, 32), (28, 7), (13, 18), (26, 25), (44, 18), (8, 41), (24, 37), (48, 18), (5, 33), (14, 19), (25, 26), (38, 11), (27, 40), (13, 26), (3, 7), (39, 38), (23, 7), (34, 4), (14, 21), (12, 29), (20, 8), (13, 40), (18, 17), (20, 36), (12, 33), (27, 12), (22, 0), (44, 27), (38, 26), (9, 26), (36, 41), (6, 42), (2, 19), (11, 14), (36, 40), (11, 25), (16, 28), (9, 32), (29, 7), (23, 31), (35, 16), (12, 41), (16, 8), (31, 12), (21, 24), (15, 3), (20, 41), (30, 17), (1, 8), (13, 41), (10, 6), (32, 14), (23, 18), (42, 21), (15, 0), (42, 29), (40, 13), (4, 31), (44, 31), (42, 0), (5, 25), (12, 24), (45, 32), (21, 29), (12, 42), (39, 35), (47, 19), (1, 28), (35, 29), (46, 1), (32, 23), (36, 26), (19, 16), (35, 5), (26, 8), (16, 20), (44, 36), (6, 35), (15, 13), (13, 5), (6, 9), (36, 19), (14, 32), (35, 19), (4, 26), (1, 2), (31, 7), (48, 14), (16, 6), (32, 34), (42, 10), (24, 17), (26, 6), (29, 2), (40, 6), (32, 24), (10, 8), (46, 18), (45, 1), (17, 18), (33, 22), (35, 6), (9, 28), (16, 40), (40, 2), (18, 7), (5, 10), (39, 22), (16, 42), (3, 28), (36, 25), (5, 28), (35, 28), (16, 10), (47, 9), (6, 34), (42, 35), (1, 1), (13, 22), (17, 11), (33, 37), (9, 34), (12, 3), (17, 15), (13, 7), (27, 1), (2, 0), (28, 27), (29, 12), (6, 30), (13, 2), (36, 20), (30, 14), (11, 18), (18, 10), (42, 25), (17, 21), (22, 20), (1, 40), (20, 0), (10, 41), (41, 22), (38, 32), (29, 31), (3, 11), (20, 34), (16, 7), (16, 23), (24, 19), (47, 7), (11, 3), (42, 42), (24, 40), (46, 8), (45, 26), (43, 28), (34, 21), (15, 2), (37, 39), (27, 4), (45, 37), (46, 33), (23, 10), (19, 34), (39, 24), (6, 18), (21, 33), (0, 22), (32, 39), (13, 37), (39, 4), (48, 21), (41, 23), (16, 4), (24, 38), (22, 10), (12, 26), (4, 8), (16, 34), (28, 31), (5, 29), (48, 25), (11, 24), (41, 2), (30, 8), (15, 17), (41, 13), (34, 32), (36, 16), (22, 4), (10, 15), (44, 11), (33, 11), (42, 26), (1, 29), (31, 29), (47, 1), (46, 21), (31, 13), (41, 40), (21, 22), (4, 0), (39, 41), (37, 13), (26, 37), (46, 36), (19, 24), (43, 19), (40, 29), (8, 40), (15, 32), (26, 29), (14, 8), (33, 42), (16, 14), (35, 13), (15, 9), (36, 38), (10, 34), (22, 37), (10, 31), (9, 20), (9, 42), (45, 42), (33, 27), (45, 6), (2, 35), (28, 4), (10, 35), (41, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 4), (19, 40), (28, 29), (44, 26), (21, 40), (1, 36), (14, 14), (24, 16), (37, 17), (2, 30), (17, 19), (19, 16), (10, 10), (31, 18), (27, 17), (17, 36), (19, 0), (37, 40), (29, 28), (40, 11), (32, 25), (42, 25), (6, 39), (42, 14), (16, 2), (4, 3), (16, 12), (18, 40), (39, 1), (23, 39), (27, 33), (22, 10), (15, 17), (41, 30), (24, 12), (20, 2), (3, 32), (34, 38), (0, 40), (40, 8), (17, 23), (0, 28), (30, 18), (14, 13), (15, 3), (2, 7), (36, 40), (30, 10), (16, 23), (7, 2), (20, 28), (41, 26), (13, 38), (0, 29), (25, 2), (28, 11), (7, 19), (40, 0), (2, 0), (2, 27), (4, 4), (16, 22), (10, 29), (29, 12), (18, 4), (26, 25), (5, 40), (18, 27), (38, 12), (37, 11), (39, 13), (7, 39), (5, 26), (40, 35), (17, 12), (27, 4), (19, 32), (34, 6), (34, 36), (37, 34), (23, 11), (17, 0), (21, 38), (25, 15), (12, 3), (16, 18), (12, 32), (17, 13), (34, 13), (33, 40), (4, 20), (19, 6), (44, 20), (36, 1), (5, 15), (13, 10), (8, 18), (35, 40), (41, 38), (21, 16), (0, 17), (42, 26), (44, 8), (25, 20), (33, 13), (41, 13), (6, 23), (42, 39), (12, 0), (15, 18), (42, 5), (3, 24), (17, 40), (0, 36), (32, 11), (43, 30), (44, 33), (22, 26), (27, 26), (39, 29), (13, 34), (23, 14), (25, 23), (40, 32), (5, 4), (24, 30), (23, 5), (10, 40), (38, 31), (30, 13), (28, 23), (30, 4), (2, 24), (24, 21), (37, 9), (36, 12), (2, 4), (26, 34), (5, 37), (23, 26), (13, 16), (10, 5), (21, 36), (2, 34), (8, 5), (18, 38), (7, 1), (33, 19), (33, 27), (3, 28), (44, 36), (31, 38), (24, 18), (5, 34), (33, 17), (36, 30), (26, 27), (14, 20), (22, 38), (32, 30), (27, 18), (37, 2), (23, 15), (24, 34), (33, 20), (7, 14), (7, 34), (13, 22), (39, 34), (42, 37), (26, 10), (1, 16), (35, 6), (8, 38), (11, 0), (28, 24), (15, 21), (18, 33), (24, 14), (26, 28), (33, 18), (12, 9), (37, 14), (33, 9), (2, 12), (26, 24), (3, 0), (3, 4), (14, 24), (11, 40), (32, 19), (32, 1), (38, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 23), (41, 33), (3, 18), (39, 24), (35, 3), (18, 9), (14, 42), (48, 42), (48, 19), (21, 2), (5, 17), (19, 12), (29, 33), (4, 21), (40, 16), (12, 39), (23, 36), (6, 29), (47, 20), (29, 21), (11, 7), (48, 18), (15, 43), (42, 28), (0, 10), (44, 33), (30, 3), (12, 25), (37, 1), (22, 28), (44, 13), (30, 4), (8, 20), (27, 20), (9, 37), (14, 15), (18, 36), (25, 37), (33, 28), (26, 33), (35, 41), (44, 6), (43, 40), (36, 40), (35, 16), (17, 17), (43, 9), (44, 39), (27, 23), (24, 28), (32, 43), (24, 27), (23, 33), (23, 29), (14, 38), (39, 41), (3, 30), (42, 9), (9, 1), (26, 20), (32, 5), (15, 2), (10, 19), (0, 35), (37, 4), (44, 20), (34, 17), (31, 12), (34, 13), (43, 10), (42, 19), (45, 0), (43, 7), (3, 14), (28, 42), (36, 20), (19, 22), (45, 36), (22, 35), (31, 31), (5, 20), (17, 18), (29, 7), (46, 23), (28, 34), (45, 6), (17, 13), (8, 23), (24, 5), (26, 24), (16, 1), (9, 27), (17, 31), (8, 11), (36, 38), (22, 4), (33, 23), (30, 24), (19, 27), (27, 17), (33, 35), (41, 43), (12, 28), (1, 18), (33, 34), (33, 3), (26, 25), (4, 6), (3, 2), (7, 14), (19, 15), (27, 25), (25, 38), (26, 34), (26, 42), (18, 8), (1, 3), (11, 39), (3, 21), (44, 35), (41, 22), (23, 35), (14, 8), (44, 3), (24, 30), (8, 39), (32, 42), (4, 5), (8, 5), (29, 15), (12, 37), (40, 2), (4, 42), (5, 0), (2, 14), (41, 39), (21, 40), (18, 21), (48, 14), (19, 6), (18, 25), (4, 0), (11, 15), (6, 33), (45, 38), (39, 40), (10, 14), (43, 13), (45, 12), (47, 37), (42, 2), (38, 1), (2, 19), (20, 1), (35, 40), (28, 16), (42, 12), (27, 36), (5, 1), (39, 42), (18, 13), (11, 14), (2, 40), (12, 2), (40, 1), (22, 0), (12, 32), (39, 6), (4, 22), (44, 37), (45, 10), (38, 42), (7, 28), (7, 34), (26, 16), (6, 21), (0, 25), (17, 39), (46, 25), (37, 9), (36, 17), (2, 18), (24, 18), (2, 6), (46, 20), (6, 37), (43, 0), (0, 6), (30, 8), (46, 13), (46, 24), (41, 26), (37, 11), (12, 23), (38, 22), (2, 33), (44, 25), (38, 20), (8, 32), (42, 10), (40, 9), (11, 9), (19, 25), (16, 0), (35, 22), (21, 42), (30, 39), (16, 13), (32, 28), (42, 16), (20, 36), (37, 17), (38, 11), (12, 43), (33, 31), (39, 38), (5, 34), (43, 34), (37, 21), (17, 41), (39, 23), (30, 11), (17, 1), (45, 2), (33, 32), (17, 24), (33, 36), (28, 15), (27, 15), (36, 16), (14, 23), (32, 27), (2, 7), (31, 27), (43, 28), (8, 19), (39, 12), (37, 39), (12, 5), (8, 17), (8, 4), (11, 3), (38, 40), (29, 43), (35, 13), (1, 13), (16, 15), (31, 23), (37, 25), (44, 22), (0, 11), (0, 14), (12, 11), (41, 25), (29, 0), (40, 21), (11, 29), (34, 33), (23, 13), (1, 22), (47, 12), (24, 42), (13, 8), (40, 35), (20, 41), (27, 18), (10, 16), (46, 34), (9, 28), (28, 27), (37, 16), (31, 3), (38, 37), (28, 29), (21, 15), (41, 9), (31, 20), (34, 16), (44, 43), (0, 20), (18, 37), (39, 17), (47, 33), (19, 20), (33, 10), (23, 43), (43, 35), (21, 25), (31, 38), (17, 14), (48, 16), (23, 12), (0, 36), (1, 27), (7, 22), (3, 4), (47, 40), (15, 29), (47, 2), (37, 42), (31, 0), (30, 5), (12, 4), (20, 9), (18, 32), (12, 33), (20, 8), (3, 7), (12, 9), (21, 4), (26, 3), (8, 3), (46, 11), (7, 19), (35, 24), (31, 33), (12, 42), (13, 38), (8, 9), (9, 9), (8, 40), (18, 17), (10, 23), (12, 14), (23, 37), (26, 14), (21, 27), (1, 23), (40, 12), (18, 18), (16, 12), (21, 18), (41, 11), (48, 10), (13, 34), (6, 32), (23, 8), (34, 9), (18, 27), (42, 23), (14, 17), (28, 23), (28, 33), (42, 43), (47, 9), (36, 9), (17, 25), (10, 7), (11, 38), (39, 33), (14, 37), (27, 43), (39, 3), (37, 23), (25, 15), (11, 30), (14, 29), (22, 5), (27, 7), (29, 12), (35, 39), (40, 30), (25, 30), (37, 3), (13, 30), (31, 22), (12, 17), (27, 13), (19, 29), (10, 17), (35, 9), (20, 22), (48, 9), (42, 27), (12, 35), (32, 11), (1, 12), (34, 22), (5, 32), (18, 12), (26, 2), (14, 12), (46, 4), (36, 28), (33, 40), (4, 18), (2, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 14), (6, 28), (28, 10), (24, 41), (38, 38), (18, 0), (8, 3), (12, 1), (15, 24), (24, 25), (33, 37), (19, 4), (26, 43), (4, 1), (6, 4), (21, 43), (5, 34), (10, 39), (19, 6), (32, 43), (3, 28), (38, 18), (34, 35), (9, 39), (20, 27), (0, 27), (2, 24), (30, 45), (6, 29), (6, 11), (17, 38), (30, 3), (28, 14), (10, 25), (18, 41), (20, 15), (29, 43), (27, 8), (13, 40), (0, 16), (28, 41), (9, 27), (15, 1), (5, 32), (0, 18), (19, 19), (39, 1), (11, 25), (21, 16), (18, 16), (32, 15), (33, 10), (14, 40), (30, 2), (25, 0), (37, 24), (26, 13), (10, 41), (9, 0), (27, 0), (23, 29), (13, 27), (35, 9), (22, 46), (8, 32), (29, 31), (21, 38), (15, 42), (37, 20), (37, 39), (35, 47), (1, 10), (11, 43), (30, 16), (20, 14), (37, 32), (37, 6), (0, 38), (32, 28), (28, 46), (14, 34), (30, 0), (28, 20), (33, 34), (7, 23), (16, 8), (21, 9), (8, 15), (33, 43), (30, 28), (12, 25), (14, 41), (9, 13), (27, 33), (36, 10), (26, 19), (34, 46), (1, 28), (36, 37), (7, 9), (14, 19), (39, 7), (6, 3), (8, 26), (33, 9), (38, 24), (32, 0), (14, 9), (24, 20), (37, 18), (37, 13), (8, 43), (35, 23), (34, 18), (28, 28), (16, 47), (19, 30), (15, 47), (15, 5), (27, 4), (0, 17), (18, 8), (19, 13), (34, 38), (16, 46), (16, 33), (30, 13), (24, 7), (15, 3), (33, 30), (2, 26), (33, 26), (32, 17), (14, 39), (8, 45), (3, 8), (31, 32), (35, 21), (0, 2), (11, 14), (18, 9), (39, 16), (9, 44), (22, 3), (11, 47), (2, 20), (19, 1), (17, 36), (22, 15), (25, 28), (32, 46), (32, 5), (30, 9), (34, 9), (15, 20), (19, 10), (18, 24), (3, 24), (25, 22), (36, 12), (18, 27), (20, 37), (36, 35), (34, 21), (36, 28), (6, 22), (28, 39), (12, 8), (31, 12), (4, 11), (6, 5), (9, 14), (33, 28), (34, 4), (29, 4), (5, 19), (26, 34), (2, 6), (1, 40), (1, 15), (28, 26), (10, 46), (34, 40), (16, 6), (17, 16), (29, 15), (18, 7), (26, 47), (16, 20), (17, 37), (37, 42), (20, 40), (38, 28), (34, 26), (16, 41), (10, 0), (18, 45), (8, 8), (13, 17), (4, 28), (27, 39), (21, 11), (21, 13), (33, 32), (37, 33), (15, 44), (11, 10), (29, 8), (15, 40), (28, 29), (0, 25), (23, 10), (22, 24), (4, 45), (7, 46), (32, 10), (28, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 21), (37, 15), (6, 11), (5, 1), (39, 31), (1, 40), (28, 11), (18, 29), (0, 47), (22, 37), (6, 22), (17, 2), (8, 24), (13, 23), (10, 24), (7, 48), (13, 13), (20, 38), (6, 13), (5, 6), (27, 36), (9, 18), (29, 38), (25, 0), (6, 43), (9, 32), (19, 47), (31, 41), (40, 32), (27, 9), (28, 44), (19, 43), (31, 38), (19, 22), (19, 34), (0, 31), (21, 25), (38, 47), (10, 17), (32, 1), (38, 6), (13, 31), (11, 37), (11, 9), (4, 42), (9, 16), (31, 42), (9, 9), (22, 43), (29, 11), (21, 4), (33, 0), (31, 22), (6, 35), (4, 28), (24, 24), (8, 19), (1, 28), (8, 35), (9, 26), (36, 17), (25, 42), (26, 28), (2, 41), (5, 42), (29, 24), (26, 14), (27, 12), (8, 18), (22, 11), (6, 1), (14, 41), (28, 26), (35, 40), (28, 48), (36, 45), (25, 10), (36, 0), (18, 38), (7, 23), (10, 37), (21, 29), (20, 44), (7, 33), (7, 17), (11, 32), (26, 35), (24, 44), (13, 16), (3, 41), (32, 40), (23, 1), (2, 21), (34, 12), (35, 45), (0, 2), (31, 0), (16, 22), (32, 3), (27, 44), (9, 44), (27, 43), (0, 18), (36, 38), (30, 46), (10, 22), (17, 19), (14, 45), (19, 40), (0, 5), (28, 17), (33, 41), (3, 0), (26, 27), (31, 10), (11, 2), (12, 33), (12, 8), (16, 36), (0, 29), (25, 36), (4, 22), (21, 27), (9, 5), (40, 25), (39, 41), (21, 33), (17, 48), (4, 13), (31, 13), (27, 8), (35, 15), (9, 14), (23, 34), (35, 3), (19, 29), (28, 20), (1, 25), (2, 29), (12, 24), (27, 10), (40, 44), (24, 40), (37, 20), (27, 16), (29, 42), (18, 47), (30, 17), (15, 16), (33, 33), (36, 6), (35, 42), (40, 33), (10, 39), (34, 31), (9, 6), (9, 27), (29, 5), (1, 30), (39, 9), (14, 39), (7, 31), (1, 43), (27, 13), (16, 43), (10, 47), (2, 27), (13, 36), (14, 25), (4, 27), (19, 35), (27, 19), (10, 40), (34, 24), (25, 11), (35, 39), (34, 29), (34, 9), (27, 1), (5, 2), (19, 2), (16, 25), (5, 25), (2, 37), (26, 47), (40, 3), (12, 40), (19, 21), (5, 10), (4, 8), (31, 40), (20, 46), (16, 38), (22, 2), (38, 36), (6, 19), (33, 14), (0, 44), (29, 15), (3, 22), (8, 48), (17, 29), (9, 42), (5, 14), (33, 24), (38, 37), (6, 31), (15, 35), (1, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 4), (17, 22), (32, 19), (23, 20), (31, 37), (41, 9), (21, 20), (42, 13), (32, 5), (25, 34), (10, 19), (11, 39), (5, 3), (22, 10), (1, 21), (38, 19), (21, 13), (13, 34), (12, 19), (30, 26), (19, 29), (42, 17), (40, 36), (1, 4), (34, 2), (8, 8), (22, 20), (18, 15), (16, 33), (1, 13), (23, 16), (41, 1), (30, 16), (31, 9), (12, 18), (21, 17), (33, 19), (35, 27), (3, 0), (4, 35), (24, 23), (9, 5), (26, 7), (38, 18), (17, 14), (21, 25), (26, 38), (37, 38), (24, 30), (10, 31), (10, 39), (5, 35), (38, 5), (28, 0), (25, 12), (2, 38), (26, 36), (3, 6), (9, 24), (12, 14), (22, 28), (35, 22), (36, 7), (29, 31), (23, 18), (19, 31), (3, 15), (4, 18), (25, 7), (11, 14), (24, 7), (4, 11), (25, 31), (0, 33), (26, 28), (31, 24), (4, 26), (28, 34), (23, 25), (18, 34), (36, 38), (20, 24), (26, 11), (24, 15), (10, 37), (35, 26), (34, 16), (5, 16), (41, 13), (2, 14), (2, 13), (24, 32), (20, 27), (28, 6), (27, 7), (30, 4), (16, 20), (7, 6), (10, 6), (37, 25), (4, 21), (14, 32), (32, 22), (21, 22), (32, 29), (37, 30), (39, 16), (2, 39), (28, 15), (9, 32), (22, 36), (3, 34), (1, 8), (20, 1), (30, 32), (16, 0), (33, 9), (15, 32), (20, 5), (39, 25), (34, 5), (30, 1), (36, 14), (37, 10), (41, 22), (37, 23), (25, 5), (32, 33), (8, 4), (4, 30), (24, 20), (38, 30), (22, 25), (33, 38), (14, 28), (27, 22), (3, 3), (15, 15), (3, 16), (13, 23), (36, 22), (27, 37), (7, 25), (42, 29), (27, 10), (14, 11), (24, 33), (12, 13), (26, 39), (4, 19), (8, 2), (22, 39), (15, 5), (14, 3), (34, 18), (39, 2), (31, 1), (16, 8), (9, 0), (5, 22), (6, 32), (35, 8), (17, 37), (34, 9), (11, 31), (22, 6), (23, 14), (16, 11), (8, 35), (10, 9), (42, 30), (2, 19), (5, 5), (22, 1), (10, 4), (5, 21), (38, 20), (28, 21), (1, 2), (22, 37), (21, 12), (17, 15), (2, 3), (27, 23), (6, 17), (39, 30), (17, 25), (5, 37), (17, 11), (1, 32), (23, 19), (27, 15), (3, 19), (33, 32), (8, 1), (0, 32), (34, 39), (15, 33), (0, 13), (31, 4), (1, 20), (38, 26), (37, 27), (0, 29), (42, 10), (19, 15), (9, 3), (9, 1), (12, 11), (41, 10), (23, 12), (19, 27), (36, 24), (24, 22), (19, 4), (32, 25), (31, 18), (29, 7), (9, 28), (9, 30), (27, 36), (12, 10), (7, 1), (30, 10), (31, 26), (24, 26), (3, 28), (33, 31), (33, 23), (20, 30), (5, 36), (0, 16), (34, 36), (20, 23), (0, 34), (7, 32), (17, 13), (35, 0), (4, 39), (35, 18), (25, 3), (2, 0), (39, 39), (41, 21), (12, 28), (14, 15), (3, 5), (9, 38), (34, 13), (18, 29), (19, 36), (11, 4), (8, 33), (31, 31), (29, 0), (3, 11), (27, 31), (31, 25), (17, 8), (31, 2), (10, 7), (16, 19), (7, 28), (0, 26), (36, 11), (34, 17), (7, 38), (37, 1), (17, 2), (26, 12), (21, 7), (33, 10), (2, 37), (22, 8), (21, 30), (42, 36), (13, 38), (23, 9), (15, 2), (17, 19), (24, 4), (40, 14), (2, 6), (41, 25), (11, 5), (31, 35), (29, 25), (9, 8), (40, 7), (28, 8), (41, 15), (14, 9), (37, 7), (37, 24), (18, 20), (26, 29), (34, 31), (19, 20), (38, 28), (6, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 9), (37, 40), (14, 41), (5, 21), (12, 30), (6, 35), (29, 31), (36, 10), (6, 5), (7, 34), (3, 7), (19, 21), (37, 28), (32, 41), (35, 4), (40, 8), (40, 41), (37, 7), (6, 18), (36, 37), (33, 37), (36, 26), (30, 41), (22, 2), (40, 0), (17, 7), (30, 45), (30, 4), (27, 11), (0, 7), (41, 30), (24, 19), (24, 45), (33, 7), (25, 45), (41, 43), (37, 13), (43, 9), (24, 22), (2, 33), (41, 15), (40, 35), (4, 37), (12, 8), (43, 22), (17, 35), (9, 9), (6, 1), (38, 34), (30, 27), (32, 42), (4, 18), (19, 42), (38, 23), (36, 36), (28, 21), (5, 34), (9, 35), (18, 29), (36, 35), (13, 23), (20, 9), (37, 29), (42, 5), (36, 34), (36, 13), (32, 4), (16, 0), (34, 18), (18, 22), (27, 44), (34, 26), (32, 33), (37, 6), (15, 3), (27, 0), (22, 15), (44, 34), (36, 4), (31, 23), (36, 23), (8, 25), (33, 44), (40, 9), (28, 23), (12, 44), (35, 13), (27, 45), (19, 19), (42, 42), (22, 35), (26, 41), (17, 11), (40, 6), (19, 6), (22, 12), (43, 24), (25, 43), (34, 8), (44, 32), (41, 13), (26, 22), (12, 24), (30, 37), (4, 41), (18, 11), (32, 25), (12, 28), (6, 11), (5, 18), (21, 3), (0, 26), (38, 27), (19, 23), (43, 42), (33, 8), (9, 25), (38, 37), (29, 34), (1, 13), (40, 44), (31, 36), (10, 8), (42, 37), (9, 30), (3, 6), (6, 21), (11, 28), (28, 39), (1, 23), (25, 0), (15, 12), (9, 6), (43, 20), (20, 6), (11, 44), (22, 36), (22, 37), (17, 2), (32, 37), (20, 12), (25, 32), (8, 11), (39, 18), (29, 40), (37, 44), (42, 3), (27, 19), (38, 15), (42, 1), (12, 17), (35, 38), (42, 15), (34, 1), (41, 32), (14, 6), (41, 28), (43, 18), (12, 15), (14, 38), (3, 29), (11, 7), (41, 37), (44, 43), (27, 28), (37, 23), (26, 15), (30, 6), (0, 12), (34, 19), (44, 35), (14, 25), (12, 21), (5, 39), (44, 27), (27, 39), (11, 4), (41, 14), (2, 28), (44, 31), (16, 42), (2, 0), (22, 31), (11, 20), (4, 31), (11, 18), (21, 6), (21, 11), (10, 37), (20, 42), (0, 13), (36, 29), (26, 40), (4, 10), (10, 16), (43, 37), (29, 26), (8, 28), (24, 25), (15, 37), (36, 28), (31, 15), (16, 37), (27, 33), (2, 32), (21, 21), (27, 40), (31, 31), (1, 29), (21, 39), (14, 45), (23, 32), (15, 16), (3, 21), (28, 27), (42, 32), (34, 31), (10, 42), (35, 20), (27, 29), (12, 13), (41, 2), (10, 25), (30, 19), (34, 17), (18, 6), (29, 16), (20, 5), (31, 24), (7, 37), (4, 38), (14, 39), (42, 19), (17, 0), (4, 15), (43, 21), (32, 17), (38, 13), (16, 7), (35, 8), (17, 18), (13, 26), (16, 17), (31, 4), (7, 43), (42, 20), (39, 38), (13, 19), (22, 40), (26, 24), (17, 6), (23, 34), (9, 14), (11, 5), (29, 20), (41, 16), (6, 2), (32, 8), (35, 7), (11, 13), (20, 32), (32, 13), (10, 45), (40, 3), (0, 18), (18, 24), (13, 21), (12, 25), (16, 13), (33, 39), (14, 14), (14, 21), (19, 30), (24, 20), (0, 14), (25, 41), (34, 30), (26, 42), (30, 5), (2, 45), (7, 10), (37, 39), (26, 36), (35, 0), (34, 44), (33, 5), (34, 21), (10, 1), (12, 33), (41, 44), (35, 25), (12, 12), (42, 14), (38, 14), (12, 41), (43, 27), (27, 24), (0, 16), (23, 26), (7, 19), (34, 38), (29, 6), (16, 30), (14, 17), (8, 10), (20, 36), (5, 35), (1, 44), (32, 20), (29, 7), (13, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (47, 0), (12, 23), (29, 4), (26, 9), (9, 3), (42, 33), (24, 22), (7, 4), (35, 24), (30, 20), (11, 13), (37, 36), (13, 8), (25, 12), (17, 19), (21, 6), (43, 39), (15, 5), (41, 27), (14, 32), (36, 38), (13, 23), (11, 37), (0, 9), (0, 20), (18, 35), (47, 18), (46, 12), (34, 10), (27, 36), (9, 26), (18, 8), (2, 21), (31, 1), (37, 30), (27, 5), (9, 0), (35, 18), (42, 42), (45, 24), (32, 18), (47, 22), (47, 42), (0, 4), (29, 6), (5, 3), (48, 16), (22, 6), (19, 41), (35, 15), (17, 2), (41, 42), (44, 8), (40, 22), (3, 34), (14, 8), (12, 19), (0, 35), (17, 40), (16, 27), (24, 21), (32, 42), (31, 33), (9, 16), (4, 23), (21, 36), (24, 33), (5, 4), (35, 28), (24, 38), (38, 38), (48, 23), (3, 27), (27, 17), (2, 7), (11, 36), (37, 23), (19, 8), (4, 2), (33, 17), (38, 29), (39, 31), (0, 14), (10, 31), (2, 27), (35, 35), (31, 40), (14, 1), (12, 31), (32, 36), (23, 24), (45, 23), (24, 8), (12, 8), (22, 0), (29, 15), (3, 17), (16, 18), (5, 30), (30, 13), (7, 31), (9, 2), (16, 37), (12, 3), (13, 38), (38, 23), (31, 21), (45, 17), (10, 12), (25, 6), (27, 3), (5, 23), (3, 33), (14, 30), (27, 10), (20, 14), (40, 33), (2, 36), (19, 14), (32, 32), (4, 12), (40, 9), (15, 15), (28, 2), (38, 5), (29, 0), (5, 1), (24, 0), (28, 22), (21, 23), (32, 22), (45, 32), (38, 35), (0, 40), (46, 1), (20, 13), (45, 4), (8, 6), (35, 22), (7, 35), (31, 19), (28, 24), (19, 17), (21, 21), (16, 38), (38, 42), (2, 9), (5, 15), (1, 10), (7, 39), (40, 29), (3, 38), (34, 23), (6, 25), (46, 22), (17, 32), (10, 26), (6, 35), (46, 40), (7, 34), (14, 4), (45, 15), (35, 20), (18, 29), (7, 29), (5, 0), (11, 22), (31, 27), (27, 27), (9, 40), (40, 0), (45, 1), (4, 41), (7, 40), (43, 9), (10, 28), (26, 27), (41, 32), (12, 0), (11, 23), (31, 4), (21, 33), (4, 30), (15, 19), (7, 23), (4, 11), (46, 29), (41, 10), (14, 15), (15, 3), (24, 15), (12, 7), (1, 5), (2, 29), (31, 35), (13, 10), (35, 11), (47, 39), (4, 1), (12, 6), (0, 3), (47, 32), (45, 35), (44, 42), (15, 34), (48, 24), (7, 26), (27, 2), (47, 28), (16, 32), (37, 1), (11, 3), (39, 24), (0, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 28), (46, 28), (35, 1), (16, 8), (40, 35), (31, 45), (11, 15), (25, 7), (40, 8), (39, 21), (24, 2), (37, 19), (7, 46), (0, 40), (23, 30), (23, 34), (1, 40), (3, 22), (1, 12), (22, 13), (27, 5), (4, 36), (41, 29), (3, 32), (15, 6), (37, 24), (12, 26), (11, 25), (0, 44), (8, 26), (34, 35), (42, 25), (38, 37), (27, 11), (14, 5), (22, 1), (46, 16), (29, 5), (26, 6), (40, 24), (6, 46), (43, 35), (6, 20), (8, 11), (1, 18), (45, 28), (31, 16), (9, 20), (29, 33), (40, 5), (17, 8), (43, 15), (24, 16), (28, 35), (28, 27), (38, 15), (13, 12), (18, 20), (39, 31), (35, 34), (7, 4), (8, 15), (44, 12), (18, 45), (3, 27), (24, 7), (42, 27), (41, 41), (6, 3), (39, 32), (39, 2), (23, 22), (10, 2), (43, 32), (45, 17), (13, 14), (12, 19), (34, 13), (40, 12), (9, 36), (34, 42), (44, 19), (34, 14), (33, 23), (19, 41), (13, 2), (31, 32), (30, 1), (45, 6), (18, 22), (33, 34), (15, 5), (8, 22), (24, 46), (44, 42), (32, 8), (17, 3), (11, 35), (38, 4), (9, 16), (3, 6), (4, 35), (28, 6), (29, 4), (35, 5), (24, 8), (38, 13), (19, 25), (4, 5), (13, 16), (7, 28), (35, 38), (0, 18), (14, 10), (31, 23), (16, 15), (39, 0), (17, 38), (41, 23), (35, 27), (39, 1), (33, 2), (14, 45), (23, 27), (7, 0), (32, 4), (10, 42), (7, 30), (33, 46), (39, 9), (45, 23), (36, 21), (13, 8), (39, 7), (8, 13), (34, 11), (29, 46), (5, 36), (13, 32), (31, 27), (22, 44), (13, 19), (22, 11), (46, 19), (9, 45), (31, 12), (36, 16), (26, 31), (34, 39), (12, 22), (17, 14), (20, 2), (31, 30), (13, 39), (31, 10), (6, 26), (20, 16), (0, 34), (15, 34), (45, 13), (36, 22), (42, 22), (7, 33), (4, 12), (32, 13), (29, 34), (14, 21), (45, 9), (17, 6), (19, 12), (33, 43), (40, 31), (5, 43), (21, 38), (44, 0), (28, 5), (38, 39), (32, 35), (35, 13), (3, 37), (7, 20), (36, 13), (38, 38), (10, 16), (32, 11), (10, 17), (39, 25), (36, 44), (46, 2), (31, 15), (35, 19), (35, 4), (24, 41), (30, 15), (27, 35), (34, 32), (19, 34), (38, 21), (17, 40), (6, 15), (36, 7), (8, 0), (4, 30), (34, 7), (43, 6), (43, 19), (31, 7), (32, 31), (15, 33), (1, 20), (17, 11), (28, 37), (16, 9), (19, 1), (9, 18), (22, 14), (2, 13), (28, 41), (14, 31), (18, 46), (11, 27), (33, 40), (34, 1), (22, 3), (40, 28), (34, 26), (7, 12), (18, 23), (43, 16), (16, 46), (9, 31), (14, 19), (20, 36), (9, 25), (36, 17), (16, 44), (18, 42), (18, 32), (14, 38), (2, 22), (13, 35), (10, 7), (7, 37), (34, 36), (26, 25), (20, 17), (11, 14), (26, 42), (19, 13), (10, 18), (46, 22), (7, 40), (34, 12), (15, 4), (43, 17), (5, 15), (41, 5), (20, 30), (37, 42), (45, 35), (23, 43), (25, 2), (3, 8), (29, 30), (24, 18), (4, 16), (6, 1), (4, 18), (15, 45), (31, 19), (2, 10), (10, 12), (34, 38), (40, 30), (38, 17), (22, 6), (10, 5), (43, 2), (26, 20), (30, 30), (46, 21), (2, 23), (33, 42), (20, 20), (29, 1), (42, 46), (12, 36), (40, 32), (4, 3), (37, 12), (3, 5), (21, 45), (45, 43), (20, 4), (17, 21), (43, 28), (19, 9), (29, 38), (26, 8), (1, 8), (23, 19), (8, 23), (45, 10), (14, 28), (36, 27), (5, 2), (43, 12), (20, 26), (10, 11), (6, 42), (12, 45), (7, 19), (27, 26), (4, 42), (21, 7), (36, 31), (8, 10), (18, 11), (19, 24), (39, 20), (35, 24), (37, 44), (7, 17), (27, 18), (26, 4), (19, 43), (5, 18), (39, 34), (23, 1), (3, 26), (5, 41), (28, 11), (37, 37), (41, 0), (37, 10), (15, 14), (5, 31), (41, 43), (44, 25), (16, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 33), (41, 3), (24, 22), (34, 29), (37, 25), (14, 22), (30, 38), (33, 12), (32, 1), (30, 4), (15, 21), (14, 5), (39, 17), (13, 32), (23, 18), (7, 13), (35, 3), (5, 23), (39, 3), (0, 24), (36, 27), (38, 18), (4, 39), (26, 14), (34, 42), (35, 22), (12, 0), (22, 27), (1, 1), (38, 0), (43, 34), (15, 32), (14, 6), (29, 3), (20, 31), (36, 32), (4, 26), (14, 8), (11, 32), (29, 12), (41, 20), (5, 42), (10, 4), (39, 33), (40, 25), (13, 35), (28, 21), (41, 35), (34, 41), (34, 33), (3, 38), (30, 20), (13, 17), (27, 37), (1, 0), (16, 31), (6, 33), (27, 19), (39, 2), (14, 27), (2, 22), (17, 18), (32, 12), (2, 8), (31, 25), (7, 32), (4, 42), (19, 11), (26, 15), (31, 19), (41, 14), (31, 36), (4, 4), (2, 5), (18, 7), (27, 29), (37, 21), (4, 22), (24, 8), (37, 19), (22, 16), (1, 14), (20, 27), (21, 3), (7, 39), (9, 7), (43, 41), (31, 20), (27, 35), (38, 4), (28, 8), (40, 2), (3, 21), (20, 18), (11, 24), (3, 28), (18, 12), (36, 9), (14, 30), (43, 13), (25, 20), (25, 33), (31, 29), (15, 17), (24, 38), (14, 18), (21, 33), (30, 19), (19, 19), (25, 34), (24, 28), (15, 14), (39, 20), (7, 36), (31, 32), (1, 35), (9, 23), (3, 22), (12, 26), (33, 7), (19, 34), (25, 11), (2, 30), (29, 11), (7, 21), (3, 6), (33, 15), (8, 28), (14, 11), (16, 35), (29, 4), (27, 27), (23, 21), (4, 12), (30, 12), (20, 39), (37, 37), (5, 2), (15, 15), (10, 9), (11, 35), (34, 40), (14, 2), (1, 22), (20, 3), (42, 23), (39, 19), (30, 24), (32, 15), (28, 9), (17, 16), (35, 28), (16, 30), (0, 6), (39, 7), (26, 1), (11, 21), (7, 4), (34, 14), (36, 5), (35, 26), (37, 4), (18, 9), (42, 10), (10, 16), (34, 10), (7, 11), (36, 38), (3, 20), (9, 2), (4, 33), (13, 42), (23, 31), (35, 32), (28, 5), (11, 23), (29, 40), (3, 11), (22, 30), (5, 5), (3, 3), (24, 7), (17, 22), (32, 36), (24, 29), (38, 23), (5, 33), (10, 35), (27, 40), (5, 3), (12, 34), (9, 33), (9, 12), (15, 29), (13, 6), (6, 15), (42, 40), (41, 30), (11, 0), (38, 16), (22, 42), (36, 1), (32, 24), (22, 2), (18, 25), (31, 13), (1, 40), (3, 0), (6, 9), (31, 7), (19, 5), (11, 22), (18, 16), (23, 37), (16, 3), (16, 32), (19, 37), (12, 41), (24, 6), (22, 31), (43, 2), (23, 5), (28, 16), (38, 20), (28, 0), (40, 30), (21, 17), (18, 29), (24, 31), (1, 15), (12, 19), (23, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 34), (28, 35), (6, 37), (33, 27), (24, 0), (29, 21), (33, 43), (7, 35), (32, 15), (17, 28), (45, 39), (13, 30), (14, 7), (11, 30), (45, 21), (12, 25), (9, 20), (40, 24), (22, 15), (27, 20), (22, 36), (3, 22), (8, 39), (1, 25), (17, 41), (34, 24), (10, 0), (10, 19), (27, 6), (27, 18), (34, 11), (5, 39), (2, 5), (21, 26), (30, 4), (46, 40), (5, 9), (43, 3), (38, 3), (15, 34), (28, 19), (44, 24), (9, 10), (7, 31), (27, 9), (16, 37), (29, 10), (11, 13), (33, 36), (25, 19), (6, 26), (9, 40), (5, 22), (4, 13), (32, 39), (42, 1), (0, 26), (15, 42), (24, 11), (17, 2), (18, 40), (2, 30), (7, 29), (44, 38), (25, 1), (34, 41), (34, 34), (32, 0), (9, 29), (21, 2), (21, 21), (37, 34), (18, 33), (14, 29), (12, 4), (30, 25), (24, 28), (13, 17), (45, 28), (10, 3), (9, 36), (31, 37), (6, 29), (3, 19), (36, 18), (2, 16), (5, 16), (27, 36), (29, 14), (41, 22), (3, 33), (4, 9), (17, 1), (2, 37), (28, 43), (12, 31), (31, 25), (28, 37), (34, 30), (44, 32), (43, 10), (32, 19), (30, 20), (30, 29), (46, 24), (30, 1), (38, 28), (11, 1), (22, 2), (46, 9), (4, 14), (38, 5), (38, 43), (9, 17), (33, 7), (2, 32), (38, 27), (15, 14), (41, 24), (25, 6), (37, 13), (7, 26), (21, 15), (1, 22), (40, 36), (24, 18), (33, 29), (25, 4), (14, 23), (24, 4), (44, 33), (7, 21), (44, 6), (42, 43), (2, 21), (17, 34), (10, 21), (9, 39), (33, 4), (3, 36), (14, 28), (44, 11), (35, 2), (30, 34), (30, 42), (23, 36), (36, 37), (11, 15), (8, 28), (3, 5), (15, 19), (24, 13), (31, 38), (40, 14), (8, 22), (45, 8), (10, 10), (1, 40), (45, 0), (44, 18), (36, 12), (44, 43), (4, 22), (18, 12), (15, 35), (20, 20), (14, 31), (38, 41), (11, 32), (36, 21), (30, 40), (19, 14), (28, 10), (4, 16), (34, 29), (36, 22), (35, 33), (24, 31), (31, 41), (4, 23), (29, 38), (37, 30), (4, 7), (26, 8), (31, 19), (27, 28), (38, 22), (20, 4), (44, 36), (22, 18), (4, 33), (14, 21), (33, 37), (11, 25), (28, 24), (29, 2), (19, 12), (9, 31), (6, 13), (0, 35), (3, 3), (42, 24), (11, 29), (23, 30), (2, 29), (19, 4), (34, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 11), (2, 24), (3, 7), (24, 23), (27, 6), (16, 26), (7, 20), (12, 29), (2, 35), (32, 25), (3, 39), (19, 6), (14, 27), (8, 10), (15, 36), (37, 19), (8, 39), (30, 21), (17, 25), (38, 28), (16, 36), (36, 26), (30, 12), (39, 33), (38, 33), (2, 11), (16, 25), (0, 8), (33, 17), (34, 3), (36, 37), (20, 8), (37, 30), (8, 34), (34, 16), (2, 18), (34, 20), (22, 1), (6, 39), (18, 29), (19, 12), (22, 3), (9, 16), (11, 20), (8, 11), (11, 8), (36, 38), (22, 11), (20, 1), (0, 9), (19, 10), (32, 14), (36, 27), (25, 14), (7, 4), (4, 28), (10, 13), (24, 28), (29, 18), (7, 39), (22, 22), (30, 30), (33, 23), (22, 21), (31, 21), (8, 3), (27, 2), (35, 9), (4, 34), (9, 4), (16, 28), (35, 5), (38, 17), (33, 12), (23, 6), (11, 11), (27, 23), (27, 16), (2, 13), (27, 20), (12, 15), (14, 33), (38, 7), (27, 22), (34, 24), (38, 31), (14, 16), (20, 15), (2, 30), (10, 3), (36, 16), (16, 37), (2, 8), (38, 14), (36, 30), (32, 28), (9, 35), (33, 25), (34, 4), (17, 14), (17, 0), (28, 15), (3, 25), (7, 5), (35, 10), (18, 6), (19, 30), (20, 35), (17, 8), (15, 22), (26, 30), (29, 37), (30, 20), (1, 2), (13, 18), (30, 3), (13, 7), (8, 13), (5, 22), (7, 27), (30, 10), (27, 30), (7, 32), (4, 22), (5, 39), (23, 27), (28, 27), (34, 19), (0, 27), (12, 8), (6, 29), (21, 3), (19, 20), (35, 39), (3, 23), (36, 22), (21, 7), (10, 28), (23, 25), (33, 9), (3, 28), (16, 7), (20, 13), (13, 12), (31, 14), (26, 15), (20, 2), (7, 13), (36, 9), (26, 23), (12, 17), (20, 17), (36, 17), (33, 2), (26, 32), (5, 15), (28, 24), (11, 2), (19, 18), (32, 35), (6, 31), (0, 25), (8, 30), (22, 8), (16, 6), (30, 2), (18, 25), (28, 16), (11, 25), (22, 9), (28, 21), (10, 10), (35, 32), (18, 16), (33, 14), (6, 17), (1, 18), (31, 3), (12, 23), (37, 23), (18, 28), (27, 7), (8, 12), (33, 1), (24, 4), (19, 0), (36, 23), (36, 5), (0, 17), (37, 32), (1, 9), (20, 14), (25, 19), (19, 33), (2, 31), (15, 33), (35, 8), (21, 24), (10, 25), (28, 39), (9, 10), (31, 5), (30, 17), (17, 7), (1, 20), (24, 20), (26, 12), (1, 23), (8, 7), (35, 38), (34, 12), (24, 5), (14, 14), (10, 11), (7, 23), (14, 29), (35, 22), (15, 35), (13, 23), (21, 2), (17, 29), (29, 25), (20, 37), (38, 36), (13, 2), (30, 36), (36, 3), (21, 20), (27, 0), (19, 14), (27, 24), (23, 8), (34, 14), (9, 20), (27, 10), (6, 28), (35, 24), (31, 7), (17, 35), (23, 17), (26, 11), (34, 17), (13, 21), (32, 26), (29, 38), (18, 10), (27, 19), (28, 23), (8, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 11), (0, 36), (14, 28), (42, 33), (31, 35), (34, 23), (5, 34), (27, 1), (38, 29), (4, 35), (26, 21), (41, 19), (21, 30), (41, 12), (13, 6), (7, 33), (18, 14), (2, 25), (32, 29), (3, 25), (21, 13), (28, 40), (33, 11), (15, 29), (0, 17), (8, 13), (25, 32), (19, 8), (12, 29), (19, 27), (41, 4), (37, 4), (21, 38), (32, 44), (16, 14), (1, 13), (13, 31), (17, 30), (27, 25), (3, 30), (12, 26), (16, 29), (27, 29), (2, 21), (1, 17), (3, 8), (23, 16), (30, 3), (42, 37), (21, 8), (27, 0), (41, 30), (2, 19), (9, 14), (42, 42), (20, 38), (8, 18), (24, 38), (4, 6), (23, 3), (8, 21), (14, 1), (30, 40), (11, 22), (8, 33), (26, 11), (33, 38), (37, 27), (37, 20), (19, 21), (19, 3), (29, 4), (15, 28), (14, 43), (35, 27), (15, 32), (7, 40), (37, 44), (31, 25), (5, 24), (18, 22), (37, 17), (24, 34), (38, 24), (2, 12), (13, 25), (37, 36), (18, 39), (34, 22), (32, 21), (11, 24), (42, 16), (1, 15), (14, 16), (14, 12), (14, 13), (8, 8), (41, 9), (29, 38), (31, 40), (26, 10), (27, 36), (30, 22), (2, 13), (7, 34), (42, 24), (1, 33), (10, 18), (1, 9), (3, 40), (3, 28), (15, 10), (26, 19), (29, 11), (13, 28), (21, 41), (3, 41), (34, 19), (2, 38), (17, 27), (30, 44), (6, 41), (18, 1), (36, 23), (30, 33), (22, 4), (26, 40), (23, 41), (11, 5), (5, 21), (10, 2), (4, 29), (23, 17), (13, 20), (13, 42), (20, 26), (35, 20), (14, 3), (1, 2), (36, 39), (32, 31), (11, 21), (37, 19), (28, 39), (30, 11), (25, 14), (22, 23), (28, 2), (34, 43), (27, 13), (9, 31), (29, 19), (27, 33), (17, 32), (16, 36), (27, 7), (14, 26), (6, 5), (34, 2), (5, 25), (18, 40), (26, 38), (41, 41), (33, 30), (26, 24), (7, 35), (26, 29), (36, 40), (24, 37), (30, 1), (25, 17), (40, 19), (38, 12), (27, 34), (17, 1), (40, 24), (39, 34), (26, 13), (24, 11), (10, 39), (3, 13), (25, 30), (19, 23), (40, 23), (20, 44), (1, 12), (35, 7), (5, 7), (29, 33), (10, 31), (17, 39), (6, 6), (39, 29), (35, 41), (16, 5), (14, 5), (25, 12), (36, 19), (23, 43), (39, 18), (32, 5), (39, 12), (7, 25), (14, 20), (4, 18), (22, 8), (0, 35), (31, 34), (13, 3), (21, 14), (35, 1), (7, 19), (28, 38), (14, 0), (12, 31), (13, 7), (12, 3), (16, 3), (19, 22), (21, 35), (41, 0), (37, 26), (0, 43), (2, 8), (0, 42), (25, 29), (7, 22), (30, 23), (6, 43), (21, 18), (22, 3), (33, 14), (9, 39), (27, 26), (0, 16), (5, 22), (15, 4), (22, 38), (11, 43), (8, 30), (40, 0), (42, 36), (17, 10), (4, 13), (25, 6), (8, 5), (23, 25), (17, 5), (10, 34), (8, 22), (25, 34), (16, 20), (19, 24), (2, 26), (40, 11), (16, 11), (38, 35), (37, 22), (10, 40), (42, 25), (12, 41), (6, 44), (7, 27), (36, 15), (23, 18), (38, 28), (4, 36), (12, 17), (23, 23), (3, 5), (18, 24), (34, 26), (24, 1), (16, 6), (20, 21), (7, 17), (1, 22), (33, 29), (30, 21), (19, 36), (5, 33), (5, 11), (22, 32), (32, 22), (20, 36), (35, 9), (9, 32), (33, 4), (0, 18), (27, 41), (41, 24), (26, 15), (13, 8), (30, 19), (29, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (8, 14), (1, 31), (28, 6), (17, 35), (4, 39), (41, 10), (8, 38), (8, 30), (12, 23), (30, 31), (33, 5), (34, 45), (16, 2), (10, 33), (1, 37), (24, 40), (30, 2), (42, 14), (2, 10), (37, 4), (41, 24), (14, 43), (41, 17), (42, 6), (4, 13), (31, 14), (42, 31), (28, 13), (12, 30), (3, 36), (10, 32), (13, 23), (28, 1), (39, 32), (42, 2), (40, 16), (7, 15), (2, 42), (6, 23), (33, 30), (5, 31), (14, 38), (34, 35), (28, 10), (3, 37), (7, 41), (0, 42), (15, 22), (24, 24), (31, 3), (34, 7), (28, 16), (39, 18), (17, 39), (3, 30), (21, 36), (31, 4), (20, 35), (21, 19), (33, 15), (24, 9), (11, 22), (25, 13), (28, 19), (22, 45), (16, 38), (22, 1), (41, 33), (35, 12), (13, 11), (31, 16), (5, 24), (38, 24), (18, 23), (31, 0), (42, 10), (7, 2), (13, 30), (14, 15), (36, 14), (8, 4), (4, 29), (7, 6), (35, 7), (27, 22), (1, 27), (30, 11), (32, 4), (25, 40), (14, 21), (6, 27), (17, 22), (31, 40), (24, 10), (7, 1), (6, 12), (22, 3), (5, 40), (1, 28), (39, 12), (27, 4), (20, 30), (13, 4), (21, 3), (29, 44), (3, 7), (5, 4), (14, 13), (23, 39), (22, 28), (22, 10), (37, 1), (14, 0), (32, 38), (19, 31), (30, 16), (33, 44), (42, 22), (39, 1), (14, 34), (27, 8), (35, 39), (21, 18), (11, 40), (17, 5), (10, 21), (31, 15), (23, 28), (36, 23), (10, 36), (26, 22), (41, 34), (31, 17), (38, 13), (35, 15), (25, 21), (18, 13), (32, 33), (36, 10), (4, 21), (9, 30), (34, 8), (11, 13), (10, 26), (10, 1), (24, 12), (5, 18), (25, 1), (34, 0), (20, 37), (30, 28), (19, 21), (19, 29), (32, 43), (37, 34), (13, 44), (16, 33), (12, 24), (38, 27), (28, 7), (36, 6), (16, 6), (31, 8), (2, 6), (9, 19), (34, 10), (6, 38), (11, 8), (24, 23), (35, 40), (33, 19), (4, 8), (27, 21), (42, 21), (17, 12), (18, 19), (26, 9), (23, 17), (24, 33), (22, 15), (30, 45), (26, 44), (20, 27), (12, 27), (8, 42), (12, 0), (1, 34), (18, 16), (4, 18), (6, 9), (3, 1), (24, 38), (16, 34), (26, 37), (36, 16), (29, 39), (28, 36), (33, 33), (2, 29), (13, 39), (8, 23), (6, 2), (42, 17), (11, 12), (2, 12), (40, 19), (16, 17), (34, 36), (24, 27), (3, 40), (38, 5), (42, 15), (0, 36), (8, 29), (8, 5), (0, 43), (9, 38), (37, 17), (25, 20), (22, 30), (18, 1), (40, 27), (22, 11), (32, 22), (38, 40), (7, 34), (31, 9), (18, 43), (8, 18), (20, 40), (11, 32), (7, 25), (12, 13), (31, 10), (36, 12), (24, 18), (1, 24), (24, 37), (37, 42), (23, 18), (21, 35), (10, 22), (8, 10), (41, 36), (34, 26), (27, 31), (37, 39), (27, 25), (29, 25), (18, 41), (6, 17), (26, 35), (30, 35), (18, 11), (25, 37), (36, 24), (9, 34), (27, 32), (37, 0), (8, 32), (32, 23), (4, 35), (3, 3), (8, 1), (6, 22), (24, 32), (18, 18), (5, 8), (15, 17), (13, 27), (29, 9), (9, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 21), (32, 29), (40, 37), (23, 27), (16, 32), (19, 33), (36, 40), (41, 29), (21, 23), (8, 0), (35, 41), (40, 14), (9, 41), (10, 39), (9, 1), (30, 31), (20, 22), (18, 6), (22, 34), (38, 3), (20, 35), (26, 3), (32, 11), (9, 4), (33, 7), (41, 41), (16, 6), (24, 39), (21, 16), (22, 36), (10, 43), (37, 26), (34, 2), (36, 23), (24, 30), (37, 36), (13, 22), (11, 23), (25, 1), (1, 33), (36, 25), (20, 12), (13, 24), (36, 13), (3, 9), (18, 9), (10, 3), (33, 1), (24, 16), (4, 13), (3, 26), (10, 41), (25, 32), (1, 32), (30, 41), (34, 6), (21, 22), (16, 38), (30, 3), (13, 10), (4, 21), (5, 11), (13, 30), (17, 24), (14, 18), (21, 39), (14, 39), (23, 24), (10, 26), (35, 28), (22, 27), (2, 24), (38, 9), (4, 7), (35, 12), (2, 33), (21, 37), (5, 26), (29, 15), (33, 29), (5, 0), (39, 33), (29, 39), (6, 38), (17, 15), (25, 37), (19, 20), (13, 12), (34, 13), (17, 2), (21, 44), (23, 5), (13, 29), (11, 12), (9, 22), (37, 31), (23, 0), (4, 44), (38, 15), (12, 41), (7, 31), (18, 8), (16, 29), (20, 30), (38, 32), (1, 20), (31, 28), (9, 3), (30, 6), (5, 8), (6, 44), (39, 24), (5, 34), (0, 24), (16, 2), (21, 31), (2, 16), (16, 5), (37, 11), (31, 5), (10, 6), (14, 3), (25, 10), (4, 26), (9, 9), (29, 14), (40, 34), (33, 3), (41, 7), (21, 5), (8, 27), (25, 13), (12, 3), (39, 44), (10, 15), (1, 35), (35, 38), (33, 36), (25, 19), (11, 21), (40, 40), (32, 7), (36, 34), (17, 36), (10, 13), (24, 19), (2, 13), (19, 14), (22, 2), (9, 13), (39, 12), (39, 35), (1, 18), (19, 32), (7, 22), (12, 12), (5, 28), (29, 24), (13, 43), (28, 30), (10, 19), (15, 17), (4, 20), (41, 3), (0, 18), (10, 23), (6, 29), (34, 16), (3, 7), (33, 17), (33, 19), (28, 11), (29, 5), (11, 14), (41, 12), (36, 8), (40, 17), (4, 10), (9, 12), (4, 31), (10, 24), (1, 22), (7, 9), (7, 27), (19, 9), (28, 6), (8, 35), (11, 8), (34, 32), (11, 32), (35, 22), (35, 39), (22, 13), (28, 12), (9, 26), (9, 25), (29, 34), (36, 20), (4, 4), (18, 29), (34, 42), (23, 19), (37, 4), (4, 17), (41, 11), (26, 39), (4, 37), (37, 9), (34, 18), (36, 5), (6, 14), (15, 1), (16, 44), (26, 33), (2, 11), (3, 40), (18, 5), (35, 13), (31, 35), (3, 2), (40, 15), (4, 19), (3, 35), (32, 8), (21, 35), (2, 27), (27, 11), (19, 42), (12, 21), (16, 39), (0, 40), (9, 18), (4, 6), (9, 38), (29, 4), (18, 11), (16, 35), (35, 1), (10, 30), (4, 27), (14, 17), (41, 39), (11, 0), (11, 6), (12, 16), (17, 6), (19, 6), (6, 13), (31, 1), (32, 2), (30, 16), (5, 5), (6, 28), (37, 3), (2, 17), (11, 26), (23, 33), (19, 36), (13, 17), (17, 26), (27, 0), (22, 12), (1, 26), (39, 23), (39, 10), (36, 28), (31, 37), (6, 10), (18, 43), (16, 42), (2, 38), (6, 17), (34, 41), (23, 25), (22, 14), (0, 37), (5, 13), (22, 5), (26, 35), (0, 7), (36, 14), (40, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 12), (33, 19), (35, 15), (34, 3), (22, 19), (13, 26), (41, 34), (33, 1), (22, 42), (17, 7), (35, 30), (10, 10), (38, 25), (33, 5), (2, 42), (43, 10), (40, 5), (20, 4), (38, 29), (6, 35), (33, 0), (26, 39), (19, 36), (41, 11), (29, 29), (39, 38), (4, 21), (6, 14), (22, 3), (15, 38), (2, 19), (5, 41), (17, 10), (17, 38), (28, 39), (10, 22), (42, 2), (10, 32), (3, 8), (11, 25), (41, 17), (11, 6), (29, 24), (26, 34), (22, 25), (22, 35), (21, 5), (28, 24), (27, 41), (42, 42), (35, 38), (37, 16), (38, 26), (11, 39), (21, 36), (29, 10), (1, 21), (3, 22), (0, 12), (36, 0), (1, 20), (16, 38), (36, 29), (39, 1), (9, 31), (37, 40), (32, 33), (13, 1), (11, 22), (16, 16), (24, 16), (27, 32), (35, 18), (30, 22), (7, 9), (9, 27), (6, 5), (8, 37), (20, 2), (5, 21), (29, 13), (32, 23), (17, 3), (18, 37), (43, 11), (10, 4), (43, 29), (35, 40), (24, 38), (28, 40), (3, 6), (3, 39), (4, 0), (41, 12), (32, 21), (10, 23), (26, 11), (3, 24), (20, 5), (35, 37), (4, 28), (39, 17), (30, 31), (41, 26), (34, 30), (32, 35), (32, 1), (0, 1), (23, 42), (35, 21), (30, 11), (2, 40), (29, 9), (37, 22), (6, 40), (28, 19), (29, 23), (35, 31), (8, 9), (38, 34), (3, 11), (18, 14), (25, 32), (10, 35), (17, 24), (37, 20), (31, 26), (17, 27), (10, 6), (26, 31), (29, 32), (25, 39), (8, 26), (23, 13), (22, 7), (35, 34), (9, 1), (35, 5), (10, 12), (18, 35), (14, 38), (38, 30), (23, 29), (9, 39), (20, 12), (3, 13), (11, 28), (5, 23), (7, 36), (21, 9), (3, 15), (1, 5), (20, 3), (12, 20), (31, 37), (5, 35), (11, 15), (41, 18), (32, 32), (26, 6), (24, 7), (34, 5), (22, 9), (23, 26), (20, 11), (15, 30), (12, 35), (13, 23), (20, 10), (8, 39), (24, 40), (16, 26), (23, 11), (31, 35), (16, 17), (5, 27), (38, 23), (15, 22), (19, 41), (5, 10), (28, 11), (0, 10), (38, 28), (0, 25), (18, 40), (8, 38), (38, 20), (20, 36), (17, 34), (21, 11), (11, 21), (1, 9), (5, 25), (11, 32), (15, 11), (15, 18), (41, 16), (37, 42), (7, 24), (37, 23), (33, 14), (38, 17), (38, 27), (35, 9), (0, 28), (22, 10), (9, 13), (39, 11), (16, 8), (41, 39), (19, 3), (37, 12), (17, 5), (23, 37), (7, 2), (42, 23), (6, 42), (28, 17), (8, 42), (40, 32), (22, 29), (26, 9), (40, 22), (43, 6), (9, 3), (27, 18), (15, 1), (7, 5), (40, 30), (21, 42), (21, 37), (22, 0), (17, 41), (34, 13), (37, 27), (19, 15), (4, 1), (11, 24), (20, 37), (27, 8), (30, 4), (17, 40), (9, 16), (24, 22), (37, 11), (4, 20), (4, 35), (3, 41), (13, 35), (11, 17), (14, 17), (28, 30), (34, 42), (33, 17), (32, 36), (43, 0), (35, 33), (19, 38), (16, 30), (20, 23), (35, 17), (37, 5), (1, 15), (43, 36), (34, 14), (14, 3), (0, 27), (1, 17), (40, 19), (0, 17), (34, 4), (6, 30), (17, 16), (36, 34), (12, 16), (13, 41), (7, 15), (6, 27), (43, 7), (15, 6), (27, 31), (33, 3), (18, 38), (20, 17), (5, 29), (11, 14), (2, 12), (13, 13), (36, 8), (14, 23), (27, 24), (12, 21), (1, 14), (27, 19), (11, 13), (36, 5), (0, 22), (15, 15), (29, 20), (34, 12), (17, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 41x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 5), (25, 45), (37, 28), (29, 44), (8, 37), (23, 22), (27, 7), (20, 11), (40, 44), (6, 32), (38, 33), (7, 44), (10, 43), (30, 15), (14, 20), (21, 38), (35, 39), (12, 16), (4, 14), (32, 0), (21, 37), (16, 11), (37, 35), (24, 1), (13, 1), (16, 9), (40, 26), (0, 26), (17, 4), (11, 1), (13, 12), (40, 4), (10, 27), (16, 31), (15, 10), (34, 7), (33, 26), (38, 15), (5, 23), (6, 35), (2, 33), (37, 23), (30, 32), (15, 31), (13, 16), (8, 35), (17, 14), (9, 10), (24, 30), (32, 40), (40, 40), (15, 22), (23, 12), (0, 27), (29, 17), (9, 28), (18, 30), (32, 26), (14, 40), (21, 40), (4, 25), (21, 23), (36, 23), (33, 36), (32, 36), (16, 4), (35, 10), (12, 13), (38, 40), (3, 30), (9, 19), (24, 0), (38, 23), (2, 21), (0, 8), (28, 16), (5, 14), (13, 11), (35, 45), (5, 12), (28, 27), (40, 38), (23, 13), (19, 29), (1, 39), (3, 8), (8, 45), (38, 3), (0, 16), (4, 0), (25, 24), (29, 40), (22, 12), (29, 14), (15, 14), (26, 12), (20, 22), (6, 36), (31, 24), (10, 35), (8, 3), (9, 20), (14, 2), (4, 36), (25, 43), (25, 1), (19, 41), (8, 8), (16, 12), (15, 32), (17, 15), (11, 24), (8, 21), (1, 18), (3, 25), (18, 38), (7, 34), (2, 39), (11, 30), (40, 30), (11, 12), (23, 34), (5, 10), (20, 10), (30, 30), (28, 11), (15, 13), (26, 9), (34, 10), (11, 11), (13, 37), (19, 13), (32, 31), (10, 18), (10, 37), (3, 39), (18, 6), (7, 19), (7, 29), (30, 34), (38, 22), (38, 35), (13, 22), (21, 32), (7, 1), (5, 8), (29, 28), (40, 33), (14, 27), (10, 38), (8, 19), (6, 20), (38, 19), (26, 25), (3, 15), (5, 6), (34, 40), (31, 32), (22, 33), (34, 44), (38, 32), (9, 39), (37, 36), (5, 40), (2, 40), (4, 31), (11, 13), (8, 12), (23, 16), (10, 32), (35, 5), (10, 7), (7, 42), (5, 4), (3, 19), (18, 19), (20, 31), (17, 20), (21, 6), (5, 37), (33, 21), (16, 1), (20, 40), (35, 18), (17, 43), (20, 34), (23, 37), (1, 31), (10, 9), (31, 3), (23, 18), (4, 10), (5, 2), (23, 35), (35, 14), (3, 0), (11, 35), (26, 40), (27, 14), (10, 28), (12, 5), (9, 13), (14, 35), (25, 23), (37, 15), (8, 30), (34, 4), (23, 15), (26, 16), (30, 44), (3, 40), (40, 37), (32, 12), (26, 14), (38, 42), (7, 28), (29, 12), (4, 9), (31, 34), (36, 8), (24, 4), (36, 39), (25, 42), (11, 43), (28, 28), (22, 0), (0, 9), (16, 45), (16, 36), (3, 45), (38, 27), (24, 36), (36, 33), (8, 25), (10, 44), (37, 30), (23, 17), (4, 3), (1, 19), (8, 43), (23, 4), (16, 14), (32, 2), (30, 40), (24, 39), (35, 27), (14, 18), (19, 21), (14, 13), (36, 13), (25, 38), (0, 41), (21, 13), (29, 16), (29, 2), (3, 33), (40, 3), (16, 21), (35, 37), (15, 0), (6, 27), (17, 27), (4, 21), (25, 31), (21, 21), (16, 22), (30, 17), (30, 12), (2, 37), (16, 33), (35, 16), (37, 0), (9, 14), (20, 21), (30, 45), (25, 15), (3, 37), (6, 11), (19, 34), (25, 11), (27, 21), (28, 15), (5, 31), (16, 44), (7, 23), (12, 17), (2, 41), (34, 6), (0, 38), (2, 17), (4, 45), (0, 39), (23, 38), (16, 13), (3, 12), (11, 26), (14, 36), (15, 4), (2, 30), (36, 26), (25, 28), (31, 2), (20, 35), (24, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 7), (17, 29), (43, 42), (17, 42), (21, 43), (47, 7), (1, 6), (38, 27), (37, 37), (8, 25), (17, 28), (14, 2), (26, 40), (10, 15), (31, 7), (47, 5), (35, 36), (6, 29), (8, 36), (44, 3), (27, 41), (35, 2), (3, 35), (12, 11), (31, 6), (37, 21), (4, 32), (16, 31), (40, 8), (8, 31), (19, 9), (0, 36), (43, 33), (10, 8), (8, 1), (20, 3), (35, 3), (43, 15), (18, 31), (13, 35), (10, 20), (6, 2), (46, 20), (43, 30), (41, 11), (2, 24), (40, 4), (21, 41), (3, 2), (20, 5), (0, 41), (19, 42), (3, 31), (10, 17), (25, 8), (44, 10), (12, 39), (2, 28), (5, 34), (45, 6), (23, 8), (30, 8), (38, 12), (3, 7), (28, 17), (25, 11), (24, 34), (35, 29), (17, 16), (16, 13), (2, 22), (11, 4), (36, 15), (47, 41), (23, 1), (21, 14), (36, 29), (2, 41), (15, 37), (14, 22), (22, 0), (34, 24), (34, 6), (23, 28), (44, 4), (33, 38), (7, 40), (43, 35), (30, 18), (22, 38), (3, 37), (27, 19), (47, 36), (39, 8), (47, 16), (17, 41), (41, 12), (41, 15), (30, 25), (40, 31), (18, 25), (14, 21), (24, 42), (17, 0), (26, 24), (13, 6), (45, 12), (37, 19), (45, 34), (21, 36), (28, 12), (24, 0), (32, 33), (19, 0), (41, 37), (22, 10), (33, 4), (5, 40), (19, 15), (32, 36), (35, 39), (16, 25), (33, 1), (43, 20), (16, 22), (18, 23), (45, 0), (28, 43), (18, 0), (7, 38), (9, 18), (32, 4), (29, 16), (14, 26), (25, 43), (20, 26), (33, 16), (46, 29), (34, 23), (13, 34), (9, 10), (10, 4), (6, 9), (43, 38), (35, 1), (34, 1), (19, 7), (31, 24), (13, 5), (9, 29), (38, 41), (38, 30), (4, 6), (1, 22), (34, 14), (0, 15), (36, 7), (5, 27), (35, 25), (5, 4), (32, 18), (26, 13), (44, 17), (25, 31), (35, 9), (37, 15), (7, 35), (39, 4), (34, 42), (32, 11), (39, 22), (35, 37), (39, 11), (27, 40), (1, 7), (36, 22), (23, 17), (21, 16), (21, 28), (17, 19), (13, 14), (36, 0), (22, 23), (37, 8), (33, 41), (8, 30), (41, 23), (2, 42), (18, 41), (18, 5), (3, 10), (31, 43), (29, 25), (1, 11), (35, 41), (19, 19), (47, 20), (15, 25), (20, 7), (7, 8), (40, 21), (28, 19), (7, 13), (13, 2), (7, 14), (25, 37), (25, 16), (33, 15), (21, 11), (33, 2), (31, 4), (46, 19), (12, 22), (28, 31), (4, 28), (1, 24), (47, 11), (24, 2), (8, 22), (18, 17), (11, 18), (32, 12), (22, 18), (24, 7), (0, 29), (8, 11), (36, 35), (4, 39), (38, 34), (9, 13), (47, 2), (9, 6), (21, 3), (43, 37), (20, 12), (9, 12), (35, 27), (20, 17), (15, 7), (42, 39), (21, 30), (40, 26), (25, 27), (18, 11), (0, 31), (4, 41), (33, 43), (20, 43), (38, 2), (22, 24), (3, 26), (22, 14), (10, 14), (7, 36), (28, 23), (1, 12), (0, 43), (23, 32), (41, 28), (44, 18), (38, 38), (33, 19), (6, 15), (16, 37), (38, 21), (6, 30), (16, 4), (32, 6), (33, 7), (39, 43), (32, 42), (44, 23), (1, 25), (2, 12), (18, 3), (47, 24), (10, 6), (26, 38), (20, 4), (38, 15), (10, 34), (13, 42), (12, 34), (40, 1), (11, 7), (7, 10), (38, 17), (45, 23), (25, 18), (20, 19), (7, 32), (47, 0), (7, 30), (42, 9), (35, 23), (25, 9), (44, 41), (8, 39), (35, 43), (26, 10), (8, 12), (10, 10), (12, 9), (46, 11), (24, 5), (33, 36), (3, 11), (32, 7), (35, 18), (32, 0), (42, 32), (2, 34), (16, 24), (11, 12), (16, 33), (14, 8), (37, 27), (14, 15), (45, 4), (20, 40), (13, 19), (31, 28), (16, 14), (5, 36), (3, 39), (5, 26), (1, 21), (2, 21), (39, 26), (32, 3), (42, 4), (42, 26), (10, 22), (20, 41), (30, 19), (42, 21), (24, 43), (8, 13), (43, 14), (26, 29), (26, 19), (12, 29), (40, 25), (6, 37), (2, 39), (30, 23), (24, 11), (30, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (19, 17), (2, 3), (34, 36), (1, 4), (45, 8), (10, 3), (14, 0), (1, 20), (22, 12), (34, 8), (26, 37), (40, 7), (1, 25), (13, 34), (31, 7), (1, 34), (2, 18), (10, 2), (27, 9), (32, 20), (45, 31), (19, 9), (19, 38), (27, 32), (43, 31), (3, 25), (38, 11), (11, 28), (33, 2), (31, 34), (15, 40), (11, 36), (18, 24), (16, 25), (0, 2), (42, 0), (34, 13), (33, 3), (36, 5), (16, 8), (18, 10), (5, 18), (3, 36), (7, 34), (19, 30), (5, 20), (3, 40), (20, 40), (9, 10), (30, 3), (37, 37), (5, 35), (44, 20), (18, 7), (15, 30), (23, 2), (33, 8), (13, 32), (31, 21), (26, 8), (6, 29), (38, 0), (15, 9), (27, 5), (28, 33), (26, 16), (32, 11), (44, 27), (39, 20), (14, 41), (4, 24), (12, 29), (29, 1), (30, 18), (1, 5), (8, 30), (36, 10), (13, 35), (30, 21), (16, 39), (18, 34), (34, 41), (38, 25), (8, 24), (0, 10), (16, 16), (42, 24), (37, 40), (18, 19), (5, 36), (37, 21), (45, 40), (2, 41), (1, 23), (23, 35), (37, 30), (35, 8), (10, 33), (1, 24), (12, 23), (41, 4), (37, 31), (17, 6), (15, 25), (17, 29), (22, 40), (22, 39), (35, 25), (36, 11), (31, 38), (29, 26), (32, 17), (17, 27), (0, 12), (27, 16), (17, 41), (21, 30), (25, 6), (9, 14), (14, 31), (15, 28), (15, 35), (24, 17), (6, 34), (42, 11), (34, 39), (39, 22), (9, 27), (39, 0), (22, 15), (34, 1), (21, 34), (39, 32), (9, 15), (30, 31), (14, 17), (34, 38), (10, 26), (22, 16), (8, 36), (22, 21), (7, 32), (15, 8), (17, 7), (4, 25), (20, 30), (18, 14), (17, 9), (19, 36), (19, 34), (28, 36), (32, 0), (13, 26), (12, 11), (24, 29), (36, 13), (27, 0), (0, 25), (33, 18), (35, 5), (31, 12), (42, 37), (43, 2), (24, 12), (25, 23), (28, 27), (10, 14), (29, 11), (7, 10), (13, 27), (40, 2), (38, 6), (1, 15), (1, 6), (11, 2), (42, 30), (4, 37), (8, 32), (24, 8), (39, 35), (9, 39), (28, 8), (42, 3), (11, 19), (41, 30), (27, 31), (45, 22), (16, 29), (40, 39), (20, 18), (2, 9), (27, 21), (22, 4), (41, 38), (20, 4), (7, 15), (16, 9), (3, 27), (21, 33), (8, 11), (21, 1), (43, 3), (15, 37), (40, 26), (28, 14), (4, 11), (30, 16), (34, 27), (40, 24), (22, 1), (17, 22), (30, 11), (37, 41), (42, 21), (3, 26), (24, 25), (30, 4), (31, 23), (38, 1), (40, 36), (26, 25), (7, 0), (38, 33), (40, 4), (8, 26), (41, 15), (36, 17), (38, 31), (9, 2), (34, 9), (11, 13), (12, 36), (24, 27), (45, 1), (33, 5), (32, 16), (40, 19), (29, 7), (2, 40), (20, 35), (29, 25), (18, 36), (40, 35), (37, 35), (4, 9), (21, 3), (45, 7), (29, 40), (37, 38), (17, 20), (40, 41), (29, 36), (25, 13), (9, 13), (7, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 17), (27, 17), (8, 1), (4, 26), (38, 24), (8, 39), (4, 29), (7, 29), (29, 15), (28, 37), (23, 43), (38, 30), (6, 31), (20, 36), (11, 21), (28, 33), (34, 0), (6, 5), (17, 23), (21, 1), (19, 0), (25, 5), (35, 26), (22, 30), (31, 32), (27, 40), (2, 15), (37, 33), (18, 32), (29, 27), (4, 12), (30, 33), (10, 31), (39, 35), (32, 20), (20, 27), (13, 22), (1, 10), (35, 42), (21, 11), (8, 12), (4, 43), (29, 18), (15, 18), (27, 10), (17, 13), (32, 11), (18, 4), (6, 39), (21, 30), (15, 31), (35, 31), (9, 23), (17, 41), (21, 26), (25, 19), (39, 24), (10, 27), (8, 6), (40, 35), (41, 21), (3, 22), (37, 36), (3, 2), (2, 34), (37, 23), (32, 6), (19, 2), (17, 22), (40, 20), (34, 11), (23, 21), (1, 36), (4, 33), (21, 37), (23, 25), (38, 23), (13, 2), (36, 34), (24, 26), (29, 2), (10, 32), (6, 9), (22, 4), (5, 36), (8, 7), (20, 16), (4, 13), (2, 4), (37, 12), (25, 32), (33, 6), (6, 43), (22, 25), (16, 26), (14, 24), (34, 31), (8, 31), (33, 34), (0, 8), (20, 1), (11, 30), (17, 4), (3, 12), (13, 30), (20, 43), (1, 26), (6, 13), (27, 14), (16, 36), (8, 4), (37, 42), (3, 31), (31, 34), (29, 43), (13, 18), (21, 13), (9, 9), (38, 8), (36, 19), (18, 18), (7, 19), (6, 1), (6, 20), (41, 11), (4, 34), (41, 30), (6, 2), (25, 30), (40, 2), (35, 5), (20, 23), (26, 29), (30, 9), (3, 28), (34, 38), (10, 41), (29, 3), (37, 9), (5, 0), (6, 19), (29, 25), (3, 9), (30, 39), (12, 33), (25, 26), (36, 29), (29, 23), (35, 3), (7, 32), (40, 36), (30, 23), (16, 32), (23, 20), (7, 12), (19, 34), (13, 34), (26, 10), (34, 19), (18, 40), (0, 4), (1, 7), (14, 23), (1, 12), (16, 2), (3, 33), (36, 6), (6, 32), (28, 31), (22, 21), (39, 3), (4, 15), (19, 18), (31, 27), (41, 6), (9, 39), (4, 41), (1, 29), (9, 27), (28, 13), (41, 12), (28, 43), (2, 36), (16, 33), (4, 6), (39, 27), (7, 9), (11, 7), (9, 38), (15, 15), (10, 5), (37, 8), (23, 14), (30, 35), (2, 2), (19, 19), (13, 27), (38, 38), (18, 34), (5, 43), (41, 35), (34, 27), (3, 41), (0, 1), (19, 31), (39, 9), (20, 40), (38, 9), (19, 14), (6, 26), (37, 19), (35, 28), (17, 34), (8, 37), (1, 40), (26, 31), (27, 0), (36, 10), (33, 43), (21, 15), (41, 41), (15, 7), (16, 16), (26, 6), (8, 29), (26, 30), (29, 42), (37, 2), (5, 3), (32, 1), (34, 30), (16, 18), (26, 2), (2, 30), (14, 26), (25, 33), (23, 40), (33, 19), (1, 21), (24, 11), (8, 22), (37, 32), (12, 23), (33, 14), (34, 14), (13, 41), (12, 13), (23, 8), (15, 40), (0, 26), (4, 32), (19, 39), (25, 20), (5, 34), (14, 3), (1, 28), (36, 22), (20, 29), (25, 9), (34, 17), (19, 21), (18, 41), (6, 17), (14, 11), (36, 39), (28, 20), (1, 11), (5, 24), (32, 3), (36, 31), (7, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 17), (21, 30), (9, 10), (32, 7), (2, 27), (9, 9), (28, 1), (40, 6), (33, 16), (32, 21), (21, 29), (15, 26), (11, 10), (37, 36), (29, 2), (14, 0), (23, 34), (8, 0), (37, 11), (38, 32), (46, 33), (2, 39), (30, 10), (20, 19), (3, 21), (25, 28), (11, 37), (27, 0), (1, 35), (43, 25), (33, 29), (37, 26), (22, 8), (6, 37), (19, 13), (28, 20), (21, 5), (20, 1), (38, 4), (46, 1), (12, 21), (25, 2), (33, 26), (3, 36), (39, 4), (17, 6), (38, 10), (33, 23), (38, 13), (32, 2), (31, 4), (19, 15), (17, 28), (40, 16), (33, 0), (31, 39), (24, 20), (17, 2), (42, 22), (9, 0), (45, 37), (44, 25), (37, 13), (19, 38), (15, 20), (34, 22), (15, 29), (37, 29), (24, 34), (45, 0), (21, 24), (34, 14), (46, 32), (24, 33), (7, 33), (10, 11), (24, 5), (43, 39), (16, 13), (25, 24), (26, 11), (24, 3), (24, 24), (16, 10), (30, 6), (9, 17), (0, 8), (36, 31), (29, 33), (45, 34), (20, 27), (4, 15), (5, 4), (7, 31), (7, 0), (23, 12), (5, 24), (24, 17), (12, 15), (27, 35), (14, 29), (19, 3), (36, 28), (43, 11), (31, 34), (26, 12), (16, 3), (6, 36), (21, 23), (22, 5), (26, 36), (3, 29), (43, 0), (13, 21), (8, 4), (34, 31), (47, 31), (16, 23), (15, 4), (13, 26), (36, 36), (33, 4), (29, 8), (28, 7), (37, 23), (0, 10), (42, 6), (4, 11), (13, 23), (47, 12), (0, 9), (22, 14), (41, 5), (31, 38), (23, 16), (12, 19), (43, 28), (16, 39), (32, 39), (32, 8), (36, 12), (44, 20), (2, 15), (3, 33), (16, 37), (39, 1), (13, 34), (18, 0), (0, 36), (11, 9), (28, 38), (43, 17), (16, 24), (23, 23), (43, 36), (32, 10), (29, 4), (8, 35), (40, 11), (39, 11), (19, 0), (20, 18), (1, 31), (40, 13), (30, 33), (3, 10), (31, 37), (33, 13), (16, 16), (18, 19), (16, 0), (2, 32), (44, 18), (0, 3), (16, 4), (47, 18), (13, 20), (24, 36), (27, 19), (13, 39), (39, 7), (24, 18), (40, 38), (20, 15), (14, 18), (27, 15), (9, 19), (17, 7), (44, 10), (37, 0), (11, 33), (41, 15), (30, 2), (15, 24), (27, 2), (35, 36), (37, 25), (40, 25), (7, 19), (10, 37), (25, 3), (5, 16), (21, 36), (40, 39), (22, 35), (1, 7), (45, 13), (9, 23), (29, 11), (35, 9), (15, 10), (33, 30), (21, 9), (16, 12), (20, 5), (46, 7), (6, 16), (1, 30), (30, 34), (23, 4), (22, 1), (23, 29), (4, 7), (24, 8), (12, 18), (31, 9), (5, 12), (32, 18), (22, 16), (2, 11), (9, 34), (14, 25), (9, 21), (45, 32), (12, 20), (40, 3), (18, 20), (14, 28), (27, 7), (3, 30), (17, 3), (1, 27), (7, 1), (6, 23), (20, 17), (20, 4), (20, 12), (45, 7), (31, 24), (34, 3), (33, 10), (7, 38), (30, 25), (29, 23), (24, 35), (35, 29), (8, 26), (14, 7), (29, 37), (17, 0), (47, 34), (25, 23), (31, 36), (38, 21), (26, 16), (34, 28), (38, 5), (37, 16), (38, 18), (37, 39), (34, 29), (28, 34), (47, 8), (12, 36), (10, 38), (15, 13), (22, 15), (41, 23), (18, 4), (39, 21), (16, 14), (19, 28), (28, 15), (34, 0), (38, 27), (11, 34), (23, 38), (13, 4), (29, 18), (24, 12), (32, 20), (6, 3), (13, 27), (46, 38), (40, 36), (37, 17), (23, 7), (15, 2), (28, 3), (15, 17), (30, 35), (18, 1), (42, 7), (37, 37), (37, 1), (9, 33), (36, 19), (44, 17), (35, 2), (8, 5), (42, 16), (26, 17), (38, 8), (46, 39), (20, 31), (11, 8), (10, 23), (4, 4), (1, 3), (45, 10), (25, 10), (23, 35), (36, 33), (3, 17), (10, 8), (43, 20), (29, 20), (23, 24), (23, 1), (12, 12), (11, 21), (15, 6), (39, 37), (27, 9), (2, 12), (1, 37), (35, 3), (24, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 31), (40, 25), (24, 12), (30, 8), (29, 16), (9, 1), (1, 28), (7, 7), (32, 17), (21, 9), (37, 36), (14, 21), (32, 12), (22, 10), (5, 29), (10, 2), (8, 4), (33, 38), (32, 30), (16, 31), (2, 4), (3, 24), (6, 29), (23, 35), (38, 28), (39, 33), (39, 42), (21, 28), (8, 8), (3, 1), (36, 32), (30, 42), (9, 14), (15, 44), (14, 43), (15, 1), (30, 29), (34, 30), (24, 11), (0, 2), (21, 44), (32, 0), (7, 28), (12, 4), (17, 25), (13, 28), (15, 16), (34, 38), (17, 40), (21, 20), (22, 31), (40, 34), (34, 44), (7, 21), (32, 2), (39, 9), (23, 17), (38, 5), (4, 28), (8, 22), (2, 41), (38, 15), (39, 11), (40, 0), (28, 15), (36, 33), (29, 7), (11, 4), (35, 36), (29, 36), (36, 0), (39, 23), (16, 26), (36, 26), (3, 8), (29, 6), (35, 16), (5, 6), (24, 0), (27, 43), (20, 31), (36, 42), (13, 27), (34, 16), (21, 12), (4, 11), (28, 18), (32, 29), (9, 36), (34, 23), (20, 41), (27, 19), (3, 6), (23, 26), (31, 43), (6, 21), (11, 28), (25, 23), (28, 19), (41, 33), (28, 28), (19, 15), (4, 34), (15, 41), (6, 24), (23, 39), (3, 12), (39, 2), (41, 12), (22, 24), (29, 41), (6, 30), (15, 15), (15, 36), (17, 7), (14, 15), (41, 34), (7, 4), (38, 20), (21, 33), (24, 10), (20, 34), (25, 40), (30, 0), (17, 32), (6, 3), (10, 39), (26, 9), (5, 44), (10, 25), (11, 29), (5, 33), (37, 25), (10, 35), (17, 10), (29, 30), (10, 44), (35, 32), (32, 7), (4, 14), (5, 24), (32, 36), (34, 10), (5, 21), (37, 2), (13, 2), (17, 44), (2, 27), (13, 34), (3, 23), (3, 4), (4, 32), (3, 34), (7, 43), (29, 34), (20, 32), (28, 20), (19, 24), (26, 38), (12, 15), (22, 40), (15, 6), (6, 27), (7, 19), (30, 17), (9, 9), (39, 27), (1, 21), (26, 27), (1, 30), (18, 25), (20, 0), (7, 42), (2, 12), (38, 0), (11, 1), (41, 35), (7, 35), (26, 40), (5, 8), (24, 32), (38, 11), (8, 16), (17, 11), (30, 34), (13, 5), (29, 42), (39, 12), (22, 33), (1, 22), (6, 38), (1, 44), (12, 6), (23, 5), (3, 18), (15, 31), (38, 35), (35, 28), (30, 30), (34, 12), (15, 19), (31, 37), (15, 24), (19, 27), (14, 13), (26, 42), (6, 34), (30, 25), (38, 25), (14, 36), (17, 13), (3, 3), (21, 13), (11, 6), (25, 22), (33, 44), (29, 3), (30, 43), (34, 40), (20, 27), (12, 25), (28, 31), (30, 5), (40, 24), (5, 7), (28, 17), (18, 27), (25, 43), (18, 16), (25, 42), (41, 0), (40, 26), (1, 23), (41, 19), (41, 15), (37, 22), (3, 35), (17, 38), (11, 32), (8, 26), (15, 9), (4, 4), (17, 8), (7, 11), (16, 11), (33, 0), (18, 21), (28, 35), (38, 40), (28, 25), (19, 2), (37, 41), (23, 21), (18, 29), (7, 0), (40, 39), (40, 23), (21, 14), (34, 15), (28, 39), (0, 8), (23, 29), (36, 38), (32, 39), (8, 19), (27, 10), (33, 33), (12, 37), (22, 14), (20, 17), (24, 24), (4, 0), (3, 5), (24, 27), (0, 28), (40, 12), (13, 7), (18, 22), (15, 40), (7, 25), (26, 6), (31, 38), (27, 27), (35, 44), (3, 38), (12, 34), (4, 35), (22, 0), (18, 15), (2, 17), (36, 7), (23, 15), (3, 44), (3, 7), (28, 14), (3, 14), (30, 18), (41, 24), (17, 6), (30, 15), (25, 18), (25, 6), (11, 17), (36, 24), (9, 43), (25, 3), (26, 22), (12, 44), (6, 13), (6, 18), (17, 23), (28, 40), (38, 23), (32, 23), (20, 1), (9, 31), (37, 5), (0, 26), (39, 6), (22, 29), (36, 40), (35, 10), (19, 12), (11, 16), (26, 26), (6, 12), (3, 27), (20, 38), (24, 23), (39, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 34), (43, 37), (32, 26), (43, 30), (16, 2), (23, 28), (44, 18), (12, 36), (41, 26), (23, 4), (38, 30), (30, 40), (39, 38), (6, 0), (2, 8), (44, 35), (41, 33), (18, 13), (37, 24), (30, 36), (21, 37), (31, 38), (11, 36), (22, 5), (39, 23), (45, 18), (18, 17), (34, 17), (24, 18), (22, 34), (14, 42), (12, 42), (40, 42), (35, 4), (15, 37), (36, 38), (1, 25), (15, 28), (42, 13), (29, 9), (32, 40), (0, 10), (29, 32), (3, 33), (5, 33), (39, 34), (11, 7), (30, 26), (7, 12), (32, 13), (13, 38), (19, 32), (23, 25), (3, 13), (39, 35), (25, 4), (3, 35), (14, 4), (34, 4), (31, 41), (7, 0), (25, 28), (41, 11), (43, 12), (29, 26), (6, 2), (37, 8), (13, 9), (5, 10), (3, 42), (31, 20), (37, 27), (8, 6), (35, 29), (6, 40), (6, 17), (13, 42), (43, 34), (22, 10), (12, 15), (11, 5), (14, 1), (27, 24), (35, 10), (41, 7), (17, 35), (25, 38), (13, 19), (1, 37), (38, 6), (27, 20), (15, 7), (7, 17), (35, 1), (6, 10), (29, 1), (29, 12), (22, 42), (3, 25), (35, 21), (37, 34), (9, 36), (1, 6), (24, 40), (35, 3), (33, 29), (19, 38), (33, 10), (16, 12), (29, 27), (38, 25), (20, 11), (25, 18), (26, 13), (0, 25), (4, 15), (34, 29), (27, 27), (7, 30), (37, 42), (20, 6), (26, 21), (27, 30), (24, 4), (8, 14), (20, 19), (27, 3), (26, 0), (14, 2), (23, 11), (30, 14), (19, 11), (0, 15), (4, 19), (19, 0), (23, 38), (45, 37), (33, 13), (27, 34), (29, 40), (29, 6), (18, 11), (35, 40), (30, 33), (37, 29), (17, 5), (30, 42), (27, 23), (2, 23), (41, 1), (33, 38), (25, 37), (19, 9), (39, 37), (44, 30), (37, 18), (37, 0), (16, 4), (27, 8), (10, 42), (45, 30), (24, 10), (42, 10), (6, 26), (43, 25), (6, 33), (7, 10), (24, 32), (17, 31), (3, 30), (8, 17), (9, 22), (33, 41), (43, 42), (13, 25), (23, 13), (2, 11), (38, 17), (33, 42), (25, 30), (33, 32), (35, 36), (33, 24), (11, 38), (33, 22), (44, 2), (10, 27), (31, 29), (37, 5), (30, 38), (17, 9), (26, 38), (31, 0), (17, 18), (45, 38), (37, 36), (27, 1), (43, 15), (37, 11), (2, 21), (34, 27), (19, 1), (23, 23), (21, 30), (33, 16), (11, 9), (23, 39), (5, 6), (0, 11), (36, 30), (2, 30), (9, 32), (44, 23), (43, 5), (27, 7), (26, 19), (12, 14), (34, 39), (37, 20), (42, 29), (36, 14), (40, 21), (12, 0), (3, 22), (7, 8), (0, 38), (18, 15), (29, 31), (4, 38), (19, 24), (12, 35), (3, 37), (4, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 10), (21, 20), (27, 37), (12, 40), (23, 41), (30, 11), (19, 17), (15, 19), (24, 36), (42, 0), (28, 37), (34, 24), (10, 38), (35, 7), (11, 1), (35, 30), (38, 0), (32, 20), (25, 27), (39, 22), (5, 21), (43, 26), (0, 16), (3, 1), (42, 23), (39, 3), (1, 9), (12, 0), (21, 25), (7, 9), (1, 3), (13, 30), (6, 38), (37, 22), (20, 3), (31, 17), (26, 35), (32, 12), (40, 9), (7, 39), (41, 36), (35, 21), (10, 7), (25, 38), (25, 12), (16, 10), (1, 33), (11, 13), (2, 26), (14, 34), (35, 40), (28, 42), (40, 41), (7, 6), (33, 17), (21, 27), (2, 18), (25, 18), (18, 41), (18, 2), (12, 38), (43, 28), (5, 29), (32, 34), (41, 28), (17, 25), (16, 30), (11, 5), (37, 41), (28, 38), (9, 27), (12, 20), (0, 9), (33, 30), (3, 38), (31, 19), (27, 0), (25, 17), (6, 33), (19, 0), (19, 28), (6, 21), (19, 40), (11, 26), (31, 1), (20, 27), (35, 0), (31, 25), (5, 13), (16, 9), (20, 10), (29, 23), (32, 22), (27, 22), (12, 23), (8, 28), (27, 9), (26, 17), (31, 27), (3, 18), (30, 14), (12, 24), (29, 26), (20, 9), (41, 41), (19, 14), (10, 10), (38, 33), (17, 1), (23, 40), (31, 23), (6, 40), (31, 34), (12, 11), (15, 2), (20, 13), (30, 37), (10, 24), (6, 8), (1, 41), (4, 14), (4, 39), (16, 0), (38, 5), (29, 39), (42, 9), (26, 11), (22, 4), (21, 19), (3, 41), (33, 3), (15, 11), (21, 32), (8, 39), (4, 31), (9, 23), (8, 25), (33, 39), (3, 2), (12, 7), (30, 6), (30, 36), (42, 13), (27, 3), (34, 36), (4, 23), (18, 22), (8, 12), (10, 14), (10, 21), (41, 23), (29, 35), (23, 26), (30, 42), (36, 1), (36, 17), (15, 35), (14, 13), (23, 27), (1, 4), (18, 17), (14, 26), (8, 37), (18, 26), (20, 33), (19, 26), (13, 39), (31, 18), (34, 19), (6, 35), (27, 16), (40, 3), (25, 29), (43, 17), (42, 33), (17, 34), (36, 28), (39, 23), (29, 17), (11, 42), (27, 15), (6, 3), (13, 4), (16, 29), (12, 3), (10, 0), (41, 1), (24, 41), (43, 12), (8, 11), (9, 7), (2, 12), (42, 7), (12, 4), (37, 10), (41, 9), (26, 21), (43, 13), (8, 35), (40, 42), (33, 0), (26, 18), (17, 37), (43, 19), (2, 22), (18, 7), (39, 38), (3, 11), (0, 38), (31, 15), (2, 33), (12, 10), (25, 11), (10, 40), (1, 14), (25, 31), (15, 25), (15, 17), (38, 39), (18, 28), (41, 14), (8, 31), (13, 29), (37, 4), (20, 34), (31, 37), (35, 42), (9, 29), (42, 37), (17, 24), (30, 18), (19, 13), (21, 17), (41, 7), (38, 3), (3, 29), (5, 31), (25, 40), (41, 4), (36, 16), (32, 29), (9, 40), (4, 10), (32, 36), (21, 22), (3, 39), (27, 34), (9, 13), (11, 19), (24, 10), (0, 13), (22, 9), (7, 1), (32, 14), (12, 14), (15, 38), (20, 17), (5, 7), (21, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 25), (38, 7), (40, 19), (5, 16), (3, 25), (23, 42), (13, 12), (6, 13), (12, 35), (29, 14), (18, 6), (35, 5), (14, 39), (25, 9), (26, 36), (20, 36), (5, 46), (18, 39), (0, 33), (10, 30), (33, 6), (8, 41), (30, 6), (16, 7), (25, 20), (22, 15), (28, 43), (25, 26), (13, 15), (27, 34), (11, 2), (8, 6), (15, 33), (9, 32), (6, 33), (22, 4), (37, 31), (11, 19), (26, 37), (1, 17), (29, 33), (2, 12), (10, 43), (33, 2), (30, 42), (12, 16), (20, 37), (20, 41), (18, 26), (13, 1), (37, 43), (13, 17), (37, 7), (15, 16), (24, 5), (5, 20), (14, 30), (7, 2), (15, 44), (7, 35), (21, 15), (6, 12), (19, 11), (37, 1), (10, 7), (21, 7), (24, 10), (24, 20), (10, 15), (31, 41), (29, 29), (25, 1), (13, 39), (23, 24), (38, 11), (24, 21), (33, 5), (25, 24), (35, 30), (28, 14), (8, 37), (18, 15), (8, 43), (15, 14), (14, 29), (5, 35), (24, 43), (40, 40), (33, 30), (16, 12), (11, 12), (25, 12), (37, 41), (11, 7), (18, 5), (5, 3), (31, 23), (8, 34), (38, 17), (18, 37), (18, 41), (30, 20), (6, 14), (9, 8), (39, 35), (31, 24), (1, 44), (23, 32), (8, 31), (10, 5), (11, 22), (7, 5), (23, 28), (25, 21), (3, 42), (3, 22), (16, 31), (33, 21), (23, 15), (33, 19), (12, 34), (2, 39), (31, 25), (0, 31), (14, 33), (12, 42), (0, 21), (3, 27), (13, 19), (36, 22), (22, 32), (21, 43), (8, 20), (26, 13), (14, 4), (6, 3), (20, 45), (24, 42), (6, 37), (14, 2), (6, 9), (26, 26), (8, 27), (37, 17), (23, 8), (5, 10), (6, 40), (10, 10), (39, 40), (23, 27), (30, 3), (10, 40), (14, 34), (25, 32), (38, 23), (34, 14), (27, 25), (9, 0), (39, 16), (32, 0), (16, 10), (15, 25), (9, 12), (37, 46), (22, 11), (17, 36), (41, 41), (9, 45), (24, 37), (11, 41), (7, 29), (12, 12), (10, 36), (31, 6), (11, 33), (26, 40), (30, 22), (35, 8), (23, 29), (19, 29), (11, 1), (41, 45), (17, 12), (25, 13), (17, 1), (33, 44), (4, 44), (23, 0), (14, 19), (22, 18), (28, 40), (21, 32), (10, 34), (18, 22), (1, 36), (2, 34), (19, 26), (39, 18), (7, 19), (19, 44), (25, 43), (40, 27), (28, 7), (14, 7), (9, 9), (35, 3), (34, 23), (26, 25), (13, 28), (34, 21), (18, 21), (31, 42), (31, 0), (38, 2), (36, 44), (25, 44), (27, 22), (18, 4), (8, 10), (39, 26), (21, 23), (24, 28), (41, 21), (12, 21), (6, 45), (6, 11), (11, 32), (20, 32), (17, 8), (25, 46), (0, 45), (40, 25), (11, 18), (24, 45), (1, 3), (3, 6), (32, 19), (38, 28), (1, 10), (3, 24), (34, 31), (4, 23), (1, 35), (38, 33), (24, 27), (37, 44), (29, 17), (2, 42), (39, 34), (28, 44), (29, 37), (8, 30), (21, 11), (30, 14), (11, 44), (36, 39), (5, 41), (20, 10), (31, 9), (20, 2), (25, 11), (1, 30), (18, 23), (38, 37), (37, 42), (22, 44), (0, 1), (5, 4), (9, 18), (41, 35), (1, 19), (8, 44), (39, 46), (9, 5), (0, 41), (11, 3), (16, 22), (15, 11), (29, 10), (14, 37), (2, 19), (0, 44), (22, 26), (29, 3), (36, 45), (37, 18), (38, 35), (2, 32), (37, 33), (16, 24), (11, 27), (20, 22), (18, 7), (25, 4), (1, 33), (17, 7), (28, 3), (40, 1), (8, 45), (21, 20), (36, 28), (1, 15), (15, 7), (6, 5), (41, 14), (7, 18), (25, 30), (33, 13), (28, 26), (0, 29), (30, 10), (4, 18), (38, 8), (11, 10), (11, 39), (35, 10), (31, 37), (12, 27), (10, 22), (20, 7), (41, 4), (2, 22), (35, 16), (16, 0), (33, 41), (6, 27), (1, 23), (1, 31), (12, 26), (7, 46), (32, 12), (41, 13), (29, 7), (40, 23), (34, 43), (35, 11), (15, 4), (1, 7), (23, 14), (19, 23), (23, 45), (9, 10), (39, 27), (38, 21), (41, 9), (35, 27), (37, 15), (40, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 46x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 37), (16, 29), (2, 4), (32, 23), (36, 20), (7, 8), (25, 25), (25, 1), (33, 17), (32, 22), (4, 7), (8, 23), (44, 26), (29, 13), (30, 16), (3, 20), (31, 31), (25, 34), (17, 11), (7, 13), (23, 33), (24, 4), (4, 26), (38, 14), (33, 31), (5, 32), (35, 31), (8, 9), (41, 6), (37, 9), (18, 38), (19, 6), (21, 26), (11, 21), (34, 16), (11, 38), (43, 7), (14, 10), (13, 34), (44, 17), (23, 38), (20, 19), (14, 2), (33, 39), (26, 38), (11, 8), (27, 38), (38, 40), (13, 9), (4, 24), (43, 9), (13, 2), (18, 7), (37, 23), (9, 1), (21, 25), (2, 20), (22, 12), (10, 11), (13, 41), (42, 33), (6, 39), (1, 23), (22, 31), (44, 3), (31, 8), (42, 35), (32, 21), (38, 7), (41, 39), (19, 26), (25, 3), (35, 5), (38, 29), (36, 18), (45, 10), (24, 36), (3, 5), (17, 36), (1, 34), (27, 2), (43, 38), (23, 31), (42, 42), (41, 30), (6, 10), (20, 27), (29, 17), (5, 9), (21, 29), (17, 9), (15, 9), (26, 41), (41, 9), (30, 9), (13, 11), (3, 29), (7, 19), (27, 10), (13, 33), (37, 35), (32, 29), (8, 13), (19, 29), (16, 28), (45, 19), (2, 17), (13, 38), (34, 13), (11, 1), (35, 41), (35, 19), (33, 36), (10, 24), (2, 26), (4, 13), (34, 27), (37, 39), (4, 39), (16, 38), (42, 32), (3, 9), (38, 20), (10, 34), (15, 6), (32, 13), (35, 13), (0, 38), (45, 3), (44, 19), (12, 33), (36, 32), (0, 37), (42, 2), (26, 24), (6, 12), (11, 20), (35, 30), (22, 34), (34, 14), (15, 38), (30, 0), (5, 30), (35, 33), (3, 30), (22, 42), (3, 16), (37, 11), (31, 11), (10, 29), (30, 7), (45, 25), (36, 15), (32, 1), (38, 8), (22, 29), (4, 23), (21, 40), (43, 26), (10, 6), (4, 5), (16, 35), (16, 41), (5, 37), (45, 17), (32, 19), (31, 30), (36, 12), (36, 35), (41, 13), (14, 0), (42, 11), (4, 10), (12, 22), (12, 1), (28, 21), (38, 17), (28, 34), (12, 17), (44, 23), (2, 21), (26, 9), (17, 22), (36, 24), (27, 21), (0, 36), (35, 21), (8, 1), (44, 32), (2, 24), (38, 6), (7, 24), (30, 33), (25, 16), (1, 10), (33, 41), (6, 13), (36, 3), (34, 39), (20, 4), (38, 18), (29, 1), (32, 16), (30, 41), (20, 23), (26, 40), (37, 27), (29, 9), (2, 32), (13, 39), (8, 14), (39, 22), (6, 9), (41, 38), (12, 42), (25, 29), (45, 5), (22, 8), (21, 7), (15, 26), (15, 24), (38, 37), (37, 14), (27, 14), (15, 39), (4, 42), (24, 17), (41, 15), (21, 23), (21, 41), (33, 35), (44, 18), (4, 29), (6, 4), (9, 0), (30, 19), (42, 27), (45, 32), (32, 37), (35, 4), (35, 7), (12, 28), (13, 16), (28, 10), (39, 9), (4, 20), (3, 37), (45, 1), (44, 0), (8, 31), (30, 30), (45, 29), (11, 19), (9, 23), (26, 18), (2, 18), (40, 32), (31, 1), (3, 26), (31, 18), (10, 26), (33, 19), (13, 26), (45, 0), (37, 32), (24, 34), (6, 34), (39, 15), (22, 7), (20, 34), (21, 33), (32, 12), (0, 25), (23, 18), (19, 25), (7, 30), (9, 21), (37, 4), (3, 7), (32, 17), (12, 2), (9, 41), (23, 28), (16, 34), (16, 22), (16, 27), (5, 36), (45, 4), (29, 6), (15, 16), (0, 11), (0, 16), (3, 33), (31, 4), (30, 25), (12, 24), (26, 12), (21, 42), (32, 38), (7, 9), (20, 21), (30, 40), (1, 22), (18, 39), (15, 41), (44, 4), (17, 35), (1, 37), (31, 38), (34, 34), (14, 42), (14, 6), (39, 6), (7, 17), (43, 34), (25, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 9), (40, 8), (17, 13), (1, 16), (41, 24), (39, 42), (29, 7), (15, 18), (23, 42), (19, 3), (3, 41), (15, 23), (39, 39), (12, 22), (18, 4), (2, 43), (41, 10), (37, 4), (37, 10), (16, 24), (21, 41), (12, 10), (8, 26), (6, 27), (12, 28), (5, 9), (21, 15), (6, 32), (9, 1), (19, 39), (32, 3), (20, 19), (3, 26), (38, 23), (23, 33), (17, 20), (8, 18), (37, 24), (16, 16), (10, 0), (29, 18), (27, 29), (9, 5), (15, 38), (8, 37), (10, 27), (31, 5), (1, 38), (16, 18), (4, 37), (7, 43), (26, 33), (22, 19), (2, 27), (6, 5), (13, 33), (37, 7), (9, 21), (19, 36), (40, 40), (14, 8), (18, 35), (30, 21), (2, 24), (35, 5), (4, 38), (12, 32), (35, 35), (37, 1), (19, 32), (21, 35), (35, 0), (14, 39), (20, 43), (23, 25), (23, 24), (19, 37), (6, 37), (31, 33), (18, 38), (18, 40), (38, 20), (27, 19), (29, 3), (9, 23), (31, 1), (8, 41), (9, 19), (16, 3), (2, 9), (11, 12), (13, 30), (38, 21), (17, 42), (14, 41), (41, 26), (9, 14), (35, 34), (11, 36), (11, 39), (4, 18), (29, 6), (6, 16), (13, 29), (28, 38), (30, 1), (34, 19), (35, 8), (1, 12), (11, 32), (18, 20), (21, 30), (26, 37), (30, 41), (0, 37), (12, 4), (10, 26), (0, 18), (8, 20), (19, 9), (11, 18), (34, 20), (20, 12), (34, 43), (19, 24), (16, 1), (27, 34), (20, 15), (4, 4), (33, 15), (0, 30), (27, 22), (3, 43), (31, 31), (37, 14), (9, 0), (27, 40), (36, 40), (29, 43), (27, 1), (40, 20), (5, 37), (20, 21), (5, 38), (15, 19), (28, 1), (25, 12), (36, 37), (12, 26), (18, 14), (9, 11), (25, 10), (5, 4), (21, 13), (22, 24), (41, 6), (11, 4), (41, 3), (16, 28), (23, 20), (33, 32), (37, 37), (30, 42), (28, 3), (14, 37), (4, 2), (20, 41), (13, 6), (12, 11), (34, 22), (29, 13), (0, 17), (5, 20), (13, 14), (19, 40), (37, 3), (18, 13), (37, 9), (2, 13), (39, 40), (29, 35), (24, 4), (2, 10), (26, 40), (23, 0), (5, 12), (39, 15), (26, 39), (12, 34), (8, 25), (5, 19), (40, 31), (24, 1), (3, 22), (27, 7), (4, 17), (2, 22), (10, 21)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 40x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 38), (25, 19), (2, 19), (5, 40), (39, 23), (16, 36), (30, 46), (37, 35), (6, 45), (17, 11), (1, 21), (12, 33), (13, 9), (21, 8), (38, 38), (27, 20), (11, 31), (39, 18), (36, 1), (32, 45), (22, 11), (2, 20), (32, 27), (14, 43), (20, 30), (29, 15), (20, 19), (37, 40), (27, 25), (13, 37), (26, 17), (37, 14), (12, 21), (5, 3), (25, 39), (5, 2), (5, 0), (8, 31), (29, 27), (6, 2), (30, 39), (0, 19), (11, 39), (29, 0), (39, 26), (0, 14), (18, 33), (1, 9), (1, 34), (12, 24), (37, 32), (30, 18), (32, 41), (4, 32), (39, 19), (2, 38), (28, 7), (20, 45), (18, 14), (10, 10), (19, 4), (32, 12), (1, 8), (37, 6), (25, 38), (21, 17), (0, 28), (11, 45), (8, 34), (39, 8), (29, 19), (22, 23), (8, 46), (4, 0), (4, 22), (33, 42), (21, 39), (17, 29), (30, 7), (26, 16), (35, 41), (26, 44), (12, 4), (38, 14), (31, 25), (16, 39), (35, 3), (18, 1), (5, 14), (30, 1), (20, 37), (27, 6), (20, 21), (32, 28), (10, 44), (4, 40), (7, 21), (16, 40), (26, 9), (7, 2), (21, 15), (22, 42), (12, 8), (4, 44), (19, 7), (34, 26), (16, 45), (31, 0), (20, 8), (36, 36), (4, 41), (12, 28), (30, 33), (9, 27), (7, 46), (8, 10), (9, 4), (38, 26), (10, 7), (37, 2), (37, 23), (22, 22), (17, 32), (17, 18), (33, 30), (33, 14), (18, 22), (27, 5), (36, 11), (10, 26), (32, 35), (39, 30), (25, 16), (36, 43), (39, 10), (37, 38), (0, 32), (14, 20), (8, 16), (19, 45), (31, 22), (13, 28), (0, 37), (2, 40), (7, 41), (39, 16), (11, 7), (25, 43), (34, 28), (18, 8), (33, 4), (14, 25), (33, 1), (13, 35), (35, 30), (8, 24), (6, 38), (3, 33), (11, 25), (13, 26), (35, 33), (32, 40), (18, 28), (36, 27), (39, 0), (13, 30), (37, 4), (32, 46), (23, 42), (4, 43), (9, 22), (5, 8), (18, 41), (9, 10), (31, 7), (32, 0), (32, 33), (39, 17), (18, 6), (20, 38), (29, 30), (11, 36), (5, 35), (6, 37), (0, 24), (4, 15), (39, 44), (36, 22), (11, 19), (18, 44), (20, 4), (33, 19), (34, 10), (32, 15), (24, 6), (14, 31), (5, 42), (23, 29), (38, 8), (38, 7), (9, 18), (36, 37), (3, 10), (12, 43), (16, 42), (1, 27), (19, 12), (17, 46), (32, 26), (34, 38), (27, 23), (26, 19), (7, 4), (31, 28), (30, 27), (32, 18), (22, 15), (18, 43), (21, 27), (26, 13), (35, 13), (1, 14), (22, 31), (31, 39), (9, 44), (1, 23), (36, 6), (2, 22), (25, 28), (4, 28), (14, 32), (24, 10), (32, 34), (30, 17), (37, 7), (12, 2), (16, 10), (16, 1), (25, 26), (18, 40), (4, 13), (24, 0), (6, 12), (39, 41), (17, 16), (27, 44), (3, 6), (35, 9), (32, 31), (37, 3), (27, 37), (5, 31), (29, 41), (35, 34), (15, 10), (0, 13), (28, 20), (39, 21), (35, 27), (27, 28), (31, 35), (11, 23), (6, 9), (0, 8), (25, 18), (25, 37), (6, 44), (13, 1), (20, 39), (1, 22), (0, 40), (9, 41), (25, 31), (32, 23), (11, 24), (34, 17), (21, 12), (14, 13), (1, 43), (4, 46), (15, 3), (36, 18), (38, 5), (27, 2), (6, 30), (28, 19), (36, 20), (4, 16), (23, 24), (31, 23), (37, 22), (38, 35), (31, 43), (15, 17), (17, 35), (11, 28), (29, 9), (30, 5), (31, 19), (19, 40), (3, 30), (11, 30), (36, 24), (3, 1), (26, 20), (9, 23), (33, 3), (4, 31), (7, 10), (30, 23), (11, 12), (8, 41), (37, 46), (12, 13), (2, 12), (8, 0), (35, 43), (34, 18), (34, 13), (14, 39), (15, 6), (11, 37), (2, 6), (16, 46), (32, 1), (29, 22), (3, 23), (28, 24), (6, 4), (26, 11), (16, 21), (22, 19), (15, 39), (23, 36), (1, 7), (11, 38), (15, 37), (18, 21), (35, 2), (3, 14), (22, 26), (6, 20), (26, 10), (30, 28), (27, 12), (7, 6), (27, 7), (29, 46), (10, 45), (14, 4), (5, 38), (6, 32), (38, 16), (1, 41), (1, 26), (35, 42), (30, 26), (19, 13), (18, 10), (39, 45), (28, 1), (6, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 6), (7, 10), (17, 14), (9, 42), (23, 19), (2, 12), (0, 27), (32, 1), (6, 36), (5, 8), (16, 28), (3, 42), (18, 16), (31, 47), (22, 8), (33, 39), (28, 34), (12, 12), (25, 9), (37, 3), (27, 43), (15, 22), (17, 29), (3, 6), (30, 25), (25, 1), (21, 20), (43, 3), (4, 43), (11, 14), (10, 14), (11, 9), (34, 29), (13, 35), (1, 34), (8, 1), (7, 21), (0, 22), (43, 22), (8, 29), (29, 4), (35, 27), (8, 45), (39, 31), (26, 10), (16, 26), (0, 31), (32, 33), (9, 23), (5, 24), (18, 19), (10, 15), (7, 16), (8, 18), (26, 17), (35, 34), (32, 16), (18, 11), (32, 5), (4, 17), (35, 5), (4, 21), (40, 7), (17, 8), (5, 6), (39, 30), (3, 14), (31, 29), (35, 14), (26, 34), (40, 6), (28, 20), (29, 13), (8, 27), (43, 24), (24, 2), (25, 10), (7, 24), (23, 13), (44, 23), (12, 29), (1, 24), (23, 9), (7, 2), (19, 39), (3, 33), (1, 14), (35, 42), (29, 0), (33, 30), (10, 34), (11, 42), (26, 16), (35, 17), (31, 4), (9, 19), (41, 20), (13, 17), (41, 17), (29, 17), (31, 30), (2, 21), (8, 13), (12, 36), (13, 0), (27, 47), (29, 31), (1, 41), (19, 23), (43, 47), (13, 13), (27, 9), (5, 41), (29, 3), (5, 45), (1, 9), (0, 25), (1, 23), (26, 28), (14, 4), (17, 42), (0, 7), (31, 16), (20, 31), (44, 17), (23, 27), (9, 43), (19, 0), (29, 43), (19, 15), (12, 45), (40, 29), (23, 11), (6, 38), (24, 21), (38, 33), (2, 0), (12, 19), (43, 20), (24, 45), (26, 33), (18, 42), (36, 9), (21, 15), (0, 16), (2, 28), (0, 30), (4, 42), (36, 10), (33, 22), (43, 0), (25, 3), (18, 23), (11, 16), (42, 21), (39, 9), (2, 18), (35, 44), (41, 28), (22, 9), (9, 2), (42, 3), (26, 46), (37, 11), (19, 25), (39, 1), (25, 17), (11, 30), (41, 27), (18, 1), (22, 47), (18, 35), (14, 5), (44, 42), (13, 32), (24, 36), (36, 38), (10, 2), (7, 36), (28, 39), (18, 0), (28, 37), (42, 8), (17, 25), (38, 9), (26, 29), (29, 9), (2, 30), (2, 33), (16, 37), (43, 4), (15, 11), (42, 6), (10, 38), (3, 18), (35, 38), (20, 41), (17, 33), (8, 9), (18, 39), (14, 41), (13, 7), (1, 46), (25, 12), (18, 24), (7, 30), (25, 27), (20, 36), (10, 44), (4, 13), (28, 8), (0, 23), (29, 44), (34, 10), (36, 0), (17, 21), (34, 19), (15, 42), (37, 45), (27, 42), (18, 18), (32, 8), (23, 24), (29, 40), (3, 37), (34, 31), (8, 14), (40, 1), (33, 4), (3, 22), (30, 16), (39, 46), (23, 16), (35, 21), (3, 44), (0, 15), (11, 19), (15, 23), (7, 9), (7, 19), (3, 30), (1, 11), (34, 3), (28, 47), (22, 4), (5, 36), (42, 11), (19, 40), (8, 2), (26, 0), (3, 24), (3, 1), (0, 17), (8, 44), (37, 12), (37, 47), (21, 19), (8, 7), (23, 29), (5, 21), (21, 30), (8, 26), (2, 47), (6, 22), (44, 1), (31, 33), (1, 20), (30, 41), (5, 32), (27, 8), (35, 12), (11, 23), (13, 19), (34, 11), (28, 46), (28, 45), (30, 8), (20, 18), (8, 46), (17, 18), (23, 22), (6, 21), (25, 47), (29, 7), (29, 6), (10, 22), (25, 4), (44, 4), (2, 32), (3, 27), (11, 18), (44, 31), (36, 5), (7, 27), (13, 21), (38, 41), (25, 0), (17, 26), (18, 25), (3, 47), (23, 38), (10, 17), (37, 39), (35, 18), (36, 30), (40, 19), (27, 28), (7, 38), (6, 3), (20, 37), (33, 2), (35, 26), (32, 45), (3, 7), (27, 40), (16, 38), (8, 15), (14, 25), (32, 31), (14, 47), (16, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 29), (22, 21), (15, 25), (6, 41), (25, 38), (34, 47), (33, 7), (16, 35), (14, 18), (30, 14), (5, 30), (22, 39), (34, 27), (11, 39), (16, 38), (0, 28), (23, 7), (5, 44), (23, 2), (22, 41), (31, 23), (18, 42), (30, 4), (8, 36), (24, 38), (0, 1), (26, 47), (20, 37), (0, 36), (35, 9), (34, 38), (18, 6), (6, 20), (26, 27), (1, 3), (24, 27), (20, 44), (30, 21), (27, 27), (27, 7), (2, 33), (34, 36), (14, 25), (33, 40), (32, 3), (3, 37), (25, 18), (17, 3), (9, 24), (28, 10), (39, 0), (22, 11), (23, 41), (19, 27), (33, 4), (14, 35), (15, 1), (16, 44), (3, 35), (9, 29), (8, 40), (4, 20), (10, 3), (15, 14), (32, 27), (19, 13), (4, 14), (21, 19), (30, 9), (9, 15), (14, 14), (26, 5), (16, 1), (36, 1), (11, 4), (38, 20), (5, 23), (19, 7), (2, 32), (28, 15), (11, 47), (38, 41), (39, 22), (2, 19), (39, 39), (2, 44), (36, 19), (17, 28), (28, 47), (7, 6), (6, 32), (5, 31), (21, 18), (17, 32), (27, 15), (22, 38), (1, 15), (32, 37), (27, 23), (29, 3), (32, 24), (22, 24), (3, 47), (26, 36), (24, 35), (28, 35), (34, 17), (25, 36), (35, 11), (10, 22), (38, 45), (14, 27), (18, 37), (31, 36), (25, 40), (35, 12), (39, 13), (18, 0), (30, 13), (28, 26), (15, 45), (25, 43), (30, 22), (25, 30), (21, 40), (8, 24), (23, 40), (26, 18), (18, 22), (9, 11), (24, 6), (15, 38), (31, 47), (16, 25), (16, 13), (22, 29), (7, 35), (8, 32), (11, 26), (1, 26), (36, 33), (12, 47), (23, 38), (39, 24), (24, 41), (17, 43), (2, 20), (8, 16), (26, 30), (15, 30), (12, 44), (31, 40), (18, 33), (24, 26), (5, 17), (9, 32), (27, 21), (34, 2), (32, 13), (13, 34), (14, 1), (19, 22), (20, 4), (32, 22), (34, 8), (32, 40), (26, 14), (25, 33), (25, 16), (20, 22), (3, 5), (32, 42), (31, 30), (37, 16), (17, 26), (38, 47), (23, 4), (20, 21), (0, 32), (38, 30), (22, 13), (25, 3), (0, 37), (4, 15), (25, 25), (5, 35), (36, 37), (25, 4), (36, 13), (32, 34), (39, 9), (17, 29), (18, 13), (1, 21), (27, 26), (16, 23), (32, 1), (33, 14), (3, 43), (15, 27), (4, 11), (26, 0), (30, 28), (7, 19), (6, 24), (23, 8), (11, 2), (33, 44), (6, 15), (21, 26), (22, 19), (19, 19), (11, 11), (27, 36), (35, 22), (29, 27), (2, 36), (21, 4), (3, 27), (16, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 2), (27, 43), (1, 36), (33, 2), (24, 26), (37, 38), (9, 30), (9, 34), (17, 10), (40, 1), (3, 26), (27, 0), (45, 14), (34, 9), (34, 8), (44, 2), (27, 33), (45, 3), (15, 28), (19, 8), (11, 16), (16, 12), (5, 41), (36, 35), (13, 18), (17, 12), (6, 5), (14, 25), (36, 15), (26, 28), (45, 23), (0, 14), (29, 22), (1, 5), (9, 43), (0, 44), (26, 21), (31, 31), (42, 8), (27, 4), (35, 34), (0, 34), (33, 8), (18, 11), (12, 32), (3, 29), (30, 30), (3, 13), (13, 11), (12, 12), (39, 28), (44, 37), (0, 35), (5, 10), (18, 28), (44, 22), (29, 31), (24, 33), (19, 37), (14, 15), (11, 17), (9, 39), (3, 18), (8, 36), (32, 33), (39, 43), (25, 26), (37, 12), (13, 43), (34, 27), (36, 0), (33, 21), (0, 22), (31, 25), (27, 18), (14, 29), (40, 23), (23, 30), (26, 44), (39, 30), (37, 19), (5, 14), (16, 41), (37, 15), (44, 6), (36, 27), (6, 1), (9, 5), (44, 30), (41, 5), (41, 42), (37, 8), (22, 28), (42, 0), (7, 7), (4, 20), (43, 35), (17, 28), (1, 41), (28, 9), (19, 35), (36, 41), (29, 7), (28, 19), (36, 1), (28, 12), (4, 2), (17, 19), (12, 6), (28, 37), (3, 35), (34, 34), (11, 34), (0, 40), (25, 24), (8, 39), (43, 14), (5, 9), (45, 4), (32, 1), (26, 6), (0, 41), (31, 36), (17, 18), (1, 30), (43, 22), (24, 37), (25, 17), (28, 31), (26, 33), (25, 4), (18, 10), (2, 5), (45, 38), (0, 42), (18, 27), (16, 29), (7, 36), (2, 29), (11, 9), (11, 41), (2, 8), (16, 17), (31, 13), (17, 7), (25, 31), (10, 13), (8, 8), (21, 15), (20, 7), (37, 39), (43, 0), (38, 31), (12, 31), (45, 13), (19, 30), (30, 19), (16, 20), (37, 3), (37, 10), (0, 17), (28, 43), (36, 3), (31, 23), (9, 32), (32, 2), (4, 44), (33, 14), (11, 30), (39, 32), (30, 11), (35, 13), (15, 11), (21, 38), (13, 15), (23, 15), (13, 8), (2, 3), (42, 22), (2, 34), (5, 16), (28, 40), (30, 13), (7, 5), (19, 31), (45, 31), (41, 3), (27, 38), (26, 37), (21, 31), (45, 1), (30, 15), (41, 9), (1, 0), (29, 19), (21, 29), (30, 23), (14, 44), (4, 9), (35, 1), (31, 37), (34, 38), (27, 23), (34, 28), (42, 14), (8, 5), (43, 32), (16, 4), (9, 40), (7, 30), (13, 17), (45, 16), (4, 37), (39, 0), (39, 29), (35, 20), (37, 24), (4, 16), (14, 17), (35, 0), (0, 27), (17, 17), (22, 37), (13, 32), (10, 1), (43, 43), (44, 25), (27, 42), (7, 13), (6, 25), (40, 41), (23, 14), (16, 21), (10, 5), (24, 43), (15, 43), (31, 7), (20, 6), (20, 15), (6, 17), (27, 15), (22, 38), (45, 11), (33, 32), (9, 7), (39, 27), (38, 4), (38, 34), (23, 3), (13, 14), (39, 12), (34, 1), (36, 10), (14, 19), (10, 32), (22, 44), (24, 23), (24, 2), (29, 25), (40, 38), (15, 44), (6, 23), (18, 16), (36, 30), (30, 31), (33, 6), (3, 30), (19, 38), (17, 23), (38, 28), (36, 33), (22, 19), (18, 13), (30, 10), (28, 16), (32, 39), (5, 7), (13, 42), (32, 9), (45, 27), (43, 40), (44, 29), (39, 41), (34, 12), (41, 6), (23, 34), (23, 24), (31, 27), (7, 42), (2, 38), (38, 13), (15, 1), (11, 12), (42, 15), (21, 4), (26, 25), (25, 37), (32, 37), (12, 24), (31, 40), (10, 22), (24, 27), (29, 28), (9, 33), (20, 12), (13, 19), (19, 17), (12, 42), (45, 30), (40, 27), (23, 8), (6, 42), (9, 31), (35, 9), (28, 26), (43, 16), (33, 18), (27, 2), (27, 34), (41, 22), (8, 34), (14, 21), (22, 31), (33, 1), (5, 30), (32, 25), (27, 26), (36, 32), (10, 28), (2, 32), (30, 35), (2, 9), (9, 8), (5, 1), (25, 30), (40, 34), (17, 11), (20, 34), (30, 27), (35, 43), (42, 34), (5, 26), (5, 38), (11, 27), (37, 41), (1, 34), (16, 27), (22, 41), (37, 4), (18, 32), (31, 32), (33, 31), (16, 1), (3, 16), (33, 42), (11, 40), (45, 25), (21, 17), (28, 20), (12, 30), (43, 12), (22, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (41, 36), (28, 41), (9, 44), (16, 21), (28, 3), (12, 1), (13, 34), (1, 9), (25, 16), (34, 41), (24, 31), (31, 38), (5, 14), (32, 22), (39, 23), (38, 0), (29, 11), (14, 19), (30, 0), (6, 31), (10, 32), (28, 14), (11, 9), (14, 46), (6, 26), (0, 18), (0, 41), (7, 10), (8, 9), (23, 18), (19, 45), (34, 27), (37, 15), (17, 38), (34, 33), (37, 28), (16, 32), (31, 18), (21, 17), (12, 40), (40, 12), (13, 28), (30, 29), (25, 27), (18, 22), (3, 1), (17, 45), (6, 42), (7, 33), (17, 33), (20, 26), (13, 23), (9, 9), (37, 33), (39, 3), (20, 34), (24, 8), (37, 10), (38, 8), (8, 29), (4, 2), (15, 23), (15, 43), (3, 27), (9, 40), (35, 0), (20, 37), (31, 37), (1, 45), (17, 32), (16, 45), (33, 13), (23, 34), (12, 9), (11, 15), (36, 11), (6, 40), (9, 25), (30, 18), (9, 3), (17, 39), (35, 12), (32, 34), (41, 33), (0, 39), (13, 27), (7, 31), (21, 42), (22, 44), (8, 43), (16, 44), (12, 46), (16, 5), (11, 42), (26, 41), (27, 34), (19, 32), (15, 35), (16, 40), (29, 10), (30, 39), (35, 9), (8, 4), (16, 33), (9, 27), (3, 12), (20, 7), (39, 16), (10, 14), (11, 43), (37, 23), (5, 32), (16, 1), (4, 38), (25, 26), (18, 17), (26, 12), (36, 41), (40, 21), (34, 34), (11, 40), (19, 38), (26, 16), (23, 23), (11, 36), (12, 2), (16, 4), (21, 39), (11, 3), (24, 5), (5, 4), (21, 20), (26, 22), (19, 40), (38, 16), (0, 3), (37, 17), (24, 25), (27, 0), (11, 31), (32, 6), (33, 4), (7, 17), (38, 1), (27, 20), (19, 22), (6, 27), (21, 24), (25, 45), (23, 20), (1, 10), (17, 26), (31, 2), (14, 12), (25, 9), (26, 2), (37, 44), (4, 30), (17, 9), (26, 29), (35, 15), (5, 11), (6, 33), (8, 24), (6, 37), (7, 32), (1, 41), (23, 14), (15, 16), (17, 21), (38, 36), (5, 38), (2, 30), (18, 2), (3, 15), (15, 0), (23, 38), (27, 19), (17, 12), (41, 41), (40, 18), (26, 15), (30, 27), (38, 45), (29, 16), (18, 19), (27, 16), (24, 27), (15, 26), (6, 17), (36, 45), (30, 21), (1, 44), (35, 32), (40, 20), (22, 24), (26, 24), (12, 14), (21, 38), (9, 31), (13, 33), (30, 11), (18, 30), (13, 39), (21, 36), (10, 29), (7, 26), (14, 1), (5, 28), (31, 42), (33, 37), (33, 42), (30, 30), (2, 29), (26, 46), (13, 20), (18, 45), (30, 25), (35, 19), (23, 42), (1, 36), (7, 3), (37, 25), (36, 15), (23, 28), (41, 42), (22, 40), (23, 24), (38, 17), (31, 10), (32, 3), (37, 16), (15, 11), (3, 24), (6, 45), (2, 8), (24, 1), (1, 22), (8, 38), (7, 7), (25, 13), (29, 28), (3, 45), (37, 1), (40, 14), (8, 34), (41, 13), (39, 29), (14, 45), (35, 20), (39, 35), (16, 29), (6, 3), (41, 23), (16, 19), (22, 18), (3, 36), (15, 45), (33, 39), (36, 32), (35, 4), (17, 34), (6, 10), (6, 21), (37, 32), (1, 42), (39, 14), (16, 22), (10, 5), (17, 17), (33, 38), (14, 10), (36, 26), (1, 24), (26, 33), (21, 3), (28, 1), (22, 42), (33, 1), (18, 1), (9, 2), (29, 29), (6, 7), (0, 20), (25, 1), (2, 3), (8, 41), (24, 34), (23, 41), (1, 6), (32, 10), (24, 28), (13, 17), (12, 29), (31, 27), (3, 19), (32, 5), (11, 23), (21, 29), (9, 38), (20, 44), (28, 26), (6, 32), (2, 18), (1, 4), (6, 16), (11, 30), (39, 15), (37, 21), (17, 29), (3, 3), (7, 12), (8, 35), (6, 24), (14, 2), (24, 38), (37, 12), (11, 29), (23, 43), (35, 25), (30, 1), (25, 12), (38, 3), (25, 28), (5, 37), (5, 16), (31, 45), (41, 3), (41, 4), (35, 2), (4, 20), (28, 38), (28, 36), (21, 8), (28, 7), (28, 0), (21, 1), (32, 25), (19, 27), (9, 7), (37, 39), (21, 33), (36, 36), (25, 18), (22, 16), (27, 11), (9, 28), (12, 7), (10, 18), (34, 0), (31, 16), (15, 19), (0, 16), (17, 11), (12, 25), (2, 21), (3, 39), (10, 44), (38, 33), (22, 37), (34, 10), (6, 12), (34, 14), (23, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 2), (31, 13), (43, 25), (44, 4), (0, 22), (44, 41), (23, 26), (0, 10), (38, 21), (33, 13), (44, 18), (17, 1), (20, 41), (20, 1), (22, 2), (15, 4), (27, 43), (44, 3), (12, 0), (16, 33), (4, 33), (5, 11), (2, 8), (23, 22), (8, 31), (1, 18), (33, 35), (39, 2), (14, 32), (18, 43), (31, 0), (23, 4), (7, 32), (35, 4), (27, 33), (39, 19), (0, 34), (32, 23), (13, 41), (8, 24), (17, 42), (21, 8), (31, 38), (23, 11), (45, 13), (25, 26), (44, 32), (33, 34), (3, 30), (20, 31), (6, 26), (42, 24), (16, 27), (24, 4), (19, 5), (11, 2), (1, 3), (38, 5), (39, 40), (4, 37), (2, 16), (34, 33), (12, 5), (30, 17), (39, 8), (18, 39), (2, 1), (42, 6), (11, 25), (12, 39), (36, 13), (12, 41), (22, 19), (1, 11), (4, 19), (22, 40), (15, 20), (42, 37), (35, 42), (13, 15), (20, 18), (6, 19), (12, 4), (18, 33), (9, 40), (16, 36), (3, 28), (31, 30), (15, 40), (27, 37), (5, 4), (19, 2), (42, 20), (26, 41), (43, 16), (6, 8), (39, 22), (18, 18), (27, 9), (20, 12), (21, 32), (16, 30), (6, 16), (15, 23), (1, 34), (26, 33), (38, 36), (4, 43), (23, 12), (2, 41), (34, 0), (29, 29), (15, 1), (13, 40), (9, 34), (2, 9), (42, 28), (0, 8), (32, 31), (46, 30), (7, 5), (35, 1), (7, 34), (33, 24), (38, 6), (38, 40), (22, 37), (13, 31), (31, 42), (41, 38), (35, 16), (12, 37), (27, 35), (34, 1), (0, 24), (6, 23), (22, 31), (9, 29), (15, 26), (46, 42), (8, 0), (46, 34), (38, 31), (7, 43), (28, 43), (9, 27), (31, 23), (37, 23), (2, 35), (9, 0), (42, 33), (21, 40), (42, 0), (40, 0), (9, 1), (0, 23), (33, 21), (7, 15), (44, 38), (30, 30), (38, 28), (2, 19), (1, 30), (17, 2), (17, 21), (46, 22), (38, 41), (11, 13), (40, 39), (30, 6), (8, 22), (35, 0), (6, 10), (45, 17), (6, 29), (19, 34), (0, 20), (40, 15), (15, 36), (4, 11), (25, 42), (40, 5), (24, 19), (26, 23), (25, 5), (4, 21), (1, 35), (22, 0), (28, 24), (37, 36), (38, 33), (0, 43), (31, 9), (37, 13), (22, 9), (17, 37), (38, 14), (4, 18), (10, 7), (27, 17), (21, 36), (21, 0), (7, 4), (27, 42), (9, 25), (38, 22), (13, 34), (1, 0), (10, 15), (9, 42), (16, 24), (33, 10), (41, 41), (13, 32), (31, 39), (36, 29), (23, 8), (42, 2), (4, 1), (42, 30), (6, 32), (36, 38), (34, 42), (46, 2), (27, 1), (11, 19), (35, 19), (36, 26), (42, 35), (36, 18), (3, 34), (16, 34), (22, 17), (19, 6), (3, 13), (22, 18), (17, 31), (1, 10), (43, 5), (29, 22), (20, 8), (26, 12), (13, 23), (38, 42), (33, 30), (4, 4), (16, 25), (14, 10), (13, 17), (39, 36), (19, 12), (8, 35), (14, 21), (21, 26), (38, 39), (3, 17), (6, 14), (27, 26), (31, 4), (10, 33), (35, 39), (36, 30), (10, 19), (3, 27), (34, 12), (41, 20), (5, 27), (18, 42), (9, 43), (43, 18), (45, 29), (43, 8), (46, 33), (44, 23), (21, 7), (33, 37), (20, 38), (9, 20), (32, 14), (12, 36), (16, 28), (1, 9), (22, 35), (31, 18), (4, 7), (19, 22), (5, 7), (34, 23), (37, 19), (39, 26), (10, 42), (1, 38), (9, 15), (8, 20), (15, 15), (1, 37), (4, 14), (32, 9), (7, 36), (46, 37), (41, 37), (12, 28), (24, 30), (41, 33), (21, 6), (16, 31), (14, 25), (19, 11), (20, 28), (32, 37), (29, 24), (3, 33), (4, 41), (38, 3), (33, 25), (26, 35), (20, 43), (39, 34), (27, 38), (38, 43), (7, 3), (22, 42), (46, 13), (6, 35), (25, 11), (42, 34), (28, 17), (26, 20), (16, 37), (38, 23), (25, 43), (17, 26), (18, 26), (37, 42), (27, 13), (23, 34), (13, 20), (30, 19), (0, 32), (32, 40), (42, 25), (6, 28), (1, 42), (0, 31), (40, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 3), (17, 17), (36, 9), (46, 34), (4, 1), (47, 17), (37, 33), (40, 2), (10, 26), (32, 17), (26, 14), (44, 30), (16, 36), (43, 23), (10, 27), (4, 40), (28, 33), (22, 35), (10, 14), (11, 37), (44, 7), (13, 2), (34, 17), (42, 26), (47, 10), (47, 16), (17, 2), (25, 25), (23, 32), (46, 36), (40, 36), (20, 13), (45, 15), (4, 24), (20, 33), (17, 10), (24, 29), (34, 25), (21, 21), (29, 1), (35, 13), (9, 41), (16, 37), (20, 6), (21, 15), (39, 33), (39, 12), (41, 30), (7, 23), (15, 13), (10, 4), (47, 2), (13, 9), (3, 5), (42, 14), (10, 29), (10, 39), (4, 41), (30, 12), (5, 26), (8, 11), (0, 41), (7, 30), (41, 19), (43, 8), (2, 29), (40, 3), (9, 25), (6, 4), (35, 12), (29, 11), (39, 37), (11, 40), (29, 19), (18, 32), (37, 17), (22, 32), (39, 26), (21, 32), (8, 4), (1, 39), (19, 17), (23, 36), (13, 10), (7, 14), (3, 23), (40, 16), (17, 37), (1, 12), (26, 17), (19, 10), (7, 21), (11, 17), (26, 40), (6, 26), (29, 2), (1, 24), (32, 37), (12, 35), (36, 38), (37, 18), (26, 2), (9, 5), (1, 38), (22, 40), (31, 38), (8, 18), (35, 26), (1, 11), (20, 10), (23, 12), (12, 7), (13, 4), (5, 4), (10, 3), (29, 17), (24, 6), (40, 25), (42, 4), (0, 33), (31, 0), (28, 16), (24, 5), (20, 12), (10, 16), (43, 16), (26, 1), (15, 21), (3, 8), (47, 28), (7, 39), (5, 2), (9, 8), (16, 13), (43, 19), (37, 1), (0, 9), (33, 9), (30, 11), (19, 40), (39, 11), (25, 4), (22, 28), (26, 13), (5, 27), (14, 40), (15, 17), (18, 22), (9, 0), (39, 18), (11, 18), (31, 18), (8, 21), (4, 36), (6, 17), (27, 14), (30, 22), (0, 19), (29, 29), (9, 23), (44, 20), (31, 7), (34, 34), (12, 18), (17, 8), (12, 16), (37, 32), (20, 28), (27, 31), (26, 3), (45, 17), (3, 7), (23, 18), (29, 0), (38, 12), (17, 4), (6, 13), (25, 39), (8, 38), (6, 18), (21, 29), (32, 16), (29, 18), (9, 16), (25, 12), (8, 15), (7, 2), (41, 21), (38, 0), (18, 3), (30, 28), (36, 3), (15, 24), (29, 7), (19, 0), (18, 40), (24, 12), (37, 6), (30, 24), (38, 26), (22, 13), (24, 8), (23, 13), (9, 24), (22, 15), (21, 14), (2, 2), (3, 4), (45, 34), (3, 25), (4, 27), (37, 8), (4, 7), (34, 16), (20, 7), (42, 2), (32, 24), (12, 37), (12, 27), (5, 23), (38, 27), (32, 33), (25, 18), (40, 38), (29, 6), (9, 29), (26, 21), (43, 20), (27, 36), (42, 25), (24, 9), (34, 18), (18, 35), (10, 18), (20, 16), (4, 6), (26, 29), (5, 9), (43, 34), (30, 39), (28, 6), (31, 39), (29, 15), (25, 36), (14, 32), (14, 6), (32, 6), (6, 28), (11, 14), (31, 15), (11, 32), (24, 30), (16, 22), (17, 30), (24, 31), (3, 24), (40, 29), (39, 17), (29, 4), (8, 1), (40, 12), (41, 27), (37, 28), (38, 31), (8, 10), (38, 30), (42, 36), (4, 4), (9, 28), (40, 31), (44, 36), (4, 32), (27, 24), (15, 30), (15, 41), (2, 34), (31, 9), (32, 34), (14, 13), (22, 2), (34, 8), (23, 1), (35, 33), (28, 32), (43, 29), (28, 8), (37, 20), (45, 20), (9, 4), (22, 31), (46, 19), (33, 15), (1, 32), (9, 20), (3, 15), (14, 29), (46, 38), (1, 5), (7, 4), (12, 22), (30, 40), (33, 39), (8, 22), (3, 29), (38, 23), (19, 13), (12, 33), (24, 16), (33, 27), (2, 11), (39, 2), (34, 4), (5, 40), (39, 22), (15, 16), (17, 34), (3, 16), (33, 26), (5, 24), (7, 1), (41, 5), (21, 11), (30, 14), (11, 6), (10, 28), (7, 18), (45, 23), (47, 15), (8, 37), (33, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (21, 20), (8, 9), (23, 2), (21, 37), (12, 19), (42, 28), (15, 44), (42, 35), (12, 12), (20, 11), (20, 13), (5, 3), (19, 37), (30, 3), (31, 33), (10, 38), (17, 26), (6, 16), (23, 7), (24, 21), (29, 45), (13, 32), (41, 17), (16, 35), (25, 3), (23, 20), (5, 7), (11, 17), (13, 9), (14, 0), (6, 21), (25, 40), (1, 45), (17, 8), (24, 41), (11, 28), (32, 5), (25, 22), (6, 9), (39, 22), (22, 14), (31, 41), (32, 12), (17, 30), (2, 16), (17, 18), (11, 40), (13, 25), (17, 10), (34, 15), (16, 4), (16, 47), (7, 46), (34, 16), (34, 8), (44, 13), (8, 37), (36, 23), (6, 7), (8, 19), (17, 9), (24, 20), (18, 12), (27, 39), (14, 16), (24, 13), (30, 42), (32, 44), (38, 43), (8, 20), (43, 35), (27, 14), (24, 3), (24, 39), (42, 11), (5, 42), (32, 23), (3, 23), (34, 33), (30, 40), (29, 20), (8, 10), (17, 19), (28, 10), (1, 44), (19, 1), (4, 13), (19, 35), (16, 36), (38, 7), (23, 19), (4, 41), (1, 3), (12, 15), (9, 28), (31, 6), (2, 15), (9, 1), (10, 2), (29, 22), (38, 44), (21, 5), (11, 7), (17, 44), (20, 47), (32, 15), (16, 29), (27, 6), (2, 9), (38, 47), (16, 34), (28, 6), (5, 4), (1, 0), (41, 24), (22, 21), (41, 4), (37, 22), (7, 6), (12, 18), (20, 34), (28, 20), (10, 27), (15, 30), (18, 43), (37, 15), (33, 14), (15, 41), (41, 0), (5, 20), (5, 22), (7, 9), (4, 11), (17, 40), (38, 33), (29, 18), (31, 27), (37, 13), (37, 39), (40, 3), (40, 8), (30, 30), (24, 27), (26, 15), (42, 4), (30, 46), (5, 47), (22, 20), (44, 21), (30, 2), (14, 4), (8, 26), (4, 44), (5, 6), (9, 16), (5, 0), (8, 31), (34, 31), (28, 37), (0, 29), (27, 8), (29, 24), (4, 37), (7, 29), (18, 32), (27, 37), (14, 45), (21, 44), (2, 37), (32, 42), (0, 24), (37, 10), (30, 45), (9, 36), (20, 38), (30, 34), (4, 2), (38, 16), (18, 19), (44, 41), (40, 34), (19, 42), (11, 12), (21, 35), (25, 14), (5, 40), (0, 30), (4, 20), (0, 4), (42, 30), (29, 43), (2, 33), (20, 40), (12, 13), (43, 29), (14, 29), (4, 24), (26, 34), (43, 18), (29, 32), (12, 29), (15, 31), (10, 39), (31, 16), (6, 28), (21, 17), (5, 31), (26, 38), (15, 16), (14, 25), (6, 5), (14, 11), (35, 46), (36, 26), (34, 35), (16, 38), (36, 14), (0, 31), (3, 29), (26, 30), (15, 1), (17, 27), (2, 12), (2, 25), (3, 11), (31, 8), (1, 46), (17, 22), (37, 19), (34, 1), (37, 32), (12, 27), (25, 31), (5, 32), (41, 35), (34, 19), (42, 5), (6, 26), (33, 4), (16, 8), (0, 14), (18, 24), (23, 45), (25, 39), (14, 9), (31, 32), (39, 31), (22, 40), (31, 35), (10, 44), (8, 13), (31, 19), (32, 4), (13, 36), (1, 5), (4, 6), (13, 8), (15, 40), (14, 20), (14, 40), (31, 25), (19, 17)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 2), (8, 8), (35, 0), (30, 25), (19, 47), (6, 29), (19, 48), (16, 40), (33, 0), (18, 29), (29, 31), (4, 6), (3, 15), (33, 18), (0, 25), (10, 10), (19, 35), (26, 34), (19, 16), (0, 5), (39, 31), (11, 32), (27, 25), (6, 6), (1, 40), (6, 10), (28, 31), (37, 17), (8, 10), (15, 2), (22, 16), (35, 28), (2, 1), (38, 48), (20, 45), (5, 6), (17, 18), (39, 32), (16, 0), (35, 44), (23, 45), (22, 30), (24, 29), (6, 25), (20, 27), (40, 33), (31, 32), (1, 24), (18, 4), (29, 34), (20, 1), (29, 5), (8, 32), (8, 33), (12, 22), (29, 43), (23, 5), (20, 2), (22, 22), (19, 33), (9, 42), (26, 5), (33, 11), (20, 34), (38, 23), (30, 46), (37, 38), (18, 39), (2, 8), (19, 13), (24, 40), (4, 13), (7, 43), (39, 2), (20, 43), (3, 44), (41, 38), (35, 42), (35, 15), (18, 38), (11, 2), (5, 9), (28, 18), (15, 19), (10, 28), (13, 12), (15, 28), (4, 25), (21, 35), (30, 41), (15, 27), (7, 23), (1, 0), (13, 18), (35, 38), (6, 11), (20, 18), (37, 28), (25, 2), (10, 1), (20, 48), (23, 25), (5, 46), (33, 16), (7, 37), (31, 3), (21, 24), (39, 37), (8, 4), (5, 13), (39, 3), (18, 5), (30, 3), (24, 28), (22, 9), (30, 10), (35, 27), (38, 25), (6, 30), (23, 10), (10, 46), (6, 46), (24, 38), (23, 44), (12, 9), (28, 16), (19, 8), (11, 14), (15, 45), (23, 47), (15, 15), (7, 22), (26, 35), (21, 16), (25, 17), (6, 19), (9, 6), (19, 2), (20, 40), (32, 41), (28, 24), (6, 12), (2, 0), (1, 6), (13, 5), (10, 18), (13, 11), (7, 17), (37, 46), (40, 41), (29, 21), (28, 38), (27, 12), (16, 42), (30, 5), (19, 14), (17, 4), (12, 41), (28, 5), (5, 8), (30, 14), (26, 19), (41, 10), (36, 12), (31, 7), (22, 3), (37, 1), (41, 46), (39, 29), (38, 19), (18, 42), (19, 30), (28, 12), (3, 12), (1, 44), (2, 36), (22, 29), (35, 14), (27, 6), (30, 32), (40, 31), (6, 41), (39, 11), (4, 0), (19, 3), (36, 17), (11, 27), (41, 14), (36, 43), (8, 12), (8, 21), (34, 21), (19, 34), (34, 1), (2, 22), (21, 23), (19, 21), (14, 29), (30, 27), (23, 13), (19, 15), (15, 36), (0, 35), (18, 48), (22, 42), (19, 18), (40, 22), (9, 0), (23, 23), (2, 33), (5, 10), (29, 8), (6, 22), (33, 14), (33, 33), (12, 32), (6, 21), (13, 33), (1, 20), (26, 38), (5, 19), (31, 47), (2, 45), (4, 7), (9, 21), (25, 34), (30, 36), (37, 34), (37, 31), (11, 6), (26, 29), (38, 9), (38, 44), (29, 38), (20, 29), (9, 48), (11, 39), (40, 47), (0, 21), (22, 8), (23, 9), (28, 15), (26, 2), (6, 43), (41, 19), (19, 4), (34, 15), (38, 46), (40, 42), (7, 3), (13, 37), (21, 6), (16, 3), (26, 36), (20, 33), (24, 47), (6, 3), (11, 10), (9, 9), (31, 22), (10, 24), (25, 6), (30, 1), (22, 2), (26, 28), (32, 6), (15, 41), (24, 14), (24, 27), (41, 21), (7, 1), (26, 24), (28, 11), (4, 37), (37, 10), (27, 23), (30, 38), (39, 13), (18, 6), (8, 22), (12, 8), (4, 3), (22, 46), (5, 30), (8, 38), (33, 19), (40, 7), (18, 11), (3, 0), (36, 29), (10, 40), (21, 28), (5, 42), (3, 14), (9, 15), (18, 23), (6, 26), (26, 48), (24, 18), (7, 0), (29, 39), (24, 34), (2, 47), (23, 46), (9, 14), (15, 29), (41, 6), (15, 11), (41, 9), (14, 46), (41, 44), (16, 25), (38, 47), (28, 28), (41, 29), (36, 37), (25, 22), (37, 0), (24, 4), (38, 28), (33, 40), (30, 19), (7, 21), (3, 38), (36, 11), (35, 48), (20, 24), (40, 8), (32, 42), (5, 21), (19, 20), (3, 22), (40, 9), (12, 27), (23, 6), (18, 26), (38, 10), (39, 33), (7, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 5), (19, 0), (18, 15), (20, 2), (11, 42), (0, 12), (23, 21), (31, 21), (23, 44), (36, 40), (38, 30), (3, 48), (7, 10), (31, 6), (25, 16), (39, 1), (40, 13), (5, 29), (45, 43), (23, 40), (41, 30), (46, 23), (32, 19), (39, 15), (40, 15), (32, 7), (43, 21), (30, 21), (22, 42), (32, 25), (15, 12), (36, 25), (6, 18), (16, 22), (13, 41), (19, 45), (28, 38), (9, 46), (2, 27), (7, 15), (38, 22), (8, 32), (25, 10), (18, 29), (20, 35), (33, 6), (11, 39), (7, 4), (44, 48), (14, 21), (46, 47), (22, 11), (26, 16), (9, 41), (7, 27), (40, 30), (41, 18), (5, 11), (40, 12), (22, 23), (5, 3), (15, 31), (40, 34), (13, 6), (29, 17), (6, 35), (19, 21), (30, 40), (29, 1), (46, 13), (30, 4), (10, 26), (34, 45), (25, 38), (2, 36), (29, 20), (12, 25), (6, 34), (42, 17), (23, 45), (34, 28), (40, 44), (27, 20), (14, 23), (19, 43), (10, 13), (16, 20), (8, 33), (17, 28), (8, 27), (32, 5), (13, 16), (36, 42), (29, 10), (46, 2), (21, 39), (47, 17), (24, 20), (10, 16), (42, 23), (32, 13), (26, 41), (35, 26), (21, 20), (48, 22), (39, 30), (39, 27), (23, 41), (6, 19), (36, 5), (41, 44), (9, 24), (38, 0), (5, 38), (22, 45), (29, 2), (45, 16), (21, 4), (32, 11), (42, 25), (21, 30), (42, 20), (26, 25), (18, 11), (4, 14), (3, 18), (29, 12), (48, 41), (19, 23), (28, 39), (26, 6), (34, 6), (46, 41), (28, 0), (34, 48), (43, 32), (35, 3), (29, 7), (30, 37), (34, 2), (10, 31), (20, 17), (45, 13), (32, 8), (6, 37), (17, 45), (26, 38), (36, 36), (39, 18), (4, 37), (11, 48), (0, 2), (39, 7), (13, 0), (29, 36), (1, 21), (0, 5), (4, 46), (10, 3), (40, 40), (8, 48), (10, 2), (19, 20), (13, 18), (14, 10), (12, 9), (4, 17), (48, 3), (43, 17), (1, 5), (35, 40), (1, 8), (47, 12), (24, 3), (22, 0), (37, 27), (2, 47), (26, 19), (26, 12), (42, 5), (6, 28), (14, 33), (19, 37), (2, 40), (19, 3), (18, 45), (24, 17), (37, 24), (10, 24), (45, 28), (12, 36), (20, 27), (36, 31), (3, 26), (11, 8), (13, 26), (16, 12), (13, 45), (14, 13), (15, 7), (31, 22), (5, 2), (44, 4), (47, 26), (23, 39), (17, 27), (0, 47), (15, 15), (42, 10), (10, 12), (46, 19), (45, 7), (3, 39), (12, 12), (14, 15), (44, 38), (32, 0), (6, 13), (28, 16), (31, 16), (31, 11), (7, 44), (17, 41), (14, 42), (44, 9), (2, 4), (45, 23), (31, 1), (14, 43), (34, 33), (46, 16), (5, 23), (26, 30), (1, 22), (43, 47), (4, 12), (48, 2), (40, 19), (43, 5), (1, 15), (23, 22), (48, 19), (15, 1), (47, 39), (42, 7), (44, 33), (23, 11), (12, 4), (46, 15), (34, 24), (41, 10), (18, 3), (45, 29), (44, 36), (28, 2), (22, 15), (7, 28), (27, 26), (34, 19), (6, 43), (21, 41), (35, 16), (35, 15), (27, 48), (31, 3), (37, 35), (2, 17), (24, 8), (8, 14), (40, 25), (29, 30), (25, 7), (38, 47), (10, 40), (11, 38), (28, 34), (43, 38), (26, 31), (18, 23), (46, 28), (34, 23), (0, 42), (29, 33), (37, 13), (16, 32), (0, 1), (25, 27), (5, 15), (0, 46), (20, 22), (35, 29), (25, 44), (41, 35), (36, 18), (16, 42), (28, 4), (22, 19), (33, 43), (36, 34), (37, 42), (44, 31), (7, 34), (9, 38), (35, 36), (29, 42), (34, 30), (43, 43), (28, 48), (40, 23), (14, 32), (36, 47), (20, 3), (0, 26), (13, 4), (25, 15), (4, 2), (26, 18), (35, 30), (48, 21), (5, 1), (47, 43), (7, 33), (20, 13), (9, 1), (36, 4), (34, 25), (37, 15), (12, 37), (22, 1), (29, 23), (10, 30), (9, 32), (5, 6), (40, 9), (11, 43), (10, 8), (47, 47), (48, 26), (12, 39), (7, 38), (30, 22), (21, 19), (22, 28), (31, 25), (47, 28), (24, 19), (28, 33), (47, 31), (0, 18), (26, 17), (36, 32), (3, 34), (5, 10), (26, 32), (42, 14), (33, 23), (4, 41), (8, 46), (10, 27), (39, 8), (39, 6), (37, 23), (9, 22), (14, 30), (13, 3), (30, 13), (7, 45), (22, 20), (16, 14), (13, 43), (35, 14), (18, 21), (22, 35), (6, 3), (37, 16), (18, 28), (30, 30), (12, 13), (23, 24), (16, 16), (17, 10), (17, 42), (23, 43), (45, 9), (9, 4), (25, 43), (48, 28), (12, 14), (29, 4), (23, 29), (21, 38), (0, 11), (11, 9), (3, 31), (14, 19), (4, 22), (32, 42), (8, 13), (4, 42), (0, 3), (10, 15), (8, 24), (14, 4), (3, 47), (27, 45), (28, 9), (2, 16), (13, 12), (13, 15), (32, 6), (0, 15), (31, 26), (48, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (14, 17), (40, 28), (7, 44), (12, 15), (24, 45), (35, 30), (4, 6), (4, 11), (41, 38), (40, 24), (28, 14), (28, 35), (9, 23), (5, 5), (21, 42), (28, 2), (42, 2), (18, 10), (3, 34), (38, 21), (0, 38), (5, 21), (30, 11), (36, 8), (6, 43), (2, 40), (10, 15), (21, 20), (37, 40), (16, 28), (32, 22), (31, 32), (24, 47), (40, 33), (26, 32), (38, 3), (37, 17), (21, 11), (7, 28), (7, 24), (0, 3), (14, 41), (37, 12), (38, 24), (20, 31), (12, 32), (17, 43), (31, 7), (3, 45), (2, 44), (42, 20), (32, 37), (24, 8), (38, 14), (41, 19), (7, 10), (35, 16), (32, 14), (5, 0), (23, 13), (14, 35), (9, 0), (2, 35), (26, 13), (20, 34), (25, 40), (8, 38), (27, 42), (31, 43), (30, 8), (21, 16), (31, 18), (21, 19), (5, 31), (7, 42), (42, 43), (10, 42), (11, 30), (44, 40), (0, 36), (41, 44), (23, 24), (43, 7), (5, 24), (11, 40), (9, 17), (33, 24), (19, 8), (8, 20), (5, 38), (29, 40), (6, 31), (26, 17), (34, 32), (24, 17), (9, 3), (8, 24), (27, 8), (35, 18), (2, 37), (4, 20), (37, 14), (1, 11), (10, 40), (37, 3), (29, 0), (13, 14), (7, 5), (27, 22), (2, 0), (11, 42), (28, 34), (25, 4), (20, 5), (41, 45), (1, 17), (40, 23), (6, 47), (40, 40), (25, 14), (12, 19), (6, 4), (21, 27), (24, 44), (4, 35), (31, 24), (44, 19), (12, 6), (17, 5), (34, 45), (9, 45), (26, 4), (15, 15), (19, 26), (37, 0), (26, 43), (5, 14), (0, 35), (3, 17), (33, 26), (3, 31), (1, 22), (29, 23), (4, 17), (36, 28), (38, 39), (27, 25), (16, 18), (26, 47), (12, 41), (26, 8), (10, 13), (12, 27), (18, 18), (30, 29), (38, 12), (22, 22), (30, 36), (17, 9), (1, 3), (24, 31), (1, 43), (9, 7), (20, 20), (0, 25), (8, 45), (13, 10), (14, 29), (44, 39), (34, 43), (36, 25), (11, 23), (8, 27), (0, 42), (25, 29), (5, 45), (41, 11), (14, 22), (1, 42), (39, 18), (16, 20), (35, 24), (41, 33), (13, 20), (5, 39), (18, 25), (7, 23), (38, 25), (7, 38), (0, 27), (16, 40), (17, 24), (27, 16), (42, 1), (5, 7), (6, 24), (33, 35), (19, 41), (0, 7), (14, 37), (19, 17), (3, 14), (21, 35), (27, 7), (33, 40), (1, 15), (24, 32), (40, 7), (37, 27), (9, 2), (5, 46), (22, 39), (18, 3), (13, 36), (40, 22), (33, 7), (19, 25), (44, 33), (17, 28), (21, 8), (35, 7), (1, 12), (33, 20), (3, 19), (7, 30), (31, 37), (24, 46), (40, 27), (4, 1), (29, 8), (36, 5), (16, 23), (25, 7), (14, 46), (39, 37), (27, 31), (12, 45), (15, 29), (17, 19), (24, 33), (8, 1), (34, 36), (15, 24), (38, 2), (21, 47), (41, 8), (19, 4), (18, 22), (44, 36), (29, 31), (38, 8), (42, 6), (9, 36), (15, 20), (18, 17), (3, 6), (28, 32), (29, 2), (23, 21), (29, 12), (15, 30), (42, 17), (30, 37), (33, 13), (14, 38), (30, 12), (30, 16), (25, 5), (3, 38), (27, 4), (27, 41), (12, 1), (32, 8), (4, 26), (41, 23), (34, 18), (17, 0), (37, 44), (44, 42), (14, 0), (13, 5), (34, 33), (15, 17), (27, 3), (21, 15), (17, 27), (23, 37), (17, 16), (25, 23), (33, 30), (23, 9), (36, 40), (41, 36), (19, 34), (11, 22), (2, 23), (0, 23), (34, 3), (39, 42), (21, 23), (18, 32), (22, 40), (41, 26), (17, 23), (4, 44), (9, 34), (18, 31), (6, 26), (36, 7), (10, 44), (2, 41), (37, 7), (19, 47), (40, 44), (22, 9), (33, 21), (18, 43), (38, 7), (17, 32), (7, 4), (35, 28), (3, 47), (29, 17), (2, 22), (9, 18), (39, 24), (5, 33), (8, 34), (39, 25), (24, 13), (27, 13), (38, 16), (25, 39), (3, 25), (1, 37), (22, 8), (31, 8), (26, 44), (35, 33), (8, 41), (34, 41), (0, 10), (42, 47), (2, 32), (42, 45), (10, 39), (42, 9), (43, 47), (4, 9), (19, 5), (38, 0), (29, 36), (26, 31), (37, 34), (37, 13), (28, 21), (18, 41), (35, 46), (9, 11), (7, 37), (10, 33), (36, 23), (37, 26), (0, 46), (29, 26), (41, 9), (6, 21), (22, 6), (17, 7), (39, 27), (24, 39), (13, 8), (36, 34), (13, 31), (27, 27), (42, 39), (11, 47), (20, 22), (10, 11), (43, 24), (28, 11), (44, 31), (21, 46), (19, 39), (2, 28), (41, 32), (29, 46), (36, 22), (16, 43), (32, 35), (25, 9), (6, 38), (20, 39), (14, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 47x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 4), (31, 22), (12, 14), (24, 35), (30, 26), (2, 16), (44, 12), (11, 25), (25, 30), (8, 34), (22, 4), (28, 17), (17, 33), (23, 18), (18, 13), (1, 12), (16, 3), (7, 32), (12, 22), (20, 37), (26, 32), (26, 29), (27, 7), (33, 16), (3, 15), (22, 39), (42, 34), (36, 17), (46, 33), (13, 27), (16, 30), (9, 5), (0, 3), (45, 26), (13, 17), (16, 2), (10, 19), (4, 18), (28, 35), (24, 15), (5, 19), (31, 28), (39, 29), (21, 36), (4, 19), (38, 4), (7, 37), (34, 14), (39, 26), (18, 17), (18, 34), (14, 34), (1, 28), (36, 39), (38, 11), (21, 10), (21, 4), (28, 1), (22, 38), (5, 27), (31, 13), (33, 3), (37, 0), (10, 24), (28, 8), (38, 14), (46, 29), (35, 31), (14, 7), (32, 14), (38, 33), (5, 8), (1, 5), (37, 7), (45, 30), (25, 24), (29, 25), (16, 9), (27, 2), (0, 19), (44, 35), (24, 4), (34, 23), (30, 32), (29, 31), (24, 14), (43, 23), (23, 23), (39, 21), (5, 4), (6, 22), (6, 10), (19, 22), (42, 8), (36, 5), (15, 13), (22, 16), (29, 12), (17, 13), (7, 4), (41, 11), (34, 12), (41, 32), (37, 22), (3, 11), (42, 35), (17, 14), (36, 0), (37, 25), (32, 15), (22, 18), (13, 37), (36, 38), (18, 24), (45, 33), (11, 20), (24, 34), (39, 38), (33, 17), (11, 11), (28, 3), (29, 3), (45, 27), (18, 26), (33, 39), (8, 0), (26, 27), (30, 9), (29, 11), (35, 3), (44, 3), (17, 34), (8, 39), (35, 5), (44, 28), (35, 2), (3, 36), (45, 4), (6, 23), (31, 2), (21, 8), (13, 35), (26, 36), (45, 17), (0, 2), (26, 7), (36, 19), (17, 9), (7, 22), (30, 14), (7, 24), (25, 4), (15, 33), (13, 29), (27, 0), (13, 6), (19, 15), (2, 1), (44, 20), (28, 22), (7, 15), (41, 20), (2, 20), (5, 20), (2, 23), (39, 11), (34, 32), (30, 16), (2, 8), (12, 39), (43, 12), (1, 39), (8, 8), (29, 29), (15, 39), (2, 10), (25, 21), (31, 29), (9, 26), (30, 21), (39, 9), (42, 19), (9, 35), (46, 27), (8, 3), (33, 33), (35, 23), (5, 32), (24, 25), (36, 34), (42, 27), (40, 39), (11, 17), (5, 2), (26, 2), (6, 26), (13, 3), (40, 38), (7, 2), (46, 23), (37, 27), (18, 19), (8, 10), (30, 25), (33, 10), (28, 9), (46, 22), (29, 17), (21, 17), (36, 18), (43, 7), (3, 23), (8, 2), (9, 30), (43, 19), (29, 15), (38, 20), (13, 7), (44, 38), (19, 0), (39, 17), (31, 0), (45, 18), (22, 13), (16, 36), (10, 15), (26, 13), (10, 8), (9, 32), (16, 13), (44, 39), (28, 14), (25, 23), (4, 35), (11, 16), (29, 16), (0, 34), (36, 26), (39, 30), (46, 26), (8, 30), (0, 30), (0, 31), (26, 11), (4, 5), (37, 9), (20, 21), (18, 6), (44, 33), (17, 1), (14, 26), (11, 1), (6, 14), (40, 10), (41, 8), (30, 27), (42, 38), (22, 22), (35, 19), (44, 8), (26, 33), (4, 17), (40, 2), (33, 6), (13, 32), (11, 26), (29, 35), (0, 37), (1, 2), (3, 9), (18, 0), (23, 32), (5, 39), (29, 14), (20, 28), (34, 31), (16, 25), (4, 36), (42, 9), (46, 6), (13, 12), (36, 36), (12, 28), (23, 19), (18, 20), (12, 25), (1, 19), (27, 16), (20, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (23, 31), (5, 2), (25, 22), (37, 33), (27, 25), (0, 26), (0, 44), (13, 12), (10, 26), (1, 22), (18, 38), (31, 29), (14, 35), (28, 8), (17, 7), (7, 21), (12, 45), (40, 43), (24, 25), (15, 15), (25, 7), (17, 29), (40, 25), (38, 17), (25, 43), (15, 24), (21, 14), (33, 15), (6, 5), (13, 30), (29, 0), (25, 44), (7, 41), (16, 44), (3, 44), (34, 27), (26, 19), (13, 13), (18, 6), (29, 7), (32, 15), (23, 38), (34, 15), (37, 22), (4, 36), (39, 4), (9, 6), (16, 2), (9, 32), (25, 10), (8, 40), (13, 4), (4, 31), (9, 26), (22, 38), (18, 40), (13, 41), (12, 17), (31, 11), (35, 7), (28, 39), (28, 3), (15, 14), (13, 19), (15, 29), (17, 23), (13, 21), (20, 10), (35, 33), (1, 41), (17, 40), (16, 15), (26, 21), (8, 10), (31, 2), (22, 41), (30, 38), (40, 22), (11, 19), (31, 6), (33, 22), (35, 5), (31, 26), (4, 19), (36, 42), (18, 27), (13, 38), (10, 24), (28, 23), (37, 0), (26, 31), (39, 11), (27, 19), (39, 36), (29, 8), (4, 39), (23, 33), (17, 39), (38, 7), (29, 15), (7, 20), (4, 16), (17, 21), (11, 25), (5, 7), (22, 21), (11, 35), (19, 35), (34, 39), (7, 0), (23, 0), (39, 38), (1, 30), (39, 10), (37, 31), (35, 41), (27, 23), (20, 2), (19, 33), (2, 17), (25, 17), (12, 39), (36, 41), (7, 25), (21, 15), (21, 22), (22, 2), (35, 2), (30, 6), (39, 14), (13, 17), (14, 42), (33, 27), (0, 19), (28, 41), (39, 12), (2, 42), (3, 42), (19, 45), (0, 5), (3, 34), (40, 18), (6, 24), (21, 27), (4, 22), (30, 5), (5, 42), (31, 30), (28, 34), (40, 32), (37, 15), (31, 41), (27, 44), (18, 7), (6, 36), (35, 14), (20, 14), (37, 42), (13, 45), (33, 45), (22, 18), (27, 3), (24, 9), (5, 34), (10, 45), (14, 10), (21, 0), (32, 8), (6, 13), (32, 22), (23, 15), (9, 2), (27, 41), (25, 0), (29, 24), (21, 3), (15, 31), (1, 33), (10, 42), (28, 10), (27, 4), (18, 20), (22, 45), (3, 7), (30, 14), (14, 18), (22, 7), (1, 19), (12, 9), (23, 41), (5, 40), (27, 39), (12, 23), (19, 4), (0, 39), (18, 4), (40, 37), (12, 19), (4, 20), (36, 25), (1, 42), (7, 40), (40, 17), (17, 5), (29, 26), (21, 23), (22, 29), (12, 5), (22, 44), (15, 8), (1, 16), (25, 12), (14, 3), (19, 5), (28, 28), (18, 41), (32, 35), (34, 20), (12, 33), (10, 32), (36, 13), (19, 37), (36, 32), (20, 18), (32, 7), (26, 32), (28, 6), (18, 30), (37, 34), (14, 13), (36, 39), (32, 11), (10, 36), (17, 4), (38, 18), (38, 37), (31, 37), (36, 26), (10, 12), (40, 2), (30, 45), (14, 8), (9, 39), (7, 45), (38, 8), (20, 9), (39, 1), (38, 21), (20, 1), (32, 12), (21, 13), (12, 43), (39, 16), (34, 34), (9, 34), (39, 31), (27, 1), (3, 36), (23, 32), (34, 37), (27, 8), (39, 42), (26, 13), (38, 41), (2, 43), (33, 40), (20, 41), (5, 27), (23, 19), (33, 42), (30, 20), (29, 16), (4, 28), (38, 31), (34, 22), (34, 9), (29, 32), (30, 24), (9, 35), (28, 11), (18, 43), (34, 11), (0, 21), (7, 44), (13, 2), (34, 36), (22, 8), (8, 37), (32, 28), (3, 18), (1, 9), (34, 33), (4, 40), (20, 43), (38, 36), (7, 22), (29, 9), (5, 17), (24, 28), (30, 28), (25, 28), (33, 30), (1, 21), (23, 29), (28, 7), (2, 40), (5, 11), (27, 22), (27, 27), (11, 9), (0, 41), (36, 40), (25, 16), (5, 30), (32, 36), (14, 12), (36, 18), (0, 6), (24, 39), (6, 34), (17, 37), (12, 20), (3, 31), (39, 15), (20, 15), (30, 18), (40, 29), (27, 42), (13, 23), (36, 23), (1, 32), (30, 7), (1, 39), (11, 13), (11, 26), (33, 7), (26, 29), (21, 8), (14, 32), (4, 14), (33, 0), (29, 10), (19, 17), (27, 38), (34, 5), (16, 8), (6, 37), (10, 8), (15, 30), (29, 27), (27, 0), (28, 0), (0, 38), (27, 15), (2, 24), (40, 7), (40, 35), (35, 20), (8, 33), (7, 10), (25, 20), (25, 35), (33, 1), (6, 38), (23, 2), (4, 44), (32, 4), (6, 1), (8, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 11), (22, 40), (31, 25), (25, 43), (12, 7), (30, 2), (19, 31), (34, 10), (21, 37), (31, 1), (41, 20), (10, 45), (40, 24), (31, 40), (8, 45), (13, 44), (26, 38), (36, 6), (8, 32), (14, 0), (41, 2), (20, 14), (26, 30), (25, 15), (11, 26), (19, 38), (24, 20), (39, 12), (1, 0), (17, 6), (18, 14), (30, 27), (3, 11), (8, 21), (11, 30), (18, 9), (5, 42), (26, 14), (37, 45), (38, 6), (6, 25), (40, 44), (23, 31), (18, 16), (3, 37), (28, 41), (22, 34), (3, 30), (23, 41), (0, 5), (16, 43), (29, 3), (35, 30), (24, 2), (39, 6), (24, 31), (0, 19), (26, 23), (0, 40), (20, 26), (27, 30), (21, 34), (10, 39), (28, 35), (13, 1), (25, 29), (7, 20), (26, 44), (2, 23), (36, 4), (23, 43), (38, 26), (35, 18), (34, 14), (17, 37), (15, 7), (9, 27), (15, 38), (8, 5), (34, 0), (4, 8), (32, 1), (36, 18), (41, 25), (0, 46), (21, 31), (20, 9), (40, 19), (8, 26), (7, 33), (3, 34), (5, 36), (34, 27), (12, 8), (19, 13), (17, 5), (34, 46), (35, 25), (19, 8), (37, 10), (6, 4), (22, 4), (1, 29), (8, 6), (28, 29), (10, 20), (32, 3), (20, 32), (28, 44), (29, 15), (19, 3), (32, 12), (37, 14), (26, 3), (41, 24), (11, 44), (2, 1), (31, 38), (16, 46), (9, 28), (11, 29), (33, 41), (30, 47), (40, 2), (16, 18), (5, 31), (21, 33), (29, 26), (12, 43), (10, 19), (1, 25), (1, 46), (15, 41), (2, 19), (39, 27), (21, 5), (41, 15), (9, 2), (29, 47), (16, 3), (1, 28), (18, 24), (28, 42), (34, 2), (4, 30), (25, 24), (16, 34), (26, 31), (0, 32), (33, 40), (26, 32), (38, 34), (4, 24), (23, 12), (7, 0), (1, 34), (25, 33), (35, 21), (30, 33), (0, 39), (17, 26), (14, 13), (13, 47), (18, 22), (21, 26), (38, 7), (3, 10), (26, 24), (16, 28), (35, 24), (19, 12), (11, 5), (9, 37), (1, 16), (3, 22), (29, 10), (4, 25), (15, 32), (34, 6), (17, 9), (19, 29), (36, 31), (3, 2), (26, 18), (6, 7), (6, 13), (17, 30), (16, 38), (23, 37), (40, 36), (40, 42), (39, 33), (28, 7), (38, 43), (15, 9), (11, 43), (25, 13), (1, 26), (31, 42), (30, 18), (8, 22), (8, 28), (14, 30), (15, 33), (28, 36), (2, 30), (10, 9), (39, 5), (20, 8), (25, 25), (23, 44), (10, 4), (23, 4), (7, 47), (3, 16), (30, 34), (3, 23), (39, 38), (18, 27), (11, 35), (32, 13), (32, 41), (11, 42), (24, 30), (31, 4), (39, 39), (9, 14), (35, 10), (34, 32), (15, 25), (32, 37), (40, 12), (31, 23), (34, 13), (16, 7), (16, 0), (12, 26), (2, 33), (7, 21), (26, 22), (12, 27), (38, 14), (35, 38), (15, 8), (2, 35), (2, 25), (38, 13), (2, 20), (11, 3), (7, 12), (29, 19), (34, 26), (13, 38), (15, 44), (34, 25), (12, 21), (6, 36), (5, 46), (27, 26), (18, 43), (22, 22), (8, 19), (22, 45), (23, 39), (1, 12), (16, 4), (12, 22), (7, 16), (0, 45), (19, 39), (19, 25), (29, 41), (3, 14), (23, 8), (10, 7), (15, 42), (19, 34), (10, 16), (13, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 35), (42, 39), (26, 14), (12, 6), (35, 23), (1, 27), (28, 27), (15, 45), (19, 12), (15, 2), (24, 1), (21, 2), (38, 46), (26, 15), (36, 25), (37, 29), (10, 41), (30, 2), (8, 21), (38, 37), (26, 37), (41, 24), (29, 38), (23, 34), (14, 41), (39, 29), (19, 25), (30, 42), (5, 32), (22, 35), (38, 4), (39, 3), (33, 26), (13, 39), (16, 35), (43, 14), (20, 39), (24, 12), (45, 17), (8, 33), (42, 31), (27, 30), (19, 32), (28, 30), (37, 13), (45, 15), (36, 21), (14, 43), (37, 30), (18, 12), (6, 3), (7, 42), (24, 33), (8, 24), (20, 9), (47, 45), (11, 27), (9, 44), (0, 11), (25, 10), (39, 36), (42, 45), (1, 41), (0, 21), (45, 13), (39, 14), (30, 45), (13, 14), (42, 14), (32, 11), (32, 15), (36, 38), (20, 24), (15, 6), (47, 24), (40, 5), (2, 42), (45, 31), (4, 30), (20, 42), (9, 22), (27, 44), (31, 10), (39, 45), (9, 29), (22, 2), (15, 31), (23, 33), (23, 43), (10, 14), (36, 43), (12, 43), (2, 41), (18, 16), (3, 2), (28, 19), (5, 0), (39, 2), (35, 24), (27, 20), (11, 16), (33, 17), (3, 6), (27, 6), (2, 25), (45, 24), (35, 21), (11, 21), (23, 42), (38, 7), (27, 13), (43, 16), (47, 26), (4, 35), (5, 8), (28, 31), (39, 16), (10, 1), (36, 14), (17, 9), (34, 42), (33, 42), (32, 10), (23, 12), (41, 13), (36, 1), (11, 4), (24, 23), (13, 17), (26, 4), (6, 6), (36, 3), (6, 46), (29, 19), (36, 39), (7, 9), (19, 10), (39, 13), (26, 29), (47, 9), (0, 7), (0, 14), (40, 29), (32, 4), (22, 40), (1, 1), (0, 13), (2, 21), (38, 22), (40, 30), (24, 30), (37, 3), (23, 5), (10, 3), (33, 27), (2, 8), (22, 45), (41, 9), (17, 39), (7, 15), (43, 17), (1, 24), (39, 39), (46, 41), (22, 18), (29, 5), (39, 42), (0, 27), (16, 15), (26, 25), (3, 28), (25, 12), (39, 10), (5, 24), (7, 26), (26, 22), (24, 40), (5, 36), (23, 13), (35, 19), (3, 7), (20, 30), (22, 19), (30, 24), (23, 11), (22, 11), (9, 33), (40, 20), (9, 0), (32, 20), (18, 3), (21, 10), (39, 43), (19, 40), (35, 35), (34, 31), (47, 5), (7, 24), (0, 32), (30, 6), (14, 18), (37, 37), (17, 44), (16, 34), (16, 9), (45, 43), (38, 13), (25, 22), (0, 12), (4, 26), (19, 45), (38, 16), (35, 36), (15, 37), (44, 36), (28, 14), (3, 37), (22, 46), (10, 12), (0, 23), (28, 10), (21, 4), (5, 41), (22, 33), (28, 42), (3, 15), (33, 14), (46, 40), (1, 17), (25, 27), (29, 2), (10, 44)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 30), (14, 21), (31, 5), (35, 6), (2, 36), (27, 40), (45, 32), (5, 15), (9, 18), (5, 4), (44, 27), (13, 37), (19, 35), (20, 12), (16, 25), (36, 38), (2, 3), (22, 4), (44, 16), (13, 5), (24, 11), (37, 32), (24, 16), (36, 25), (7, 16), (6, 26), (42, 21), (5, 16), (35, 30), (29, 8), (21, 37), (37, 0), (7, 9), (34, 30), (27, 34), (18, 9), (42, 29), (28, 0), (14, 25), (0, 3), (16, 31), (36, 8), (16, 0), (42, 15), (6, 22), (18, 23), (45, 40), (46, 15), (31, 36), (3, 25), (32, 13), (27, 26), (8, 40), (27, 30), (5, 25), (6, 0), (29, 31), (32, 16), (8, 27), (44, 23), (12, 23), (27, 2), (2, 15), (4, 12), (18, 2), (34, 12), (11, 30), (44, 3), (16, 40), (42, 38), (25, 4), (33, 14), (3, 27), (34, 0), (38, 30), (9, 32), (9, 10), (26, 3), (0, 20), (20, 4), (44, 18), (2, 30), (31, 1), (33, 34), (17, 14), (35, 20), (9, 23), (31, 28), (15, 17), (1, 6), (34, 6), (5, 7), (34, 32), (18, 6), (39, 24), (43, 31), (5, 14), (11, 14), (33, 31), (11, 16), (12, 20), (23, 5), (35, 5), (45, 22), (40, 6), (46, 9), (36, 33), (30, 5), (23, 24), (6, 18), (5, 40), (17, 17), (4, 30), (11, 10), (13, 40), (20, 9), (31, 17), (25, 21), (11, 9), (28, 24), (21, 39), (15, 21), (41, 35), (30, 22), (0, 29), (29, 25), (38, 34), (4, 20), (34, 31), (17, 36), (43, 27), (7, 40), (14, 9), (16, 37), (39, 8), (24, 8), (42, 32), (0, 10), (8, 26), (23, 27), (45, 37), (22, 8), (23, 3), (7, 23), (12, 38), (1, 27), (16, 16), (28, 6), (7, 6), (11, 1), (5, 1), (18, 38), (5, 8), (44, 19), (25, 30), (22, 26), (43, 10), (4, 26), (2, 33), (12, 24), (35, 23), (41, 34), (5, 32), (26, 7), (34, 21), (45, 3), (24, 7), (27, 16), (43, 23), (46, 23), (4, 11), (1, 16), (30, 11), (13, 33), (0, 9), (2, 5), (6, 37), (13, 3), (9, 6), (16, 29), (6, 17), (2, 4), (4, 28), (10, 20), (39, 6), (27, 32), (2, 21), (40, 25), (29, 21), (20, 11), (32, 31), (41, 5), (19, 5), (19, 11), (28, 1), (8, 5), (26, 4), (3, 36), (10, 38), (3, 23), (22, 28), (1, 9), (33, 9), (15, 6), (9, 27), (18, 17), (44, 35), (15, 18), (36, 35), (13, 17), (18, 10), (1, 17), (43, 37), (25, 31), (12, 27), (15, 4), (0, 34), (6, 2), (26, 14), (42, 27), (42, 26), (45, 10), (8, 25), (40, 10), (2, 20), (39, 15), (34, 35), (14, 31), (22, 5), (40, 34), (38, 3), (26, 39), (18, 13), (27, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 48x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 40), (22, 11), (39, 11), (22, 15), (14, 40), (2, 35), (38, 41), (43, 38), (38, 25), (14, 37), (4, 15), (0, 13), (18, 16), (13, 43), (36, 16), (36, 13), (7, 43), (1, 12), (0, 31), (33, 5), (0, 9), (24, 1), (33, 25), (42, 39), (46, 35), (21, 11), (40, 32), (3, 37), (5, 38), (24, 36), (10, 36), (4, 17), (27, 10), (7, 37), (14, 36), (2, 21), (45, 4), (46, 17), (19, 7), (42, 20), (39, 25), (29, 2), (26, 36), (21, 10), (40, 4), (23, 17), (4, 22), (24, 42), (16, 2), (1, 27), (7, 28), (23, 25), (41, 20), (3, 19), (27, 1), (28, 36), (13, 28), (25, 22), (16, 14), (16, 37), (26, 37), (6, 7), (18, 28), (2, 7), (18, 23), (19, 31), (3, 20), (15, 41), (18, 17), (16, 10), (25, 32), (36, 6), (23, 36), (1, 18), (8, 27), (39, 19), (47, 9), (19, 14), (46, 19), (18, 10), (18, 11), (8, 26), (14, 29), (30, 38), (31, 9), (17, 8), (15, 31), (46, 11), (37, 3), (21, 13), (3, 39), (14, 24), (39, 27), (38, 28), (0, 25), (47, 23), (34, 8), (33, 8), (28, 40), (28, 17), (19, 26), (45, 22), (9, 36), (29, 20), (29, 32), (2, 3), (35, 24), (18, 24), (5, 17), (44, 14), (46, 24), (17, 4), (37, 12), (25, 38), (14, 27), (29, 0), (19, 23), (7, 14), (37, 2), (33, 14), (0, 8), (46, 15), (8, 30), (32, 29), (6, 0), (17, 28), (39, 29), (39, 9), (21, 7), (5, 15), (10, 7), (12, 39), (40, 39), (16, 39), (1, 14), (27, 2), (19, 44), (35, 31), (30, 26), (8, 3), (19, 18), (28, 7), (13, 44), (43, 22), (2, 28), (3, 35), (43, 1), (0, 3), (25, 2), (20, 11), (28, 41), (35, 15), (31, 5), (17, 7), (0, 4), (16, 4), (2, 41), (34, 12), (37, 38), (2, 34), (32, 9), (15, 10), (21, 22), (16, 16), (5, 1), (17, 19), (29, 10), (6, 20), (34, 27), (15, 0), (12, 44), (25, 30), (11, 25), (16, 19), (27, 28), (7, 10), (9, 6), (32, 8), (45, 3), (2, 31), (35, 5), (36, 11), (26, 24), (5, 27), (47, 1), (46, 22), (2, 26), (3, 23), (10, 35), (45, 17), (19, 5), (38, 43), (40, 19), (43, 24), (1, 34), (46, 40), (33, 35), (5, 19), (35, 18), (7, 15), (28, 14), (5, 21), (35, 41), (14, 38), (4, 41), (33, 11), (17, 27), (15, 37), (3, 38), (9, 2), (35, 42), (33, 26), (31, 40), (16, 0), (26, 20), (12, 41), (25, 19), (40, 26), (29, 36), (14, 41), (3, 12), (41, 40), (21, 9), (28, 6), (21, 16), (22, 42), (8, 7), (47, 7), (19, 20), (45, 20), (39, 7), (13, 33), (8, 8), (18, 0), (26, 32), (15, 3), (41, 33), (5, 2), (19, 40), (41, 36), (44, 42), (47, 18), (20, 0), (10, 9), (23, 23), (28, 39), (27, 36), (33, 36), (41, 4), (6, 22), (19, 6), (10, 8), (3, 43), (46, 8), (16, 13), (5, 26), (4, 32), (44, 37), (33, 40), (28, 4), (40, 18), (26, 16), (21, 8), (35, 36), (38, 38), (25, 13), (12, 37), (36, 1), (36, 7), (14, 33), (7, 7), (17, 30), (36, 26), (30, 5), (35, 32), (18, 1), (7, 42), (39, 23), (42, 33), (9, 22), (29, 22), (27, 32), (40, 5), (34, 19), (39, 20), (4, 16), (17, 36), (16, 12), (31, 21), (40, 23), (10, 13), (12, 27), (25, 8), (38, 11), (35, 23), (25, 18), (23, 32), (4, 30), (13, 40), (7, 40), (29, 41), (19, 11), (41, 43), (25, 37), (17, 43), (46, 41), (47, 3), (5, 11), (8, 19), (5, 30), (32, 18), (27, 6), (32, 13), (24, 6), (23, 30), (3, 1), (29, 21), (29, 39), (38, 31), (33, 13), (6, 9), (44, 43), (15, 34), (6, 34), (2, 42), (30, 34), (37, 35), (26, 10), (21, 20), (22, 36), (23, 41), (32, 30), (13, 29), (20, 14), (12, 26), (6, 27), (9, 17), (4, 23), (17, 20), (13, 32), (1, 11), (46, 4), (21, 4), (38, 8), (45, 33), (25, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 29), (9, 19), (5, 17), (24, 41), (1, 16), (20, 23), (13, 38), (9, 32), (34, 28), (24, 18), (11, 4), (40, 17), (16, 7), (18, 15), (10, 26), (11, 10), (21, 44), (25, 28), (38, 7), (0, 29), (29, 7), (31, 30), (22, 9), (17, 36), (13, 32), (38, 14), (38, 42), (3, 39), (4, 5), (0, 25), (35, 4), (38, 40), (8, 20), (37, 10), (14, 44), (16, 40), (29, 6), (2, 15), (6, 29), (20, 5), (21, 27), (25, 21), (16, 34), (23, 1), (16, 1), (34, 15), (37, 0), (8, 40), (11, 2), (4, 6), (15, 24), (18, 2), (23, 3), (5, 42), (5, 38), (25, 16), (14, 33), (13, 43), (16, 6), (40, 14), (15, 35), (21, 0), (3, 41), (3, 21), (7, 14), (37, 14), (31, 35), (34, 29), (5, 35), (32, 15), (0, 39), (2, 26), (38, 15), (15, 23), (32, 11), (30, 10), (33, 2), (27, 12), (14, 29), (14, 15), (13, 30), (38, 8), (12, 12), (2, 22), (21, 13), (35, 38), (12, 37), (36, 3), (35, 35), (15, 2), (3, 12), (27, 0), (25, 36), (18, 9), (16, 9), (5, 30), (36, 40), (25, 42), (32, 39), (4, 10), (40, 29), (1, 38), (6, 14), (1, 14), (26, 40), (30, 26), (27, 40), (33, 15), (0, 41), (23, 19), (19, 37), (28, 22), (23, 6), (5, 21), (13, 18), (30, 43), (19, 17), (16, 18), (16, 42), (36, 42), (5, 12), (32, 12), (34, 1), (28, 13), (16, 2), (19, 41), (24, 28), (21, 43), (31, 14), (11, 42), (3, 13), (27, 34), (37, 42), (3, 43), (4, 25), (35, 33), (0, 43), (10, 23), (7, 0), (26, 11), (17, 7), (5, 22), (19, 44), (8, 15), (18, 36), (34, 4), (40, 26), (16, 44), (26, 10), (37, 3), (11, 12), (31, 16), (18, 43), (22, 14), (15, 26), (27, 19), (18, 13), (35, 11), (12, 40), (12, 30), (34, 24), (14, 0), (30, 13), (28, 24), (40, 22), (25, 5), (12, 36), (9, 27), (18, 14), (30, 0), (20, 39), (18, 24), (21, 6), (10, 37), (7, 22), (37, 5), (17, 16), (35, 21), (28, 29), (15, 19), (38, 20), (39, 38), (18, 23), (33, 22), (11, 21), (18, 37), (20, 44), (24, 15), (34, 20), (2, 36), (16, 11), (27, 1), (39, 13), (34, 16), (5, 8), (1, 6), (20, 26), (36, 8), (24, 30), (17, 23), (7, 23), (36, 18), (0, 38), (37, 2), (34, 37), (8, 9), (27, 41), (9, 17), (30, 37), (13, 19), (1, 28), (3, 14), (0, 19), (16, 36), (12, 33), (33, 40), (32, 26), (12, 28), (29, 11), (22, 5), (2, 3), (18, 4), (38, 38), (25, 43), (12, 24), (31, 11), (40, 9), (30, 5), (18, 27), (1, 25), (23, 41), (32, 14), (1, 31), (11, 15), (34, 41), (26, 44), (1, 15), (38, 6), (19, 12), (38, 27), (26, 8), (19, 4), (10, 29), (17, 27), (1, 7), (40, 5), (3, 22), (33, 35), (11, 39), (36, 9), (13, 37), (12, 2), (21, 30), (4, 4), (20, 3), (29, 39), (7, 13), (27, 14), (19, 43), (10, 17), (8, 30), (37, 43), (5, 7), (19, 30), (23, 18), (29, 37), (10, 5), (37, 36), (36, 5), (22, 18), (19, 35), (4, 16), (6, 28), (27, 30), (25, 15), (31, 28), (4, 3), (25, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 32), (44, 15), (28, 27), (8, 38), (34, 14), (15, 35), (35, 24), (25, 39), (33, 39), (3, 13), (43, 20), (12, 41), (46, 35), (24, 22), (43, 8), (25, 32), (28, 12), (0, 12), (40, 26), (39, 34), (31, 22), (41, 32), (22, 40), (37, 17), (30, 37), (5, 20), (32, 10), (18, 13), (11, 24), (16, 26), (9, 41), (25, 27), (12, 29), (35, 22), (38, 9), (27, 33), (34, 29), (43, 32), (32, 37), (34, 20), (0, 7), (38, 7), (16, 20), (40, 31), (3, 35), (46, 22), (39, 27), (38, 37), (40, 13), (31, 41), (42, 24), (10, 41), (23, 9), (5, 34), (11, 12), (38, 15), (22, 31), (45, 0), (26, 10), (14, 30), (14, 32), (43, 21), (31, 28), (5, 27), (21, 39), (43, 33), (10, 27), (29, 5), (44, 34), (29, 28), (41, 26), (32, 26), (0, 38), (18, 26), (30, 24), (13, 29), (0, 6), (0, 36), (7, 12), (5, 0), (32, 6), (2, 41), (41, 16), (8, 16), (0, 13), (20, 19), (12, 28), (34, 31), (14, 6), (43, 3), (34, 34), (35, 39), (13, 17), (32, 23), (13, 15), (45, 32), (2, 9), (5, 5), (40, 38), (21, 24), (40, 25), (19, 16), (17, 23), (40, 12), (23, 29), (29, 4), (12, 36), (7, 7), (1, 10), (44, 23), (20, 11), (36, 15), (21, 33), (11, 27), (26, 26), (35, 36), (29, 24), (44, 22), (13, 1), (18, 41), (39, 20), (25, 40), (22, 27), (43, 35), (8, 39), (10, 40), (42, 30), (19, 19), (19, 39), (9, 19), (27, 16), (17, 1), (46, 28), (14, 34), (1, 24), (8, 20), (7, 9), (22, 1), (32, 32), (39, 37), (36, 22), (24, 10), (25, 1), (11, 25), (30, 9), (19, 11), (28, 40), (16, 37), (37, 36), (18, 34), (33, 7), (46, 26), (31, 30), (7, 31), (6, 35), (25, 11), (7, 8), (47, 16), (36, 30), (2, 33), (42, 15), (25, 24), (30, 25), (31, 32), (24, 21), (20, 18), (3, 10), (29, 33), (23, 12), (20, 13), (13, 11), (16, 3), (31, 19), (38, 39), (13, 25), (46, 5), (47, 13), (14, 37), (36, 17), (8, 35), (41, 1), (14, 18), (15, 4), (30, 32), (19, 21), (40, 9), (36, 11), (22, 13), (4, 11), (17, 11), (33, 32), (1, 19), (4, 10), (30, 28), (34, 17), (45, 41), (46, 33), (35, 1), (4, 34), (26, 20), (45, 18), (38, 35), (11, 23), (42, 39), (47, 20), (23, 41), (22, 26), (32, 5), (41, 25), (23, 5), (26, 23), (27, 24), (6, 13), (15, 10), (23, 26), (24, 24), (9, 31), (20, 23), (11, 26), (2, 34), (33, 30), (29, 3), (29, 8), (18, 16), (10, 8), (21, 21), (8, 2), (40, 11), (28, 29), (29, 19), (38, 8), (32, 11), (24, 13), (31, 40), (19, 31), (1, 28), (31, 39), (3, 23), (36, 12), (16, 18), (8, 32), (46, 38), (37, 19), (26, 5), (32, 33), (15, 14), (46, 12), (45, 2), (47, 37), (7, 0), (26, 11), (22, 12), (45, 20), (34, 26), (35, 5), (18, 1), (42, 36), (21, 16), (29, 35), (7, 3), (13, 22), (0, 27), (11, 31), (22, 22), (46, 11), (30, 12), (44, 32), (47, 34), (36, 38), (2, 18), (2, 10), (0, 23), (15, 20), (43, 12), (31, 21), (38, 30), (14, 21), (37, 24), (28, 33), (29, 18), (14, 36), (10, 20), (18, 40), (10, 2), (16, 30), (7, 23), (46, 24), (42, 32), (44, 9), (12, 2), (22, 28), (32, 29), (23, 20), (44, 11), (26, 4), (18, 27), (11, 29), (31, 7), (43, 1), (38, 23), (12, 6), (46, 13), (11, 7), (18, 29), (47, 21), (26, 38), (37, 9), (3, 12), (19, 0), (28, 32), (24, 0), (9, 29), (3, 17), (41, 14), (34, 32), (23, 4), (29, 1), (34, 0), (36, 27), (41, 15), (16, 7), (27, 22), (5, 16), (23, 7), (7, 4), (2, 40), (11, 14), (26, 32), (44, 6), (24, 36), (37, 0), (16, 35), (40, 10), (6, 18), (32, 35), (27, 34), (6, 3), (13, 26), (25, 18), (42, 35), (31, 10), (34, 7), (26, 0), (30, 38), (26, 13), (3, 15), (27, 25), (22, 30), (19, 2), (15, 36), (45, 27), (34, 37), (19, 25), (0, 19), (22, 10), (30, 1), (40, 1), (35, 26), (18, 17), (37, 13), (36, 3), (23, 19), (8, 11), (27, 7), (12, 31), (31, 13), (9, 24), (6, 36), (43, 39), (39, 17), (18, 5), (11, 40), (45, 8), (17, 36), (5, 10), (16, 5), (35, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 40x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (36, 12), (5, 1), (0, 38), (5, 22), (21, 9), (3, 25), (1, 40), (17, 35), (16, 2), (23, 9), (30, 25), (5, 21), (7, 25), (0, 24), (3, 35), (32, 26), (19, 16), (7, 6), (13, 19), (0, 11), (13, 18), (28, 3), (23, 1), (29, 33), (29, 22), (4, 19), (13, 30), (29, 37), (34, 22), (7, 34), (38, 3), (26, 1), (21, 17), (29, 32), (1, 31), (3, 30), (37, 6), (39, 19), (4, 31), (1, 4), (39, 13), (35, 38), (35, 28), (21, 27), (30, 19), (19, 1), (25, 18), (31, 24), (29, 8), (12, 5), (22, 24), (18, 27), (31, 33), (5, 24), (14, 10), (15, 29), (21, 22), (20, 22), (26, 23), (21, 2), (3, 5), (10, 7), (3, 7), (22, 4), (25, 29), (2, 39), (14, 18), (3, 33), (38, 7), (19, 30), (10, 6), (19, 11), (35, 14), (23, 21), (9, 19), (9, 17), (39, 2), (21, 13), (17, 0), (38, 26), (31, 28), (2, 10), (12, 35), (16, 28), (27, 13), (38, 30), (12, 32), (17, 2), (14, 15), (25, 5), (4, 3), (10, 15), (9, 0), (23, 31), (39, 4), (35, 12), (27, 37), (17, 18), (31, 26), (26, 25), (31, 14), (31, 17), (23, 15), (0, 29), (15, 30), (37, 19), (27, 10), (33, 2), (39, 20), (24, 19), (0, 27), (3, 17), (18, 26), (35, 8), (12, 8), (12, 25), (22, 9), (33, 30), (17, 5), (28, 12), (38, 22), (7, 17), (20, 29), (29, 2), (30, 0), (23, 28), (18, 38), (7, 0), (12, 19), (36, 6), (2, 37), (33, 39), (24, 2), (37, 26), (13, 14), (4, 13), (10, 1), (29, 0), (1, 36), (7, 5), (8, 5), (0, 3), (22, 21), (8, 21), (13, 22), (18, 37), (21, 5), (32, 19), (28, 6), (30, 17), (31, 15), (21, 24), (19, 38), (5, 31), (14, 12), (28, 0), (15, 18), (14, 9), (32, 24), (15, 36), (17, 39), (19, 19), (28, 18), (38, 36), (32, 32), (35, 31), (14, 8), (29, 36), (23, 27), (23, 3), (20, 31), (13, 32), (10, 30), (38, 6), (26, 30), (22, 26), (26, 18), (10, 33), (23, 19), (13, 40), (32, 7), (32, 37), (32, 29), (30, 14), (2, 32), (4, 16), (37, 21), (18, 29), (1, 15), (2, 13), (27, 18), (36, 16), (23, 36), (12, 2), (33, 32), (28, 2), (22, 3), (30, 5), (38, 8), (2, 11), (6, 34), (30, 18), (30, 16), (28, 35), (29, 34), (38, 27), (8, 31), (36, 26), (31, 10), (4, 15), (11, 7), (20, 34), (25, 8), (7, 1), (22, 2), (1, 14), (34, 34), (17, 26), (17, 15), (36, 7), (5, 32), (8, 26), (27, 15), (19, 34), (26, 3), (11, 39), (38, 25), (25, 15), (38, 18), (31, 4), (0, 40), (18, 11), (24, 23), (20, 15), (34, 12), (39, 25), (10, 40), (22, 0), (13, 1), (6, 8), (2, 9), (5, 20), (17, 25), (34, 18), (16, 9), (1, 21), (26, 24), (16, 38), (26, 15), (1, 24), (17, 9), (38, 16), (16, 20), (35, 23), (7, 21), (20, 3), (32, 28), (39, 7), (29, 4), (32, 1), (34, 21), (25, 35), (24, 16), (13, 35), (38, 23), (39, 29), (26, 32), (9, 39), (28, 1), (37, 32), (16, 29), (34, 40), (6, 33), (1, 10), (39, 35), (39, 3), (37, 33), (1, 25), (26, 10), (19, 8), (14, 36), (21, 18), (38, 29), (37, 30), (35, 27), (33, 28), (25, 20), (5, 39), (24, 33), (10, 20), (14, 24), (23, 32), (27, 22), (30, 34), (26, 28), (27, 26), (34, 16), (39, 15), (10, 2), (18, 34), (22, 7), (39, 1), (23, 17), (22, 13), (17, 28), (8, 13), (0, 4), (13, 28), (30, 7), (16, 24), (2, 15), (32, 9), (25, 32), (4, 2)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 41x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 30), (5, 12), (7, 29), (17, 34), (17, 10), (26, 22), (26, 38), (39, 12), (10, 32), (24, 24), (17, 38), (17, 11), (40, 11), (20, 26), (37, 1), (4, 9), (17, 32), (2, 18), (18, 13), (29, 26), (32, 38), (13, 30), (30, 39), (10, 3), (7, 25), (3, 1), (0, 19), (35, 30), (7, 24), (39, 18), (5, 8), (39, 8), (37, 37), (30, 1), (6, 13), (26, 39), (17, 39), (39, 27), (27, 34), (33, 15), (10, 8), (39, 10), (22, 14), (40, 20), (3, 8), (12, 4), (25, 0), (2, 8), (32, 31), (18, 11), (11, 3), (19, 7), (20, 31), (25, 11), (32, 3), (19, 38), (23, 19), (6, 38), (2, 28), (21, 25), (6, 23), (1, 17), (38, 29), (19, 6), (5, 15), (1, 8), (7, 10), (21, 23), (4, 3), (12, 23), (10, 7), (19, 10), (26, 3), (8, 28), (12, 6), (5, 30), (28, 27), (12, 33), (32, 0), (22, 34), (14, 33), (19, 17), (39, 19), (39, 2), (21, 13), (26, 23), (37, 32), (5, 18), (13, 33), (11, 16), (30, 21), (18, 21), (20, 20), (8, 3), (2, 9), (18, 1), (18, 26), (30, 12), (8, 37), (28, 30), (27, 25), (37, 0), (23, 25), (10, 37), (6, 7), (36, 27), (7, 5), (21, 17), (35, 31), (23, 11), (1, 26), (29, 6), (16, 14), (20, 23), (38, 17), (20, 12), (32, 29), (21, 39), (37, 18), (5, 1), (33, 9), (32, 18), (39, 9), (8, 18), (29, 38), (6, 6), (4, 38), (38, 38), (36, 1), (9, 2), (31, 14), (17, 30), (22, 11), (35, 12), (30, 13), (13, 9), (36, 3), (31, 13), (30, 24), (20, 13), (0, 8), (11, 34), (14, 27), (38, 8), (0, 5), (13, 27), (12, 13), (11, 33), (29, 17), (22, 32), (11, 29), (37, 39), (26, 30), (4, 14), (39, 33), (10, 13), (25, 14), (21, 19), (0, 11), (9, 16), (31, 34), (20, 32), (31, 4), (29, 19), (11, 38), (27, 31), (30, 29), (1, 16), (14, 24), (24, 12), (13, 29), (3, 28), (4, 35), (7, 12), (24, 7), (5, 20), (15, 26), (23, 24), (16, 37), (37, 9), (3, 5), (22, 3), (5, 39), (31, 23), (34, 17), (28, 36), (24, 21), (17, 19), (24, 16), (21, 10), (34, 9), (21, 8), (20, 11), (14, 35), (31, 33), (9, 13), (11, 0), (13, 5), (18, 33), (28, 11), (29, 1), (33, 30), (21, 3), (14, 12), (30, 36), (28, 21), (1, 24), (2, 13), (16, 34), (29, 21), (26, 14), (36, 15), (8, 17), (5, 0), (1, 25), (28, 22), (35, 38), (13, 39), (15, 7), (39, 20), (33, 0), (12, 9), (37, 3), (27, 6), (7, 11), (40, 28), (16, 4), (14, 26), (29, 3), (8, 19), (25, 21), (2, 2), (0, 16), (1, 35), (20, 2), (13, 26), (14, 34), (16, 8), (16, 12), (8, 35), (6, 0), (38, 22), (28, 3), (26, 24), (33, 11), (2, 16), (0, 15), (3, 2), (1, 6), (7, 0), (25, 37), (0, 28), (17, 20), (19, 23), (16, 2), (9, 11), (12, 5), (36, 35), (32, 25), (12, 0), (8, 6), (32, 19), (35, 16), (5, 36), (10, 33), (9, 10), (4, 18), (10, 17), (23, 21), (18, 8), (19, 35), (23, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 25), (32, 23), (35, 7), (5, 10), (9, 4), (10, 9), (26, 30), (33, 37), (12, 14), (9, 19), (33, 5), (38, 21), (34, 25), (37, 18), (10, 20), (30, 36), (24, 36), (27, 17), (24, 14), (29, 23), (29, 32), (28, 13), (18, 39), (12, 13), (13, 21), (15, 30), (37, 34), (40, 38), (23, 21), (19, 16), (1, 8), (4, 27), (8, 12), (24, 2), (10, 25), (26, 29), (36, 11), (36, 19), (7, 10), (23, 39), (0, 27), (24, 34), (14, 5), (35, 36), (31, 37), (11, 4), (7, 0), (36, 33), (4, 31), (2, 24), (39, 27), (31, 13), (23, 30), (9, 17), (2, 34), (12, 29), (11, 5), (40, 10), (13, 38), (5, 27), (18, 17), (30, 14), (30, 13), (30, 38), (12, 0), (40, 15), (2, 18), (21, 20), (6, 12), (13, 0), (26, 18), (18, 0), (31, 6), (24, 21), (26, 16), (26, 1), (1, 39), (10, 32), (17, 28), (41, 4), (22, 18), (19, 12), (27, 37), (22, 4), (17, 31), (34, 10), (3, 30), (30, 8), (38, 13), (11, 38), (32, 34), (18, 22), (27, 36), (14, 34), (19, 39), (34, 15), (0, 35), (32, 15), (7, 8), (4, 24), (24, 0), (3, 34), (38, 20), (41, 2), (36, 3), (17, 8), (25, 38), (22, 3), (19, 10), (27, 27), (35, 15), (4, 38), (2, 25), (23, 23), (26, 28), (32, 39), (0, 3), (5, 18), (30, 35), (12, 22), (3, 23), (3, 35), (38, 35), (8, 39), (3, 0), (26, 26), (2, 0), (5, 19), (22, 29), (24, 3), (5, 35), (27, 5), (15, 27), (15, 10), (8, 34), (40, 33), (30, 3), (11, 26), (32, 19), (34, 30), (36, 32), (17, 7), (1, 34), (35, 23), (11, 21), (28, 1), (1, 13), (6, 14), (38, 25), (27, 31), (36, 34), (10, 24), (2, 4), (3, 32), (15, 28), (23, 6), (25, 11), (6, 15), (6, 5), (21, 26), (4, 22), (0, 21), (4, 4), (5, 11), (30, 18), (1, 26), (10, 1), (20, 17), (32, 18), (24, 28), (19, 40), (39, 35), (9, 1), (35, 28), (36, 36), (6, 36), (18, 2), (8, 32), (33, 23), (20, 36), (9, 3), (6, 7), (6, 27), (22, 23), (32, 38), (18, 12), (31, 27), (10, 2), (5, 32), (31, 30), (24, 15), (20, 31), (16, 16), (18, 38), (18, 35), (29, 36), (9, 27), (6, 31), (37, 4), (0, 39), (31, 23), (11, 34), (14, 37), (34, 27), (21, 24), (36, 14), (31, 21), (6, 35), (0, 19), (28, 21), (36, 20), (29, 16), (2, 13), (9, 8), (33, 21), (36, 23), (11, 37), (33, 24), (27, 29), (8, 0), (33, 35), (8, 33), (8, 21), (39, 34), (26, 32), (21, 37), (3, 22), (3, 26), (23, 20), (8, 23), (38, 30), (1, 11), (1, 22), (14, 15), (24, 23), (18, 25), (0, 7), (40, 30), (39, 29), (37, 38), (36, 16), (1, 35), (38, 23), (30, 26), (30, 1), (33, 25), (3, 28), (21, 9), (41, 23), (9, 6), (26, 20), (26, 14), (7, 28), (8, 31), (33, 33), (40, 21), (11, 32), (8, 35), (14, 14), (28, 26), (34, 17), (29, 25), (38, 10), (2, 38), (17, 3), (24, 39), (16, 39), (0, 1), (28, 35), (19, 15), (29, 34), (13, 20), (2, 30), (30, 19), (22, 37), (13, 1), (29, 6), (14, 10), (10, 15), (29, 27), (8, 2), (34, 35), (40, 6), (11, 19), (25, 30), (34, 39), (37, 27), (23, 19), (22, 38), (32, 8), (34, 36), (5, 40), (35, 35), (32, 21), (14, 36), (22, 17), (6, 0), (20, 25), (25, 2), (22, 39), (17, 38), (1, 19), (11, 35), (15, 7), (30, 16), (24, 32), (4, 23), (38, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 17), (13, 23), (27, 12), (19, 24), (1, 6), (21, 15), (37, 11), (33, 3), (36, 28), (23, 41), (11, 17), (17, 40), (27, 17), (26, 38), (3, 32), (14, 3), (31, 17), (29, 4), (5, 11), (27, 16), (5, 41), (15, 26), (7, 38), (29, 2), (24, 10), (9, 35), (4, 5), (38, 19), (34, 16), (30, 38), (20, 21), (10, 32), (26, 3), (33, 24), (37, 32), (5, 3), (39, 30), (27, 24), (10, 28), (21, 27), (5, 38), (6, 10), (14, 35), (1, 2), (35, 1), (37, 0), (34, 34), (35, 0), (21, 9), (41, 17), (35, 16), (26, 10), (35, 31), (20, 4), (30, 25), (10, 30), (35, 4), (10, 5), (35, 37), (20, 15), (40, 18), (40, 34), (11, 0), (30, 23), (12, 33), (25, 4), (31, 12), (24, 7), (38, 22), (36, 16), (28, 6), (18, 26), (15, 21), (39, 20), (38, 39), (18, 3), (2, 35), (12, 5), (25, 11), (42, 20), (33, 16), (29, 19), (4, 22), (16, 3), (0, 38), (34, 32), (5, 4), (6, 33), (23, 25), (14, 0), (2, 15), (24, 5), (24, 0), (6, 27), (13, 5), (17, 42), (4, 39), (24, 20), (12, 25), (7, 25), (2, 26), (2, 16), (23, 0), (20, 34), (16, 29), (26, 9), (24, 27), (30, 12), (35, 7), (36, 7), (2, 30), (33, 11), (37, 12), (19, 28), (23, 12), (18, 14), (8, 35), (10, 10), (16, 30), (29, 25), (13, 18), (27, 41), (0, 25), (5, 23), (40, 17), (40, 8), (9, 31), (1, 30), (20, 32), (13, 4), (37, 24), (19, 6), (42, 2), (35, 38), (29, 23), (7, 6), (20, 40), (21, 19), (14, 24), (9, 22), (9, 15), (31, 33), (21, 39), (25, 6), (2, 0), (11, 22), (4, 29), (35, 34), (30, 8), (39, 5), (19, 8), (34, 19), (22, 30), (20, 27), (15, 6), (16, 41), (8, 15), (42, 32), (32, 22), (38, 38), (14, 16), (29, 38), (41, 16), (0, 39), (29, 1), (2, 31), (40, 21), (18, 13), (3, 7), (40, 27), (1, 25), (0, 40), (23, 34), (27, 9), (41, 27), (36, 27), (37, 30), (2, 39), (27, 19), (3, 5), (31, 7), (30, 6), (1, 22), (33, 22), (8, 20), (3, 4), (30, 17), (11, 41), (42, 40), (0, 3), (4, 27), (34, 9), (2, 11), (29, 39), (16, 39), (15, 25), (9, 1), (22, 26), (4, 0), (10, 25), (7, 24), (27, 26), (19, 29), (30, 2), (25, 20), (27, 37), (15, 36), (7, 36), (6, 30), (30, 10), (13, 14), (11, 30), (2, 25), (42, 24), (30, 39), (26, 21), (11, 5), (24, 15), (19, 23), (18, 23), (30, 26), (19, 36), (25, 15), (42, 39), (9, 38), (2, 24), (15, 11), (31, 27), (25, 24), (9, 32), (1, 4), (2, 12), (6, 9), (22, 11), (30, 37), (15, 42), (32, 41), (9, 13), (41, 10), (4, 16), (28, 22), (29, 30), (14, 40), (10, 38), (34, 4), (6, 2), (31, 9), (32, 7), (32, 25), (34, 11), (42, 1), (30, 7), (19, 11), (10, 29), (12, 40), (31, 42), (10, 34), (15, 2), (18, 16), (17, 23), (40, 1), (28, 13), (6, 34), (21, 14), (12, 15), (8, 9), (42, 17), (25, 30), (4, 21), (32, 29), (25, 1), (13, 11), (20, 12), (37, 39), (9, 42), (32, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 11), (31, 13), (23, 32), (20, 39), (39, 32), (22, 30), (13, 39), (3, 40), (9, 2), (31, 27), (37, 8), (0, 20), (0, 37), (24, 39), (38, 34), (29, 8), (3, 17), (10, 27), (17, 29), (37, 21), (8, 41), (26, 18), (14, 18), (15, 11), (42, 11), (6, 38), (1, 6), (23, 23), (39, 24), (25, 33), (23, 14), (23, 20), (20, 12), (12, 2), (34, 13), (30, 32), (26, 7), (16, 27), (35, 41), (16, 23), (38, 23), (32, 3), (39, 36), (20, 25), (27, 6), (34, 17), (9, 14), (0, 39), (1, 9), (20, 13), (29, 38), (13, 2), (24, 15), (33, 23), (25, 19), (21, 33), (23, 38), (11, 37), (27, 21), (30, 24), (4, 37), (18, 11), (21, 21), (31, 6), (38, 19), (8, 14), (14, 20), (27, 3), (19, 32), (12, 33), (6, 34), (26, 39), (20, 31), (33, 4), (18, 38), (36, 18), (7, 1), (35, 21), (24, 6), (12, 21), (40, 19), (26, 13), (4, 22), (22, 2), (24, 8), (28, 42), (3, 31), (5, 19), (37, 0), (17, 42), (38, 17), (17, 6), (40, 22), (6, 14), (17, 8), (23, 18), (3, 22), (22, 33), (11, 30), (41, 0), (35, 1), (2, 3), (2, 27), (5, 32), (6, 21), (38, 13), (15, 14), (1, 7), (29, 25), (30, 40), (34, 39), (10, 42), (37, 36), (24, 2), (23, 2), (7, 39), (9, 3), (29, 15), (20, 20), (28, 7), (16, 21), (32, 1), (1, 20), (40, 29), (30, 35), (16, 41), (11, 22), (22, 35), (37, 26), (17, 24), (17, 37), (37, 42), (19, 26), (34, 10), (33, 34), (0, 24), (41, 29), (21, 24), (30, 7), (39, 42), (11, 4), (38, 12), (17, 11), (34, 33), (6, 4), (30, 17), (39, 4), (9, 26), (8, 37), (28, 21), (34, 25), (38, 39), (20, 16), (20, 36), (32, 28), (8, 22), (37, 12), (13, 16), (1, 39), (16, 17), (22, 27), (29, 36), (21, 10), (4, 15), (19, 15), (0, 1), (4, 35), (5, 3), (1, 36), (36, 13), (23, 5), (4, 5), (29, 30), (22, 24), (0, 32), (0, 42), (21, 30), (25, 20), (7, 19), (6, 13), (29, 10), (16, 37), (25, 18), (41, 1), (26, 2), (15, 21), (29, 33), (34, 42), (14, 36), (27, 41), (33, 22), (28, 37), (0, 36), (32, 35), (29, 20), (26, 34), (12, 34), (15, 7), (29, 35), (10, 4), (0, 26), (40, 2), (13, 30), (5, 30), (12, 22), (32, 18), (8, 35), (37, 6), (42, 41), (8, 34), (13, 28), (26, 41), (12, 10), (32, 2), (29, 7), (31, 31), (5, 34), (12, 9), (27, 36), (36, 21), (12, 1), (30, 20), (35, 17), (34, 20), (3, 37), (24, 16), (21, 32), (0, 31), (39, 16), (41, 39), (23, 35), (24, 5), (18, 22), (2, 11), (5, 42), (18, 24), (10, 1), (38, 41), (8, 3), (20, 40), (19, 42), (23, 29), (37, 9), (18, 5), (18, 13), (32, 15), (4, 23), (12, 41), (28, 10), (25, 25), (24, 10), (28, 15), (29, 14), (23, 24), (7, 36), (15, 34), (6, 25), (12, 32), (26, 6), (39, 6), (30, 5), (26, 37), (15, 20), (3, 9), (36, 16), (16, 40), (26, 0), (28, 23), (17, 4), (35, 13), (5, 21), (10, 38), (8, 10), (34, 4), (31, 26), (3, 11), (24, 14), (31, 3), (13, 6), (16, 19), (15, 42), (11, 28), (6, 18), (26, 11), (10, 23)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 33), (10, 21), (48, 24), (30, 34), (4, 23), (26, 11), (5, 34), (3, 33), (28, 41), (6, 5), (0, 26), (46, 24), (38, 33), (39, 3), (10, 10), (24, 14), (47, 38), (43, 40), (30, 38), (22, 14), (10, 28), (47, 21), (24, 39), (29, 33), (3, 27), (10, 37), (31, 15), (17, 6), (45, 24), (43, 5), (6, 22), (46, 9), (1, 10), (28, 15), (11, 15), (5, 31), (47, 18), (41, 39), (43, 42), (31, 33), (1, 23), (40, 39), (2, 28), (3, 35), (34, 12), (44, 27), (12, 6), (32, 17), (41, 17), (26, 1), (44, 15), (3, 0), (37, 21), (3, 1), (40, 21), (19, 31), (20, 9), (12, 36), (12, 2), (8, 0), (0, 41), (3, 28), (48, 7), (15, 31), (8, 6), (5, 5), (48, 0), (0, 9), (23, 34), (17, 39), (7, 40), (21, 14), (34, 24), (23, 16), (23, 9), (32, 29), (2, 39), (31, 2), (1, 18), (24, 7), (16, 24), (37, 5), (6, 7), (8, 18), (7, 12), (48, 10), (21, 42), (37, 32), (31, 30), (37, 2), (19, 30), (13, 30), (20, 5), (22, 22), (28, 42), (31, 37), (31, 7), (47, 39), (13, 23), (41, 28), (4, 43), (7, 41), (39, 30), (23, 15), (22, 12), (18, 9), (11, 24), (39, 13), (26, 3), (19, 29), (24, 32), (4, 36), (30, 21), (45, 20), (8, 36), (46, 5), (22, 32), (10, 11), (32, 4), (18, 31), (46, 37), (30, 32), (46, 0), (16, 16), (27, 35), (26, 16), (40, 28), (34, 9), (29, 3), (44, 1), (15, 26), (42, 1), (34, 13), (45, 29), (29, 26), (38, 31), (16, 18), (12, 40), (17, 33), (3, 9), (28, 27), (27, 21), (2, 8), (28, 33), (17, 15), (5, 10), (15, 39), (32, 39), (48, 35), (31, 39), (25, 38), (44, 18), (18, 18), (42, 40), (32, 30), (1, 13), (43, 8), (12, 41), (7, 11), (23, 26), (9, 24), (42, 31), (13, 15), (9, 7), (26, 0), (9, 0), (44, 2), (38, 17), (19, 19), (27, 23), (34, 30), (35, 21), (41, 19), (23, 32), (35, 7), (27, 11), (30, 36), (43, 27), (16, 9), (42, 36), (34, 39), (12, 43), (46, 35), (1, 5), (17, 4), (16, 31), (6, 12), (10, 33), (33, 6), (8, 15), (7, 0), (26, 37), (17, 12), (0, 8), (24, 37), (39, 14), (24, 20), (37, 31), (28, 43), (14, 30), (20, 14), (34, 18), (41, 41), (47, 17), (28, 40), (16, 5), (44, 23), (10, 18), (32, 21), (40, 16), (45, 2), (21, 22), (0, 32), (46, 33), (30, 37), (40, 5), (45, 16), (8, 30), (16, 4), (42, 41), (45, 34), (48, 31), (8, 20), (1, 15), (48, 20), (4, 4), (24, 43), (27, 1), (4, 25), (41, 31), (5, 26), (33, 38), (1, 0), (12, 5), (36, 12), (41, 18), (0, 3), (13, 3), (47, 9), (4, 39), (15, 33), (47, 27), (12, 14), (7, 3), (14, 4), (15, 16), (48, 23), (15, 36), (37, 7), (38, 35), (7, 22), (14, 14), (32, 37), (37, 36), (8, 10), (26, 9), (31, 14), (9, 33), (33, 2), (15, 13), (43, 33), (34, 19), (1, 34), (28, 21), (18, 1), (1, 1), (34, 34), (0, 40), (0, 12), (14, 17), (40, 40), (41, 29), (42, 15), (6, 3), (4, 19), (14, 24), (14, 5), (10, 22), (8, 23), (20, 1), (15, 43), (26, 24), (32, 23), (33, 29), (13, 6), (28, 23), (16, 41), (22, 16), (2, 42), (18, 33), (24, 8), (13, 36), (38, 18), (37, 33), (43, 0), (17, 32), (24, 18), (26, 34), (7, 24), (20, 32), (15, 22), (35, 41), (27, 8), (42, 42), (46, 13), (12, 37), (8, 32), (45, 4), (28, 32), (18, 0), (8, 13), (7, 8), (13, 29), (33, 20), (14, 32), (23, 40), (10, 35), (12, 42), (38, 15), (36, 17), (35, 11), (37, 18), (8, 12), (42, 43), (44, 7), (35, 40), (27, 43), (8, 5), (17, 13), (13, 16), (25, 40), (14, 26), (9, 37), (24, 17), (35, 16), (1, 38), (21, 21), (1, 42), (27, 2), (44, 34), (13, 39), (21, 0), (1, 6), (45, 43), (36, 11), (37, 40), (14, 1), (20, 7), (4, 14), (20, 36), (22, 35), (41, 11), (15, 7), (23, 27), (10, 31), (46, 23), (22, 28), (33, 1), (11, 28), (17, 19), (39, 1), (6, 10), (38, 36), (26, 35), (42, 3), (21, 27), (46, 43), (2, 25), (23, 11), (9, 3), (37, 38), (29, 20), (6, 29), (40, 30), (36, 2), (47, 35), (4, 5), (44, 11), (0, 34), (35, 19), (16, 13), (23, 36), (42, 2), (6, 26), (32, 1), (8, 1), (23, 17), (37, 6), (16, 14), (32, 12), (5, 40), (24, 3), (45, 10), (25, 17), (7, 6), (28, 8), (43, 34), (3, 13), (18, 37), (23, 3), (44, 35), (45, 42), (20, 17), (33, 27), (2, 14), (45, 13), (13, 17), (16, 19), (33, 34), (45, 28), (1, 11), (45, 1), (42, 29), (25, 41), (44, 28), (45, 18), (11, 31), (34, 23), (36, 21), (10, 5), (33, 25), (35, 4), (44, 31), (12, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 33), (10, 7), (23, 26), (35, 1), (6, 30), (41, 41), (30, 42), (14, 35), (12, 11), (37, 27), (3, 37), (25, 32), (27, 20), (1, 40), (39, 17), (11, 11), (28, 7), (4, 38), (44, 32), (34, 7), (47, 22), (5, 11), (8, 9), (27, 39), (17, 0), (22, 23), (5, 21), (37, 14), (13, 14), (44, 17), (6, 0), (43, 40), (31, 18), (30, 9), (29, 41), (28, 43), (31, 24), (37, 22), (1, 13), (8, 8), (35, 38), (26, 40), (39, 10), (11, 16), (18, 24), (45, 43), (47, 33), (42, 3), (46, 12), (34, 33), (25, 37), (15, 13), (10, 19), (1, 31), (16, 16), (45, 25), (17, 32), (36, 11), (19, 32), (37, 32), (3, 21), (40, 12), (5, 19), (16, 36), (42, 29), (13, 35), (22, 32), (26, 7), (18, 15), (17, 40), (33, 17), (21, 29), (23, 30), (39, 23), (24, 38), (0, 21), (37, 1), (26, 39), (6, 31), (9, 12), (24, 43), (15, 7), (36, 6), (44, 36), (41, 16), (16, 4), (43, 36), (35, 2), (23, 28), (26, 16), (40, 39), (13, 21), (28, 19), (17, 12), (44, 35), (45, 4), (31, 33), (46, 13), (10, 18), (34, 24), (39, 20), (41, 1), (26, 18), (18, 4), (17, 6), (9, 32), (29, 32), (15, 30), (16, 40), (43, 15), (44, 13), (47, 25), (24, 4), (20, 26), (9, 34), (28, 31), (18, 20), (41, 4), (41, 33), (21, 42), (26, 28), (17, 9), (36, 4), (22, 24), (21, 30), (41, 3), (22, 16), (39, 22), (5, 17), (13, 3), (9, 24), (36, 5), (7, 43), (17, 8), (14, 4), (42, 40), (40, 38), (21, 9), (30, 12), (46, 9), (9, 5), (10, 28), (4, 7), (46, 8), (33, 33), (30, 2), (30, 29), (4, 42), (24, 36), (24, 0), (13, 29), (0, 11), (3, 27), (12, 40), (14, 10), (20, 4), (10, 39), (38, 25), (39, 26), (12, 10), (12, 8), (42, 41), (8, 6), (17, 22), (18, 32), (11, 28), (24, 31), (18, 38), (3, 11), (18, 9), (36, 16), (29, 14), (31, 30), (13, 30), (16, 23), (41, 35), (6, 6), (32, 12), (35, 8), (28, 29), (37, 21), (22, 18), (15, 28), (16, 14), (27, 40), (39, 33), (12, 3), (17, 13), (19, 3), (18, 30), (6, 10), (29, 21), (8, 33), (32, 5), (4, 29), (34, 3), (18, 3), (21, 16), (27, 29), (7, 29), (36, 13), (1, 14), (45, 39), (24, 22), (16, 22), (36, 31), (27, 26), (6, 18), (43, 14), (29, 9), (38, 40), (9, 37), (9, 39), (24, 7), (18, 12), (1, 39), (9, 35), (34, 15), (32, 41), (33, 43), (14, 16), (25, 42), (14, 36), (37, 6), (47, 20), (42, 22), (26, 33), (30, 40), (40, 0), (46, 6), (41, 2), (29, 27), (9, 18), (24, 15), (22, 5), (0, 24), (37, 8), (32, 28), (28, 2), (6, 32), (9, 1), (7, 3), (27, 9), (1, 16), (21, 40), (32, 24), (33, 7), (42, 23), (25, 12), (28, 39), (22, 38), (21, 13), (36, 22), (24, 6), (24, 23), (1, 20), (10, 10), (18, 21), (28, 37), (38, 5), (9, 42), (46, 18), (6, 7), (43, 39), (41, 32), (43, 2), (40, 34), (45, 35), (40, 41), (26, 31), (1, 36), (14, 23), (42, 37), (39, 38), (44, 39), (39, 39), (5, 5), (35, 0), (1, 0), (45, 16), (29, 30), (27, 17), (27, 11), (5, 35), (33, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 6), (42, 38), (10, 1), (9, 27), (30, 19), (28, 28), (36, 31), (43, 24), (5, 15), (10, 9), (14, 17), (25, 42), (36, 11), (30, 11), (47, 39), (7, 18), (6, 23), (22, 32), (35, 6), (16, 14), (43, 8), (9, 38), (9, 32), (9, 4), (21, 41), (24, 1), (6, 18), (22, 43), (4, 35), (30, 31), (12, 32), (9, 7), (28, 25), (9, 16), (31, 0), (41, 35), (42, 32), (16, 38), (37, 35), (18, 11), (2, 28), (8, 30), (27, 20), (27, 6), (46, 10), (21, 28), (13, 39), (12, 26), (43, 33), (19, 5), (5, 26), (0, 39), (16, 16), (22, 41), (39, 20), (27, 33), (20, 33), (15, 14), (4, 44), (6, 26), (37, 7), (7, 36), (15, 16), (0, 6), (0, 17), (32, 9), (38, 41), (41, 1), (45, 29), (21, 27), (17, 1), (41, 9), (39, 41), (11, 0), (11, 20), (14, 26), (15, 22), (14, 39), (34, 38), (28, 42), (3, 2), (5, 32), (11, 44), (14, 11), (37, 11), (1, 25), (31, 29), (36, 29), (42, 12), (27, 18), (18, 17), (44, 42), (47, 29), (2, 6), (17, 19), (27, 26), (3, 0), (21, 39), (31, 16), (20, 16), (1, 1), (23, 25), (38, 27), (29, 30), (44, 39), (28, 2), (42, 9), (30, 30), (42, 28), (1, 4), (21, 32), (20, 31), (21, 13), (32, 25), (34, 3), (0, 14), (29, 2), (34, 32), (3, 33), (5, 38), (31, 41), (43, 39), (20, 32), (25, 5), (17, 24), (11, 14), (42, 15), (13, 12), (43, 26), (5, 4), (47, 42), (29, 40), (7, 29), (21, 29), (38, 19), (43, 32), (31, 23), (17, 30), (22, 39), (21, 21), (20, 38), (35, 12), (4, 1), (20, 42), (3, 29), (21, 34), (45, 26), (27, 19), (44, 0), (11, 6), (0, 25), (15, 25), (1, 11), (10, 24), (27, 23), (8, 34), (34, 8), (11, 43), (3, 7), (4, 36), (34, 0), (38, 36), (0, 43), (26, 1), (30, 8), (23, 23), (9, 10), (35, 38), (30, 42), (37, 12), (26, 7), (2, 18), (41, 8), (42, 31), (23, 42), (21, 9), (16, 8), (17, 16), (42, 16), (1, 31), (30, 35), (45, 4), (24, 24), (25, 14), (5, 31), (2, 31), (16, 23), (33, 11), (26, 41), (6, 9), (16, 17), (31, 37), (47, 13), (1, 10), (43, 22), (19, 40), (7, 22), (16, 29), (36, 37), (17, 26), (36, 42), (40, 16), (33, 42), (32, 12), (24, 21), (40, 22), (15, 11), (5, 41), (7, 27), (7, 15), (19, 43), (44, 29), (45, 45), (24, 20), (16, 6), (25, 32), (39, 14), (33, 29), (33, 5), (31, 17), (8, 9), (17, 2), (9, 31), (19, 12), (5, 23), (26, 17), (34, 44), (8, 16), (27, 7), (24, 39), (10, 8), (46, 34), (32, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 43), (4, 43), (7, 18), (9, 48), (31, 36), (17, 11), (4, 12), (19, 27), (0, 28), (37, 14), (16, 2), (22, 16), (29, 13), (38, 43), (16, 46), (41, 40), (4, 45), (24, 15), (10, 24), (29, 18), (34, 10), (16, 48), (32, 1), (5, 30), (27, 13), (13, 0), (35, 8), (26, 24), (27, 5), (5, 35), (36, 6), (26, 1), (40, 15), (17, 2), (31, 16), (12, 3), (25, 21), (15, 8), (26, 10), (30, 32), (33, 33), (0, 26), (40, 9), (16, 6), (10, 6), (14, 36), (27, 12), (32, 14), (23, 19), (39, 45), (11, 18), (11, 19), (18, 6), (28, 0), (12, 13), (24, 44), (30, 35), (35, 5), (18, 15), (20, 31), (19, 46), (9, 6), (41, 17), (8, 46), (28, 12), (25, 40), (19, 15), (2, 13), (33, 22), (3, 18), (23, 28), (21, 5), (37, 24), (29, 45), (14, 26), (8, 38), (3, 34), (13, 31), (17, 39), (34, 47), (28, 32), (31, 10), (12, 34), (41, 0), (1, 44), (14, 5), (41, 37), (37, 29), (0, 42), (3, 46), (5, 44), (15, 2), (3, 37), (40, 8), (11, 7), (37, 8), (23, 27), (6, 11), (6, 29), (36, 29), (17, 9), (5, 27), (7, 24), (11, 9), (21, 4), (6, 20), (6, 9), (38, 0), (22, 21), (32, 24), (25, 47), (12, 46), (28, 40), (25, 24), (24, 23), (3, 20), (11, 10), (38, 38), (8, 11), (29, 35), (4, 8), (7, 40), (7, 21), (40, 3), (9, 22), (22, 40), (24, 29), (39, 18), (5, 3), (28, 38), (40, 25), (6, 46), (3, 26), (37, 16), (6, 23), (29, 15), (36, 31), (36, 18), (30, 23), (9, 18), (19, 10), (27, 7), (29, 25), (29, 12), (9, 10), (30, 28), (11, 24), (19, 40), (2, 33), (12, 8), (39, 38), (3, 13), (14, 37), (13, 20), (22, 3), (8, 26), (29, 37), (9, 14), (19, 34), (9, 4), (28, 13), (2, 1), (30, 3), (33, 44), (32, 4), (11, 21), (40, 2), (19, 23), (41, 46), (40, 26), (8, 35), (3, 28), (0, 12), (33, 23), (27, 8), (0, 17), (1, 1), (18, 34), (14, 40), (23, 30), (30, 18), (20, 48), (10, 27), (15, 46), (5, 8), (27, 42), (16, 39), (19, 42), (31, 43), (31, 34), (39, 15), (23, 22), (19, 22), (12, 23), (28, 19), (23, 45), (21, 35), (8, 6), (39, 8), (19, 37), (41, 29), (10, 15), (9, 16), (41, 13), (11, 42), (25, 32), (38, 11), (35, 19), (41, 7), (41, 34), (18, 47), (34, 44), (23, 1), (1, 12), (4, 38), (35, 43), (27, 19), (22, 32), (28, 34), (10, 16), (22, 23), (17, 38), (26, 42), (19, 19), (1, 24), (5, 47), (8, 10), (37, 40), (32, 30), (31, 45), (6, 34), (13, 27), (1, 5), (4, 9), (15, 21), (24, 30), (5, 33), (21, 25), (14, 10), (21, 7), (37, 25), (37, 32), (14, 23), (4, 47), (39, 29), (36, 28), (19, 33), (31, 1), (25, 12), (24, 43), (26, 9), (16, 17), (29, 41), (12, 1), (1, 40), (17, 0), (14, 44), (40, 13), (27, 21), (34, 33), (3, 33), (26, 25), (14, 15), (16, 8), (13, 46), (1, 33), (28, 22), (33, 29), (1, 21), (18, 16), (18, 7), (38, 35), (35, 13), (32, 23), (15, 13), (1, 10), (33, 19), (13, 4), (20, 13), (11, 44), (11, 36), (5, 6), (37, 15), (29, 38), (4, 17), (32, 11), (16, 24), (32, 16), (23, 25), (38, 17), (30, 14), (6, 22), (16, 32), (18, 29), (35, 32), (5, 22), (34, 28), (6, 17), (22, 39), (2, 19), (18, 36), (7, 28), (23, 21), (20, 21), (1, 36), (14, 31), (24, 42), (31, 2), (29, 48), (39, 35), (38, 21), (20, 41), (13, 37), (27, 4), (40, 37), (40, 35), (15, 47), (31, 3), (20, 11), (18, 4), (27, 45), (35, 39), (13, 18), (38, 31), (3, 40), (4, 27), (27, 18), (5, 10), (40, 40), (23, 13), (34, 0), (6, 3), (40, 32), (15, 10), (1, 8), (13, 10), (12, 10), (2, 21), (17, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 45x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 45), (10, 8), (27, 35), (31, 7), (34, 8), (20, 39), (20, 27), (7, 21), (43, 5), (25, 18), (7, 9), (34, 17), (23, 44), (19, 2), (38, 37), (16, 39), (30, 14), (31, 36), (31, 32), (38, 32), (33, 41), (21, 2), (23, 32), (13, 38), (44, 5), (44, 24), (6, 31), (7, 34), (8, 14), (37, 31), (5, 25), (39, 42), (24, 9), (25, 23), (19, 44), (33, 29), (8, 13), (36, 5), (32, 13), (25, 40), (9, 28), (44, 2), (38, 21), (37, 5), (16, 1), (11, 42), (38, 14), (23, 36), (41, 18), (22, 38), (13, 12), (18, 23), (12, 10), (37, 8), (11, 35), (21, 22), (23, 26), (0, 46), (25, 33), (2, 23), (13, 32), (35, 31), (3, 24), (43, 39), (11, 30), (39, 41), (32, 26), (22, 34), (23, 2), (34, 29), (43, 1), (3, 41), (15, 46), (15, 31), (7, 33), (8, 6), (13, 28), (3, 11), (29, 9), (3, 35), (16, 31), (5, 20), (17, 23), (4, 21), (29, 39), (38, 42), (11, 17), (18, 7), (31, 21), (32, 44), (2, 32), (19, 4), (33, 9), (17, 10), (12, 34), (26, 30), (44, 13), (27, 19), (39, 44), (43, 36), (6, 9), (28, 11), (28, 0), (20, 44), (7, 23), (18, 36), (17, 5), (16, 8), (5, 21), (15, 18), (11, 18), (4, 37), (23, 43), (2, 21), (28, 32), (26, 4), (16, 3), (18, 34), (18, 21), (21, 26), (1, 7), (34, 33), (26, 44), (8, 36), (11, 43), (9, 35), (28, 19), (22, 12), (11, 15), (44, 4), (28, 1), (36, 2), (6, 19), (18, 0), (40, 47), (39, 15), (2, 13), (18, 6), (17, 27), (10, 33), (13, 45), (3, 18), (29, 38), (43, 11), (12, 9), (22, 20), (40, 38), (44, 11), (27, 17), (16, 2), (31, 17), (9, 45), (28, 26), (17, 12), (32, 37), (36, 3), (13, 43), (27, 6), (31, 0), (27, 16), (24, 38), (33, 28), (43, 31), (25, 9), (36, 29), (40, 16), (5, 11), (32, 12), (4, 27), (33, 43), (21, 24), (3, 23), (10, 19), (7, 18), (30, 33), (38, 8), (7, 35), (27, 28), (7, 44), (6, 14), (19, 13), (23, 5), (29, 21), (7, 20), (39, 19), (43, 23), (43, 4), (26, 27), (39, 4), (18, 40), (42, 14), (13, 31), (0, 25), (20, 14), (24, 25), (13, 37), (22, 9), (21, 32), (0, 15), (28, 7), (25, 26), (2, 17), (10, 37), (6, 30), (9, 20), (6, 8), (8, 17), (26, 43), (15, 36), (36, 13), (29, 37), (13, 21), (30, 13), (29, 15), (34, 34), (3, 26), (24, 34), (44, 28), (39, 27), (33, 45), (21, 3), (41, 47), (1, 40), (3, 47), (33, 31), (10, 9), (21, 28), (4, 23), (32, 14), (19, 20), (40, 33), (32, 24), (22, 41), (1, 9), (30, 46), (5, 24), (30, 32), (15, 30), (34, 21), (21, 42), (6, 45), (33, 10), (36, 20), (38, 20), (1, 2), (23, 42), (21, 10), (6, 27), (42, 33), (30, 5), (11, 1), (6, 0), (36, 9), (8, 28), (44, 21), (20, 26), (28, 18), (42, 12), (35, 35), (21, 4), (38, 47), (3, 2), (1, 41), (19, 19), (2, 40), (16, 4), (42, 19), (24, 13), (36, 4), (40, 27), (37, 4), (20, 41), (27, 27), (35, 46), (17, 39), (28, 41), (12, 11), (15, 11), (30, 16), (22, 1), (11, 32), (40, 14), (5, 47), (27, 22), (15, 35), (30, 15), (28, 28), (8, 39), (4, 28), (19, 31), (24, 45), (18, 46), (13, 23), (39, 30), (29, 11), (24, 36), (0, 12), (33, 24), (16, 20), (9, 24), (6, 7), (42, 29), (34, 6), (8, 7), (7, 30), (13, 22), (25, 11), (44, 41), (20, 9), (12, 23), (25, 17), (17, 42), (21, 38), (29, 31), (20, 42), (6, 1), (23, 38), (5, 23), (19, 15), (30, 27), (5, 16), (20, 2), (12, 22), (32, 15), (0, 2), (23, 9), (1, 3), (26, 22), (30, 28), (34, 26), (17, 38), (1, 23), (1, 10), (14, 37), (2, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (46, 29), (20, 40), (3, 21), (45, 41), (18, 4), (24, 40), (34, 6), (46, 11), (3, 34), (36, 36), (15, 8), (34, 23), (28, 21), (18, 12), (26, 10), (10, 43), (24, 28), (36, 7), (9, 7), (20, 18), (1, 19), (25, 15), (46, 39), (13, 9), (34, 17), (8, 15), (13, 20), (21, 25), (30, 19), (45, 39), (22, 41), (6, 25), (8, 41), (32, 37), (20, 4), (27, 1), (35, 33), (16, 3), (46, 3), (15, 23), (6, 5), (28, 26), (1, 34), (17, 5), (29, 29), (1, 8), (4, 15), (5, 44), (21, 0), (30, 22), (9, 35), (0, 28), (12, 18), (44, 1), (37, 23), (5, 34), (9, 5), (41, 7), (10, 19), (34, 14), (11, 18), (47, 3), (2, 0), (27, 31), (35, 15), (8, 36), (1, 11), (20, 32), (14, 4), (4, 2), (42, 45), (18, 8), (39, 33), (22, 12), (25, 21), (46, 17), (32, 41), (10, 26), (15, 15), (38, 14), (39, 45), (20, 27), (26, 36), (34, 44), (34, 35), (11, 7), (39, 9), (23, 14), (40, 23), (20, 3), (10, 36), (1, 42), (6, 26), (10, 10), (4, 25), (15, 45), (26, 16), (16, 7), (45, 35), (27, 13), (25, 18), (13, 5), (1, 31), (14, 16), (24, 33), (1, 18), (35, 35), (47, 41), (22, 37), (7, 20), (11, 44), (35, 12), (8, 24), (2, 15), (3, 38), (42, 5), (15, 10), (41, 23), (17, 18), (2, 35), (30, 21), (33, 27), (48, 17), (6, 17), (2, 43), (21, 7), (33, 25), (6, 33), (37, 14), (23, 27), (30, 13), (13, 13), (13, 29), (22, 19), (43, 31), (45, 40), (7, 2), (8, 12), (35, 36), (31, 15), (37, 10), (34, 1), (26, 3), (30, 31), (37, 36), (6, 44), (16, 20), (30, 35), (44, 32), (12, 16), (24, 21), (18, 6), (12, 1), (44, 21), (14, 24), (27, 45), (4, 11), (44, 44), (43, 33), (10, 41), (26, 31), (46, 23), (32, 7), (11, 10), (25, 40), (36, 45), (6, 38), (33, 45), (28, 16), (22, 24), (26, 32), (16, 24), (29, 23), (12, 13), (0, 7), (36, 33), (5, 33), (18, 23), (13, 36), (46, 1), (6, 12), (0, 26), (6, 3), (41, 3), (30, 26), (43, 20), (38, 29), (21, 5), (27, 12), (13, 6), (15, 17), (16, 13), (23, 39), (24, 35), (4, 4), (3, 8), (21, 24), (17, 41), (44, 16), (29, 2), (18, 43), (36, 44), (0, 39), (39, 31), (29, 8), (15, 27), (39, 10), (40, 11), (33, 18), (16, 4), (26, 40), (15, 35), (42, 22), (9, 23), (48, 1), (41, 42), (31, 25), (35, 4), (47, 11), (19, 13), (44, 9), (30, 44), (0, 45), (10, 40), (31, 34), (19, 30), (12, 5), (21, 4), (2, 19), (41, 29), (19, 23), (33, 21), (10, 31), (48, 2), (47, 36), (5, 9), (15, 24), (1, 1), (21, 15), (26, 11), (28, 12), (2, 21), (18, 35), (19, 1), (7, 1), (14, 1), (48, 18), (6, 43), (45, 23), (33, 4), (30, 45), (22, 42), (31, 41), (20, 28), (5, 7), (32, 19), (16, 11), (20, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 35), (23, 27), (9, 30), (42, 35), (45, 11), (46, 1), (27, 12), (18, 44), (30, 13), (32, 18), (12, 32), (27, 5), (45, 39), (44, 11), (4, 14), (19, 8), (5, 13), (25, 22), (29, 12), (25, 41), (37, 47), (0, 20), (34, 24), (12, 2), (0, 36), (41, 46), (28, 27), (37, 6), (43, 17), (23, 12), (4, 21), (40, 29), (20, 8), (28, 18), (9, 38), (15, 15), (23, 17), (17, 17), (9, 7), (26, 42), (25, 21), (2, 7), (12, 3), (19, 35), (27, 43), (6, 8), (32, 48), (28, 24), (16, 2), (4, 8), (9, 48), (22, 20), (36, 20), (34, 46), (7, 46), (14, 37), (31, 29), (31, 18), (33, 40), (27, 15), (7, 5), (5, 1), (10, 44), (38, 33), (30, 33), (45, 20), (22, 36), (16, 26), (34, 2), (2, 18), (11, 31), (7, 12), (43, 26), (34, 30), (10, 25), (8, 28), (2, 30), (44, 38), (5, 41), (36, 24), (39, 32), (35, 43), (41, 6), (15, 4), (41, 15), (34, 47), (39, 21), (33, 0), (45, 42), (42, 45), (21, 33), (13, 37), (42, 18), (12, 7), (6, 23), (14, 42), (20, 42), (27, 21), (5, 16), (12, 9), (35, 17), (18, 3), (29, 41), (24, 47), (23, 13), (7, 7), (10, 32), (33, 30), (34, 10), (37, 21), (7, 27), (38, 29), (23, 30), (22, 38), (19, 19), (31, 26), (33, 36), (33, 39), (38, 7), (8, 27), (21, 42), (3, 2), (44, 42), (24, 12), (35, 35), (20, 23), (0, 19), (39, 15), (38, 25), (17, 28), (20, 36), (2, 5), (32, 36), (42, 31), (41, 34), (14, 19), (26, 29), (17, 40), (38, 3), (23, 34), (11, 46), (9, 4), (41, 0), (15, 45), (44, 34), (39, 1), (16, 19), (43, 18), (10, 19), (8, 3), (11, 5), (9, 5), (24, 2), (12, 21), (18, 43), (46, 26), (17, 35), (12, 24), (24, 29), (8, 45), (30, 12), (8, 47), (43, 9), (9, 29), (2, 23), (20, 18), (2, 32), (15, 27), (10, 21), (40, 14), (34, 37), (5, 4), (41, 14), (31, 33), (44, 48), (24, 19), (27, 44), (15, 40), (34, 28), (34, 31), (8, 9), (12, 36), (41, 12), (33, 28), (36, 3), (45, 46), (29, 9), (14, 46), (28, 47), (40, 5), (25, 5), (22, 9), (27, 39), (26, 27), (18, 27), (16, 38), (34, 19), (36, 13), (1, 5), (34, 45), (23, 2), (2, 43), (20, 15), (14, 14), (42, 4), (36, 37), (2, 20), (35, 21), (38, 41), (12, 14), (1, 14), (26, 13), (5, 2), (32, 28), (11, 4), (24, 17), (37, 22), (26, 21), (32, 14), (32, 35), (31, 41), (14, 21), (32, 47), (30, 40), (19, 26), (36, 9), (37, 34), (17, 7), (25, 19), (6, 22), (12, 5), (42, 46), (42, 48), (1, 47), (28, 21), (21, 15), (39, 30), (31, 31), (31, 43), (39, 47), (36, 25), (44, 36), (4, 15), (30, 28), (7, 31), (0, 42), (21, 46), (25, 39), (8, 42), (31, 21), (15, 25), (33, 3), (0, 44), (6, 0), (8, 46), (26, 7), (23, 41), (2, 29), (41, 9), (18, 29), (14, 41), (19, 33), (26, 22), (6, 47)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 43x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 4), (15, 25), (30, 38), (9, 32), (29, 34), (31, 26), (0, 29), (19, 4), (32, 29), (6, 8), (25, 21), (2, 41), (13, 33), (34, 42), (37, 7), (24, 30), (18, 25), (0, 14), (42, 1), (40, 39), (6, 19), (34, 10), (40, 14), (24, 1), (18, 28), (35, 38), (8, 9), (29, 14), (3, 18), (12, 12), (0, 24), (20, 30), (31, 1), (38, 22), (6, 42), (3, 27), (34, 35), (7, 21), (17, 0), (31, 33), (7, 1), (17, 10), (11, 3), (22, 26), (14, 19), (7, 26), (2, 17), (25, 18), (5, 24), (2, 22), (28, 30), (34, 22), (25, 32), (36, 41), (40, 5), (11, 28), (23, 33), (12, 16), (32, 13), (14, 16), (34, 39), (2, 24), (33, 18), (3, 42), (11, 21), (21, 38), (36, 14), (22, 23), (23, 29), (15, 32), (10, 40), (32, 22), (28, 14), (8, 6), (34, 19), (41, 39), (36, 31), (19, 36), (13, 37), (39, 6), (17, 42), (17, 32), (38, 39), (40, 25), (4, 41), (35, 33), (23, 9), (9, 27), (12, 32), (29, 30), (2, 40), (10, 6), (2, 38), (14, 21), (41, 4), (12, 24), (27, 3), (20, 2), (16, 13), (42, 26), (38, 29), (11, 38), (42, 32), (7, 36), (14, 14), (37, 34), (4, 1), (29, 41), (35, 35), (23, 10), (9, 10), (12, 15), (32, 2), (40, 24), (32, 7), (28, 31), (17, 27), (18, 16), (38, 28), (24, 25), (11, 16), (2, 39), (37, 28), (27, 36), (36, 30), (12, 0), (25, 28), (42, 14), (40, 10), (38, 35), (8, 32), (28, 5), (0, 4), (15, 20), (42, 2), (14, 10), (24, 37), (19, 1), (0, 21), (2, 33), (7, 29), (42, 17), (8, 1), (3, 8), (32, 40), (17, 4), (27, 35), (1, 35), (5, 25), (40, 33), (38, 7), (3, 5), (36, 9), (5, 33), (13, 39), (30, 7), (12, 9), (8, 21), (16, 32), (31, 24), (16, 19), (42, 28), (9, 22), (26, 40), (21, 34), (28, 42), (18, 10), (40, 16), (31, 36), (17, 41), (3, 36), (29, 23), (39, 38), (8, 12), (18, 39), (4, 18), (30, 25), (29, 9), (26, 17), (8, 37), (1, 41), (33, 41), (27, 21), (9, 23), (5, 26), (33, 19), (10, 37), (16, 8), (3, 26), (22, 17), (4, 37), (13, 7), (33, 0), (37, 26), (27, 29), (15, 31), (6, 35), (23, 17), (35, 27), (32, 1), (1, 16), (11, 8), (20, 27), (10, 15), (10, 32), (20, 39), (9, 36), (42, 31), (25, 27), (19, 18), (17, 17), (18, 36), (32, 38), (9, 3), (15, 3), (0, 33), (0, 34), (2, 2), (42, 9), (35, 15), (22, 13), (40, 4), (1, 18), (42, 20), (5, 34), (1, 28), (35, 4), (4, 16), (11, 30), (33, 35), (23, 20), (25, 7), (19, 33), (16, 18), (36, 2), (32, 26), (14, 15), (29, 38), (19, 40), (15, 36), (37, 6), (2, 4), (6, 21), (5, 13), (20, 23), (34, 9), (12, 29), (3, 20), (28, 3), (13, 11), (17, 29), (21, 12), (13, 29), (36, 26), (31, 17), (22, 1), (41, 40), (4, 17), (32, 20), (33, 28), (8, 31), (7, 19), (26, 25), (31, 6), (41, 37), (32, 41), (22, 12), (12, 25), (14, 17), (23, 5), (23, 15), (33, 5), (4, 26), (6, 38), (30, 1), (21, 42)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 46x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (22, 29), (35, 29), (25, 25), (22, 41), (13, 8), (0, 23), (8, 20), (23, 33), (7, 14), (35, 15), (35, 5), (43, 28), (4, 37), (22, 18), (30, 15), (19, 0), (31, 2), (25, 36), (30, 31), (37, 47), (16, 36), (37, 38), (42, 9), (23, 2), (10, 39), (45, 2), (15, 7), (40, 46), (28, 11), (39, 33), (14, 37), (35, 7), (43, 37), (14, 10), (32, 47), (14, 2), (35, 33), (23, 21), (28, 15), (16, 13), (19, 14), (3, 2), (25, 18), (33, 14), (43, 36), (28, 39), (31, 4), (0, 2), (16, 40), (10, 12), (6, 40), (3, 10), (43, 34), (43, 4), (9, 44), (25, 30), (44, 23), (29, 16), (37, 39), (32, 17), (19, 13), (4, 7), (31, 27), (44, 20), (11, 29), (39, 4), (12, 32), (21, 10), (20, 31), (40, 30), (13, 7), (19, 18), (39, 0), (32, 43), (35, 6), (15, 47), (5, 47), (6, 1), (22, 32), (38, 29), (38, 24), (22, 34), (42, 6), (32, 38), (17, 28), (19, 42), (4, 5), (6, 17), (39, 42), (9, 41), (45, 23), (25, 41), (26, 6), (19, 37), (26, 9), (27, 47), (20, 44), (11, 31), (4, 30), (21, 46), (34, 22), (33, 7), (12, 47), (31, 33), (33, 47), (11, 38), (10, 34), (7, 17), (31, 31), (9, 29), (19, 9), (26, 4), (34, 27), (14, 0), (27, 0), (45, 44), (3, 12), (0, 41), (41, 10), (42, 11), (43, 18), (11, 34), (26, 41), (4, 8), (42, 41), (21, 48), (7, 11), (32, 11), (21, 2), (35, 45), (29, 21), (31, 46), (4, 4), (44, 32), (23, 6), (5, 12), (9, 10), (21, 14), (22, 2), (14, 11), (5, 46), (33, 30), (33, 34), (9, 37), (28, 46), (41, 5), (10, 17), (11, 11), (10, 8), (15, 30), (31, 26), (11, 46), (15, 39), (11, 47), (6, 10), (6, 0), (38, 12), (30, 21), (21, 37), (24, 0), (22, 12), (21, 28), (19, 11), (41, 31), (5, 35), (34, 12), (5, 5), (45, 43), (7, 25), (14, 17), (18, 46), (28, 38), (16, 22), (17, 4), (1, 20), (22, 25), (33, 44), (4, 41), (10, 47), (4, 23), (15, 40), (5, 10), (24, 23), (0, 16), (4, 48), (29, 0), (43, 35), (16, 1), (5, 4), (6, 11), (22, 37), (42, 1), (13, 16), (39, 16), (40, 24), (42, 36), (7, 26), (36, 22), (3, 19), (25, 2), (6, 8), (34, 1), (12, 11), (28, 44), (22, 8), (26, 10), (41, 3), (34, 45), (38, 27), (1, 3), (42, 15), (33, 1), (35, 22), (2, 26), (7, 24), (34, 19), (37, 2), (36, 4), (42, 8), (45, 41), (31, 8), (42, 29), (23, 24), (33, 22), (40, 47), (30, 48), (17, 6), (39, 28), (9, 6), (27, 26), (37, 19), (34, 34), (0, 3), (10, 16), (10, 38), (12, 0), (21, 43), (9, 14), (25, 45), (42, 28), (0, 8), (20, 42), (27, 20), (11, 21), (45, 40), (8, 36), (23, 7), (42, 38), (25, 29), (21, 31), (34, 6), (18, 14), (37, 16), (16, 32), (26, 44), (29, 2), (39, 24), (45, 42), (12, 17), (13, 36), (1, 2), (37, 14), (35, 26), (19, 16), (23, 19), (15, 33), (23, 47), (36, 26), (42, 45), (2, 7), (19, 36), (18, 41), (25, 23), (18, 48), (21, 22), (26, 7), (30, 3), (35, 12), (29, 38), (43, 8), (5, 9), (21, 8), (26, 42), (9, 43), (36, 45), (31, 28), (1, 44), (44, 5), (26, 47), (9, 15), (39, 37), (8, 6), (36, 37), (26, 17), (1, 42), (12, 10), (29, 28), (19, 22), (11, 6), (38, 14), (9, 1), (29, 3), (40, 34), (21, 5), (9, 0), (37, 41), (0, 13), (27, 45), (33, 10), (20, 43), (38, 0), (7, 31), (3, 37), (31, 10), (26, 22), (6, 15), (35, 36), (18, 22), (10, 31), (33, 8), (16, 2), (38, 18), (2, 46), (33, 27), (45, 17), (25, 3), (2, 32), (45, 7), (44, 26), (13, 39), (18, 37), (7, 44), (31, 36), (36, 46), (20, 13), (40, 6), (2, 21), (5, 23), (27, 43), (25, 11), (12, 19), (38, 47), (9, 3), (0, 36), (11, 48), (9, 9), (24, 47), (39, 38), (45, 28), (36, 18), (13, 28), (28, 21), (5, 14), (5, 29), (7, 33), (2, 42), (34, 48), (18, 38), (34, 17), (27, 42), (39, 34), (41, 12), (45, 46), (40, 32), (19, 33), (42, 30), (17, 34), (25, 35), (24, 1), (21, 44), (25, 38), (40, 1), (9, 27), (7, 39), (35, 4), (37, 10), (45, 47), (40, 14), (25, 16), (29, 31), (8, 5), (5, 8), (34, 21), (45, 24), (9, 25), (10, 13), (21, 15), (14, 23), (25, 6), (11, 25), (22, 19), (19, 43), (17, 11), (16, 37), (41, 13), (23, 23), (3, 33), (33, 26), (3, 38), (20, 8), (35, 30), (15, 34), (40, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 26), (32, 39), (28, 9), (36, 2), (9, 41), (29, 30), (15, 13), (3, 12), (0, 22), (31, 21), (13, 36), (7, 12), (24, 22), (25, 36), (7, 23), (15, 17), (9, 7), (12, 3), (38, 33), (0, 17), (35, 42), (12, 21), (32, 26), (22, 10), (38, 31), (18, 39), (20, 2), (25, 19), (5, 27), (32, 5), (4, 29), (1, 30), (0, 40), (34, 21), (33, 6), (21, 10), (30, 3), (36, 43), (5, 28), (39, 1), (27, 7), (3, 42), (13, 5), (10, 27), (30, 16), (12, 18), (15, 10), (18, 15), (36, 42), (36, 28), (30, 28), (14, 15), (11, 13), (29, 20), (6, 31), (3, 29), (7, 40), (31, 5), (15, 39), (34, 13), (21, 9), (11, 27), (16, 28), (12, 28), (32, 16), (23, 26), (14, 6), (27, 17), (11, 2), (18, 36), (3, 36), (2, 0), (8, 30), (36, 15), (22, 38), (23, 25), (28, 31), (20, 15), (9, 25), (37, 39), (28, 44), (5, 21), (22, 13), (32, 37), (27, 24), (9, 28), (11, 9), (15, 42), (25, 24), (28, 10), (28, 11), (13, 25), (8, 17), (16, 16), (12, 8), (34, 40), (35, 16), (11, 44), (34, 23), (8, 32), (21, 35), (28, 3), (39, 41), (0, 41), (1, 2), (7, 34), (8, 3), (23, 14), (5, 5), (22, 18), (21, 25), (0, 10), (9, 6), (19, 41), (39, 21), (36, 13), (20, 10), (21, 17), (4, 31), (24, 31), (7, 43), (11, 16), (14, 21), (36, 4), (28, 7), (24, 26), (11, 39), (31, 18), (12, 33), (6, 13), (15, 44), (9, 44), (41, 39), (39, 37), (34, 44), (31, 14), (40, 31), (35, 34), (41, 23), (26, 6), (40, 34), (38, 18), (10, 7), (21, 8), (19, 29), (34, 20), (35, 12), (29, 13), (28, 27), (26, 14), (19, 32), (39, 30), (33, 2), (3, 43), (19, 21), (15, 20), (13, 14), (10, 4), (30, 43), (14, 24), (22, 37), (12, 41), (40, 26), (34, 10), (29, 9), (27, 9), (25, 20), (2, 6), (33, 9), (5, 10), (38, 42), (4, 19), (18, 2), (2, 42), (4, 39), (34, 29), (23, 6), (33, 11), (38, 23), (28, 25), (10, 2), (22, 44), (14, 2), (11, 1), (33, 33), (11, 6), (17, 21), (19, 4), (1, 42), (41, 9), (7, 2), (33, 5), (35, 30), (32, 8), (40, 25), (36, 22), (35, 29), (23, 34), (31, 4), (10, 9), (2, 35), (24, 15), (33, 4), (10, 16), (7, 42), (13, 27), (31, 33), (21, 20), (10, 32), (30, 13), (20, 18), (25, 13), (37, 5), (10, 3), (38, 13), (39, 17), (11, 36), (9, 32), (38, 28), (29, 3), (24, 41), (23, 7), (17, 4), (39, 6), (24, 13), (32, 6), (2, 14), (1, 31), (14, 5), (22, 2), (13, 6), (1, 1), (27, 8), (18, 38), (40, 44), (26, 30), (31, 42), (34, 16), (1, 43), (18, 24), (38, 4), (20, 24), (21, 37), (32, 36), (31, 13), (1, 21), (23, 11), (0, 23), (25, 33), (13, 22), (19, 7), (6, 25), (4, 9), (41, 11), (1, 28), (40, 17), (13, 12), (39, 20), (26, 29), (8, 23), (0, 5), (6, 44), (19, 22), (26, 36), (4, 0), (21, 19), (39, 5), (13, 28), (16, 4), (28, 33), (35, 11), (26, 28), (13, 41), (34, 17), (25, 26), (29, 5), (12, 29), (41, 18), (38, 27), (25, 38), (9, 29), (15, 27), (18, 30), (1, 0), (22, 42), (7, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 49x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 40), (18, 22), (10, 30), (29, 28), (3, 7), (42, 23), (4, 8), (48, 19), (13, 38), (22, 38), (43, 12), (9, 0), (32, 9), (10, 38), (9, 4), (22, 1), (33, 42), (30, 34), (34, 12), (6, 23), (40, 37), (20, 20), (46, 21), (46, 37), (28, 4), (22, 43), (4, 37), (2, 20), (48, 15), (42, 8), (10, 6), (46, 15), (12, 6), (3, 2), (6, 17), (36, 30), (10, 19), (0, 32), (18, 42), (38, 26), (4, 35), (11, 5), (10, 41), (7, 20), (2, 36), (16, 43), (7, 44), (2, 30), (41, 18), (8, 17), (43, 3), (29, 0), (39, 30), (12, 43), (28, 12), (10, 33), (17, 37), (21, 41), (44, 11), (5, 20), (18, 37), (33, 14), (22, 14), (26, 27), (35, 23), (0, 9), (31, 36), (47, 40), (16, 21), (30, 0), (31, 3), (19, 24), (47, 13), (43, 34), (44, 29), (39, 36), (3, 26), (37, 37), (26, 20), (23, 42), (12, 38), (18, 26), (20, 33), (4, 39), (44, 40), (18, 14), (32, 27), (7, 2), (11, 39), (2, 44), (17, 23), (16, 37), (0, 41), (18, 1), (22, 35), (44, 37), (16, 36), (17, 19), (1, 19), (41, 12), (26, 26), (17, 13), (12, 40), (18, 35), (45, 40), (6, 20), (38, 10), (25, 10), (46, 27), (4, 14), (31, 15), (43, 29), (15, 2), (4, 6), (15, 42), (41, 0), (17, 30), (32, 22), (43, 22), (11, 15), (37, 24), (6, 7), (18, 25), (12, 26), (26, 16), (28, 23), (30, 36), (17, 43), (25, 4), (20, 32), (21, 32), (38, 5), (47, 35), (33, 38), (0, 1), (43, 10), (1, 2), (14, 3), (47, 29), (12, 25), (1, 23), (47, 15), (30, 32), (34, 3), (44, 35), (0, 43), (40, 31), (44, 42), (13, 37), (8, 29), (46, 19), (23, 31), (12, 3), (42, 20), (16, 4), (43, 20), (48, 5), (28, 43), (2, 43), (30, 9), (21, 37), (0, 14), (37, 39), (31, 13), (7, 28), (44, 44), (16, 32), (7, 9), (4, 1), (31, 2), (22, 6), (41, 2), (28, 10), (25, 25), (19, 40), (46, 22), (19, 30), (37, 13), (22, 34), (47, 43), (35, 15), (46, 28), (2, 42), (36, 5), (34, 33), (33, 7), (13, 6), (44, 43), (48, 25), (28, 34), (38, 23), (38, 42), (40, 27), (18, 11), (13, 15), (37, 19), (9, 25), (41, 21), (32, 39), (38, 11), (48, 0), (25, 1), (13, 36), (14, 32), (46, 17), (41, 25), (27, 11), (30, 29), (9, 37), (45, 44), (12, 18), (4, 3), (24, 26), (33, 17), (2, 24), (7, 5), (31, 30), (33, 20), (9, 35), (36, 19), (6, 12), (30, 23), (29, 1), (30, 3), (48, 38), (24, 12), (22, 42), (12, 24), (48, 34), (23, 21), (31, 40), (42, 40), (14, 10), (32, 30), (47, 3), (6, 19), (44, 31), (24, 14), (38, 37), (35, 19), (0, 27), (26, 19), (13, 21), (39, 17), (40, 12), (8, 18), (47, 39), (31, 27), (6, 34), (37, 25), (16, 15), (22, 7), (42, 18), (45, 10), (18, 23), (23, 23), (42, 33), (27, 26), (11, 4), (12, 13), (44, 6), (42, 2), (47, 24), (46, 26), (7, 38), (23, 16), (16, 19), (2, 34), (29, 39), (14, 7), (6, 9), (25, 33), (5, 43), (34, 18), (31, 28), (38, 27), (36, 22), (19, 20), (25, 29), (32, 25), (4, 16), (19, 4), (18, 20), (35, 26), (41, 29), (17, 38), (21, 38), (24, 29), (26, 13), (1, 7), (13, 42), (36, 9), (14, 41), (0, 33), (4, 41), (38, 18), (36, 7), (39, 18), (34, 37), (41, 27), (30, 39), (36, 35), (45, 13), (38, 6), (10, 42), (28, 22), (31, 26), (24, 35), (28, 30), (9, 32), (31, 25), (43, 2), (32, 1), (8, 24), (43, 6), (47, 34), (39, 33), (6, 0), (36, 6), (42, 41), (3, 23), (7, 19), (24, 9), (31, 44), (10, 44), (43, 40), (45, 38), (21, 7), (15, 13), (19, 1), (36, 39), (4, 12), (26, 15), (43, 16), (20, 5), (10, 21), (37, 10), (38, 9), (48, 28), (9, 18), (29, 38), (16, 13), (29, 16), (16, 33), (11, 18), (16, 26), (15, 5), (40, 14), (4, 32), (8, 43), (44, 18), (24, 0), (45, 2), (36, 10), (25, 28), (27, 6), (8, 37), (31, 11), (1, 10), (29, 2), (30, 35), (1, 16), (44, 32), (41, 20), (29, 30), (32, 20), (21, 9), (12, 20), (20, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 41), (48, 41), (14, 40), (45, 20), (1, 2), (39, 36), (16, 33), (44, 12), (13, 25), (27, 12), (45, 35), (23, 6), (42, 22), (40, 15), (22, 21), (1, 13), (32, 8), (38, 22), (40, 3), (37, 9), (3, 0), (11, 13), (8, 37), (24, 30), (9, 12), (5, 38), (10, 22), (13, 19), (16, 28), (41, 33), (16, 27), (27, 35), (12, 12), (8, 21), (44, 26), (18, 14), (43, 36), (22, 35), (26, 7), (26, 26), (21, 30), (33, 23), (11, 12), (17, 10), (16, 19), (40, 21), (45, 4), (2, 11), (44, 3), (31, 2), (11, 14), (15, 4), (28, 12), (5, 36), (33, 19), (48, 26), (9, 34), (11, 16), (8, 22), (6, 0), (0, 15), (8, 19), (31, 31), (28, 8), (30, 42), (0, 4), (16, 2), (3, 30), (20, 7), (43, 24), (7, 15), (42, 37), (39, 31), (20, 40), (27, 20), (47, 3), (19, 7), (1, 33), (6, 27), (23, 31), (41, 5), (9, 3), (28, 34), (28, 41), (40, 37), (8, 15), (26, 6), (17, 42), (40, 14), (10, 42), (46, 36), (42, 4), (15, 38), (8, 8), (44, 40), (31, 32), (15, 3), (47, 18), (35, 10), (3, 13), (47, 0), (34, 1), (4, 22), (2, 36), (34, 26), (21, 39), (14, 7), (13, 38), (33, 22), (38, 42), (32, 25), (25, 32), (29, 9), (6, 12), (48, 15), (47, 1), (35, 24), (41, 38), (36, 41), (19, 36), (38, 33), (3, 28), (30, 23), (22, 0), (14, 17), (31, 21), (0, 25), (32, 41), (25, 8), (14, 19), (32, 29), (28, 28), (4, 9), (27, 32), (48, 31), (2, 34), (7, 38), (14, 25), (15, 41), (11, 20), (43, 34), (14, 14), (44, 21), (27, 19), (18, 39), (2, 28), (34, 3), (6, 17), (15, 31), (25, 24), (10, 23), (25, 2), (19, 26), (29, 27), (11, 25), (32, 36), (18, 16), (45, 39), (14, 20), (21, 28), (10, 2), (34, 22), (0, 31), (20, 24), (46, 10), (38, 35), (4, 17), (24, 4), (0, 41), (45, 40), (26, 23), (28, 24), (19, 14), (25, 30), (22, 6), (14, 5), (48, 3), (46, 32), (35, 5), (26, 12), (40, 16), (13, 21), (13, 30), (44, 5), (34, 6), (18, 31), (37, 13), (13, 37), (36, 37), (16, 24), (47, 30), (6, 38), (38, 29), (38, 15), (22, 42), (11, 15), (30, 33), (34, 0), (30, 24), (13, 2), (16, 30), (10, 34), (38, 8), (8, 26), (33, 4), (21, 11), (29, 29), (31, 11), (32, 24), (12, 39), (38, 40), (45, 28), (35, 11), (32, 9), (44, 20), (40, 29), (30, 10), (12, 21), (26, 9), (39, 33), (33, 33), (7, 32), (7, 23), (24, 22), (17, 28), (10, 28), (26, 10), (4, 14), (39, 32), (25, 7), (26, 33), (1, 31), (35, 37), (44, 42), (11, 29), (36, 11), (4, 15), (45, 13), (22, 8), (48, 33), (43, 42), (31, 39), (20, 34), (47, 12), (23, 38), (14, 24), (32, 13), (34, 37), (40, 25), (39, 19), (38, 17), (32, 16), (33, 35), (18, 8), (1, 35), (27, 17), (38, 1), (14, 27), (36, 30), (42, 2), (5, 24), (4, 33), (21, 0), (22, 31), (7, 5), (29, 30), (46, 21), (6, 29), (42, 17), (22, 23), (4, 29), (9, 22), (11, 4), (7, 2), (45, 25), (46, 39), (16, 25), (34, 25), (22, 10), (25, 27), (42, 15), (1, 24), (32, 20), (7, 21), (41, 1), (47, 16), (19, 25), (42, 11), (10, 25), (17, 41), (0, 12), (32, 5), (17, 24), (17, 17), (16, 21), (20, 8), (38, 20), (5, 7), (29, 42), (33, 9), (20, 4), (34, 39), (22, 29), (17, 23), (5, 32), (35, 25), (5, 22), (40, 17), (47, 31), (48, 8), (45, 12), (8, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 3), (17, 0), (23, 20), (46, 13), (36, 8), (6, 21), (37, 42), (11, 30), (31, 13), (6, 25), (8, 22), (26, 38), (28, 35), (9, 24), (46, 5), (18, 27), (11, 31), (42, 15), (45, 16), (5, 21), (30, 13), (30, 28), (16, 30), (24, 11), (37, 32), (6, 4), (43, 13), (22, 7), (45, 39), (46, 2), (46, 23), (14, 11), (44, 25), (21, 15), (14, 12), (31, 11), (35, 24), (40, 37), (3, 40), (23, 2), (3, 41), (33, 20), (38, 31), (7, 12), (13, 30), (10, 23), (22, 40), (19, 24), (38, 40), (10, 26), (1, 19), (3, 0), (20, 42), (30, 32), (13, 18), (43, 15), (45, 37), (21, 16), (16, 1), (12, 17), (24, 32), (17, 22), (26, 25), (47, 22), (3, 27), (8, 38), (6, 38), (8, 6), (37, 35), (45, 22), (41, 26), (11, 28), (36, 28), (28, 30), (12, 30), (35, 32), (45, 2), (0, 39), (3, 15), (26, 6), (7, 34), (33, 1), (3, 6), (44, 24), (27, 2), (9, 9), (24, 0), (26, 14), (33, 40), (2, 1), (20, 32), (8, 39), (1, 5), (20, 18), (46, 34), (22, 3), (40, 42), (7, 42), (0, 8), (20, 38), (43, 4), (19, 16), (3, 26), (36, 5), (4, 21), (2, 20), (46, 28), (27, 17), (32, 17), (32, 26), (36, 26), (18, 17), (46, 38), (28, 22), (38, 22), (21, 7), (29, 21), (48, 11), (26, 16), (2, 16), (35, 2), (37, 9), (38, 34), (42, 19), (25, 4), (25, 39), (42, 31), (36, 21), (4, 27), (40, 24), (35, 0), (12, 4), (21, 26), (14, 19), (35, 11), (41, 4), (28, 13), (42, 12), (25, 25), (21, 5), (43, 31), (28, 19), (9, 34), (6, 28), (2, 17), (32, 28), (47, 39), (46, 15), (47, 10), (11, 32), (6, 27), (41, 31), (26, 33), (20, 6), (18, 0), (11, 17), (40, 15), (34, 0), (43, 2), (7, 3), (47, 16), (8, 9), (39, 41), (37, 16), (21, 21), (39, 18), (33, 36), (46, 30), (0, 14), (9, 4), (42, 42), (21, 33), (24, 4), (27, 40), (37, 36), (8, 29), (33, 17), (8, 21), (46, 3), (16, 35), (42, 21), (15, 41), (9, 2), (38, 39), (3, 7), (2, 22), (47, 15), (39, 19), (20, 19), (24, 15), (34, 20), (44, 26), (25, 1), (42, 32), (17, 24), (44, 28), (42, 3), (0, 27), (45, 23), (42, 36), (22, 17), (13, 9), (5, 34), (48, 18), (20, 36), (43, 11), (3, 1), (20, 12), (10, 13), (20, 26), (36, 2), (31, 33), (34, 10), (17, 39), (39, 27), (48, 4), (24, 19), (5, 6), (13, 5), (39, 40), (3, 28), (43, 42), (30, 20), (22, 13), (27, 42), (38, 21), (33, 35), (11, 9), (8, 16), (46, 39), (1, 41), (35, 13), (43, 41), (13, 38), (14, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 33), (12, 10), (26, 9), (13, 7), (8, 36), (44, 34), (40, 36), (47, 43), (11, 5), (8, 16), (9, 4), (2, 45), (10, 46), (2, 2), (43, 39), (3, 30), (8, 32), (4, 38), (5, 12), (44, 23), (15, 29), (6, 40), (41, 33), (27, 33), (4, 20), (17, 40), (28, 11), (16, 16), (9, 11), (39, 11), (32, 29), (8, 28), (48, 11), (40, 30), (48, 35), (7, 44), (38, 41), (28, 44), (11, 22), (23, 5), (44, 17), (20, 23), (40, 14), (33, 23), (34, 14), (16, 10), (19, 36), (24, 17), (40, 39), (31, 21), (43, 16), (22, 34), (13, 17), (24, 27), (34, 29), (36, 43), (31, 20), (27, 11), (23, 44), (10, 5), (32, 7), (46, 14), (9, 1), (32, 34), (12, 2), (2, 32), (12, 44), (42, 34), (40, 27), (11, 12), (2, 12), (43, 31), (32, 46), (47, 5), (13, 25), (4, 43), (8, 37), (1, 2), (29, 44), (14, 13), (22, 12), (25, 27), (41, 5), (48, 21), (7, 11), (42, 16), (42, 44), (10, 23), (45, 45), (36, 17), (28, 31), (31, 40), (22, 5), (3, 28), (48, 37), (3, 13), (34, 45), (2, 26), (35, 43), (9, 37), (47, 25), (30, 32), (8, 5), (35, 42), (42, 12), (25, 29), (18, 20), (26, 11), (31, 25), (22, 26), (34, 17), (46, 15), (32, 28), (18, 46), (24, 15), (8, 30), (4, 39), (1, 3), (14, 12), (31, 5), (36, 32), (6, 14), (20, 43), (25, 40), (17, 17), (38, 26), (11, 0), (6, 36), (44, 15), (24, 30), (22, 41), (25, 6), (9, 18), (25, 14), (5, 13), (13, 13), (1, 30), (21, 4), (19, 3), (26, 42), (43, 6), (17, 19), (32, 22), (32, 9), (31, 32), (28, 13), (33, 17), (31, 14), (7, 6), (26, 26), (21, 39), (14, 14), (1, 37), (18, 23), (10, 45), (4, 35), (2, 39), (12, 41), (42, 24), (20, 5), (20, 34), (12, 12), (48, 23), (10, 1), (33, 36), (8, 40), (6, 0), (18, 22), (14, 28), (22, 44), (9, 19), (1, 32), (31, 12), (13, 31), (38, 11), (41, 10), (30, 5), (40, 15), (46, 34), (42, 47), (8, 42), (36, 23), (14, 9), (6, 8), (46, 25), (46, 47), (9, 39), (44, 46), (35, 17), (17, 0), (11, 31), (7, 30), (30, 6), (38, 25), (9, 25), (38, 6), (20, 41), (25, 9), (31, 4), (19, 13), (30, 43), (48, 42), (32, 10), (20, 18), (27, 37), (15, 15), (5, 29), (24, 23), (22, 42), (32, 25), (2, 8), (36, 40), (29, 26), (23, 29), (11, 11), (22, 43), (34, 46), (10, 20), (35, 7), (8, 27), (28, 21), (18, 17), (38, 20), (30, 21), (30, 26), (26, 41), (32, 27), (12, 46), (38, 0), (6, 41), (32, 42), (17, 28), (17, 38), (32, 21), (40, 40), (38, 19), (6, 32), (8, 7), (45, 8), (23, 17), (48, 18), (5, 8), (44, 14), (8, 29), (14, 40), (26, 2), (48, 46), (12, 42), (48, 22), (9, 16), (20, 15), (15, 7), (31, 36), (11, 19), (42, 33), (31, 19), (35, 40), (24, 34), (47, 41), (14, 24), (32, 15), (0, 27), (37, 46), (15, 24), (42, 23), (22, 4), (38, 10), (47, 10), (12, 15), (10, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 19), (2, 23), (41, 16), (9, 12), (19, 26), (39, 33), (3, 16), (15, 30), (20, 31), (42, 29), (30, 24), (31, 4), (7, 21), (8, 13), (6, 39), (3, 18), (21, 39), (40, 19), (42, 23), (2, 6), (1, 32), (20, 27), (32, 32), (14, 26), (4, 3), (7, 26), (36, 11), (34, 23), (6, 4), (42, 10), (8, 30), (7, 30), (31, 25), (40, 21), (24, 3), (30, 29), (2, 30), (41, 30), (7, 3), (18, 24), (1, 2), (5, 11), (27, 10), (40, 1), (25, 22), (22, 2), (40, 32), (27, 32), (30, 9), (17, 20), (5, 19), (33, 17), (27, 16), (39, 25), (20, 12), (32, 18), (33, 2), (6, 33), (29, 27), (21, 21), (31, 33), (5, 6), (9, 29), (9, 17), (29, 20), (28, 19), (37, 33), (26, 14), (15, 22), (16, 22), (1, 1), (21, 34), (25, 13), (1, 38), (25, 4), (25, 32), (33, 34), (25, 17), (1, 9), (2, 39), (40, 10), (18, 10), (29, 18), (24, 34), (33, 22), (2, 36), (26, 6), (23, 29), (28, 16), (36, 37), (26, 3), (10, 12), (10, 36), (20, 11), (30, 0), (21, 15), (12, 31), (30, 8), (19, 18), (29, 4), (22, 21), (4, 25), (41, 26), (17, 22), (32, 0), (4, 16), (24, 11), (23, 4), (15, 9), (4, 14), (29, 25), (12, 10), (37, 28), (14, 15), (6, 14), (1, 30), (26, 17), (35, 31), (35, 36), (17, 31), (16, 6), (32, 5), (11, 15), (43, 28), (36, 13), (27, 30), (14, 3), (28, 34), (28, 39), (3, 31), (3, 5), (40, 36), (38, 27), (11, 14), (29, 39), (16, 17), (0, 15), (25, 14), (3, 7), (18, 2), (20, 3), (4, 12), (0, 1), (7, 8), (0, 17), (7, 28), (19, 29), (5, 12), (28, 18), (26, 23), (12, 21), (13, 27), (30, 12), (18, 18), (26, 27), (17, 16), (2, 21), (16, 23), (34, 10), (8, 5), (27, 11), (38, 38), (20, 25), (27, 37), (40, 24), (14, 27), (38, 6), (8, 32), (39, 39), (25, 27), (35, 16), (17, 4), (1, 6), (32, 24), (13, 1), (27, 35), (41, 10), (0, 23), (41, 3), (3, 1), (38, 25), (1, 34), (7, 38), (43, 7), (11, 23), (23, 30), (37, 11), (14, 37), (37, 2), (28, 5), (0, 26), (0, 34), (26, 15), (30, 27), (9, 36), (5, 16), (28, 6), (4, 21), (43, 33), (19, 34), (42, 37), (1, 29), (15, 12), (29, 12), (8, 25), (1, 35), (35, 11), (32, 28), (15, 27), (34, 21), (18, 14), (25, 38), (10, 34), (26, 4), (38, 23), (26, 9), (39, 36), (20, 18), (3, 17), (1, 17), (1, 23), (28, 10), (12, 30), (8, 27), (14, 9), (20, 32), (30, 26), (35, 26), (40, 11), (0, 24), (15, 37), (6, 17), (18, 7), (11, 10), (6, 2), (30, 21), (32, 37), (37, 13), (0, 5), (18, 13), (29, 9), (33, 18), (1, 11), (15, 13), (41, 24), (43, 4), (7, 39), (26, 8), (28, 8), (29, 0), (32, 25), (23, 17), (0, 30), (17, 2), (19, 4), (24, 23), (43, 13), (22, 4), (37, 5), (23, 36), (2, 19), (38, 11), (38, 18), (37, 14), (18, 34), (39, 9), (38, 15), (29, 1), (19, 17), (3, 37), (7, 18), (22, 39), (36, 26), (33, 32), (3, 28), (18, 25), (20, 36), (10, 19), (21, 26), (35, 5), (40, 3), (41, 11), (13, 4), (13, 32), (28, 3), (27, 13), (8, 39), (19, 31), (41, 27), (18, 21), (4, 9), (0, 18), (24, 22), (9, 27), (5, 9), (33, 8), (11, 35), (13, 36), (13, 6), (9, 25), (6, 10), (13, 13), (40, 26), (28, 28), (32, 2), (18, 35), (35, 4), (37, 19), (38, 19), (19, 1), (5, 0), (30, 33), (42, 19), (8, 37), (22, 26), (20, 23), (15, 7), (29, 32), (40, 39), (33, 20), (31, 21), (1, 13), (14, 36), (22, 25), (5, 22), (42, 9), (36, 4)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 5), (42, 41), (26, 4), (43, 35), (1, 5), (3, 11), (10, 32), (1, 13), (46, 10), (30, 19), (35, 0), (43, 31), (39, 17), (43, 37), (5, 20), (2, 26), (23, 10), (26, 10), (31, 0), (7, 27), (30, 29), (24, 5), (28, 41), (36, 12), (33, 7), (48, 17), (21, 13), (44, 9), (37, 12), (4, 17), (4, 11), (5, 0), (20, 2), (4, 34), (40, 14), (46, 6), (15, 5), (5, 7), (5, 30), (36, 13), (44, 32), (42, 39), (37, 33), (45, 8), (42, 15), (22, 37), (38, 3), (13, 22), (32, 36), (22, 1), (6, 37), (46, 22), (25, 41), (23, 19), (24, 28), (6, 23), (33, 38), (1, 21), (4, 36), (12, 11), (19, 0), (18, 6), (25, 26), (44, 27), (11, 14), (36, 7), (40, 28), (38, 14), (33, 41), (11, 24), (32, 37), (16, 13), (8, 2), (28, 39), (44, 18), (39, 15), (14, 32), (1, 3), (24, 34), (20, 24), (25, 33), (46, 7), (2, 17), (10, 6), (8, 1), (8, 27), (16, 29), (19, 37), (1, 24), (19, 12), (41, 16), (28, 37), (32, 27), (21, 19), (31, 34), (15, 15), (0, 9), (42, 19), (8, 40), (8, 5), (38, 32), (2, 22), (28, 34), (47, 31), (25, 29), (27, 6), (40, 27), (28, 2), (9, 8), (7, 17), (14, 21), (12, 3), (8, 16), (14, 37), (11, 30), (1, 12), (39, 20), (13, 5), (0, 2), (19, 30), (8, 8), (47, 23), (29, 41), (28, 29), (7, 34), (41, 5), (12, 16), (30, 30), (19, 26), (38, 28), (39, 1), (42, 40), (20, 0), (48, 8), (27, 31), (28, 40), (20, 19), (37, 20), (11, 28), (10, 23), (7, 40), (8, 4), (48, 20), (19, 4), (45, 21), (44, 21), (41, 11), (7, 15), (12, 6), (33, 16), (27, 2), (26, 24), (24, 21), (40, 41), (3, 31), (9, 21), (15, 39), (44, 17), (23, 6), (0, 11), (21, 3), (48, 2), (46, 40), (37, 0), (31, 38), (48, 7), (39, 27), (39, 24), (18, 41), (5, 22), (14, 40), (35, 11), (13, 4), (2, 4), (36, 40), (20, 21), (14, 41), (6, 25), (39, 4), (7, 30), (6, 26), (15, 11), (21, 4), (46, 11), (2, 12), (34, 16), (23, 18), (2, 29), (43, 22), (0, 25), (45, 24), (45, 16), (28, 26), (37, 18), (45, 0), (11, 4), (12, 1), (7, 8), (10, 34), (3, 10), (35, 17), (44, 31), (28, 28), (14, 12), (46, 23), (15, 35), (14, 11), (16, 23), (48, 14), (44, 29), (14, 28), (9, 6), (29, 17), (37, 30), (27, 21), (0, 38), (27, 13), (32, 12), (3, 30), (9, 35), (24, 1), (22, 5), (25, 13), (25, 8), (32, 11), (28, 18), (25, 14), (10, 0), (39, 35), (15, 12), (6, 1), (0, 40), (42, 11), (23, 5), (43, 26), (31, 17), (1, 31), (41, 23), (3, 32), (7, 35), (20, 11), (8, 29), (7, 33), (23, 13), (0, 26), (39, 32), (40, 24), (27, 5), (2, 21), (35, 34), (14, 1), (13, 9), (36, 11), (22, 20), (46, 12), (23, 17), (6, 7), (17, 11), (13, 14), (42, 12), (15, 40), (13, 16), (8, 12), (42, 1), (36, 15), (3, 3), (45, 4), (30, 32), (20, 23), (16, 20), (6, 16), (44, 25), (48, 6), (1, 39), (35, 18), (19, 1), (16, 37), (15, 1), (4, 8), (34, 3), (47, 36), (18, 28), (48, 19), (36, 35), (29, 2), (4, 19), (25, 21), (7, 3), (47, 15), (26, 39), (22, 18), (48, 36), (13, 17), (24, 37), (47, 32), (35, 2), (18, 20), (38, 19), (47, 13), (6, 38), (7, 4), (15, 13), (39, 37), (28, 20), (8, 34), (20, 33), (16, 32), (30, 35), (44, 28), (41, 1), (12, 28), (43, 4), (22, 15), (26, 37), (1, 17), (39, 21), (35, 30), (39, 10), (31, 15), (6, 2), (43, 38), (38, 0), (24, 12), (41, 9), (23, 2), (44, 33), (21, 40), (41, 31), (25, 40), (48, 13), (41, 7), (32, 34), (14, 18), (11, 5), (30, 22), (41, 38), (27, 4), (21, 41), (4, 41), (31, 35), (37, 23), (15, 27), (6, 29), (31, 8), (19, 27), (33, 22), (42, 10), (0, 30), (13, 34), (7, 32), (2, 32), (35, 15), (39, 25), (18, 11), (6, 27), (48, 1), (37, 5), (2, 40), (46, 4), (5, 19), (20, 40), (31, 11), (44, 41), (20, 30), (47, 8), (10, 12), (4, 32), (4, 30), (34, 41), (26, 6), (9, 24), (17, 30), (31, 1), (23, 26), (40, 6), (45, 9), (9, 41), (27, 18), (26, 36), (33, 19), (18, 22), (45, 6), (3, 36), (30, 11), (17, 17), (47, 25)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 44x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 13), (5, 3), (33, 20), (15, 18), (19, 39), (40, 9), (41, 39), (32, 21), (21, 21), (39, 40), (19, 37), (20, 0), (21, 25), (0, 17), (22, 16), (19, 15), (12, 12), (29, 8), (9, 13), (4, 13), (35, 26), (21, 0), (24, 26), (4, 15), (27, 38), (1, 19), (42, 20), (10, 22), (30, 21), (34, 20), (22, 23), (25, 6), (42, 2), (15, 38), (29, 22), (6, 27), (39, 15), (43, 38), (21, 38), (16, 18), (29, 3), (6, 7), (8, 38), (23, 30), (20, 1), (4, 14), (17, 27), (43, 29), (38, 39), (10, 20), (10, 18), (38, 6), (9, 10), (35, 40), (5, 0), (34, 17), (28, 17), (4, 22), (2, 38), (6, 28), (12, 27), (14, 37), (15, 27), (13, 12), (5, 7), (42, 16), (38, 5), (35, 8), (17, 7), (5, 8), (30, 8), (40, 33), (28, 19), (28, 22), (1, 12), (36, 21), (34, 21), (7, 25), (37, 17), (40, 22), (15, 21), (43, 31), (21, 5), (25, 12), (36, 4), (33, 13), (12, 21), (2, 35), (31, 18), (23, 6), (9, 11), (23, 40), (33, 31), (10, 29), (14, 5), (11, 10), (29, 1), (0, 13), (35, 31), (3, 11), (35, 21), (6, 37), (40, 34), (33, 39), (43, 28), (24, 31), (35, 20), (12, 4), (31, 5), (26, 10), (31, 14), (35, 16), (25, 8), (19, 20), (3, 15), (0, 16), (26, 15), (6, 10), (20, 12), (11, 2), (22, 22), (7, 19), (22, 17), (27, 29), (7, 20), (8, 31), (39, 29), (1, 3), (11, 5), (6, 19), (14, 16), (43, 2), (12, 20), (19, 38), (9, 21), (22, 29), (16, 1), (16, 9), (32, 35), (3, 37), (36, 17), (37, 21), (19, 32), (14, 13), (20, 17), (18, 1), (42, 1), (32, 11), (11, 8), (7, 12), (20, 4), (25, 22), (28, 33), (42, 32), (13, 23), (12, 39), (5, 26), (15, 19), (30, 37), (32, 10), (23, 15), (9, 22), (17, 12), (30, 39), (36, 12), (4, 23), (2, 13), (0, 38), (38, 19), (18, 34), (39, 39), (29, 17), (6, 13), (12, 3), (17, 15), (1, 10), (27, 9), (8, 0), (14, 26), (32, 6), (17, 17), (43, 33), (1, 30), (4, 19), (15, 4), (21, 16), (36, 8), (30, 34), (15, 16), (40, 28), (28, 18), (36, 26), (0, 8), (21, 36), (6, 34), (19, 29), (24, 0), (7, 34), (9, 25), (25, 34), (15, 10), (35, 0), (32, 37), (24, 21), (22, 6), (15, 30), (33, 37), (14, 27), (30, 40), (27, 5), (27, 39), (11, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 2), (28, 0), (3, 23), (19, 28), (1, 41), (34, 7), (2, 41), (36, 24), (0, 9), (0, 24), (23, 6), (48, 34), (1, 32), (32, 20), (42, 21), (37, 2), (16, 36), (36, 37), (19, 29), (3, 21), (7, 13), (6, 0), (31, 25), (7, 25), (26, 33), (22, 2), (37, 6), (12, 6), (39, 10), (17, 28), (19, 32), (13, 1), (39, 25), (2, 25), (40, 11), (14, 26), (28, 13), (48, 1), (12, 39), (29, 38), (16, 33), (36, 4), (2, 42), (18, 40), (29, 13), (5, 14), (18, 39), (1, 13), (11, 26), (24, 40), (40, 12), (14, 37), (30, 11), (41, 9), (14, 14), (20, 16), (27, 26), (31, 5), (48, 26), (11, 13), (48, 31), (23, 28), (28, 12), (19, 8), (14, 3), (8, 39), (2, 16), (48, 35), (17, 37), (10, 2), (10, 42), (46, 24), (38, 22), (38, 1), (10, 22), (18, 35), (4, 39), (11, 10), (4, 4), (31, 26), (15, 5), (10, 11), (47, 1), (42, 13), (0, 37), (17, 23), (24, 18), (11, 20), (48, 33), (40, 30), (46, 28), (32, 22), (45, 2), (27, 22), (22, 29), (15, 37), (8, 0), (34, 38), (35, 25), (20, 11), (40, 23), (16, 27), (15, 29), (44, 26), (12, 22), (4, 32), (30, 26), (39, 4), (21, 17), (20, 8), (1, 28), (46, 26), (29, 19), (29, 18), (30, 7), (27, 34), (36, 7), (18, 27), (26, 41), (39, 12), (6, 41), (22, 22), (9, 21), (2, 5), (18, 38), (47, 29), (28, 11), (27, 2), (18, 37), (13, 12), (24, 24), (40, 38), (5, 25), (17, 25), (46, 7), (2, 18), (43, 34), (26, 18), (4, 8), (33, 34), (10, 10), (35, 23), (29, 23), (16, 8), (1, 9), (8, 40), (25, 28), (22, 27), (28, 26), (3, 35), (45, 8), (5, 3), (14, 21), (6, 19), (43, 13), (34, 31), (35, 1), (0, 21), (27, 40), (22, 1), (41, 16), (19, 24), (30, 10), (11, 39), (39, 39), (9, 34), (27, 0), (41, 12), (2, 23), (26, 3), (7, 37), (7, 30), (42, 30), (14, 38), (7, 39), (14, 39), (9, 7), (40, 20), (15, 7), (38, 37), (17, 1), (27, 30), (33, 36), (12, 32), (21, 20), (20, 40), (13, 0), (13, 5), (15, 8), (8, 27), (13, 42), (39, 32), (0, 12), (20, 27), (14, 1), (24, 41), (4, 1), (28, 18), (21, 0), (16, 3), (41, 36), (13, 20), (4, 16), (1, 33), (32, 34), (1, 18), (13, 15), (44, 38), (13, 3), (24, 27), (21, 10), (7, 9), (21, 27), (37, 39), (43, 33), (19, 41), (26, 25), (5, 17), (0, 41), (1, 39), (38, 11), (27, 25), (26, 34), (30, 4), (12, 33), (3, 24), (15, 41), (17, 36), (42, 24), (2, 14), (8, 19), (31, 31), (27, 11), (28, 38), (25, 0), (46, 36), (9, 26), (38, 7), (44, 23), (48, 29), (10, 5), (34, 32), (38, 36), (13, 29), (9, 12), (21, 26), (3, 37), (42, 27), (32, 27), (47, 5), (0, 25), (2, 7), (44, 4), (21, 19), (35, 20), (4, 24), (27, 21), (16, 38), (7, 18), (31, 23), (39, 24), (41, 2), (20, 36), (14, 27), (30, 12), (10, 29), (26, 22), (18, 31), (25, 34), (29, 16), (17, 26), (34, 29), (12, 11), (25, 29), (1, 30), (33, 9), (5, 39), (48, 32), (18, 33), (18, 10), (7, 40), (17, 13), (47, 23), (17, 31), (5, 7), (43, 40), (44, 32), (28, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (17, 23), (12, 27), (28, 42), (0, 33), (36, 41), (1, 14), (38, 19), (38, 36), (21, 5), (20, 36), (26, 16), (2, 38), (4, 7), (31, 37), (10, 37), (37, 20), (19, 26), (15, 18), (9, 0), (24, 44), (11, 41), (22, 23), (20, 18), (1, 36), (26, 18), (5, 16), (41, 25), (16, 33), (5, 18), (2, 33), (36, 0), (13, 32), (15, 43), (15, 28), (19, 22), (1, 15), (4, 13), (25, 5), (3, 1), (29, 34), (4, 42), (38, 16), (31, 18), (26, 4), (35, 38), (24, 35), (40, 14), (24, 6), (0, 39), (36, 36), (24, 42), (10, 26), (35, 8), (34, 15), (12, 18), (39, 13), (26, 5), (39, 1), (16, 31), (38, 8), (1, 35), (35, 2), (31, 7), (4, 1), (17, 43), (18, 44), (38, 13), (30, 27), (4, 30), (8, 2), (15, 14), (29, 11), (40, 19), (16, 28), (6, 0), (40, 26), (26, 7), (11, 29), (10, 21), (16, 6), (18, 27), (34, 29), (15, 22), (5, 8), (39, 40), (11, 36), (12, 14), (6, 3), (39, 11), (32, 44), (32, 10), (12, 37), (4, 18), (30, 38), (1, 2), (10, 30), (15, 4), (27, 43), (8, 19), (41, 19), (3, 7), (31, 4), (12, 19), (10, 23), (32, 16), (13, 39), (17, 39), (2, 34), (22, 3), (18, 16), (21, 0), (32, 24), (40, 44), (28, 31), (4, 25), (21, 10), (31, 36), (2, 17), (23, 20), (36, 43), (2, 12), (25, 6), (31, 26), (25, 33), (28, 40), (23, 25), (14, 16), (11, 25), (26, 29), (8, 5), (25, 17), (39, 4), (36, 9), (1, 10), (3, 10), (29, 7), (40, 5), (8, 3), (21, 2), (38, 12), (35, 25), (23, 35), (37, 29), (12, 10), (16, 9), (31, 44), (10, 17), (14, 17), (11, 44), (41, 26), (40, 27), (34, 32), (7, 21), (26, 0), (16, 14), (38, 42), (27, 33), (0, 23), (30, 33), (27, 10), (1, 18), (21, 18), (8, 1), (19, 3), (10, 28), (18, 9), (18, 39), (4, 33), (41, 8), (20, 26), (20, 3), (32, 41), (17, 2), (29, 23), (32, 0), (15, 3), (15, 8), (41, 12), (4, 16), (19, 31), (15, 34), (1, 39), (6, 35), (5, 15), (34, 6), (37, 19), (34, 25), (17, 31), (7, 14), (36, 44), (9, 6), (32, 12), (40, 42), (21, 29), (2, 1), (27, 32), (39, 37), (18, 11), (12, 31), (16, 24), (6, 24), (18, 42), (12, 17), (26, 26), (30, 25), (3, 21), (12, 35), (41, 31), (40, 2), (13, 10), (41, 28), (7, 22), (22, 43), (18, 6), (11, 40), (2, 9), (15, 11), (12, 39), (38, 35), (1, 4), (27, 44), (33, 42), (23, 11), (32, 30), (33, 37), (17, 7), (37, 30), (18, 34), (35, 37), (9, 28), (0, 19), (17, 32), (18, 2), (33, 16), (7, 12), (30, 39), (31, 25), (33, 1), (9, 10), (2, 10), (21, 6), (15, 33), (36, 20), (11, 9), (6, 25), (21, 25), (8, 7), (41, 2), (24, 10), (41, 35), (21, 39), (8, 38), (4, 10), (41, 37), (22, 9), (37, 3), (29, 8), (38, 10), (27, 1), (35, 43), (21, 32), (7, 5), (32, 22), (24, 20), (36, 26), (40, 34), (31, 6), (6, 26), (3, 24), (7, 11), (29, 26), (13, 43), (19, 25), (28, 44), (37, 32), (33, 41), (31, 38), (37, 41), (17, 30), (17, 22), (30, 18), (26, 38), (12, 42), (13, 19), (15, 16), (28, 20), (11, 5), (3, 8), (1, 7), (33, 29), (3, 19), (18, 13), (18, 19), (0, 40), (36, 2), (31, 2), (40, 43), (3, 32), (9, 39), (17, 5), (10, 31), (28, 22), (40, 23), (12, 0), (1, 24), (28, 41), (22, 10), (41, 29), (3, 44), (28, 0), (23, 12), (39, 31), (29, 14), (10, 33), (0, 6), (2, 43), (23, 39), (25, 10), (0, 26), (7, 9), (4, 12), (24, 31), (23, 24), (27, 17), (2, 11), (13, 4), (1, 12), (21, 28), (36, 4), (13, 28), (39, 39), (38, 30), (11, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 43x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 5), (34, 7), (10, 20), (6, 21), (2, 39), (12, 35), (23, 37), (24, 25), (24, 14), (5, 18), (14, 10), (19, 39), (11, 19), (37, 9), (25, 39), (34, 9), (9, 20), (11, 21), (8, 19), (21, 34), (7, 31), (0, 33), (33, 20), (5, 22), (32, 0), (32, 33), (2, 38), (39, 20), (19, 0), (2, 34), (40, 40), (6, 4), (30, 40), (34, 10), (19, 41), (9, 24), (2, 1), (13, 34), (1, 31), (7, 20), (41, 2), (30, 8), (17, 37), (41, 20), (20, 2), (30, 22), (31, 37), (39, 0), (10, 40), (6, 33), (40, 10), (10, 10), (30, 36), (33, 24), (14, 37), (20, 24), (38, 27), (40, 32), (13, 25), (42, 32), (41, 1), (24, 4), (21, 25), (3, 2), (6, 36), (14, 12), (28, 5), (27, 21), (23, 18), (1, 33), (37, 11), (31, 10), (17, 5), (1, 4), (12, 15), (39, 5), (18, 28), (25, 41), (15, 17), (37, 34), (37, 30), (15, 32), (5, 24), (37, 13), (26, 37), (36, 11), (41, 26), (36, 18), (5, 37), (12, 7), (20, 17), (6, 26), (32, 24), (38, 37), (37, 17), (4, 4), (12, 5), (27, 40), (19, 16), (31, 0), (30, 39), (38, 7), (2, 35), (20, 0), (5, 36), (18, 13), (0, 10), (17, 23), (20, 5), (35, 31), (12, 13), (6, 13), (17, 28), (37, 36), (2, 30), (38, 34), (1, 10), (11, 36), (17, 18), (4, 28), (29, 13), (36, 40), (36, 7), (22, 12), (15, 4), (1, 6), (31, 12), (27, 10), (27, 15), (42, 23), (32, 34), (39, 14), (28, 23), (1, 25), (29, 28), (22, 32), (32, 37), (27, 25), (39, 22), (0, 7), (18, 26), (3, 29), (16, 18), (41, 9), (19, 26), (1, 29), (37, 21), (36, 0), (8, 30), (18, 5), (26, 8), (41, 29), (32, 16), (23, 36), (2, 11), (4, 9), (1, 27), (32, 5), (31, 15), (14, 6), (1, 21), (37, 32), (14, 25), (3, 26), (6, 41), (0, 35), (25, 0), (29, 34), (42, 2), (6, 37), (17, 1), (21, 33), (13, 38), (14, 41), (10, 28), (10, 3), (9, 17), (12, 39), (21, 1), (1, 39), (40, 0), (39, 30), (13, 16), (8, 1), (18, 23), (25, 3), (42, 33), (40, 30), (20, 23), (29, 23), (29, 25), (15, 18), (39, 23), (28, 10), (33, 26), (15, 5), (8, 10), (20, 35), (12, 9), (19, 17), (31, 14), (10, 15), (35, 9), (5, 9), (10, 35), (30, 27), (28, 39), (4, 33), (14, 17), (36, 19), (29, 32), (10, 31), (12, 30), (20, 18), (10, 1), (9, 2), (19, 33), (35, 18), (8, 8), (23, 21), (36, 16), (22, 11), (6, 14), (8, 21), (3, 6), (17, 40), (28, 9), (42, 22), (6, 23), (5, 2), (32, 32), (34, 2), (4, 41), (19, 36), (15, 20), (42, 5), (23, 31), (5, 34), (9, 33), (41, 15), (30, 2), (17, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 31), (11, 1), (25, 10), (30, 32), (3, 22), (12, 17), (34, 15), (14, 32), (23, 38), (42, 38), (4, 3), (20, 27), (24, 20), (6, 7), (21, 22), (13, 0), (9, 20), (6, 28), (3, 29), (13, 28), (29, 2), (19, 28), (32, 9), (22, 22), (2, 15), (24, 28), (40, 9), (5, 33), (40, 42), (34, 30), (30, 22), (25, 33), (28, 27), (12, 2), (25, 43), (18, 21), (28, 37), (22, 23), (31, 5), (33, 26), (29, 36), (32, 30), (0, 7), (3, 41), (43, 24), (11, 38), (18, 26), (7, 26), (1, 36), (26, 16), (5, 0), (26, 20), (4, 31), (1, 37), (1, 15), (9, 5), (4, 23), (35, 21), (15, 37), (41, 3), (20, 25), (12, 39), (11, 6), (21, 29), (45, 3), (25, 6), (13, 16), (1, 40), (32, 17), (44, 12), (22, 43), (39, 28), (8, 31), (25, 44), (24, 7), (19, 19), (38, 6), (3, 37), (20, 23), (1, 10), (29, 9), (35, 29), (35, 8), (38, 33), (34, 33), (17, 19), (30, 43), (4, 20), (1, 21), (28, 12), (38, 19), (43, 12), (0, 17), (4, 41), (41, 6), (2, 18), (17, 4), (33, 39), (29, 17), (22, 36), (30, 17), (28, 42), (29, 3), (9, 16), (31, 27), (24, 41), (41, 30), (45, 2), (15, 7), (13, 30), (43, 40), (7, 9), (45, 43), (40, 3), (31, 24), (19, 15), (20, 2), (4, 38), (29, 14), (24, 31), (44, 36), (7, 41), (26, 3), (32, 23), (15, 31), (31, 35), (40, 17), (41, 36), (21, 30), (33, 4), (6, 14), (0, 41), (28, 22), (31, 42), (16, 10), (5, 22), (27, 20), (22, 7), (17, 6), (5, 17), (3, 13), (15, 25), (34, 3), (21, 26), (0, 31), (24, 36), (32, 44), (3, 23), (10, 14), (16, 25), (37, 18), (30, 44), (40, 7), (2, 5), (21, 0), (7, 7), (0, 6), (26, 12), (33, 1), (27, 25), (42, 16), (12, 28), (23, 39), (23, 4), (25, 7), (5, 12), (21, 23), (35, 36), (28, 33), (44, 27), (14, 40), (9, 10), (6, 42), (18, 29), (11, 32), (43, 6), (42, 8), (36, 32), (15, 35), (15, 16), (16, 20), (14, 38), (22, 9), (38, 30), (38, 40), (23, 40), (36, 12), (3, 36), (30, 40), (29, 4), (10, 38), (22, 38), (3, 28), (39, 38), (22, 16), (6, 0), (8, 43), (24, 11), (35, 25), (43, 1), (28, 44), (16, 38), (34, 6), (18, 19), (20, 22), (45, 34), (5, 38), (32, 43), (8, 2), (3, 39), (15, 17), (30, 12), (41, 37), (17, 28), (19, 5), (14, 42), (43, 21), (12, 7), (6, 44), (0, 37), (10, 12), (17, 2), (11, 33), (11, 40), (1, 24), (40, 13), (37, 3), (7, 32), (1, 14), (14, 35), (19, 41), (42, 13), (31, 3), (29, 32), (43, 20), (14, 3), (14, 17), (18, 12), (36, 19), (27, 7), (27, 31), (40, 19), (30, 7), (12, 34), (30, 31), (24, 24), (36, 39), (19, 37), (18, 13), (34, 29), (40, 32), (19, 32), (0, 35), (9, 35), (22, 24), (15, 29), (42, 35), (22, 42), (1, 18), (27, 30), (43, 15), (26, 25), (37, 31), (34, 40), (16, 24), (33, 10), (44, 17), (43, 43), (28, 24), (23, 6), (35, 12), (22, 41), (36, 4), (6, 25), (25, 30), (4, 33), (8, 5), (16, 28), (24, 22), (12, 18), (1, 44), (13, 31), (26, 21), (2, 21), (5, 35), (10, 6), (15, 13), (35, 2), (15, 38), (4, 1), (32, 20), (7, 25), (37, 44), (4, 29), (45, 4), (35, 22), (5, 20), (1, 3), (26, 40), (32, 16), (13, 22), (35, 26), (23, 26), (9, 21), (39, 33), (35, 13), (20, 7), (27, 18), (25, 39), (31, 7), (2, 10), (28, 4), (27, 40), (14, 22), (43, 26), (33, 40), (14, 24), (36, 30), (44, 15), (18, 25), (9, 31), (27, 35), (14, 31), (32, 19), (31, 29), (36, 27), (0, 8), (38, 23), (0, 32), (38, 42), (0, 26), (35, 42), (27, 43), (9, 17), (33, 22), (41, 5), (33, 37), (33, 9), (3, 8), (12, 12), (3, 44), (13, 23), (13, 37), (8, 4), (42, 11), (9, 18), (4, 21), (2, 17), (16, 23), (41, 41), (12, 32), (45, 42), (3, 31), (11, 20), (38, 1), (29, 31), (10, 9), (11, 34), (12, 13), (39, 10), (39, 40), (1, 1), (39, 15), (36, 14), (10, 35), (25, 12), (34, 42), (42, 32), (16, 41), (40, 22), (5, 23), (37, 24), (26, 38), (36, 23), (22, 29), (7, 8), (9, 40), (24, 42), (37, 10), (20, 29), (45, 14), (25, 41), (39, 30), (30, 11), (12, 37), (21, 21), (27, 26), (20, 28), (35, 24), (36, 29), (29, 23), (41, 7), (44, 20), (7, 4), (42, 18), (8, 14), (35, 15), (37, 36), (28, 30), (37, 34), (25, 0), (24, 43), (43, 8), (3, 32)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 46x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (13, 16), (27, 15), (14, 4), (39, 35), (6, 22), (23, 2), (4, 5), (41, 31), (17, 3), (30, 37), (4, 41), (41, 34), (26, 13), (10, 20), (41, 20), (9, 20), (3, 37), (28, 40), (2, 28), (36, 9), (7, 4), (14, 36), (3, 17), (14, 16), (0, 31), (12, 13), (17, 28), (31, 17), (17, 23), (32, 17), (0, 25), (12, 15), (29, 30), (29, 27), (2, 26), (15, 26), (5, 23), (40, 17), (1, 17), (22, 18), (18, 21), (30, 14), (8, 14), (26, 26), (24, 3), (3, 39), (44, 18), (44, 29), (41, 21), (8, 35), (42, 2), (25, 34), (39, 23), (7, 38), (29, 5), (9, 16), (12, 22), (36, 41), (8, 3), (9, 31), (12, 37), (45, 33), (20, 17), (33, 39), (33, 41), (12, 5), (29, 25), (27, 19), (24, 1), (34, 41), (15, 15), (24, 39), (13, 23), (43, 36), (37, 2), (27, 32), (38, 39), (9, 11), (33, 32), (16, 37), (44, 28), (8, 39), (20, 1), (32, 2), (17, 29), (14, 29), (18, 36), (4, 18), (34, 31), (32, 3), (11, 40), (30, 4), (39, 6), (41, 27), (37, 35), (21, 27), (10, 33), (30, 39), (39, 25), (9, 21), (23, 19), (0, 23), (26, 19), (11, 15), (17, 19), (11, 9), (31, 25), (38, 8), (22, 22), (22, 5), (31, 30), (36, 19), (13, 12), (8, 7), (44, 26), (38, 16), (26, 4), (26, 31), (43, 15), (15, 3), (9, 23), (1, 29), (42, 9), (44, 27), (36, 36), (8, 20), (1, 24), (39, 36), (26, 25), (7, 8), (27, 7), (43, 1), (4, 19), (6, 6), (19, 8), (18, 28), (32, 7), (6, 31), (38, 15), (27, 40), (9, 37), (31, 10), (33, 8), (43, 21), (25, 7), (29, 33), (23, 38), (31, 36), (19, 31), (23, 24), (24, 8), (1, 35), (27, 21), (28, 20), (26, 20), (45, 40), (12, 12), (7, 28), (41, 15), (39, 33), (0, 32), (14, 6), (17, 16), (40, 9), (15, 19), (16, 31), (43, 7), (26, 6), (0, 20), (27, 1), (14, 14), (36, 4), (44, 20), (10, 1), (17, 38), (43, 8), (33, 7), (9, 6), (0, 7), (26, 0), (38, 11), (35, 17), (14, 10), (18, 14), (31, 2), (28, 26), (45, 0), (22, 40), (10, 11), (37, 1), (28, 19), (39, 11), (9, 19), (30, 36), (31, 34), (17, 37), (28, 11), (40, 25), (20, 7), (12, 18), (33, 33), (23, 31), (7, 16), (24, 37), (44, 35), (21, 4), (35, 24), (17, 39), (24, 7), (37, 7), (12, 28), (40, 30), (33, 13), (29, 14), (20, 3), (37, 37), (40, 22), (24, 21), (4, 10), (18, 6), (35, 32), (19, 4), (24, 22), (1, 40), (1, 12), (40, 29), (1, 19), (6, 33), (25, 15), (0, 8), (39, 18), (15, 37), (8, 37), (1, 14), (30, 2), (45, 14), (45, 28), (3, 20), (13, 30), (0, 6), (26, 32), (43, 41), (30, 15), (26, 10), (13, 8), (9, 15), (0, 30), (38, 2), (19, 30), (7, 23), (40, 31), (5, 14), (11, 39), (34, 3), (11, 6), (28, 22), (14, 12), (32, 34), (16, 11), (40, 7), (7, 39), (8, 0), (38, 29), (39, 34), (37, 23), (5, 0), (22, 39), (28, 9), (17, 6), (34, 28), (11, 22), (9, 29), (37, 19), (12, 7), (32, 33), (40, 4), (43, 37), (16, 30), (5, 32), (39, 40), (43, 26), (5, 16), (5, 6), (33, 20), (25, 24), (4, 25), (37, 17), (1, 0), (25, 3), (22, 29), (5, 3), (39, 7), (23, 23), (0, 4), (24, 31), (1, 7), (38, 26), (28, 6), (42, 18), (11, 5), (37, 9), (28, 41), (11, 4), (20, 37), (39, 9), (29, 11), (45, 7), (1, 13), (7, 6), (7, 17), (18, 2), (9, 22), (3, 34), (24, 35), (5, 18), (17, 8), (38, 32), (17, 14), (45, 10), (29, 39), (12, 11), (19, 29), (25, 36), (16, 6), (38, 35), (34, 30), (35, 36), (42, 26), (7, 21), (35, 39), (31, 9), (16, 17), (17, 32), (26, 22), (13, 33), (7, 14), (23, 25), (42, 5), (39, 31), (32, 15), (44, 12), (13, 34), (8, 4), (18, 5), (7, 0), (41, 25), (13, 20), (3, 9), (9, 1), (21, 33), (29, 23), (32, 8), (14, 9), (0, 35), (23, 14), (3, 6), (7, 5), (26, 28), (8, 31), (6, 21), (25, 28), (20, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 44x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 1), (35, 1), (13, 4), (20, 44), (24, 24), (6, 21), (22, 29), (7, 39), (40, 44), (12, 5), (26, 44), (6, 26), (24, 36), (21, 12), (43, 38), (30, 23), (1, 1), (24, 35), (19, 1), (36, 26), (25, 33), (13, 34), (41, 26), (33, 16), (10, 14), (30, 33), (7, 16), (3, 5), (31, 20), (7, 30), (13, 16), (37, 27), (25, 38), (13, 37), (16, 21), (15, 44), (8, 1), (22, 43), (30, 19), (14, 26), (17, 16), (12, 31), (32, 42), (12, 0), (43, 37), (25, 18), (7, 33), (2, 5), (23, 33), (19, 17), (17, 7), (36, 42), (27, 1), (25, 27), (23, 31), (39, 11), (39, 36), (6, 14), (30, 7), (3, 19), (23, 47), (24, 42), (14, 31), (19, 43), (43, 10), (43, 36), (8, 3), (21, 40), (33, 11), (35, 32), (17, 4), (5, 42), (43, 9), (9, 14), (26, 6), (34, 44), (20, 4), (35, 33), (41, 0), (35, 9), (14, 25), (41, 10), (33, 19), (20, 27), (15, 26), (6, 31), (1, 8), (1, 14), (32, 11), (10, 36), (6, 23), (4, 36), (8, 5), (25, 3), (21, 17), (41, 8), (17, 25), (36, 29), (26, 9), (14, 32), (33, 6), (24, 45), (13, 11), (0, 37), (7, 42), (16, 40), (9, 4), (35, 3), (29, 44), (14, 29), (2, 13), (31, 4), (11, 12), (31, 22), (43, 44), (26, 46), (28, 47), (14, 2), (23, 2), (13, 32), (1, 47), (35, 28), (19, 34), (1, 29), (7, 13), (20, 22), (20, 38), (11, 45), (29, 8), (26, 19), (12, 7), (2, 30), (23, 45), (39, 48), (1, 3), (20, 26), (22, 24), (42, 42), (25, 9), (11, 18), (43, 12), (27, 39), (10, 26), (12, 30), (21, 19), (3, 20), (35, 16), (10, 32), (18, 24), (37, 31), (15, 0), (28, 15), (4, 10), (14, 21), (39, 17), (38, 25), (43, 22), (32, 36), (29, 4), (36, 16), (2, 15), (13, 17), (31, 17), (4, 40), (42, 38), (41, 38), (11, 46), (12, 35), (36, 19), (32, 40), (29, 30), (18, 1), (19, 9), (27, 38), (35, 47), (27, 35), (2, 34), (20, 10), (38, 0), (5, 11), (33, 7), (42, 44), (29, 22), (13, 2), (9, 15), (0, 14), (3, 41), (32, 3), (35, 17), (8, 34), (39, 21), (21, 46), (34, 35), (34, 24), (27, 41), (42, 0), (32, 24), (36, 7), (15, 40), (7, 1), (17, 0), (2, 44), (11, 38), (18, 7), (32, 38), (34, 29), (33, 20), (3, 24), (29, 41), (0, 5), (7, 32), (27, 19), (38, 24), (10, 20), (1, 42), (4, 44), (28, 42), (37, 46), (22, 42), (5, 45), (12, 27), (28, 44), (35, 30), (33, 22), (28, 43), (19, 26), (10, 30), (30, 5), (37, 30), (24, 7), (10, 2), (20, 17), (38, 22), (8, 44), (5, 25), (16, 4), (0, 19), (8, 47), (42, 32), (6, 12), (36, 37), (5, 43), (42, 2), (27, 24), (16, 13), (9, 35), (35, 19), (6, 20), (29, 29), (38, 37), (39, 5), (4, 0), (18, 37), (20, 33), (0, 32), (42, 16), (13, 0), (18, 42), (30, 48), (0, 23), (22, 31), (39, 10), (10, 6), (32, 39), (1, 40), (7, 47), (0, 40), (23, 18), (3, 10), (12, 42), (39, 46), (14, 1), (19, 48), (11, 3), (32, 19), (8, 46), (19, 36), (30, 14), (42, 39), (34, 1), (17, 24), (43, 40), (18, 29), (8, 0), (36, 8), (41, 12), (12, 33), (6, 17), (19, 16), (0, 7), (29, 0), (8, 23), (21, 14), (26, 41), (7, 31), (40, 34), (39, 13), (19, 30), (24, 21), (14, 15), (29, 33), (20, 7), (40, 42), (41, 48), (6, 27), (42, 43), (5, 17), (25, 40), (20, 1), (23, 4), (23, 39), (30, 43), (21, 32), (26, 26), (21, 15), (36, 41), (7, 19), (18, 16), (38, 39), (11, 39), (12, 21), (14, 20), (36, 36), (33, 18), (40, 10), (35, 36), (12, 20), (25, 48), (39, 28), (32, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 25), (9, 36), (45, 22), (4, 1), (33, 6), (23, 39), (24, 23), (13, 13), (36, 27), (19, 31), (34, 20), (9, 4), (28, 2), (22, 30), (10, 4), (28, 20), (38, 10), (39, 7), (7, 13), (38, 26), (44, 6), (15, 22), (7, 17), (41, 32), (25, 18), (42, 13), (22, 16), (6, 3), (36, 35), (4, 17), (42, 25), (27, 32), (39, 24), (32, 8), (34, 24), (1, 20), (23, 4), (12, 0), (35, 27), (45, 30), (40, 25), (2, 19), (42, 6), (25, 22), (26, 38), (42, 32), (10, 34), (6, 24), (21, 27), (26, 2), (25, 32), (25, 21), (41, 23), (7, 22), (3, 16), (35, 28), (5, 24), (24, 40), (15, 16), (5, 27), (10, 40), (42, 19), (17, 36), (15, 14), (2, 25), (26, 23), (23, 5), (29, 30), (36, 17), (44, 36), (14, 38), (40, 37), (0, 8), (40, 6), (23, 16), (15, 32), (36, 21), (12, 20), (28, 0), (43, 38), (5, 25), (34, 28), (10, 3), (5, 34), (45, 4), (43, 31), (2, 3), (11, 40), (6, 16), (34, 36), (21, 3), (36, 29), (13, 35), (31, 27), (26, 29), (26, 33), (25, 28), (10, 36), (8, 37), (31, 23), (40, 26), (0, 19), (24, 29), (9, 33), (15, 26), (28, 11), (37, 20), (30, 17), (17, 16), (14, 17), (42, 17), (32, 36), (39, 19), (21, 33), (32, 18), (33, 30), (40, 36), (31, 29), (39, 26), (6, 4), (1, 32), (6, 37), (9, 12), (30, 1), (39, 27), (34, 0), (8, 8), (40, 12), (43, 10), (29, 37), (4, 31), (35, 5), (45, 8), (41, 2), (13, 3), (21, 19), (33, 23), (2, 4), (40, 8), (34, 40), (11, 19), (34, 6), (0, 32), (19, 13), (30, 2), (44, 7), (16, 18), (21, 24), (26, 17), (28, 22), (11, 3), (25, 11), (39, 18), (34, 32), (42, 15), (19, 29), (36, 30), (10, 37), (43, 29), (2, 13), (36, 19), (5, 19), (25, 23), (24, 32), (37, 29), (16, 1), (44, 32), (28, 8), (38, 9), (31, 11), (30, 33), (1, 11), (38, 3), (41, 39), (30, 14), (10, 0), (11, 24), (14, 2), (4, 18), (20, 23), (43, 14), (11, 16), (34, 10), (9, 20), (4, 11), (23, 40), (45, 32), (18, 38), (7, 31), (44, 17), (5, 20), (17, 17), (12, 34), (32, 27), (44, 10), (15, 2), (36, 7), (1, 3), (18, 27), (4, 39), (28, 25), (19, 6), (0, 34), (43, 17), (12, 37), (22, 13), (12, 14), (39, 33), (35, 26), (37, 21), (34, 14), (26, 6), (18, 9), (22, 35), (5, 33), (23, 34), (17, 6), (3, 34), (11, 28), (18, 12), (20, 15), (17, 29), (19, 19), (44, 0), (22, 31), (34, 4), (22, 2), (22, 7), (12, 33), (16, 39), (39, 12), (28, 40), (31, 39), (38, 16), (0, 3), (24, 12), (17, 4), (13, 29), (19, 38), (9, 30), (41, 3), (40, 13), (25, 12), (0, 39), (42, 23), (8, 24), (9, 21), (0, 1), (1, 27), (25, 38), (5, 31), (12, 29), (35, 1), (7, 25), (8, 7), (8, 9), (42, 39), (11, 17), (16, 9), (15, 5), (8, 32), (35, 13), (15, 20), (38, 35), (35, 29), (16, 23), (33, 38), (38, 6), (19, 35), (10, 28), (1, 34), (45, 12), (32, 12), (3, 8), (24, 38), (38, 23), (27, 34), (9, 26), (5, 2), (1, 13), (12, 24), (8, 22), (5, 40), (24, 25), (27, 35), (10, 22), (35, 2), (16, 29), (27, 31), (10, 13), (40, 15), (39, 23), (22, 19), (23, 0), (15, 6), (8, 29), (29, 16), (17, 3), (15, 30), (3, 0), (22, 27), (19, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 31), (39, 5), (28, 4), (9, 37), (15, 1), (10, 28), (9, 12), (36, 28), (8, 19), (25, 33), (0, 37), (24, 6), (0, 17), (9, 36), (46, 21), (48, 9), (13, 26), (46, 20), (8, 17), (7, 31), (35, 1), (11, 0), (3, 17), (2, 3), (5, 23), (26, 10), (1, 21), (8, 26), (24, 34), (44, 17), (28, 1), (21, 32), (20, 27), (42, 20), (38, 34), (31, 29), (25, 26), (1, 1), (3, 16), (6, 0), (41, 0), (21, 0), (20, 9), (31, 17), (16, 18), (4, 20), (31, 7), (42, 18), (37, 1), (9, 4), (4, 0), (32, 41), (29, 4), (25, 37), (6, 7), (40, 5), (15, 29), (10, 18), (45, 34), (13, 30), (28, 33), (24, 23), (44, 19), (16, 11), (48, 20), (38, 17), (8, 8), (28, 6), (17, 2), (26, 25), (23, 10), (14, 22), (42, 10), (30, 29), (27, 10), (44, 1), (39, 29), (37, 33), (18, 13), (43, 19), (10, 8), (36, 8), (0, 15), (4, 9), (46, 25), (11, 19), (43, 13), (5, 12), (12, 12), (16, 17), (11, 10), (16, 23), (46, 26), (6, 14), (43, 9), (28, 29), (12, 1), (46, 38), (22, 7), (35, 16), (6, 24), (5, 20), (9, 10), (40, 18), (46, 3), (11, 37), (43, 4), (36, 4), (46, 27), (41, 33), (30, 12), (12, 13), (46, 22), (22, 16), (16, 27), (10, 11), (24, 4), (13, 3), (15, 17), (13, 40), (9, 38), (43, 12), (26, 18), (10, 27), (35, 25), (11, 18), (21, 22), (45, 25), (0, 28), (10, 19), (30, 9), (19, 8), (39, 9), (21, 34), (16, 20), (8, 39), (9, 1), (13, 21), (14, 26), (7, 10), (13, 37), (17, 0), (17, 19), (32, 17), (28, 27), (29, 15), (33, 9), (46, 23), (41, 32), (0, 36), (23, 39), (3, 7), (24, 41), (16, 29), (28, 38), (31, 9), (17, 37), (33, 39), (35, 41), (30, 5), (20, 3), (2, 0), (34, 38), (1, 0), (42, 30), (16, 28), (21, 41), (17, 18), (33, 37), (9, 7), (33, 38), (43, 38), (24, 36), (38, 30), (15, 41), (32, 28), (31, 23), (25, 3), (30, 24), (11, 24), (40, 7), (46, 4), (22, 4), (20, 25), (43, 0), (24, 19), (12, 34), (39, 32), (40, 20), (40, 0), (19, 32), (38, 9), (30, 27), (21, 27), (31, 38), (42, 39), (3, 20), (18, 12), (29, 9), (41, 14), (41, 16), (40, 32), (5, 8), (23, 15), (41, 41), (41, 35), (6, 34), (40, 2), (15, 30), (19, 33), (25, 36), (2, 25), (40, 35), (20, 34), (10, 36), (22, 23), (17, 26), (20, 31), (27, 38), (24, 7), (24, 8), (19, 22), (28, 40), (32, 31), (42, 35), (5, 15), (22, 39), (9, 9), (0, 10), (10, 34), (13, 23), (23, 14), (24, 24), (15, 13), (1, 11), (1, 16), (31, 41), (38, 32), (34, 27), (6, 1), (27, 7), (17, 31), (31, 28), (15, 25), (7, 1), (17, 33), (25, 28), (25, 18), (24, 25), (20, 33), (42, 9), (8, 15), (21, 10), (14, 20), (47, 31), (18, 18), (6, 23), (19, 24), (34, 31), (15, 8), (7, 11), (1, 31), (26, 31), (12, 22), (7, 35), (36, 40), (13, 7), (25, 39), (2, 8), (1, 26), (18, 21), (1, 29), (10, 12), (18, 10), (33, 11), (36, 7), (19, 12), (17, 7), (37, 32), (12, 24), (17, 27), (36, 24), (45, 2), (45, 40), (42, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 40x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 20), (21, 17), (31, 16), (1, 37), (25, 2), (20, 27), (37, 1), (13, 25), (25, 11), (26, 1), (35, 10), (23, 10), (0, 26), (37, 21), (36, 6), (25, 20), (38, 17), (36, 45), (18, 3), (18, 25), (9, 13), (8, 11), (34, 45), (25, 1), (0, 17), (7, 34), (27, 38), (27, 33), (12, 33), (23, 47), (33, 19), (6, 37), (22, 26), (27, 13), (35, 28), (4, 27), (12, 23), (2, 5), (5, 5), (6, 45), (0, 42), (6, 6), (10, 31), (31, 30), (6, 17), (33, 37), (4, 8), (2, 22), (9, 0), (13, 28), (36, 20), (31, 6), (20, 11), (2, 39), (27, 48), (24, 39), (25, 10), (30, 33), (12, 39), (17, 47), (6, 0), (7, 11), (11, 25), (21, 42), (11, 16), (31, 43), (39, 17), (36, 17), (23, 42), (34, 24), (25, 17), (22, 48), (0, 38), (10, 8), (5, 2), (19, 34), (13, 11), (15, 13), (32, 21), (13, 19), (24, 14), (27, 32), (14, 15), (14, 30), (14, 29), (34, 33), (14, 8), (11, 28), (18, 28), (25, 0), (26, 14), (12, 19), (37, 18), (6, 13), (28, 46), (23, 38), (11, 46), (38, 4), (2, 36), (9, 8), (36, 43), (32, 3), (35, 0), (22, 17), (26, 23), (34, 20), (2, 17), (37, 14), (29, 46), (5, 21), (18, 2), (21, 10), (33, 5), (1, 31), (20, 45), (21, 4), (11, 19), (20, 30), (29, 33), (9, 9), (10, 42), (24, 48), (27, 9), (37, 38), (5, 45), (24, 7), (1, 36), (28, 38), (20, 15), (22, 32), (25, 16), (24, 17), (30, 15), (0, 21), (13, 20), (28, 33), (25, 14), (4, 47), (39, 0), (34, 32), (1, 48), (39, 47), (15, 1), (10, 38), (2, 31), (12, 24), (14, 38), (28, 37), (11, 35), (18, 17), (13, 21), (37, 11), (2, 28), (16, 21), (33, 20), (35, 38), (28, 12), (25, 31), (20, 5), (12, 5), (15, 22), (3, 37), (3, 6), (21, 26), (9, 33), (33, 34), (12, 9), (27, 5), (23, 29), (17, 38), (33, 33), (25, 37), (31, 37), (19, 16), (30, 9), (14, 18), (12, 47), (10, 17), (0, 44), (17, 23), (8, 47), (27, 47), (20, 48), (19, 18), (33, 42), (19, 2), (1, 7), (7, 10), (35, 47), (6, 27), (25, 23), (7, 30), (15, 26), (2, 21), (15, 42), (23, 16), (4, 20), (15, 44), (34, 47), (30, 10), (18, 1), (27, 42), (23, 19), (6, 25), (5, 17), (1, 26), (38, 12), (3, 25), (37, 7), (3, 16), (16, 1), (5, 48), (14, 26), (9, 6), (39, 36), (20, 1), (21, 39), (14, 16), (21, 30), (16, 38), (9, 7), (39, 1), (2, 7), (22, 36), (14, 11), (34, 29), (37, 33), (31, 4), (3, 3), (32, 5), (16, 31), (8, 32), (12, 1), (7, 35), (37, 48), (18, 30), (33, 2), (39, 31), (4, 12), (20, 36), (24, 1), (17, 8), (33, 23), (34, 3), (4, 38), (16, 40), (24, 30), (0, 12), (21, 43), (18, 11), (26, 10), (17, 9), (21, 37), (31, 24), (34, 1), (10, 29), (38, 43), (2, 19), (28, 44), (13, 31), (1, 9), (19, 20), (39, 15), (17, 19), (3, 45), (28, 48), (5, 26), (4, 29), (1, 24), (27, 41), (6, 28), (29, 32), (32, 9), (39, 26), (14, 9), (19, 40), (8, 34), (38, 34), (31, 17), (2, 43), (24, 35), (9, 29), (21, 33), (10, 33), (39, 40), (6, 23), (22, 37), (3, 31), (4, 46), (27, 27), (3, 42), (2, 12), (31, 40), (22, 33)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 28), (41, 33), (21, 18), (13, 1), (29, 19), (13, 0), (12, 6), (32, 44), (14, 40), (6, 28), (26, 44), (30, 17), (28, 25), (46, 13), (22, 5), (34, 2), (21, 6), (30, 15), (38, 15), (36, 25), (28, 6), (42, 27), (32, 23), (37, 39), (24, 44), (22, 42), (26, 32), (32, 1), (18, 3), (4, 17), (24, 38), (20, 8), (3, 12), (34, 29), (32, 28), (30, 16), (21, 34), (2, 4), (34, 44), (1, 34), (4, 13), (37, 30), (21, 45), (33, 30), (27, 33), (26, 8), (15, 44), (6, 35), (34, 43), (27, 2), (22, 40), (40, 21), (30, 7), (36, 34), (17, 24), (20, 31), (39, 11), (19, 33), (3, 3), (34, 19), (12, 27), (20, 12), (11, 14), (30, 29), (15, 26), (19, 29), (4, 39), (20, 43), (43, 21), (37, 8), (12, 29), (45, 41), (13, 33), (46, 14), (10, 3), (31, 16), (30, 9), (25, 28), (19, 19), (40, 5), (24, 4), (37, 9), (38, 37), (15, 0), (34, 37), (19, 15), (31, 31), (5, 15), (42, 10), (17, 35), (32, 33), (7, 27), (11, 8), (18, 37), (14, 23), (28, 21), (40, 12), (21, 27), (7, 43), (46, 4), (41, 11), (0, 2), (26, 3), (42, 12), (33, 12), (10, 4), (38, 27), (4, 37), (45, 23), (14, 31), (20, 5), (23, 26), (28, 26), (46, 7), (41, 41), (6, 13), (9, 23), (2, 12), (12, 13), (10, 24), (34, 45), (35, 30), (3, 16), (36, 2), (44, 6), (9, 35), (12, 17), (1, 32), (43, 30), (12, 1), (40, 27), (24, 35), (22, 17), (2, 32), (9, 18), (35, 35), (25, 12), (11, 28), (45, 31), (28, 19), (21, 29), (25, 3), (13, 41), (31, 13), (34, 39), (6, 7), (2, 19), (12, 32), (34, 30), (42, 1), (26, 21), (41, 7), (41, 43), (3, 20), (37, 43), (3, 35), (34, 24), (45, 35), (9, 26), (22, 1), (16, 19), (14, 20), (41, 13), (36, 3), (23, 22), (11, 27), (43, 11), (7, 21), (21, 25), (13, 10), (41, 1), (27, 25), (42, 21), (4, 30), (28, 4), (36, 31), (19, 40), (35, 45), (37, 13), (36, 43), (8, 26), (21, 31), (8, 17), (1, 24), (24, 17), (30, 13), (25, 7), (0, 40), (38, 9), (8, 27), (9, 32), (30, 34), (4, 21), (44, 39), (35, 1), (42, 3), (15, 4), (14, 9), (33, 11), (21, 22), (16, 33), (0, 34), (26, 23), (30, 37), (27, 40), (12, 16), (15, 11), (23, 27), (25, 6), (35, 12), (42, 34), (40, 17), (33, 9), (14, 8), (9, 44), (30, 10), (9, 39), (34, 13), (25, 41), (4, 0), (24, 16), (11, 2), (9, 27), (45, 38), (5, 13), (13, 30), (11, 45), (46, 43), (10, 17), (9, 45), (35, 17), (15, 27), (28, 5), (7, 12), (30, 23), (38, 26), (12, 10), (9, 5), (28, 8), (16, 18), (21, 40), (20, 24), (28, 17), (13, 27), (27, 6), (39, 44), (10, 36), (18, 31), (34, 1), (0, 45), (11, 21), (11, 24), (32, 26), (5, 29), (7, 1)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 8), (24, 5), (26, 8), (36, 19), (17, 42), (40, 14), (27, 8), (12, 22), (3, 25), (38, 26), (17, 0), (22, 36), (40, 8), (20, 19), (38, 9), (32, 2), (14, 32), (29, 18), (8, 31), (23, 38), (1, 38), (30, 21), (30, 9), (39, 14), (1, 42), (37, 10), (9, 0), (22, 32), (25, 1), (29, 11), (26, 9), (28, 35), (37, 28), (0, 16), (2, 13), (2, 35), (10, 32), (33, 39), (32, 41), (33, 42), (2, 8), (21, 19), (20, 32), (25, 22), (19, 32), (18, 0), (12, 7), (8, 27), (5, 15), (39, 21), (7, 4), (27, 16), (9, 40), (11, 5), (0, 12), (21, 7), (32, 7), (39, 40), (38, 38), (9, 9), (17, 30), (12, 15), (11, 24), (30, 33), (29, 34), (13, 1), (28, 32), (37, 40), (26, 6), (17, 40), (9, 8), (20, 34), (0, 24), (26, 16), (11, 25), (6, 20), (7, 41), (17, 27), (2, 11), (19, 21), (29, 36), (34, 6), (7, 9), (4, 24), (8, 37), (5, 0), (9, 32), (24, 17), (12, 17), (11, 41), (11, 35), (4, 18), (19, 2), (32, 27), (21, 21), (22, 8), (23, 36), (13, 36), (11, 0), (9, 36), (22, 38), (24, 25), (30, 16), (27, 27), (18, 2), (18, 10), (5, 38), (29, 40), (33, 2), (4, 40), (33, 32), (20, 17), (29, 6), (30, 15), (26, 30), (3, 17), (19, 13), (23, 31), (8, 16), (8, 14), (8, 30), (26, 11), (28, 31), (28, 26), (27, 33), (38, 8), (40, 37), (32, 35), (16, 42), (20, 26), (38, 34), (24, 41), (7, 7), (8, 41), (15, 40), (37, 35), (7, 39), (10, 28), (7, 28), (36, 34), (30, 14), (20, 30), (33, 34), (11, 14), (7, 6), (25, 10), (3, 36), (2, 42), (35, 37), (26, 3), (19, 23), (31, 39), (16, 3), (39, 39), (13, 23), (5, 3), (25, 30), (40, 25), (15, 21), (18, 21), (10, 5), (3, 38), (15, 18), (37, 7), (10, 8), (39, 19), (13, 8), (24, 29), (14, 15), (16, 25), (37, 2), (14, 41), (18, 36), (23, 6), (40, 6), (4, 32), (10, 13), (23, 27), (31, 12), (21, 8), (31, 22), (14, 12), (35, 13), (34, 5), (18, 4), (26, 4), (8, 28), (9, 1), (6, 31), (16, 0), (15, 24), (21, 16), (2, 0), (37, 31), (11, 37), (9, 10), (10, 20), (19, 10), (17, 39), (21, 13), (13, 27), (3, 30), (19, 12), (20, 29), (5, 12), (39, 37), (39, 15), (4, 42), (22, 31), (40, 18), (34, 15), (1, 33), (31, 15), (37, 0), (36, 2), (26, 2), (35, 20), (26, 41), (9, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 20), (8, 41), (0, 26), (7, 5), (0, 16), (35, 35), (22, 42), (31, 26), (11, 21), (19, 3), (26, 33), (14, 29), (25, 1), (27, 38), (5, 7), (26, 25), (31, 7), (26, 23), (34, 46), (10, 47), (35, 14), (29, 18), (25, 36), (4, 9), (14, 43), (25, 9), (4, 20), (12, 38), (27, 11), (16, 27), (0, 27), (25, 17), (5, 17), (31, 3), (9, 16), (0, 17), (30, 17), (14, 30), (1, 28), (29, 37), (15, 40), (29, 39), (27, 35), (17, 33), (36, 32), (32, 29), (15, 41), (28, 35), (38, 13), (34, 25), (32, 24), (31, 18), (5, 44), (14, 7), (25, 34), (26, 45), (39, 0), (39, 7), (31, 20), (8, 27), (6, 18), (0, 2), (1, 47), (19, 0), (11, 4), (2, 22), (19, 34), (13, 8), (2, 11), (3, 46), (24, 25), (23, 8), (34, 40), (17, 16), (4, 22), (27, 19), (30, 37), (2, 4), (10, 16), (5, 22), (29, 34), (23, 19), (12, 18), (30, 31), (4, 21), (7, 47), (19, 4), (39, 13), (27, 4), (27, 33), (27, 0), (9, 11), (32, 21), (1, 31), (26, 35), (6, 24), (5, 8), (6, 13), (39, 11), (12, 35), (0, 1), (19, 18), (32, 8), (8, 19), (28, 10), (22, 32), (17, 21), (34, 33), (25, 4), (3, 24), (31, 4), (31, 24), (29, 17), (37, 44), (21, 15), (23, 0), (18, 4), (16, 47), (7, 11), (4, 15), (5, 21), (26, 4), (12, 4), (22, 30), (22, 1), (6, 3), (31, 19), (24, 14), (33, 21), (6, 17), (33, 14), (23, 28), (33, 30), (29, 47), (16, 13), (19, 45), (27, 22), (12, 39), (18, 28), (35, 16), (18, 45), (5, 37), (38, 29), (33, 40), (23, 6), (16, 35), (17, 22), (27, 23), (3, 42), (9, 13), (4, 23), (24, 28), (12, 44), (35, 12), (4, 0), (36, 20), (29, 14), (10, 24), (4, 30), (22, 7), (27, 30), (15, 24), (14, 21), (38, 35), (5, 15), (25, 11), (1, 8), (2, 16), (27, 21), (25, 6), (13, 14), (37, 5), (6, 6), (32, 17), (18, 18), (39, 32), (0, 14), (9, 34), (19, 29), (33, 27), (8, 18), (8, 22), (37, 34), (30, 25), (13, 33), (20, 42), (39, 23), (32, 35), (11, 25), (16, 5), (0, 42), (12, 24), (20, 20), (28, 26), (3, 28), (20, 28), (3, 11), (21, 27), (35, 27), (27, 14), (29, 32), (9, 9), (32, 4), (32, 37), (15, 34), (17, 32), (35, 21), (1, 7), (8, 46), (38, 38), (2, 37), (36, 46), (24, 10), (36, 3), (23, 12), (15, 19), (11, 23), (37, 16), (15, 37), (5, 40), (30, 11), (27, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 28), (26, 10), (8, 24), (21, 5), (34, 30), (25, 32), (5, 15), (40, 29), (23, 0), (1, 41), (9, 32), (31, 15), (40, 16), (42, 39), (37, 13), (26, 0), (20, 25), (38, 22), (26, 34), (3, 14), (14, 11), (39, 43), (9, 33), (22, 40), (41, 36), (23, 4), (25, 15), (13, 18), (16, 10), (39, 26), (37, 23), (37, 37), (27, 11), (38, 31), (9, 22), (42, 17), (5, 37), (42, 14), (2, 43), (8, 45), (29, 44), (29, 10), (36, 31), (5, 5), (20, 26), (15, 15), (34, 25), (33, 16), (8, 37), (32, 22), (27, 21), (9, 47), (35, 12), (6, 5), (42, 5), (34, 1), (39, 39), (6, 42), (1, 45), (33, 18), (25, 18), (29, 47), (31, 16), (2, 42), (11, 39), (1, 19), (7, 16), (4, 0), (41, 45), (3, 38), (39, 21), (30, 11), (6, 31), (42, 4), (42, 0), (25, 13), (38, 5), (23, 7), (4, 35), (17, 22), (30, 16), (40, 11), (4, 2), (15, 42), (9, 40), (26, 28), (26, 18), (19, 25), (3, 45), (20, 29), (4, 9), (5, 14), (22, 5), (31, 10), (18, 7), (28, 17), (32, 36), (33, 47), (11, 40), (27, 6), (39, 12), (2, 38), (4, 25), (18, 20), (0, 12), (11, 0), (16, 7), (10, 6), (22, 23), (5, 13), (28, 43), (30, 46), (9, 43), (15, 1), (40, 40), (5, 21), (34, 10), (19, 27), (41, 24), (17, 3), (36, 6), (36, 37), (27, 0), (28, 44), (23, 1), (42, 32), (33, 14), (33, 10), (40, 36), (20, 4), (33, 1), (11, 41), (2, 35), (12, 6), (30, 14), (22, 35), (7, 7), (26, 42), (38, 21), (41, 12), (26, 1), (28, 9), (13, 13), (1, 38), (12, 42), (27, 43), (35, 46), (15, 3), (30, 22), (29, 5), (8, 33), (41, 35), (13, 14), (35, 19), (28, 21), (28, 39), (8, 38), (11, 43), (8, 7), (25, 19), (38, 4), (16, 29), (19, 38), (2, 28), (36, 22), (19, 45), (35, 18), (38, 36), (27, 9), (4, 34), (0, 29), (31, 12), (31, 4), (40, 32), (10, 23), (32, 21), (19, 7), (32, 3), (32, 12), (31, 34), (42, 46), (0, 28), (5, 18), (27, 46), (7, 26), (5, 12), (24, 15), (39, 30), (33, 38), (14, 32), (41, 46), (40, 17), (40, 45), (29, 46), (34, 20), (41, 10), (36, 0), (41, 4), (28, 45), (26, 24), (27, 24), (39, 25), (41, 21), (15, 7), (37, 20), (18, 3), (35, 6), (18, 24), (33, 40), (26, 12), (28, 31), (25, 4), (16, 11), (40, 33), (12, 4), (41, 8), (39, 2), (38, 27), (33, 5), (1, 18), (28, 3), (26, 41), (7, 44), (34, 32), (29, 0), (29, 18), (7, 19), (42, 22), (3, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 43x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 19), (5, 27), (25, 4), (11, 11), (19, 20), (16, 3), (7, 32), (35, 4), (12, 30), (4, 35), (2, 39), (18, 11), (21, 38), (15, 5), (35, 32), (25, 7), (6, 28), (9, 31), (27, 3), (41, 45), (29, 9), (28, 34), (10, 33), (37, 17), (10, 2), (26, 38), (42, 8), (2, 38), (28, 38), (13, 13), (29, 20), (25, 15), (7, 3), (10, 27), (1, 26), (28, 2), (12, 9), (40, 16), (41, 41), (11, 12), (31, 0), (2, 12), (22, 29), (4, 16), (41, 43), (6, 25), (17, 17), (34, 47), (1, 15), (14, 26), (28, 32), (2, 6), (7, 28), (35, 9), (36, 22), (21, 2), (33, 8), (14, 24), (16, 25), (38, 9), (11, 37), (19, 17), (28, 46), (22, 27), (5, 48), (14, 12), (39, 36), (11, 14), (4, 32), (42, 46), (0, 35), (11, 43), (28, 20), (8, 36), (17, 36), (23, 37), (7, 20), (6, 18), (22, 16), (42, 11), (17, 9), (40, 10), (37, 45), (25, 9), (1, 42), (37, 46), (42, 5), (2, 42), (9, 7), (15, 22), (25, 43), (33, 26), (16, 18), (38, 18), (37, 3), (19, 38), (42, 24), (29, 28), (26, 24), (23, 24), (40, 40), (27, 29), (12, 28), (21, 26), (38, 4), (11, 10), (17, 3), (27, 48), (14, 17), (27, 21), (20, 17), (18, 33), (16, 1), (10, 38), (35, 33), (19, 39), (21, 39), (27, 7), (1, 35), (42, 9), (0, 32), (32, 2), (5, 17), (29, 33), (28, 19), (8, 40), (23, 38), (42, 14), (28, 23), (42, 33), (22, 48), (22, 20), (18, 46), (9, 8), (33, 17), (37, 30), (11, 46), (5, 28), (41, 47), (15, 31), (18, 2), (33, 42), (34, 11), (32, 3), (12, 44), (21, 25), (40, 4), (42, 45), (13, 18), (24, 1), (35, 41), (38, 26), (42, 20), (32, 42), (42, 43), (5, 15), (31, 13), (17, 29), (33, 14), (7, 1), (29, 23), (16, 32), (39, 28), (8, 34), (2, 3), (25, 31), (16, 5), (30, 44), (28, 16), (12, 19), (0, 44), (21, 32), (11, 1), (31, 47), (19, 34), (32, 0), (1, 17), (37, 13), (40, 14), (27, 46), (7, 10), (7, 17), (3, 16), (33, 38), (18, 40), (25, 42), (17, 0), (26, 2), (36, 36), (7, 47), (11, 31), (20, 10), (4, 8), (31, 30), (36, 17), (11, 13), (22, 43), (21, 42), (30, 2), (24, 7), (25, 23), (6, 27), (0, 21), (27, 2), (42, 12), (22, 12), (8, 32), (18, 41), (41, 17), (23, 7), (40, 26), (13, 29), (39, 12), (17, 13), (42, 21), (0, 41), (30, 19), (6, 3), (22, 4), (17, 33), (26, 17), (0, 12), (21, 16), (34, 27), (40, 11), (29, 29), (35, 25), (18, 37), (27, 32), (35, 17), (25, 21), (42, 26), (6, 10), (1, 40), (41, 24), (11, 9), (35, 11), (3, 8), (39, 48)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 47x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 39), (5, 7), (22, 39), (7, 12), (31, 45), (22, 11), (15, 37), (33, 15), (35, 31), (18, 12), (14, 1), (5, 19), (10, 33), (18, 5), (3, 13), (21, 3), (44, 19), (21, 31), (4, 13), (16, 35), (6, 44), (36, 7), (3, 10), (3, 7), (16, 3), (7, 42), (38, 13), (17, 19), (13, 42), (45, 38), (37, 35), (37, 20), (1, 32), (28, 27), (42, 7), (44, 13), (32, 19), (25, 39), (34, 20), (35, 44), (11, 34), (29, 42), (13, 27), (21, 10), (16, 40), (4, 26), (28, 10), (10, 29), (33, 37), (39, 18), (20, 3), (32, 12), (15, 42), (40, 8), (31, 13), (17, 24), (4, 11), (45, 2), (30, 43), (19, 28), (45, 12), (31, 8), (8, 1), (0, 38), (29, 31), (40, 40), (26, 0), (24, 20), (11, 1), (18, 43), (39, 29), (29, 37), (7, 10), (31, 5), (19, 43), (4, 45), (34, 14), (36, 29), (25, 42), (40, 25), (13, 33), (4, 34), (43, 34), (4, 19), (40, 19), (36, 43), (20, 37), (24, 8), (45, 17), (32, 33), (26, 16), (33, 39), (19, 2), (46, 35), (14, 19), (36, 3), (30, 28), (41, 7), (8, 16), (23, 20), (34, 32), (27, 27), (34, 27), (29, 44), (46, 41), (22, 1), (35, 32), (16, 44), (14, 6), (20, 0), (33, 32), (39, 38), (21, 44), (12, 33), (6, 33), (33, 14), (3, 0), (31, 22), (27, 0), (12, 20), (6, 21), (11, 19), (29, 32), (1, 36), (0, 35), (6, 16), (13, 23), (25, 26), (21, 42), (41, 28), (20, 24), (27, 18), (23, 12), (13, 30), (6, 14), (19, 6), (36, 6), (45, 35), (17, 15), (41, 14), (0, 37), (10, 16), (41, 39), (35, 8), (30, 33), (4, 4), (37, 1), (12, 15), (1, 21), (45, 11), (44, 9), (1, 12), (32, 10), (6, 1), (1, 1), (28, 30), (29, 8), (20, 18), (25, 37), (12, 32), (8, 13), (28, 6), (8, 11), (8, 28), (12, 1), (20, 25), (3, 23), (36, 21), (14, 12), (31, 34), (2, 22), (2, 10), (11, 41), (6, 19), (23, 17), (15, 35), (24, 2), (38, 35), (30, 14), (46, 22), (13, 36), (14, 34), (41, 44), (43, 16), (44, 39), (24, 33), (20, 36), (18, 16), (21, 19), (2, 23), (21, 29), (18, 27), (21, 43), (11, 3), (13, 34), (20, 10), (0, 23), (45, 9), (45, 37), (24, 42), (22, 34), (9, 21), (2, 42), (3, 27), (23, 22), (20, 4), (40, 6), (7, 45), (33, 3), (29, 4), (40, 28), (23, 33), (36, 12), (24, 0), (5, 25), (26, 10), (30, 20), (14, 37), (45, 42), (11, 20), (22, 5), (39, 9), (18, 35), (36, 27), (27, 43), (38, 42), (4, 38), (24, 16), (40, 30), (31, 19), (14, 4), (3, 8), (31, 37), (8, 41), (39, 13), (19, 11), (30, 26), (16, 11), (12, 14), (30, 31), (13, 0), (30, 2), (26, 14), (21, 14), (37, 39), (24, 14), (7, 9), (30, 3), (10, 9), (13, 28), (2, 4), (4, 39), (38, 24), (40, 14), (8, 27), (21, 21), (6, 11), (34, 13), (34, 31), (17, 27), (9, 42), (3, 25), (1, 44), (38, 3), (36, 45), (2, 1), (14, 45), (5, 38), (32, 16), (15, 6), (20, 27), (17, 37), (11, 24), (15, 45), (10, 28), (25, 32), (24, 11), (29, 18), (40, 39), (44, 29), (22, 30), (39, 22), (40, 38), (44, 34), (16, 6), (8, 20), (0, 7), (10, 14), (32, 40), (44, 23), (22, 28), (23, 11), (43, 42), (46, 13), (5, 4), (24, 35), (1, 6), (12, 42), (5, 33), (1, 7), (45, 26), (0, 45), (36, 34), (27, 22), (19, 23), (41, 1), (12, 7), (6, 45), (44, 26), (33, 34), (13, 43), (46, 27), (2, 16), (35, 14), (35, 20), (10, 23), (18, 33), (43, 41), (26, 40), (34, 35), (30, 21), (29, 36), (45, 33), (41, 30), (16, 15), (4, 0), (25, 10), (12, 17), (32, 30), (0, 8), (44, 8), (31, 38), (41, 21), (13, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 7), (6, 13), (14, 26), (2, 35), (15, 1), (32, 37), (4, 7), (10, 26), (26, 19), (12, 16), (3, 0), (26, 28), (31, 23), (38, 1), (1, 12), (39, 27), (19, 7), (26, 20), (31, 15), (20, 18), (6, 7), (34, 32), (39, 3), (21, 30), (8, 35), (38, 37), (5, 12), (10, 39), (30, 34), (34, 24), (29, 32), (39, 29), (34, 17), (40, 4), (29, 4), (1, 3), (16, 17), (22, 35), (0, 4), (35, 9), (18, 6), (6, 10), (27, 43), (38, 36), (24, 40), (11, 8), (35, 43), (32, 31), (34, 30), (15, 17), (26, 10), (35, 2), (5, 36), (13, 7), (10, 2), (4, 12), (10, 33), (11, 5), (0, 39), (12, 8), (28, 15), (35, 29), (20, 38), (12, 33), (21, 12), (38, 29), (19, 11), (35, 17), (19, 19), (38, 6), (5, 38), (24, 20), (33, 8), (19, 12), (36, 17), (1, 32), (10, 28), (27, 2), (37, 11), (33, 7), (36, 8), (26, 11), (6, 38), (39, 35), (18, 30), (7, 1), (21, 37), (24, 43), (29, 8), (18, 4), (3, 9), (26, 13), (34, 33), (35, 25), (40, 27), (23, 19), (14, 6), (13, 35), (20, 29), (24, 9), (17, 2), (20, 20), (34, 38), (25, 42), (34, 39), (18, 38), (24, 33), (13, 6), (6, 32), (0, 20), (0, 9), (5, 33), (11, 0), (36, 29), (11, 32), (0, 36), (14, 10), (1, 29), (23, 43), (18, 39), (0, 32), (2, 43), (6, 3), (21, 20), (4, 27), (29, 24), (32, 3), (29, 10), (13, 16), (10, 5), (11, 23), (33, 36), (16, 19), (23, 1), (0, 14), (0, 41), (39, 15), (37, 34), (5, 5), (16, 26), (19, 23), (26, 38), (34, 25), (33, 13), (8, 34), (17, 43), (9, 11), (29, 5), (19, 27), (34, 3), (21, 26), (4, 5), (13, 14), (8, 29), (26, 5), (12, 27), (34, 9), (34, 7), (23, 0), (5, 28), (29, 29), (13, 3), (16, 32), (2, 18), (19, 25), (12, 31), (6, 16), (9, 6), (34, 21), (2, 7), (18, 8), (11, 2), (30, 11), (33, 40), (40, 35), (5, 19), (13, 1), (18, 5), (1, 2), (26, 34), (28, 37), (40, 31), (26, 21), (9, 1), (33, 38), (7, 18), (26, 6), (32, 26), (8, 37), (7, 14), (27, 40), (32, 22), (27, 3), (4, 36), (18, 41), (25, 40), (38, 17), (15, 24), (39, 30), (37, 1), (11, 29), (16, 36), (6, 26), (4, 28), (2, 11), (38, 2), (20, 42), (0, 34), (7, 31), (7, 8), (30, 36), (27, 12), (36, 22), (20, 19), (37, 39), (19, 13), (28, 13), (38, 0), (2, 38), (34, 13), (3, 19), (40, 20), (33, 37), (6, 12), (30, 13), (35, 10), (23, 41), (7, 37), (16, 8), (12, 7), (27, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 20), (33, 21), (0, 17), (21, 23), (22, 7), (29, 18), (18, 38), (5, 40), (36, 27), (15, 17), (4, 26), (6, 36), (21, 22), (3, 12), (11, 0), (16, 19), (13, 22), (18, 39), (16, 28), (11, 13), (12, 25), (19, 2), (15, 14), (22, 34), (6, 35), (11, 5), (2, 26), (10, 12), (27, 31), (21, 10), (16, 16), (10, 33), (36, 17), (12, 9), (10, 35), (19, 41), (23, 8), (11, 6), (25, 11), (27, 24), (6, 28), (16, 18), (22, 39), (16, 33), (10, 19), (34, 15), (26, 34), (6, 12), (10, 14), (23, 42), (39, 20), (37, 38), (4, 18), (35, 4), (33, 15), (21, 38), (28, 6), (33, 26), (5, 26), (18, 22), (28, 13), (40, 22), (3, 41), (32, 37), (3, 23), (39, 27), (34, 4), (28, 10), (23, 32), (17, 5), (7, 35), (30, 9), (19, 7), (36, 22), (7, 39), (16, 0), (7, 13), (3, 34), (34, 21), (6, 9), (30, 11), (29, 37), (21, 24), (15, 23), (7, 6), (32, 14), (3, 6), (34, 24), (7, 10), (34, 1), (23, 3), (16, 30), (22, 40), (4, 3), (7, 14), (27, 25), (25, 19), (2, 38), (36, 19), (28, 23), (16, 14), (29, 38), (4, 10), (23, 30), (34, 18), (1, 38), (3, 2), (33, 25), (24, 36), (35, 38), (38, 11), (30, 37), (27, 33), (2, 12), (12, 11), (31, 5), (11, 39), (30, 1), (18, 2), (19, 20), (28, 22), (9, 25), (4, 13), (9, 29), (34, 25), (40, 4), (15, 21), (35, 35), (9, 34), (20, 18), (35, 16), (33, 31), (13, 6), (36, 32), (9, 5), (34, 11), (35, 7), (2, 27), (14, 6), (0, 9), (4, 27), (16, 25), (23, 1), (18, 36), (15, 22), (6, 26), (39, 39), (29, 16), (4, 11), (24, 26), (34, 9), (20, 34), (20, 33), (10, 27), (11, 7), (38, 35), (22, 12), (4, 24), (16, 7), (22, 18), (18, 28), (22, 14), (37, 18), (14, 30), (0, 31), (12, 27), (39, 33), (2, 23), (38, 24), (1, 40), (9, 33), (30, 34), (27, 13), (35, 17), (2, 11), (28, 2), (1, 6), (10, 25), (23, 14), (40, 21), (26, 24), (5, 11), (29, 12), (26, 16), (12, 36), (13, 10), (35, 23), (21, 34), (28, 21), (37, 20), (33, 2), (15, 42), (38, 27), (32, 19), (40, 16), (5, 7), (5, 33), (35, 5), (16, 27), (5, 39), (27, 38), (24, 6), (9, 35), (40, 39), (32, 39), (19, 28), (14, 23), (16, 9), (28, 36), (40, 18), (22, 1), (6, 38), (26, 14), (25, 32), (31, 34), (25, 4), (36, 7), (4, 14), (31, 41), (14, 36), (20, 12), (11, 21), (7, 16), (37, 37), (1, 14), (26, 28), (32, 10), (4, 20), (19, 4), (30, 40), (0, 14), (31, 17), (15, 6), (3, 22), (36, 20), (39, 21), (17, 30), (19, 29), (29, 39), (0, 29), (21, 0), (37, 32), (5, 1), (25, 25), (5, 0), (7, 33), (38, 3), (4, 9), (14, 8), (37, 21), (12, 34), (3, 27), (17, 39), (7, 12), (28, 28), (21, 37), (28, 12), (22, 37), (4, 25), (26, 33), (32, 36), (7, 27), (38, 9), (16, 10), (39, 32), (1, 39), (18, 5), (18, 10), (20, 6), (25, 22), (5, 12), (36, 11), (13, 5), (6, 8), (5, 32), (11, 37), (1, 8), (6, 18), (25, 8), (35, 28), (21, 29), (36, 6), (12, 0), (19, 27), (33, 32), (3, 38), (1, 3), (2, 34), (27, 42), (23, 13), (8, 11), (32, 1), (11, 42), (7, 4), (11, 33), (10, 30), (27, 18), (26, 30), (24, 27), (17, 20), (24, 37), (39, 2), (20, 25), (32, 2), (29, 25), (14, 10), (17, 41), (38, 40), (2, 29), (39, 9), (14, 38), (23, 21), (15, 9), (31, 4), (38, 23), (0, 13), (12, 6), (3, 0), (3, 28), (37, 39), (12, 24), (15, 15), (37, 1), (13, 25), (21, 33), (7, 23), (19, 6), (4, 12), (13, 23), (9, 10), (6, 11), (18, 34), (11, 41), (11, 17), (22, 6), (5, 18), (32, 18), (21, 32), (20, 5), (39, 22), (24, 39), (20, 21), (37, 10), (8, 31), (25, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 48x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (13, 40), (3, 22), (25, 38), (43, 36), (12, 1), (14, 9), (8, 35), (21, 0), (18, 5), (22, 16), (8, 30), (7, 12), (21, 34), (15, 15), (10, 29), (11, 28), (18, 33), (47, 15), (1, 40), (11, 33), (1, 8), (23, 30), (34, 34), (37, 2), (28, 26), (15, 29), (29, 25), (30, 38), (39, 20), (34, 6), (22, 29), (33, 34), (29, 35), (21, 11), (28, 6), (42, 3), (14, 26), (1, 10), (27, 3), (15, 35), (43, 26), (11, 22), (24, 4), (33, 19), (8, 20), (47, 32), (1, 26), (20, 39), (14, 0), (12, 23), (8, 9), (21, 39), (17, 25), (32, 2), (36, 40), (32, 27), (16, 34), (17, 2), (13, 41), (15, 20), (19, 31), (16, 18), (19, 33), (40, 11), (39, 17), (29, 27), (25, 35), (13, 1), (6, 36), (36, 12), (16, 0), (33, 2), (25, 28), (32, 39), (36, 1), (31, 1), (20, 0), (6, 16), (22, 28), (12, 31), (33, 29), (13, 3), (23, 39), (6, 23), (37, 7), (21, 14), (30, 3), (1, 3), (6, 27), (26, 10), (4, 1), (26, 2), (8, 40), (4, 38), (31, 16), (40, 22), (34, 13), (7, 26), (34, 24), (37, 29), (5, 40), (44, 17), (1, 0), (38, 22), (36, 33), (31, 13), (47, 35), (6, 1), (33, 22), (28, 1), (11, 6), (19, 39), (10, 22), (44, 39), (39, 6), (46, 38), (29, 39), (39, 10), (5, 2), (17, 5), (23, 0), (20, 23), (38, 20), (44, 40), (45, 1), (41, 17), (40, 8), (40, 2), (44, 12), (40, 31), (17, 1), (38, 8), (9, 2), (7, 11), (35, 38), (14, 27), (34, 17), (24, 20), (6, 31), (13, 37), (46, 30), (38, 26), (19, 24), (38, 12), (20, 29), (0, 39), (5, 31), (20, 40), (36, 13), (16, 40), (0, 6), (12, 22), (44, 36), (14, 7), (41, 7), (21, 41), (26, 38), (8, 0), (9, 40), (22, 35), (5, 34), (20, 6), (13, 21), (45, 2), (24, 7), (5, 3), (38, 24), (5, 19), (8, 12), (46, 21), (45, 6), (34, 35), (9, 5), (0, 23), (25, 39), (43, 17), (22, 26), (26, 6), (27, 5), (40, 40), (46, 13), (18, 32), (30, 27), (31, 34), (22, 3), (40, 14), (10, 39), (21, 15), (0, 29), (13, 17), (39, 36), (9, 27), (30, 24), (8, 33), (7, 21), (13, 39), (20, 38), (20, 10), (37, 26), (19, 22), (21, 13), (7, 31), (2, 18), (15, 40), (22, 34), (0, 7), (47, 33), (44, 22), (8, 41), (25, 1), (11, 23), (9, 37), (46, 22), (16, 9), (23, 20), (16, 26), (45, 27), (35, 33), (7, 24), (41, 19), (25, 30), (2, 7), (31, 9), (6, 20), (18, 38), (46, 8), (47, 38), (42, 33), (26, 13), (11, 12), (1, 28), (46, 20), (19, 21), (3, 38), (41, 38), (10, 0), (37, 15), (8, 10), (29, 38), (32, 25), (5, 33), (5, 1), (0, 12), (6, 25), (8, 5), (9, 25), (45, 41), (28, 41), (4, 10), (17, 4), (22, 7), (27, 27), (15, 9), (45, 13), (39, 0), (47, 11), (35, 40), (46, 11), (27, 8), (28, 24), (39, 39), (31, 23), (23, 12), (21, 20), (43, 11), (24, 11), (32, 6), (14, 3), (46, 15), (30, 19), (5, 28), (6, 21), (45, 29), (47, 19), (27, 4), (9, 4), (13, 22), (5, 15), (12, 36), (24, 19), (27, 22), (30, 29), (27, 15), (41, 5), (20, 35), (3, 9), (28, 18), (41, 15), (47, 28), (47, 26), (13, 27), (5, 22), (10, 21), (30, 39), (38, 2), (0, 30), (14, 13), (38, 16), (14, 40), (26, 36), (26, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 49x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (43, 3), (21, 2), (26, 6), (43, 15), (45, 39), (35, 1), (3, 19), (39, 29), (29, 7), (37, 5), (44, 8), (38, 40), (47, 22), (37, 40), (14, 41), (11, 8), (38, 20), (46, 1), (21, 32), (38, 11), (32, 23), (19, 35), (22, 9), (18, 21), (31, 20), (36, 39), (34, 26), (18, 42), (15, 14), (24, 11), (26, 27), (25, 33), (8, 21), (5, 12), (37, 14), (7, 33), (16, 21), (5, 21), (40, 12), (26, 25), (3, 36), (31, 14), (20, 18), (28, 6), (45, 34), (22, 36), (29, 37), (25, 24), (18, 22), (8, 30), (34, 2), (21, 24), (4, 13), (4, 12), (37, 32), (14, 23), (48, 12), (38, 0), (28, 5), (27, 8), (32, 22), (18, 23), (34, 25), (47, 39), (41, 5), (20, 25), (6, 6), (43, 18), (16, 20), (48, 18), (45, 6), (46, 26), (5, 27), (13, 14), (2, 17), (10, 26), (17, 31), (29, 18), (39, 34), (18, 25), (23, 4), (28, 23), (27, 38), (40, 8), (1, 5), (21, 4), (1, 30), (8, 18), (1, 36), (14, 13), (48, 19), (12, 16), (12, 30), (16, 36), (48, 3), (7, 19), (41, 40), (45, 32), (16, 9), (22, 27), (37, 38), (2, 33), (38, 26), (46, 25), (19, 38), (16, 14), (48, 22), (8, 19), (0, 38), (26, 29), (9, 6), (40, 36), (14, 7), (28, 40), (18, 34), (13, 39), (4, 40), (43, 32), (12, 3), (26, 23), (45, 35), (4, 5), (13, 31), (46, 32), (43, 9), (45, 23), (14, 39), (34, 18), (5, 18), (16, 12), (46, 5), (43, 4), (6, 27), (10, 24), (24, 14), (32, 13), (1, 20), (2, 41), (6, 34), (25, 29), (33, 35), (22, 33), (38, 21), (30, 17), (14, 19), (20, 34), (28, 42), (4, 24), (27, 15), (19, 19), (34, 34), (43, 26), (16, 28), (2, 29), (20, 22), (9, 5), (13, 16), (4, 36), (3, 27), (32, 14), (29, 15), (30, 13), (47, 19), (9, 10), (23, 28), (33, 11), (48, 28), (2, 6), (40, 11), (44, 2), (41, 22), (33, 21), (10, 27), (10, 30), (2, 9), (7, 40), (3, 21), (20, 12), (15, 4), (38, 32), (6, 16), (26, 38), (7, 38), (12, 0), (20, 28), (34, 10), (35, 17), (35, 21), (0, 7), (31, 15), (16, 6), (5, 3), (31, 33), (26, 7), (10, 14), (35, 2), (48, 41), (28, 37), (7, 7), (6, 9), (0, 13), (5, 40), (17, 35), (38, 5), (34, 11), (27, 36), (31, 26), (17, 41), (2, 15), (9, 30), (10, 31), (23, 13), (28, 26), (1, 35), (15, 20), (0, 27), (48, 32), (45, 19), (28, 32), (13, 35), (37, 6), (44, 36), (44, 27), (6, 19), (18, 16), (38, 7), (37, 8), (10, 39), (35, 26), (34, 31), (47, 23), (14, 30), (47, 30), (5, 26), (22, 15), (1, 9), (42, 16), (23, 3), (27, 9), (41, 35), (7, 37), (45, 38), (37, 21), (9, 14), (32, 36), (19, 32), (15, 15), (19, 8), (42, 0), (15, 36), (24, 41), (38, 41), (26, 40), (24, 22), (13, 15), (47, 13), (4, 18), (22, 29), (13, 1), (15, 3), (0, 31), (6, 35), (38, 8), (6, 11), (42, 37), (25, 38), (3, 33), (7, 22), (1, 29), (44, 9), (0, 34), (9, 28), (17, 2), (15, 25), (15, 17), (39, 31), (20, 41), (24, 2), (24, 7), (30, 12), (11, 27), (25, 16), (47, 4), (0, 20), (23, 22), (6, 5), (12, 29), (13, 9), (32, 34), (0, 23), (42, 21), (4, 32), (1, 28), (3, 12), (43, 35), (8, 24), (30, 23), (18, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (9, 36), (22, 3), (34, 12), (39, 2), (3, 9), (21, 39), (0, 30), (23, 7), (22, 25), (44, 26), (46, 11), (38, 24), (43, 3), (45, 33), (36, 2), (26, 17), (23, 26), (38, 20), (45, 23), (5, 31), (1, 5), (2, 10), (44, 34), (24, 32), (35, 39), (40, 6), (9, 35), (8, 8), (0, 10), (40, 26), (39, 18), (34, 19), (4, 18), (22, 1), (26, 31), (7, 29), (4, 12), (21, 19), (0, 22), (8, 23), (37, 40), (14, 17), (43, 9), (35, 7), (30, 10), (8, 2), (42, 26), (9, 21), (31, 38), (29, 36), (9, 33), (39, 39), (41, 36), (29, 23), (9, 12), (11, 1), (36, 4), (10, 22), (18, 31), (27, 38), (29, 24), (46, 7), (22, 23), (35, 25), (44, 11), (21, 18), (45, 30), (24, 15), (1, 36), (21, 0), (10, 23), (4, 22), (13, 13), (37, 32), (21, 21), (32, 18), (22, 22), (23, 27), (2, 29), (28, 21), (29, 0), (2, 6), (5, 12), (8, 13), (44, 18), (24, 1), (38, 4), (23, 17), (5, 24), (22, 20), (45, 7), (35, 8), (29, 13), (28, 22), (4, 40), (5, 26), (28, 39), (11, 32), (33, 30), (19, 10), (15, 39), (32, 26), (21, 22), (6, 7), (42, 18), (30, 29), (2, 25), (39, 6), (20, 13), (27, 30), (18, 30), (42, 32), (20, 26), (21, 13), (22, 39), (16, 28), (3, 34), (38, 9), (44, 4), (26, 19), (0, 17), (8, 12), (2, 12), (16, 0), (31, 4), (22, 18), (6, 33), (2, 31), (39, 17), (4, 15), (41, 20), (27, 23), (25, 23), (35, 4), (23, 31), (24, 27), (29, 27), (46, 14), (38, 12), (28, 1), (28, 10), (28, 32), (8, 15), (31, 36), (21, 14), (42, 9), (17, 34), (18, 27), (6, 12), (18, 2), (29, 5), (7, 3), (6, 16), (41, 19), (7, 25), (26, 28), (44, 14), (11, 29), (38, 17), (46, 23), (3, 19), (15, 37), (37, 18), (31, 24), (41, 13), (3, 25), (15, 27), (0, 26), (39, 10), (37, 23), (25, 13), (43, 13), (8, 36), (39, 13), (26, 13), (40, 12), (17, 21), (44, 35), (31, 27), (3, 31), (25, 37), (34, 0), (20, 0), (3, 20), (17, 6), (36, 24), (40, 23), (32, 23), (32, 33), (4, 4), (18, 24), (17, 19), (43, 28), (4, 20), (35, 22), (5, 5), (3, 39), (39, 29), (34, 20), (42, 5), (35, 11), (40, 1), (14, 39), (9, 31), (11, 17), (45, 38), (21, 16), (38, 2), (27, 22), (7, 11), (31, 15), (42, 37), (7, 17), (21, 35), (30, 18), (2, 5), (14, 12), (7, 18), (45, 25), (15, 28), (40, 36), (14, 24), (15, 21), (37, 3), (25, 8), (16, 29), (14, 21), (17, 5), (45, 28), (44, 33), (43, 33), (30, 25), (14, 10), (7, 15), (41, 21), (10, 37), (2, 19), (45, 12), (7, 38), (46, 5), (21, 3), (21, 30), (40, 32), (14, 34), (10, 11), (36, 22), (23, 13), (14, 32), (34, 23), (46, 21), (34, 36), (10, 38), (39, 23), (46, 25), (46, 16), (40, 0), (14, 35), (23, 24), (11, 23), (37, 14), (30, 33), (33, 19), (4, 33), (40, 11), (28, 19), (32, 22), (33, 16), (19, 35), (9, 17), (32, 0), (45, 15), (32, 4), (5, 38), (34, 27), (43, 11), (0, 25), (37, 20), (8, 28), (6, 34), (12, 31), (15, 17), (43, 2), (36, 15), (32, 1), (11, 24), (3, 33), (1, 3), (14, 27), (12, 32), (7, 2), (12, 2), (26, 24), (41, 37), (41, 4), (36, 20), (12, 37), (14, 33), (14, 29), (5, 28), (36, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (6, 37), (35, 38), (31, 28), (20, 34), (20, 9), (12, 19), (40, 28), (24, 22), (10, 40), (6, 39), (37, 36), (13, 24), (7, 28), (0, 33), (23, 37), (43, 13), (18, 2), (39, 24), (4, 40), (2, 9), (29, 32), (5, 39), (9, 37), (19, 1), (35, 24), (4, 23), (14, 6), (38, 35), (30, 33), (36, 11), (1, 35), (10, 39), (28, 10), (44, 31), (35, 4), (22, 30), (38, 34), (8, 25), (36, 27), (24, 16), (23, 34), (6, 10), (19, 13), (36, 2), (10, 33), (35, 32), (9, 1), (18, 17), (44, 1), (29, 9), (15, 26), (14, 8), (33, 36), (11, 7), (15, 17), (6, 3), (14, 1), (3, 31), (30, 39), (13, 5), (16, 19), (24, 5), (19, 40), (9, 29), (26, 27), (28, 25), (21, 39), (24, 15), (8, 12), (23, 18), (4, 15), (18, 31), (18, 27), (36, 1), (13, 38), (39, 38), (14, 16), (1, 5), (4, 14), (44, 4), (1, 12), (41, 21), (20, 3), (1, 23), (39, 15), (41, 9), (13, 7), (10, 16), (1, 27), (21, 32), (25, 13), (21, 33), (14, 35), (38, 16), (24, 32), (17, 23), (31, 21), (22, 29), (36, 15), (41, 11), (19, 15), (25, 25), (28, 21), (20, 23), (35, 40), (5, 2), (43, 26), (32, 37), (16, 13), (7, 6), (18, 22), (6, 6), (31, 11), (14, 30), (41, 40), (9, 2), (9, 10), (3, 15), (42, 38), (43, 9), (1, 7), (7, 31), (16, 7), (22, 20), (38, 36), (13, 21), (17, 28), (2, 4), (0, 38), (39, 35), (30, 20), (21, 3), (40, 27), (4, 34), (44, 25), (10, 8), (32, 11), (7, 18), (34, 17), (1, 36), (10, 2), (37, 4), (33, 18), (28, 27), (36, 14), (6, 2), (28, 12), (26, 39), (2, 7), (11, 35), (35, 23), (14, 33), (26, 23), (44, 5), (36, 40), (16, 2), (14, 5), (15, 1), (39, 25), (23, 40), (40, 12), (7, 29), (30, 27), (35, 8), (5, 28), (22, 34), (35, 13), (40, 16), (19, 28), (33, 0), (39, 9), (3, 0), (7, 14), (16, 33), (1, 37), (19, 26), (20, 31), (5, 31), (32, 28), (41, 30), (13, 34), (8, 11), (21, 28), (5, 35), (30, 16), (21, 27), (32, 2), (24, 12), (39, 6), (39, 40), (40, 3), (39, 2), (3, 36), (43, 4), (15, 28), (4, 18), (29, 8), (35, 7), (7, 34), (37, 10), (16, 21), (31, 39), (33, 28), (9, 3), (6, 24), (38, 29), (39, 13), (19, 30), (15, 35), (0, 2), (40, 14), (42, 16), (3, 1), (25, 11), (8, 1), (30, 19), (1, 26), (13, 35), (1, 32), (38, 0), (31, 20), (15, 4), (19, 19), (38, 27), (3, 2), (39, 7), (43, 17), (6, 36), (12, 34), (7, 9), (18, 5), (3, 17), (12, 12), (37, 27), (29, 27), (28, 24), (37, 40), (35, 35), (16, 12), (16, 40), (34, 40), (26, 29), (2, 36), (10, 10), (35, 19), (42, 6), (32, 31), (15, 9), (40, 34), (37, 38), (29, 22), (31, 24), (19, 10), (31, 8), (37, 37), (0, 11), (19, 6), (4, 39), (44, 19), (38, 12), (38, 25), (25, 33), (42, 28), (8, 20), (2, 15), (20, 39), (38, 19)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 41x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 7), (19, 23), (13, 0), (15, 2), (22, 39), (15, 37), (17, 29), (18, 4), (0, 41), (20, 16), (30, 14), (39, 16), (21, 37), (21, 1), (36, 7), (22, 35), (4, 40), (37, 33), (25, 9), (39, 24), (39, 32), (32, 6), (10, 26), (3, 41), (4, 37), (6, 42), (36, 21), (4, 28), (30, 12), (27, 14), (36, 29), (29, 24), (14, 41), (39, 23), (14, 27), (17, 32), (4, 18), (7, 7), (3, 4), (38, 2), (39, 30), (30, 30), (38, 3), (29, 17), (24, 10), (25, 13), (30, 22), (5, 34), (30, 10), (22, 42), (30, 26), (19, 28), (39, 19), (20, 33), (18, 7), (4, 39), (33, 45), (23, 38), (22, 23), (27, 2), (21, 17), (25, 32), (17, 20), (3, 13), (11, 25), (22, 20), (35, 28), (0, 8), (27, 31), (7, 17), (31, 12), (37, 20), (6, 32), (6, 8), (12, 42), (22, 37), (30, 20), (33, 11), (17, 44), (35, 25), (15, 33), (29, 7), (6, 0), (28, 35), (27, 21), (21, 16), (24, 33), (9, 31), (19, 38), (22, 4), (11, 15), (19, 13), (6, 33), (21, 2), (5, 32), (33, 18), (25, 10), (2, 19), (15, 22), (6, 23), (35, 2), (22, 34), (33, 4), (5, 3), (30, 35), (31, 24), (36, 6), (23, 16), (35, 40), (22, 2), (19, 26), (8, 19), (4, 22), (11, 14), (39, 6), (38, 22), (37, 6), (9, 12), (8, 14), (11, 34), (24, 31), (35, 30), (35, 23), (30, 43), (35, 17), (36, 8), (13, 43), (29, 14), (36, 37), (3, 21), (18, 15), (10, 1), (38, 14), (9, 6), (21, 3), (6, 14), (7, 11), (16, 21), (20, 35), (36, 3), (33, 25), (14, 35), (0, 17), (4, 31), (13, 9), (5, 9), (11, 36), (31, 42), (7, 41), (9, 44), (23, 9), (32, 13), (20, 2), (38, 17), (37, 24), (36, 45), (18, 34), (8, 38), (38, 28), (19, 29), (39, 44), (16, 7), (10, 14), (12, 43), (21, 26), (11, 26), (10, 38), (24, 2), (18, 36), (4, 20), (11, 20), (32, 1), (9, 18), (10, 7), (3, 15), (8, 32), (17, 23), (29, 11), (10, 23), (0, 24), (25, 3), (38, 5), (26, 42), (37, 4), (10, 22), (19, 35), (28, 9), (2, 16), (31, 23), (25, 21), (0, 31), (29, 2), (26, 43), (1, 5), (13, 3), (21, 40), (3, 2), (36, 14), (17, 25), (25, 36), (8, 31), (34, 36), (10, 12), (12, 45), (9, 38), (30, 19), (35, 3), (18, 39), (12, 27), (33, 38), (4, 3), (15, 4), (21, 22), (5, 7), (34, 33), (4, 42), (12, 37), (6, 15), (4, 36), (21, 33), (18, 33), (37, 28), (6, 12), (32, 26), (15, 17), (19, 20), (27, 33), (36, 1), (30, 4), (32, 40), (3, 29), (26, 14), (14, 15), (31, 27), (27, 38), (23, 39), (34, 5), (7, 27), (26, 15), (12, 34), (22, 33), (3, 44), (39, 27), (27, 6), (6, 4), (39, 34), (33, 2), (35, 29), (33, 9), (10, 35), (5, 10), (26, 34), (25, 12), (3, 27), (25, 1), (34, 38), (40, 27), (10, 24), (27, 36), (19, 36), (25, 0), (22, 5), (40, 13), (11, 45), (35, 26), (18, 17), (24, 16), (20, 3), (17, 15), (12, 23), (5, 12), (19, 45), (8, 23), (2, 27), (24, 35), (37, 16), (6, 31), (17, 4), (15, 29), (20, 6), (21, 8), (21, 23), (29, 32), (37, 12), (38, 0), (20, 36), (7, 43), (0, 32), (38, 30), (29, 8), (15, 11), (3, 11), (40, 23), (13, 4), (27, 12), (12, 17), (17, 30), (32, 31), (13, 17), (28, 19), (22, 9), (40, 25), (37, 10), (35, 38), (23, 37), (27, 29), (8, 10), (36, 11), (9, 28), (22, 0), (16, 14), (39, 31), (28, 43), (34, 13), (8, 22), (11, 43), (38, 21), (40, 31), (15, 30), (13, 14), (7, 38), (33, 44), (21, 28), (5, 5), (7, 25), (3, 5), (35, 37), (38, 34), (18, 14), (6, 39), (36, 17), (30, 17), (9, 23), (15, 20), (32, 32), (40, 40), (5, 16), (32, 35), (11, 3), (30, 8), (40, 34), (22, 24), (35, 0), (21, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 44x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (35, 14), (3, 34), (7, 46), (34, 34), (9, 11), (33, 20), (12, 17), (5, 21), (34, 23), (22, 39), (3, 6), (10, 10), (4, 35), (41, 25), (40, 8), (31, 45), (33, 23), (1, 17), (32, 41), (26, 15), (21, 43), (24, 15), (14, 7), (9, 18), (9, 3), (37, 18), (31, 34), (14, 30), (8, 29), (28, 9), (11, 21), (11, 41), (29, 48), (6, 41), (10, 22), (14, 37), (7, 16), (37, 47), (41, 23), (33, 15), (1, 40), (4, 7), (1, 24), (37, 46), (1, 41), (32, 11), (39, 12), (37, 6), (5, 5), (16, 27), (9, 41), (16, 18), (29, 3), (3, 2), (33, 24), (12, 2), (5, 24), (29, 18), (2, 40), (20, 35), (8, 36), (29, 2), (2, 14), (19, 48), (19, 22), (39, 35), (35, 44), (21, 34), (23, 17), (13, 22), (37, 41), (25, 13), (12, 47), (20, 1), (38, 27), (20, 0), (42, 10), (34, 7), (20, 28), (39, 17), (15, 36), (40, 30), (15, 45), (42, 41), (6, 20), (1, 28), (31, 11), (36, 3), (16, 31), (13, 3), (2, 43), (22, 12), (23, 40), (13, 21), (40, 36), (20, 22), (13, 39), (5, 42), (28, 2), (28, 4), (1, 35), (24, 37), (36, 44), (36, 11), (30, 26), (32, 35), (24, 7), (22, 2), (8, 28), (15, 2), (14, 3), (30, 6), (41, 44), (21, 4), (24, 35), (34, 38), (42, 8), (10, 5), (4, 33), (19, 33), (14, 42), (32, 30), (38, 30), (19, 45), (21, 45), (12, 13), (37, 39), (30, 32), (42, 44), (21, 19), (33, 26), (28, 44), (4, 47), (19, 7), (1, 20), (28, 38), (3, 24), (0, 33), (3, 28), (1, 36), (1, 38), (18, 35), (12, 11), (23, 13), (32, 27), (26, 10), (38, 2), (14, 9), (25, 18), (15, 37), (29, 37), (11, 19), (42, 15), (9, 10), (4, 29), (15, 33), (2, 37), (29, 40), (16, 32), (20, 34), (15, 30), (39, 37), (20, 43), (36, 30), (14, 22), (39, 7), (36, 34), (24, 31), (21, 1), (16, 34), (14, 12), (42, 34), (10, 27), (39, 22), (8, 15), (22, 40), (16, 5), (14, 41), (24, 43), (23, 29), (7, 24), (35, 1), (2, 1), (9, 16), (42, 4), (8, 11), (13, 0), (38, 37), (12, 8), (12, 41), (34, 2), (0, 15), (23, 43), (4, 30), (16, 26), (18, 32), (43, 47), (37, 32), (30, 46), (5, 8), (15, 17), (23, 32), (10, 7), (13, 43), (40, 12), (27, 27), (37, 33), (17, 40), (21, 27), (24, 20), (8, 9), (6, 33), (11, 38), (29, 38), (26, 41), (41, 37), (11, 43), (15, 22), (21, 31), (14, 11), (29, 35), (15, 8), (26, 14), (16, 46), (43, 42), (31, 3), (41, 21), (19, 36), (31, 5), (32, 37), (34, 11), (0, 21), (35, 36), (19, 27), (3, 13), (17, 45), (14, 2), (40, 16), (1, 47), (11, 9), (12, 31), (40, 21), (3, 21), (25, 2), (34, 31), (7, 28), (13, 4), (7, 43), (38, 15), (28, 21), (43, 25), (36, 7), (43, 41), (4, 48), (14, 1), (38, 9), (6, 4), (43, 11), (22, 10), (9, 37), (8, 19), (32, 33), (41, 30), (14, 5), (15, 48), (7, 45), (28, 0), (1, 31), (12, 37), (16, 33), (39, 40), (43, 45), (26, 12), (5, 10), (32, 44), (22, 15), (23, 30), (8, 10), (33, 28), (5, 27), (11, 42), (26, 23), (41, 26), (34, 6), (31, 9), (30, 13), (39, 30), (14, 43), (16, 11), (10, 31), (31, 0), (3, 35), (1, 26), (24, 47), (22, 35), (6, 15), (27, 1), (2, 24), (22, 32), (35, 35), (4, 37), (15, 18), (32, 21), (43, 1), (30, 33), (5, 36), (18, 40), (33, 42), (15, 31), (37, 43), (8, 4), (0, 4), (28, 26), (20, 3), (27, 23), (37, 2), (41, 9), (15, 24), (13, 10), (30, 18), (37, 29), (36, 45), (13, 18), (2, 6), (31, 14), (21, 28), (19, 42), (7, 33), (13, 27), (35, 32), (43, 26), (0, 20), (31, 25), (28, 29), (29, 42), (4, 42), (41, 22), (40, 11), (19, 1), (24, 42), (0, 3), (25, 19), (17, 30), (20, 16), (30, 22), (14, 26), (18, 8), (24, 32), (14, 25), (11, 4), (0, 12), (32, 46), (18, 11), (17, 17), (30, 16), (15, 5), (38, 38), (38, 34), (42, 2), (23, 42), (7, 30), (40, 19), (29, 44), (38, 13), (11, 1), (37, 35), (26, 45), (43, 28), (15, 39), (7, 40), (30, 14), (0, 39), (18, 30), (40, 4), (35, 45), (9, 13), (11, 32), (8, 44), (13, 24), (16, 8), (6, 32), (31, 6), (34, 40), (34, 22), (26, 11), (16, 1), (42, 13), (34, 35), (34, 30)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (44, 35), (1, 31), (35, 29), (27, 18), (0, 1), (24, 6), (45, 14), (5, 2), (47, 35), (37, 11), (28, 20), (30, 20), (32, 23), (28, 15), (24, 37), (10, 12), (24, 41), (3, 34), (6, 34), (45, 32), (9, 38), (32, 41), (39, 33), (37, 6), (43, 7), (4, 28), (26, 16), (26, 35), (4, 19), (33, 14), (7, 35), (0, 18), (17, 30), (4, 17), (45, 40), (26, 17), (27, 3), (15, 16), (27, 24), (23, 21), (13, 3), (3, 35), (33, 37), (0, 4), (5, 11), (35, 7), (28, 18), (24, 18), (8, 6), (40, 39), (28, 25), (15, 25), (0, 39), (5, 5), (28, 41), (25, 8), (18, 16), (36, 39), (42, 4), (41, 39), (6, 28), (11, 28), (19, 23), (27, 15), (27, 17), (24, 10), (41, 1), (26, 28), (14, 3), (33, 9), (24, 36), (12, 32), (48, 38), (11, 31), (9, 35), (23, 39), (25, 17), (19, 8), (32, 39), (41, 37), (32, 1), (23, 4), (9, 41), (43, 20), (46, 32), (41, 41), (47, 20), (31, 3), (45, 7), (11, 37), (23, 38), (2, 14), (16, 26), (24, 24), (47, 39), (25, 34), (33, 12), (17, 37), (18, 13), (39, 8), (36, 24), (26, 2), (20, 3), (41, 20), (4, 35), (44, 5), (33, 36), (41, 25), (9, 16), (37, 29), (48, 30), (2, 39), (46, 9), (37, 27), (11, 14), (8, 9), (24, 33), (3, 23), (31, 4), (34, 13), (31, 17), (41, 31), (29, 13), (7, 33), (41, 24), (18, 33), (31, 1), (48, 1), (0, 38), (2, 37), (5, 35), (13, 22), (24, 22), (5, 7), (2, 10), (39, 24), (45, 33), (15, 8), (42, 3), (25, 22), (45, 1), (48, 11), (12, 11), (7, 38), (37, 3), (39, 15), (35, 8), (7, 26), (30, 36), (25, 29), (37, 22), (42, 1), (22, 36), (10, 4), (27, 7), (20, 23), (1, 39), (46, 21), (26, 22), (15, 10), (12, 5), (24, 38), (45, 6), (16, 17), (48, 14), (35, 3), (17, 22), (37, 15), (19, 5), (3, 17), (2, 25), (7, 20), (44, 37), (28, 3), (44, 17), (2, 12), (34, 11), (26, 19), (0, 33), (1, 35), (25, 5), (21, 9), (34, 4), (45, 29), (33, 29), (42, 6), (26, 39), (25, 9), (47, 8), (31, 11), (17, 40), (7, 9), (28, 19), (5, 38), (36, 16), (37, 21), (25, 37), (42, 36), (45, 5), (37, 36), (41, 13), (10, 26), (32, 2), (41, 33), (20, 27), (7, 24), (40, 32), (33, 1), (39, 6), (7, 36), (2, 28), (33, 7), (9, 40), (44, 11), (34, 19), (11, 41), (15, 18), (15, 31), (10, 24), (38, 23), (38, 3), (12, 37), (26, 7), (46, 35), (45, 20), (15, 28), (1, 19), (31, 27), (31, 16), (17, 21), (7, 40), (14, 36), (11, 34), (37, 19), (14, 6), (15, 4), (13, 40), (30, 13), (16, 5), (42, 9), (46, 29), (31, 38), (39, 4), (16, 28), (6, 7), (36, 36), (45, 8), (32, 7), (44, 13), (37, 7), (22, 37), (34, 26), (25, 35), (36, 33), (9, 2), (9, 24), (27, 30), (20, 22), (46, 3), (14, 2), (14, 40), (8, 19), (46, 41), (6, 2), (1, 37), (46, 14), (14, 25), (38, 27), (27, 25), (8, 29), (35, 19), (44, 4), (15, 6), (1, 20), (36, 18), (16, 38), (9, 37), (43, 37), (14, 31), (41, 0), (29, 29), (8, 15), (33, 3), (37, 16), (7, 1), (9, 4), (20, 31), (44, 26), (23, 5), (11, 5), (46, 27), (14, 11), (13, 37), (38, 17), (29, 12), (23, 29), (11, 6), (27, 41), (39, 37), (38, 33), (19, 36), (30, 7), (18, 24), (20, 21), (27, 12), (7, 6), (13, 19), (46, 16), (42, 28), (20, 16), (16, 23), (47, 16), (37, 5), (24, 12), (26, 3), (1, 27), (37, 33), (24, 17), (21, 19), (3, 13), (5, 41), (21, 36), (17, 7), (16, 12), (37, 8), (10, 34), (33, 16), (34, 3), (7, 13), (30, 12), (8, 2), (1, 11), (5, 25), (4, 7)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 23), (41, 27), (26, 17), (43, 16), (25, 21), (27, 23), (26, 42), (23, 9), (10, 40), (39, 1), (33, 39), (28, 38), (26, 21), (21, 35), (39, 2), (14, 33), (39, 31), (40, 34), (43, 0), (31, 43), (23, 15), (31, 19), (33, 27), (36, 30), (4, 6), (24, 29), (10, 1), (30, 42), (43, 30), (36, 32), (16, 9), (38, 9), (2, 38), (5, 24), (19, 31), (15, 31), (39, 41), (6, 16), (21, 6), (28, 19), (43, 14), (18, 9), (37, 24), (5, 8), (19, 38), (22, 21), (13, 1), (43, 12), (9, 35), (36, 23), (39, 15), (14, 36), (15, 41), (1, 32), (22, 5), (40, 37), (38, 10), (39, 13), (6, 28), (13, 26), (13, 40), (24, 44), (36, 3), (24, 0), (34, 0), (41, 39), (5, 17), (33, 32), (36, 17), (4, 24), (42, 37), (4, 7), (30, 26), (8, 30), (17, 7), (34, 21), (30, 14), (17, 2), (21, 32), (40, 4), (17, 44), (5, 28), (33, 14), (18, 12), (26, 44), (8, 20), (8, 25), (13, 24), (32, 31), (10, 3), (11, 17), (30, 5), (18, 28), (35, 5), (0, 10), (15, 30), (0, 23), (39, 16), (0, 2), (37, 32), (11, 0), (12, 30), (35, 17), (5, 13), (35, 36), (43, 37), (28, 13), (15, 14), (43, 5), (2, 14), (41, 30), (5, 43), (25, 14), (6, 30), (23, 24), (23, 2), (32, 22), (41, 2), (34, 37), (8, 36), (42, 10), (12, 14), (25, 1), (26, 36), (39, 42), (34, 6), (17, 23), (29, 39), (41, 0), (32, 29), (8, 43), (16, 7), (13, 17), (22, 4), (1, 7), (4, 9), (31, 44), (18, 43), (42, 0), (33, 9), (42, 7), (18, 32), (8, 2), (42, 4), (17, 34), (20, 24), (30, 33), (8, 8), (26, 12), (26, 43), (1, 3), (4, 27), (11, 27), (7, 4), (19, 19), (18, 38), (4, 42), (13, 41), (17, 13), (24, 14), (22, 7), (43, 21), (22, 42), (38, 37), (18, 6), (26, 2), (20, 9), (24, 43), (11, 5), (11, 26), (27, 19), (39, 25), (0, 6), (39, 32), (5, 11), (17, 40), (40, 20), (16, 13), (32, 27), (23, 13), (41, 33), (17, 41), (2, 1), (10, 22), (13, 18), (18, 14), (13, 4), (6, 43), (29, 11), (7, 38), (36, 7), (17, 37), (8, 42), (3, 22), (21, 9), (5, 4), (5, 35), (3, 10), (30, 16), (5, 27), (30, 29), (36, 4), (26, 8), (42, 2), (31, 21), (11, 24), (14, 7), (36, 26), (43, 8), (33, 11), (28, 9), (35, 10), (36, 16), (42, 26), (37, 38), (33, 1), (30, 34), (38, 3), (10, 17), (12, 24), (17, 1), (17, 12), (32, 5), (36, 18), (27, 13), (11, 44), (15, 39), (12, 18), (4, 28), (32, 2), (16, 16), (7, 23), (11, 30), (18, 23), (1, 18), (19, 21), (4, 17), (37, 44), (31, 29), (4, 34), (13, 19), (40, 31), (42, 18), (16, 23), (22, 30), (27, 24), (41, 34), (8, 22), (34, 20), (41, 12), (21, 12), (21, 22), (15, 28), (1, 11), (13, 35), (22, 41), (28, 0), (38, 42), (9, 44), (9, 18), (31, 41), (39, 34), (17, 21), (21, 26), (30, 11), (5, 40), (41, 24), (3, 30), (15, 36), (22, 28), (15, 20), (6, 25), (33, 18), (23, 29), (12, 7), (26, 9), (30, 31), (13, 11), (14, 18), (14, 19), (23, 30), (24, 42), (16, 32), (39, 14), (24, 21), (20, 0), (18, 16), (20, 2), (33, 38), (3, 44), (27, 32), (12, 2), (32, 7), (22, 19), (17, 4), (35, 25), (4, 13), (22, 18), (42, 6), (1, 4), (38, 4), (20, 32), (21, 17), (10, 2), (16, 36), (12, 19), (39, 0), (14, 42), (40, 17), (2, 17), (28, 8), (32, 38), (15, 2), (3, 11), (12, 10), (10, 5), (25, 0), (8, 4), (20, 13), (32, 43), (9, 23), (27, 10), (1, 13), (43, 17), (6, 18), (32, 39), (40, 6), (5, 3), (2, 16)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (45, 38), (36, 27), (39, 21), (35, 35), (33, 37), (45, 11), (6, 27), (47, 29), (15, 22), (10, 8), (43, 1), (28, 10), (23, 9), (44, 32), (28, 13), (46, 6), (21, 29), (47, 5), (34, 41), (44, 24), (13, 43), (37, 32), (1, 20), (8, 31), (18, 34), (1, 34), (40, 25), (0, 7), (15, 36), (29, 0), (45, 40), (47, 31), (2, 13), (16, 25), (10, 13), (45, 10), (4, 24), (38, 30), (9, 16), (5, 9), (45, 28), (20, 8), (10, 30), (46, 8), (34, 32), (37, 23), (22, 6), (6, 0), (36, 35), (36, 9), (43, 11), (1, 3), (25, 42), (44, 29), (10, 34), (33, 0), (26, 27), (29, 23), (16, 30), (8, 16), (17, 25), (47, 26), (42, 27), (39, 18), (2, 11), (22, 20), (43, 7), (47, 17), (9, 35), (14, 40), (26, 13), (42, 22), (30, 15), (33, 26), (41, 1), (25, 6), (36, 31), (44, 28), (43, 21), (8, 5), (12, 30), (36, 42), (24, 33), (4, 40), (17, 14), (31, 8), (35, 0), (23, 4), (40, 27), (1, 39), (21, 28), (35, 30), (4, 36), (12, 13), (44, 30), (41, 22), (32, 39), (5, 16), (25, 7), (38, 22), (4, 12), (39, 15), (0, 6), (36, 20), (6, 24), (40, 23), (19, 11), (28, 27), (27, 7), (18, 40), (10, 36), (40, 2), (11, 9), (19, 23), (46, 3), (28, 12), (5, 12), (42, 3), (46, 34), (25, 1), (2, 6), (23, 23), (3, 36), (8, 35), (34, 29), (6, 41), (42, 13), (1, 4), (33, 12), (22, 19), (28, 38), (32, 26), (7, 17), (36, 23), (5, 24), (25, 43), (46, 28), (28, 9), (32, 22), (14, 32), (35, 5), (7, 43), (21, 2), (30, 4), (4, 22), (15, 29), (27, 11), (10, 1), (38, 29), (43, 26), (40, 18), (17, 5), (34, 12), (31, 36), (32, 40), (33, 43), (27, 14), (46, 12), (17, 36), (3, 27), (31, 18), (23, 7), (14, 25), (31, 26), (15, 41), (45, 36), (47, 40), (34, 33), (15, 14), (21, 3), (1, 0), (41, 6), (39, 33), (46, 1), (5, 35), (34, 18), (0, 12), (23, 0), (23, 27), (17, 6), (36, 40), (22, 26), (22, 12), (12, 17), (17, 18), (34, 17), (39, 12), (37, 38), (20, 25), (37, 13), (14, 31), (30, 12), (39, 36), (3, 18), (24, 14), (43, 29), (19, 16), (11, 1), (41, 21), (40, 0), (46, 31), (39, 39), (31, 3), (43, 22), (0, 22), (29, 39), (25, 11), (0, 37), (6, 16), (32, 3), (47, 35), (1, 10), (19, 3), (15, 43), (41, 20), (43, 0), (1, 43), (28, 0), (12, 18), (2, 14), (37, 16), (29, 7), (4, 27), (37, 41), (24, 3), (23, 17), (30, 39), (9, 14), (3, 21), (10, 16), (18, 31), (37, 0), (15, 42), (20, 36), (13, 12), (21, 38), (14, 38), (14, 12), (3, 43), (3, 17), (36, 6), (46, 15), (33, 29), (47, 7), (11, 0), (8, 26), (13, 39), (29, 15), (37, 37), (34, 11), (24, 24), (4, 4), (4, 30), (2, 18), (7, 7), (38, 17), (23, 26), (2, 38), (11, 42), (38, 20), (3, 19), (24, 4), (14, 13), (44, 4), (31, 5), (30, 36), (39, 43), (15, 18), (28, 40), (1, 38), (18, 15), (38, 6), (8, 21), (18, 3), (42, 21), (45, 3), (21, 13), (6, 37), (6, 14), (17, 8), (37, 31), (27, 22), (17, 3), (32, 14), (42, 0), (39, 24), (34, 35), (15, 25), (19, 6), (7, 41), (14, 4), (35, 10), (12, 43), (32, 24), (24, 10), (3, 23), (0, 42), (12, 16), (41, 33), (25, 28), (41, 41), (38, 42), (13, 22), (0, 33), (7, 31), (13, 41), (29, 41), (29, 29), (1, 14), (3, 7), (31, 7), (15, 5), (0, 16), (28, 30), (23, 8), (34, 34), (45, 29), (17, 15), (5, 25), (12, 6), (21, 32), (22, 18), (24, 0), (12, 8), (8, 38), (40, 8), (10, 35), (16, 29), (31, 25), (11, 8), (13, 29), (26, 18), (0, 35), (23, 15), (42, 8), (25, 38), (2, 25), (24, 22), (11, 39), (47, 21), (44, 0), (2, 29), (21, 19), (21, 4), (5, 40)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 49x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (2, 41), (21, 21), (43, 1), (32, 34), (26, 45), (48, 38), (9, 33), (6, 38), (30, 4), (5, 32), (23, 24), (2, 23), (46, 3), (4, 3), (2, 0), (29, 1), (33, 0), (36, 34), (46, 22), (44, 3), (14, 19), (6, 17), (18, 28), (6, 0), (18, 0), (31, 16), (40, 44), (0, 29), (7, 42), (8, 39), (12, 39), (23, 34), (40, 18), (20, 11), (1, 43), (3, 22), (15, 17), (20, 18), (45, 3), (22, 41), (28, 22), (14, 22), (5, 2), (42, 24), (8, 8), (44, 9), (31, 34), (1, 27), (34, 7), (14, 7), (11, 20), (28, 19), (8, 6), (28, 5), (6, 6), (17, 21), (44, 39), (17, 18), (33, 31), (46, 41), (1, 12), (32, 15), (29, 19), (38, 31), (31, 42), (47, 44), (22, 1), (9, 22), (15, 44), (29, 0), (9, 20), (13, 16), (31, 6), (35, 32), (0, 13), (6, 11), (26, 39), (39, 20), (10, 28), (22, 12), (48, 30), (3, 40), (46, 13), (47, 25), (44, 13), (47, 9), (37, 36), (10, 18), (25, 37), (24, 13), (46, 35), (7, 15), (27, 6), (0, 11), (13, 20), (30, 35), (38, 5), (6, 4), (20, 0), (4, 12), (12, 32), (27, 3), (8, 36), (32, 35), (9, 45), (24, 38), (20, 40), (46, 43), (9, 12), (15, 13), (25, 0), (22, 25), (11, 44), (1, 41), (29, 13), (28, 28), (39, 36), (0, 40), (30, 23), (33, 10), (10, 20), (27, 5), (45, 29), (31, 11), (9, 44), (14, 45), (42, 45), (40, 0), (2, 7), (39, 14), (43, 34), (31, 13), (7, 2), (6, 28), (36, 13), (4, 26), (4, 34), (22, 31), (44, 10), (7, 14), (20, 38), (19, 24), (42, 18), (38, 29), (20, 3), (45, 43), (39, 6), (41, 26), (45, 24), (19, 6), (38, 24), (37, 21), (18, 26), (15, 19), (1, 21), (14, 27), (30, 8), (40, 43), (4, 10), (3, 31), (6, 25), (23, 4), (32, 39), (18, 31), (16, 32), (14, 39), (12, 45), (6, 15), (46, 2), (47, 43), (45, 42), (21, 17), (1, 8), (12, 28), (9, 15), (42, 39), (15, 27), (46, 24), (4, 8), (34, 10), (0, 45), (41, 8), (21, 29), (20, 2), (44, 0), (37, 8), (24, 3), (30, 15), (19, 44), (42, 28), (17, 27), (26, 44), (44, 33), (18, 29), (8, 23), (37, 24), (13, 35), (33, 27), (22, 29), (35, 44), (40, 41), (16, 18), (41, 9), (37, 16), (28, 3), (26, 33), (39, 16), (14, 28), (42, 20), (21, 23), (36, 0), (13, 44), (25, 39), (25, 43), (47, 28), (23, 7), (23, 30), (14, 35), (16, 7), (16, 35), (39, 31), (28, 33), (0, 8), (31, 19), (15, 3), (3, 9), (45, 10), (44, 24), (30, 37), (8, 33), (12, 17), (9, 26), (8, 27), (38, 30), (10, 22), (23, 8), (1, 37), (38, 17), (13, 5), (18, 10), (2, 6), (6, 23), (15, 39), (12, 36), (1, 30), (3, 20), (9, 43), (4, 23), (39, 37), (22, 38), (35, 31), (13, 11), (2, 35), (20, 8), (11, 18), (31, 21), (34, 13), (26, 25), (8, 16), (35, 42), (31, 7), (17, 36), (1, 33), (48, 34), (1, 28), (16, 16), (37, 30), (21, 2), (4, 38), (21, 28), (26, 30), (41, 29), (48, 37), (43, 8), (23, 31), (29, 16), (23, 26), (48, 18), (46, 42), (26, 27), (41, 24), (13, 9), (19, 36), (18, 40), (14, 31), (31, 32), (28, 0), (34, 17), (23, 41), (17, 20), (4, 20), (41, 16), (40, 5), (12, 31), (1, 22), (6, 9), (23, 43), (16, 8), (43, 22), (5, 7), (20, 41), (38, 2), (2, 31), (26, 2), (36, 42), (14, 11), (6, 12), (29, 43), (2, 4), (1, 1), (27, 0), (14, 8), (39, 41), (5, 1), (34, 5), (38, 21), (29, 44), (14, 25), (26, 8), (0, 41), (18, 44), (12, 3), (7, 0), (5, 4), (28, 7), (7, 8), (17, 35), (45, 2), (23, 27), (34, 27), (39, 39), (28, 13), (30, 36), (28, 25), (22, 23), (35, 41), (38, 12), (22, 3), (33, 7), (10, 39), (5, 22), (2, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 42x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 37), (34, 26), (18, 17), (28, 18), (8, 26), (27, 1), (22, 4), (7, 0), (41, 35), (40, 30), (40, 29), (0, 14), (6, 26), (2, 24), (28, 37), (12, 2), (1, 22), (2, 33), (11, 21), (27, 26), (6, 38), (30, 8), (35, 36), (8, 31), (11, 25), (1, 27), (10, 24), (14, 0), (27, 25), (3, 6), (8, 16), (14, 10), (14, 35), (24, 31), (40, 11), (2, 16), (16, 38), (16, 28), (25, 35), (23, 22), (20, 28), (25, 1), (38, 7), (23, 8), (28, 6), (25, 2), (8, 39), (0, 18), (30, 29), (8, 9), (40, 39), (14, 9), (34, 3), (33, 6), (40, 31), (22, 30), (27, 4), (22, 39), (17, 11), (3, 38), (23, 16), (40, 10), (29, 8), (22, 27), (3, 33), (31, 28), (23, 27), (19, 22), (24, 24), (17, 14), (0, 20), (35, 38), (33, 39), (0, 12), (19, 0), (0, 3), (9, 2), (29, 4), (27, 31), (41, 36), (8, 7), (10, 19), (1, 33), (15, 11), (31, 37), (30, 6), (22, 32), (10, 35), (11, 27), (39, 29), (2, 23), (6, 32), (30, 32), (30, 14), (23, 33), (16, 26), (32, 34), (16, 36), (25, 31), (38, 14), (1, 35), (25, 13), (26, 32), (24, 39), (19, 19), (17, 20), (16, 1), (1, 32), (25, 0), (5, 1), (13, 37), (26, 35), (12, 34), (21, 14), (9, 8), (11, 7), (6, 19), (40, 21), (32, 15), (32, 38), (11, 17), (0, 38), (31, 19), (40, 20), (17, 26), (38, 17), (1, 15), (6, 20), (33, 34), (37, 6), (16, 27), (8, 36), (9, 22), (14, 5), (39, 18), (29, 6), (38, 19), (20, 19), (37, 15), (16, 15), (33, 19), (5, 11), (35, 4), (22, 3), (0, 22), (22, 22), (13, 35), (11, 0), (6, 9), (39, 10), (26, 22), (29, 29), (28, 33), (30, 28), (10, 14), (26, 8), (5, 31), (20, 29), (24, 1), (37, 9), (2, 9), (0, 34), (14, 27), (5, 17), (35, 25), (25, 39), (20, 4), (13, 31), (23, 30), (41, 1), (12, 19), (33, 26), (11, 28), (6, 12), (9, 34), (26, 3), (38, 13), (0, 25), (19, 8), (28, 23), (33, 28), (24, 21), (20, 24), (0, 7), (7, 10), (0, 37), (36, 10), (37, 33), (22, 18), (31, 20), (38, 20), (13, 26), (40, 19), (11, 22), (13, 11), (15, 12), (7, 31), (34, 37), (16, 11), (5, 21), (28, 22), (6, 8), (14, 28), (3, 1), (22, 5), (29, 28), (36, 30), (0, 30), (3, 21), (23, 24), (36, 8), (16, 19), (10, 21), (39, 14), (28, 35), (27, 6), (32, 35), (6, 5), (41, 20), (24, 36), (24, 35), (27, 22), (17, 15), (10, 25), (9, 18), (19, 6), (17, 38), (41, 4), (10, 11), (18, 23), (27, 32), (3, 18), (21, 29), (24, 26), (36, 4), (6, 27), (2, 18), (3, 35), (0, 31), (28, 24), (9, 33), (24, 20), (9, 30), (16, 3), (32, 12), (15, 1), (19, 14), (28, 1), (22, 0), (3, 4), (16, 21), (39, 24), (36, 3), (40, 27), (17, 10), (36, 26), (9, 29), (7, 17), (20, 27), (34, 0), (25, 29), (5, 36), (7, 39), (24, 38), (22, 8), (25, 20), (11, 29), (37, 12), (34, 25), (30, 16), (2, 34), (29, 23), (31, 18), (14, 25), (25, 10), (5, 3), (13, 29), (36, 32), (5, 34), (4, 14), (32, 4), (34, 7), (31, 30), (13, 5), (34, 39), (5, 33), (4, 39), (12, 33), (29, 27), (39, 2), (5, 29), (40, 0), (33, 0), (37, 0), (12, 35), (31, 21), (27, 3), (4, 38), (4, 10), (34, 18), (7, 32), (24, 32), (18, 3), (34, 34), (12, 29), (33, 23), (2, 30), (39, 21), (23, 14), (7, 3), (26, 15), (2, 35), (20, 36), (40, 35), (36, 6), (0, 17), (8, 25), (17, 12), (39, 12), (12, 10), (31, 26), (40, 15), (20, 14), (26, 28), (16, 22), (39, 6), (4, 31), (23, 31), (6, 1), (4, 37), (6, 14), (1, 17), (14, 37), (28, 26), (16, 9)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 45x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 30), (25, 0), (17, 35), (13, 19), (42, 1), (21, 31), (17, 26), (15, 19), (27, 7), (3, 4), (39, 32), (23, 33), (1, 7), (16, 22), (21, 7), (17, 9), (29, 26), (32, 36), (11, 17), (11, 37), (8, 21), (27, 17), (28, 4), (4, 8), (16, 16), (26, 40), (15, 16), (41, 27), (28, 41), (6, 32), (5, 11), (7, 40), (40, 36), (21, 25), (27, 15), (31, 41), (35, 0), (2, 1), (17, 5), (35, 4), (33, 16), (32, 0), (18, 26), (10, 33), (22, 27), (27, 12), (35, 22), (39, 29), (31, 12), (44, 17), (2, 26), (17, 17), (1, 31), (7, 0), (12, 15), (23, 4), (4, 27), (3, 31), (37, 6), (43, 23), (38, 32), (28, 23), (36, 38), (42, 25), (26, 25), (0, 28), (26, 34), (27, 29), (35, 1), (23, 32), (44, 28), (34, 26), (17, 32), (44, 15), (25, 2), (44, 4), (40, 34), (38, 22), (20, 3), (10, 3), (9, 33), (5, 7), (3, 33), (8, 39), (36, 5), (43, 17), (35, 29), (14, 23), (13, 3), (40, 31), (29, 22), (0, 20), (24, 29), (39, 15), (39, 1), (1, 9), (16, 3), (4, 18), (8, 0), (21, 9), (38, 28), (27, 32), (41, 39), (26, 22), (35, 38), (10, 22), (30, 14), (18, 9), (20, 34), (38, 10), (37, 18), (21, 5), (9, 31), (9, 34), (6, 8), (0, 39), (25, 16), (43, 19), (29, 0), (16, 1), (27, 23), (40, 20), (1, 25), (20, 9), (41, 37), (12, 14), (0, 15), (7, 2), (29, 35), (44, 31), (14, 28), (40, 23), (22, 37), (1, 20), (23, 9), (33, 20), (12, 23), (15, 36), (28, 38), (24, 15), (39, 24), (22, 21), (42, 23), (35, 34), (40, 40), (31, 13), (24, 34), (25, 12), (7, 39), (4, 9), (4, 29), (21, 19), (20, 14), (24, 36), (14, 41), (7, 35), (6, 34), (5, 35), (9, 29), (37, 10), (12, 8), (5, 23), (31, 6), (13, 36), (44, 35), (23, 3), (15, 21), (39, 13), (11, 2), (6, 30), (7, 14), (9, 25), (37, 34), (12, 25), (13, 23), (13, 2), (18, 35), (28, 6), (21, 28), (32, 7), (11, 13), (19, 3), (3, 32), (30, 35), (17, 16), (0, 10), (9, 27), (22, 8), (27, 14), (28, 25), (5, 13), (35, 26), (44, 18), (26, 21), (30, 34), (10, 13), (4, 12), (39, 3), (25, 20), (19, 7), (17, 12)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 49x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (18, 5), (17, 4), (39, 13), (32, 8), (13, 3), (23, 11), (35, 3), (29, 8), (4, 10), (15, 32), (21, 45), (34, 42), (47, 17), (15, 8), (39, 20), (3, 8), (11, 45), (39, 3), (20, 5), (31, 42), (29, 38), (45, 0), (23, 16), (7, 34), (4, 0), (27, 32), (2, 11), (47, 7), (41, 15), (13, 0), (43, 29), (41, 41), (7, 15), (1, 33), (3, 47), (20, 24), (48, 36), (34, 33), (10, 14), (30, 14), (35, 8), (10, 21), (20, 15), (34, 23), (9, 45), (32, 44), (7, 37), (29, 29), (20, 18), (3, 11), (6, 1), (34, 32), (29, 13), (4, 31), (47, 10), (45, 8), (33, 37), (35, 42), (11, 9), (13, 14), (45, 33), (36, 18), (11, 43), (27, 2), (2, 27), (32, 3), (27, 7), (6, 6), (25, 5), (32, 38), (23, 36), (19, 8), (12, 25), (20, 46), (23, 34), (30, 21), (43, 10), (0, 44), (3, 44), (7, 12), (33, 13), (18, 26), (21, 27), (22, 28), (46, 42), (48, 46), (21, 31), (34, 2), (19, 42), (29, 43), (40, 46), (33, 11), (47, 34), (13, 19), (6, 12), (17, 40), (32, 15), (41, 2), (29, 34), (28, 12), (21, 11), (38, 19), (11, 28), (45, 47), (3, 36), (26, 39), (18, 38), (31, 12), (33, 41), (39, 46), (24, 2), (15, 26), (21, 23), (13, 41), (42, 27), (14, 42), (31, 32), (32, 45), (36, 27), (5, 29), (6, 11), (47, 35), (34, 47), (33, 7), (9, 24), (17, 0), (22, 41), (19, 25), (15, 14), (0, 45), (43, 45), (19, 2), (25, 13), (10, 4), (34, 43), (10, 30), (0, 37), (41, 46), (11, 13), (11, 6), (16, 14), (46, 8), (17, 14), (38, 5), (39, 41), (4, 8), (7, 44), (17, 10), (35, 13), (4, 47), (42, 10), (8, 23), (34, 10), (3, 35), (31, 33), (16, 7), (20, 16), (38, 20), (9, 34), (8, 29), (29, 9), (3, 23), (23, 13), (20, 32), (7, 45), (22, 6), (25, 17), (3, 3), (45, 25), (4, 46), (12, 13), (42, 28), (17, 17), (31, 21), (48, 41), (14, 16), (8, 27), (0, 42), (44, 12), (19, 17), (9, 15), (8, 40), (42, 38), (36, 39), (8, 30), (9, 46), (21, 8), (31, 36), (40, 8), (12, 38), (18, 30), (31, 14), (36, 6), (14, 12), (40, 29), (28, 34), (48, 27), (17, 47), (47, 28), (45, 20), (43, 13), (42, 30), (18, 37), (13, 43), (44, 31), (6, 36), (33, 36), (3, 39), (5, 42), (35, 30), (0, 34), (2, 40), (29, 16), (1, 45), (13, 20), (9, 37), (25, 10), (36, 2), (36, 32), (27, 18), (29, 20), (1, 12), (8, 5), (16, 24), (4, 13), (34, 31), (31, 6), (32, 28), (19, 11), (36, 35), (22, 20), (5, 31), (39, 29), (45, 11), (38, 40), (33, 21), (8, 41), (20, 23), (13, 45), (48, 25), (24, 16), (29, 4), (48, 26), (10, 5), (47, 9), (7, 6), (14, 8), (36, 41), (12, 44), (14, 30), (19, 37), (4, 9), (35, 45), (4, 22), (42, 43), (3, 20), (24, 46), (6, 4), (11, 1), (8, 32), (43, 39), (2, 41), (48, 4), (15, 34), (33, 19), (32, 35), (39, 18), (7, 18), (38, 4), (22, 31), (9, 16), (9, 44), (9, 43), (1, 28), (6, 20), (47, 37), (15, 39), (13, 17), (9, 35), (47, 2), (14, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 25), (5, 21), (1, 37), (15, 39), (12, 36), (36, 14), (26, 13), (11, 22), (27, 36), (36, 13), (6, 38), (22, 4), (2, 41), (36, 7), (9, 3), (18, 8), (9, 19), (16, 11), (23, 1), (24, 33), (35, 19), (17, 33), (11, 16), (27, 22), (33, 39), (20, 9), (11, 42), (18, 32), (27, 1), (20, 13), (32, 4), (22, 35), (39, 0), (33, 5), (14, 22), (2, 4), (29, 23), (27, 29), (25, 10), (21, 29), (23, 38), (17, 26), (1, 40), (12, 21), (20, 8), (2, 28), (30, 7), (22, 3), (15, 38), (7, 20), (36, 27), (14, 12), (14, 15), (9, 28), (12, 3), (13, 39), (21, 18), (15, 37), (14, 37), (21, 19), (21, 36), (9, 18), (34, 7), (11, 37), (36, 38), (8, 3), (20, 7), (38, 39), (35, 1), (13, 4), (32, 12), (23, 21), (24, 24), (16, 8), (31, 24), (34, 39), (28, 4), (29, 25), (14, 11), (28, 24), (19, 28), (19, 39), (28, 13), (36, 28), (8, 37), (4, 8), (12, 34), (3, 4), (29, 37), (1, 38), (0, 10), (26, 20), (19, 5), (25, 29), (24, 19), (2, 6), (34, 1), (14, 17), (29, 8), (3, 19), (26, 3), (26, 39), (39, 6), (17, 5), (9, 41), (35, 14), (37, 35), (35, 17), (32, 23), (12, 10), (5, 19), (11, 11), (22, 0), (39, 11), (29, 11), (27, 33), (10, 14), (11, 2), (12, 27), (26, 41), (26, 8), (5, 17), (33, 3), (20, 14), (6, 12), (35, 26), (20, 23), (2, 25), (17, 31), (1, 26), (30, 41), (16, 17), (35, 30), (10, 24), (24, 4), (37, 40), (16, 26), (18, 15), (2, 40), (1, 15), (36, 26), (40, 1), (1, 28), (10, 33), (38, 1), (25, 13), (19, 19), (26, 24), (10, 28), (18, 37), (29, 16), (0, 11), (25, 21), (35, 6), (36, 8), (8, 23), (31, 0), (9, 4), (32, 15), (18, 17), (2, 10), (35, 32), (13, 21), (30, 0), (2, 33), (9, 2), (40, 23), (33, 1), (39, 31), (37, 2), (6, 28), (1, 25), (19, 23), (17, 9), (3, 39), (26, 4), (38, 14), (32, 42), (30, 18), (20, 0), (29, 9), (14, 39), (4, 16), (0, 29), (29, 41), (27, 9), (5, 28), (7, 30), (33, 37), (32, 17), (35, 18), (13, 37), (15, 9), (17, 24), (0, 8), (0, 22), (25, 33), (14, 18), (13, 27), (28, 5), (26, 26), (28, 10), (6, 40), (18, 34), (18, 16), (11, 27), (6, 34), (6, 15), (39, 12), (18, 3), (10, 32), (6, 13), (14, 32), (37, 6), (20, 3), (0, 7), (36, 23), (21, 40), (29, 15), (19, 3), (19, 20), (4, 6), (23, 35), (13, 35), (26, 1), (39, 30), (1, 39), (22, 29), (35, 15), (29, 13), (39, 42), (33, 19), (10, 13), (22, 10), (3, 12), (10, 3), (2, 20), (16, 23), (7, 14), (9, 33), (9, 9), (17, 22), (34, 41), (23, 31), (33, 36), (31, 2), (7, 15), (20, 36), (24, 26), (4, 19), (12, 6), (13, 10), (26, 19), (21, 22), (24, 38), (28, 29), (1, 13), (4, 42), (24, 42), (34, 16), (37, 10), (14, 24), (38, 32), (0, 14), (19, 14), (18, 42), (20, 29), (37, 27), (9, 17), (1, 16), (2, 39), (2, 0), (4, 13), (10, 23), (29, 33), (9, 21), (35, 23), (35, 13), (32, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 40x48 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (39, 47), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 40), (13, 28), (27, 20), (29, 20), (38, 14), (4, 43), (19, 7), (34, 14), (32, 14), (38, 21), (8, 39), (36, 1), (29, 5), (18, 36), (3, 37), (15, 12), (37, 28), (28, 16), (19, 43), (4, 46), (15, 23), (36, 9), (39, 33), (0, 22), (5, 13), (37, 36), (37, 32), (9, 34), (18, 21), (9, 16), (31, 28), (1, 2), (35, 43), (12, 23), (4, 19), (23, 41), (12, 7), (36, 17), (20, 15), (25, 22), (26, 15), (0, 5), (2, 44), (0, 30), (34, 5), (17, 17), (17, 44), (36, 21), (21, 40), (31, 11), (33, 13), (38, 45), (35, 24), (10, 21), (32, 34), (9, 35), (19, 44), (7, 4), (18, 43), (18, 27), (19, 12), (21, 30), (2, 18), (7, 23), (33, 12), (34, 30), (2, 45), (18, 2), (21, 15), (12, 16), (24, 16), (23, 14), (25, 11), (27, 5), (27, 16), (5, 30), (9, 38), (32, 12), (21, 24), (5, 21), (37, 16), (39, 45), (10, 10), (38, 44), (35, 2), (38, 5), (5, 0), (8, 46), (29, 34), (12, 39), (35, 15), (32, 16), (9, 26), (21, 35), (3, 32), (24, 18), (32, 18), (37, 23), (19, 11), (6, 31), (24, 11), (4, 30), (27, 47), (30, 10), (37, 26), (18, 14), (34, 41), (23, 15), (1, 15), (6, 33), (31, 1), (14, 12), (14, 41), (20, 27), (19, 42), (7, 6), (3, 39), (13, 13), (34, 47), (33, 46), (7, 18), (16, 26), (18, 28), (27, 22), (5, 44), (10, 45), (33, 33), (27, 11), (20, 6), (33, 32), (18, 42), (14, 24), (37, 45), (0, 19), (16, 38), (17, 46), (35, 11), (20, 33), (22, 0), (6, 22), (11, 36), (25, 9), (38, 17), (13, 15), (20, 7), (9, 22), (2, 34), (21, 27), (15, 31), (17, 27), (6, 36), (39, 42), (2, 9), (16, 42), (0, 37), (2, 6), (3, 9), (1, 20), (34, 29), (23, 42), (36, 36), (28, 37), (4, 18), (36, 25), (21, 18), (14, 30), (12, 45), (39, 23), (13, 0), (12, 5), (33, 28), (10, 37), (35, 17), (37, 7), (12, 13), (4, 23), (36, 12), (38, 9), (1, 10), (35, 5), (32, 4), (34, 34), (18, 26), (10, 32), (25, 8), (10, 30), (17, 36), (32, 17), (7, 30), (29, 17), (12, 33), (10, 29), (12, 2), (37, 37), (6, 9), (3, 16), (25, 26), (21, 39), (38, 40), (15, 37), (27, 36), (27, 3), (5, 17), (12, 34), (38, 30), (9, 1), (30, 8), (27, 27), (10, 17), (36, 4), (2, 22), (22, 16), (26, 30), (6, 28), (12, 8), (15, 26), (7, 15), (20, 32), (35, 1), (0, 27), (28, 21), (29, 15), (7, 20), (3, 14), (14, 8)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (26, 13), (27, 5), (35, 14), (30, 13), (32, 36), (33, 21), (27, 33), (15, 28), (33, 26), (38, 33), (25, 4), (8, 28), (14, 29), (41, 24), (29, 34), (31, 16), (38, 12), (22, 25), (11, 2), (28, 41), (19, 40), (2, 3), (4, 37), (21, 32), (8, 41), (35, 30), (11, 3), (22, 5), (31, 29), (14, 15), (23, 11), (15, 29), (33, 35), (29, 2), (2, 20), (3, 26), (11, 36), (37, 20), (8, 25), (15, 10), (18, 39), (19, 15), (5, 21), (16, 1), (6, 13), (35, 29), (37, 25), (41, 37), (28, 30), (38, 26), (15, 39), (29, 33), (10, 21), (9, 29), (26, 30), (34, 16), (26, 20), (21, 25), (20, 26), (10, 18), (35, 32), (19, 0), (11, 41), (3, 25), (40, 42), (24, 27), (33, 39), (0, 27), (41, 8), (39, 38), (17, 25), (36, 27), (30, 17), (28, 21), (36, 18), (14, 12), (31, 8), (11, 13), (30, 16), (37, 2), (8, 26), (37, 23), (0, 11), (40, 20), (34, 5), (19, 6), (32, 7), (16, 39), (13, 11), (25, 0), (8, 6), (29, 1), (40, 15), (6, 38), (41, 32), (33, 9), (10, 16), (6, 0), (27, 29), (29, 8), (20, 0), (36, 6), (20, 12), (0, 19), (17, 38), (27, 36), (13, 4), (19, 25), (31, 23), (4, 24), (1, 42), (26, 32), (21, 15), (39, 17), (25, 37), (18, 10), (8, 18), (41, 5), (26, 35), (12, 26), (17, 42), (19, 27), (19, 10), (34, 27), (31, 18), (30, 27), (36, 30), (28, 8), (5, 11), (32, 18), (17, 12), (1, 23), (18, 33), (34, 20), (14, 28), (14, 20), (27, 40), (8, 33), (9, 32), (12, 16), (0, 4), (7, 27), (12, 3), (13, 0), (19, 42), (8, 35), (14, 39), (30, 34), (28, 31), (27, 8), (22, 7), (31, 41), (10, 3), (10, 36), (34, 18), (39, 23), (20, 29), (28, 16), (7, 19), (7, 31), (1, 0), (25, 36), (35, 15), (28, 13), (19, 41), (30, 22), (14, 33), (24, 18), (21, 14), (38, 14), (18, 16), (22, 21), (28, 20), (8, 13), (4, 17), (33, 36), (38, 0), (1, 1), (20, 10), (1, 27), (38, 19), (25, 34), (5, 26), (25, 16), (39, 36), (1, 9), (12, 2), (26, 12), (26, 37), (7, 1), (5, 15), (15, 9), (41, 34), (29, 30), (38, 3), (29, 23), (6, 8), (16, 37), (32, 33), (1, 17), (27, 6), (23, 6), (5, 20), (6, 21), (31, 27), (30, 2), (27, 34), (3, 4), (18, 37), (35, 11), (31, 0), (32, 27), (4, 21), (23, 39), (13, 28), (25, 15), (35, 28), (4, 35), (15, 26), (20, 28), (7, 34), (41, 31), (31, 42), (18, 8), (13, 41), (4, 15), (27, 19), (20, 27), (41, 28), (3, 21), (35, 21), (30, 7), (7, 10), (18, 32), (28, 4), (5, 29), (1, 6), (21, 34), (36, 26), (27, 14), (39, 7), (33, 20), (26, 41), (14, 35), (37, 9), (21, 36), (14, 1), (0, 25), (2, 36), (34, 23), (23, 9), (18, 35), (24, 7), (3, 15), (29, 37), (16, 4), (35, 20), (8, 29), (12, 42), (16, 41), (23, 13), (11, 33), (25, 28), (38, 15), (14, 16), (15, 7), (7, 39), (12, 11), (41, 12), (9, 34), (8, 27), (36, 19), (19, 28), (0, 23), (31, 39), (37, 13), (31, 30), (5, 40), (6, 30), (23, 24), (24, 17), (14, 31), (32, 25), (28, 38), (6, 41), (0, 35), (7, 14), (31, 35), (21, 8), (37, 41), (21, 6), (34, 37), (34, 8), (22, 28), (4, 1), (41, 10), (18, 29), (22, 4), (22, 18), (32, 32), (10, 22), (5, 35), (36, 4), (4, 40), (5, 39), (15, 37), (34, 21), (23, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (28, 1), (22, 1), (17, 33), (24, 28), (25, 19), (13, 38), (39, 18), (21, 28), (14, 39), (40, 11), (30, 20), (27, 41), (34, 29), (32, 36), (29, 37), (38, 20), (37, 6), (12, 40), (11, 12), (24, 33), (34, 28), (30, 23), (38, 17), (36, 40), (33, 6), (0, 31), (18, 28), (13, 18), (21, 0), (6, 28), (26, 32), (23, 22), (1, 41), (14, 11), (9, 5), (21, 13), (19, 3), (32, 37), (15, 39), (36, 8), (18, 34), (21, 2), (22, 10), (20, 3), (1, 30), (40, 33), (31, 33), (18, 6), (3, 26), (7, 13), (8, 36), (10, 37), (18, 35), (35, 32), (21, 16), (35, 25), (11, 24), (2, 25), (32, 10), (2, 17), (18, 40), (28, 12), (37, 35), (29, 10), (28, 40), (9, 38), (17, 2), (10, 4), (18, 8), (11, 26), (6, 0), (33, 17), (5, 38), (32, 8), (35, 31), (27, 16), (34, 5), (8, 41), (8, 9), (34, 30), (2, 29), (40, 39), (12, 7), (16, 20), (7, 32), (35, 24), (34, 0), (26, 33), (11, 33), (15, 42), (14, 22), (13, 1), (37, 28), (4, 3), (21, 19), (1, 6), (9, 31), (4, 30), (14, 23), (5, 15), (32, 22), (10, 25), (39, 37), (14, 0), (23, 24), (25, 35), (38, 26), (11, 6), (15, 4), (12, 29), (21, 12), (22, 25), (1, 29), (1, 9), (30, 14), (7, 21), (11, 14), (10, 1), (18, 14), (29, 41), (24, 15), (19, 13), (22, 33), (19, 9), (13, 6), (30, 9), (34, 22), (6, 20), (21, 8), (14, 9), (4, 17), (17, 20), (4, 21), (24, 6), (28, 7), (7, 23), (14, 33), (27, 37), (40, 18), (20, 42), (18, 38), (32, 25), (12, 16), (26, 8), (4, 2), (3, 23), (6, 16), (16, 8), (3, 1), (39, 41), (35, 10), (39, 17), (31, 30), (38, 21), (14, 38), (26, 18), (0, 17), (20, 41), (36, 10), (13, 23), (38, 6), (29, 30), (26, 14), (32, 9), (12, 11), (2, 37), (17, 22), (27, 23), (13, 30), (3, 11), (37, 31), (20, 32), (35, 8), (12, 36), (40, 34), (24, 39), (3, 40), (31, 32), (24, 25), (3, 8), (15, 30), (38, 1), (1, 5), (36, 14), (1, 14), (33, 14), (25, 15), (38, 27), (7, 20), (6, 13), (9, 8), (11, 13), (0, 13), (17, 11), (23, 15), (25, 16), (35, 30), (31, 19), (17, 10), (21, 31), (13, 41), (26, 2), (37, 13), (17, 0), (35, 26), (36, 21), (28, 21), (25, 17), (1, 23), (27, 39), (7, 1), (23, 38), (3, 9), (23, 26), (28, 19), (23, 29), (1, 8), (22, 12), (26, 26), (12, 21), (40, 31), (12, 27), (35, 39), (0, 8), (28, 32), (26, 39), (38, 25), (10, 30), (34, 12), (17, 7), (36, 1), (30, 18), (31, 39), (18, 41), (18, 30), (3, 4), (35, 29), (19, 11), (3, 24), (1, 19), (27, 24), (0, 28), (6, 25), (13, 28), (23, 33), (27, 30), (12, 25), (40, 22), (14, 40), (16, 6), (37, 26), (35, 11), (0, 39), (13, 26), (22, 35), (15, 10), (32, 20), (30, 27), (15, 29), (13, 37), (33, 18), (33, 22), (27, 36), (12, 32), (37, 33), (22, 38), (25, 11), (21, 4), (40, 26), (7, 22), (7, 5), (38, 15), (25, 20), (13, 5), (1, 38), (27, 14), (18, 36), (40, 12), (14, 10), (10, 34), (39, 27), (38, 10), (8, 13), (32, 27), (25, 4), (19, 26), (34, 10), (18, 22), (16, 0), (20, 33), (21, 42), (14, 41), (8, 24), (22, 14), (32, 42), (34, 18), (18, 42), (12, 19), (14, 35), (21, 6), (25, 6), (30, 32), (10, 3), (14, 3), (39, 1), (35, 7), (24, 19), (12, 1), (4, 5), (17, 36), (18, 4), (15, 17), (8, 10), (15, 24), (40, 28), (1, 37), (4, 32), (23, 21), (35, 2), (19, 38), (23, 13), (8, 11), (2, 21), (36, 38), (8, 16), (27, 34), (5, 0), (24, 29), (20, 8), (31, 29), (10, 26), (28, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 16), (46, 0), (9, 0), (0, 37), (8, 33), (42, 13), (42, 24), (2, 33), (20, 40), (28, 21), (36, 9), (18, 34), (29, 3), (42, 31), (39, 41), (8, 30), (37, 23), (6, 37), (10, 1), (41, 25), (12, 12), (19, 32), (48, 12), (38, 13), (10, 42), (37, 37), (5, 41), (44, 19), (40, 4), (34, 1), (19, 22), (1, 25), (31, 27), (3, 13), (5, 26), (45, 20), (9, 23), (29, 15), (4, 18), (30, 38), (28, 8), (11, 16), (24, 24), (25, 40), (13, 3), (23, 36), (30, 11), (32, 13), (37, 5), (29, 8), (20, 0), (35, 0), (47, 2), (28, 0), (34, 19), (38, 40), (34, 7), (12, 6), (4, 37), (11, 4), (31, 5), (26, 16), (31, 3), (39, 18), (27, 16), (6, 23), (6, 28), (5, 12), (39, 22), (43, 30), (48, 23), (19, 42), (34, 40), (27, 38), (15, 2), (32, 20), (46, 1), (0, 2), (44, 32), (5, 27), (21, 16), (26, 11), (2, 12), (16, 37), (26, 0), (41, 15), (46, 43), (6, 31), (13, 15), (32, 4), (28, 31), (25, 20), (20, 11), (7, 7), (9, 18), (2, 21), (14, 35), (35, 43), (15, 27), (29, 31), (42, 30), (20, 39), (41, 14), (42, 8), (24, 4), (7, 11), (29, 41), (23, 35), (24, 16), (41, 37), (38, 23), (40, 2), (15, 38), (21, 21), (0, 39), (43, 7), (34, 30), (0, 42), (37, 42), (35, 38), (41, 35), (34, 37), (43, 32), (24, 42), (36, 32), (6, 16), (31, 28), (19, 36), (34, 18), (41, 5), (48, 26), (36, 39), (44, 11), (20, 15), (22, 4), (21, 12), (26, 14), (40, 11), (36, 13), (0, 15), (31, 32), (48, 40), (6, 0), (3, 29), (8, 36), (47, 43), (7, 25), (4, 9), (11, 5), (33, 17), (33, 23), (30, 29), (12, 27), (28, 19), (26, 12), (2, 1), (40, 23), (44, 28), (14, 38), (23, 10), (42, 28), (20, 12), (11, 18), (37, 12), (21, 29), (13, 6), (21, 26), (28, 36), (26, 1), (35, 24), (39, 0), (2, 6), (18, 36), (42, 14), (17, 12), (28, 11), (15, 16), (6, 29), (33, 7), (38, 26), (4, 17), (15, 1), (29, 36), (34, 27), (44, 41), (44, 36), (6, 12), (26, 5), (19, 23), (32, 15), (36, 20), (47, 5), (46, 28), (37, 38), (25, 25), (1, 31), (8, 43), (37, 13), (42, 35), (2, 23), (17, 21), (31, 26), (16, 17), (8, 20), (12, 0), (14, 32), (45, 3), (5, 1), (39, 7), (37, 39), (29, 16), (12, 16), (46, 34), (2, 4), (47, 14), (35, 15), (38, 24), (8, 17), (23, 27), (22, 43), (0, 11), (15, 19), (0, 40), (43, 41), (40, 21), (18, 21), (27, 23), (23, 20), (31, 1), (29, 11), (30, 23), (1, 11), (32, 0), (18, 29), (23, 22), (36, 5), (12, 36), (29, 0), (3, 12), (25, 21), (16, 30), (45, 26), (32, 34), (17, 19), (42, 0), (24, 30), (35, 20), (4, 39), (47, 23), (28, 6), (30, 24), (10, 32), (22, 42), (34, 24), (40, 19), (39, 30), (3, 20), (32, 16), (43, 40), (10, 9), (3, 42), (30, 41), (16, 39), (21, 24), (17, 8), (29, 14), (20, 23), (35, 28), (38, 22), (36, 28), (14, 30), (44, 3), (42, 41), (25, 11), (37, 27), (22, 10), (18, 43), (23, 15), (28, 25), (0, 43), (7, 13), (1, 19), (19, 12), (33, 29), (24, 34), (20, 5), (10, 28), (40, 33), (28, 17), (24, 21), (42, 32), (38, 14), (28, 14), (31, 18), (24, 40), (46, 19), (42, 29), (1, 4), (20, 14), (12, 18), (43, 19), (22, 34), (42, 19), (27, 20), (14, 41), (19, 5), (44, 25), (2, 29), (3, 3), (36, 38), (10, 2), (32, 29), (28, 41), (17, 2), (11, 33), (5, 17), (10, 35), (28, 20), (19, 13), (41, 10), (30, 36), (40, 31), (14, 39), (48, 3), (32, 41), (30, 19), (12, 23), (32, 30), (27, 11), (44, 13), (26, 4), (39, 13), (39, 25), (15, 4), (46, 22), (11, 37), (39, 31), (6, 8), (12, 42), (15, 31), (12, 10), (24, 33), (41, 29), (29, 37), (26, 23), (0, 27), (16, 33), (31, 22), (16, 29), (2, 15), (34, 17), (45, 9), (47, 12), (4, 13), (42, 6), (17, 4), (8, 31), (36, 30), (0, 7), (21, 28), (21, 43), (29, 35), (45, 40), (12, 29), (41, 36), (27, 22), (23, 34), (33, 42), (16, 0), (24, 13), (24, 15), (38, 37), (26, 21), (38, 19), (25, 41), (16, 14), (48, 5), (28, 5), (7, 33), (17, 20), (24, 36), (21, 41), (39, 32), (18, 14), (23, 37), (9, 34), (24, 27), (30, 15), (18, 16), (36, 25), (1, 27), (41, 20), (16, 5), (3, 6), (19, 0), (35, 31), (3, 26), (8, 42), (27, 14), (46, 8), (5, 40), (23, 25), (21, 6)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "In a 44x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (11, 46), (12, 15), (33, 20), (31, 16), (19, 41), (6, 13), (20, 19), (18, 18), (1, 10), (30, 1), (6, 9), (24, 25), (25, 23), (15, 18), (15, 5), (19, 14), (6, 6), (17, 35), (38, 11), (16, 44), (18, 39), (38, 40), (31, 29), (42, 3), (22, 20), (10, 4), (31, 2), (38, 22), (16, 43), (27, 10), (16, 17), (6, 24), (27, 0), (30, 44), (42, 17), (28, 16), (4, 41), (3, 37), (36, 1), (16, 31), (30, 16), (29, 18), (18, 3), (42, 30), (32, 20), (43, 25), (32, 15), (30, 0), (22, 6), (37, 31), (32, 3), (15, 36), (30, 33), (0, 13), (19, 26), (8, 6), (43, 23), (39, 25), (43, 8), (26, 27), (32, 22), (24, 19), (16, 38), (38, 30), (36, 7), (21, 31), (41, 9), (40, 31), (0, 29), (30, 46), (41, 8), (40, 30), (29, 39), (5, 30), (24, 46), (43, 4), (43, 29), (4, 27), (6, 40), (32, 18), (42, 46), (27, 19), (5, 1), (5, 6), (20, 43), (41, 44), (37, 4), (21, 18), (12, 4), (42, 27), (10, 2), (7, 35), (3, 44), (5, 44), (17, 27), (32, 5), (26, 20), (28, 31), (19, 6), (14, 9), (24, 14), (19, 12), (33, 18), (15, 25), (28, 2), (6, 4), (33, 15), (27, 21), (13, 25), (36, 9), (40, 18), (33, 35), (16, 40), (28, 26), (39, 13), (32, 44), (22, 18), (43, 16), (19, 30), (7, 28), (11, 22), (25, 37), (35, 31), (24, 7), (22, 14), (26, 26), (24, 23), (0, 18), (38, 39), (4, 17), (33, 10), (9, 6), (28, 12), (41, 27), (30, 21), (8, 42), (19, 45), (10, 26), (37, 43), (7, 13), (11, 8), (11, 28), (17, 37), (0, 32), (17, 31), (10, 23), (32, 13), (27, 27), (20, 16), (9, 3), (39, 10), (40, 2), (3, 2), (16, 2), (13, 46), (30, 37), (27, 30), (18, 23), (10, 10), (15, 45), (14, 8), (17, 34), (25, 17), (21, 38), (17, 43), (26, 28), (28, 11), (17, 11), (11, 34), (15, 26), (3, 16), (38, 14), (18, 20), (40, 14), (6, 15), (31, 19), (33, 14), (15, 33), (35, 20), (8, 13), (41, 35), (2, 21), (35, 44), (18, 11), (16, 26), (23, 32), (32, 9), (36, 21), (27, 13), (1, 22), (23, 3), (42, 10), (9, 17), (2, 24), (39, 37), (13, 39), (30, 43), (14, 10), (26, 37), (19, 38), (12, 41), (29, 26), (8, 21), (15, 3), (22, 44), (14, 44), (40, 17), (6, 38), (41, 22), (15, 9), (4, 15), (14, 18), (33, 27), (14, 14), (24, 20), (38, 9), (27, 18), (38, 17), (20, 18), (28, 33), (34, 26), (34, 21), (21, 2), (6, 11), (43, 19), (2, 15), (3, 24), (23, 6), (23, 35), (42, 44), (32, 41), (31, 21), (15, 44), (11, 32), (4, 7), (41, 13), (15, 1), (9, 43), (3, 15), (15, 19), (6, 34), (2, 2), (15, 22), (14, 0), (27, 46), (28, 43), (11, 5), (35, 11), (33, 6), (3, 1), (14, 15), (16, 29), (25, 19), (2, 36), (34, 46), (36, 26), (7, 18), (43, 3), (37, 13), (40, 9), (37, 20), (34, 27), (7, 14), (1, 33), (32, 17), (35, 24), (40, 1), (11, 16), (8, 33), (16, 11), (3, 41), (2, 0), (5, 4), (38, 24), (31, 38), (14, 41), (34, 29), (4, 8), (19, 37), (36, 5), (20, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 41x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 13), (26, 18), (3, 30), (7, 22), (0, 23), (37, 11), (8, 14), (13, 40), (10, 13), (27, 29), (3, 3), (2, 31), (39, 8), (34, 24), (29, 11), (13, 3), (6, 35), (11, 33), (21, 40), (16, 7), (22, 39), (34, 0), (4, 17), (16, 13), (2, 13), (2, 39), (2, 16), (20, 22), (22, 31), (15, 31), (17, 7), (24, 19), (20, 2), (21, 15), (7, 40), (5, 17), (0, 7), (24, 6), (12, 5), (26, 26), (13, 39), (7, 18), (17, 32), (18, 20), (1, 7), (39, 28), (37, 16), (15, 23), (11, 14), (38, 8), (39, 13), (29, 12), (22, 2), (5, 29), (15, 19), (39, 5), (27, 27), (23, 13), (8, 33), (29, 23), (19, 24), (2, 21), (35, 22), (25, 2), (4, 1), (17, 0), (18, 6), (10, 36), (5, 36), (8, 39), (26, 13), (35, 2), (34, 7), (1, 6), (26, 25), (3, 15), (11, 40), (35, 37), (15, 2), (8, 30), (24, 5), (21, 11), (6, 34), (2, 36), (34, 16), (34, 37), (22, 38), (34, 20), (18, 14), (4, 3), (37, 2), (35, 6), (7, 20), (1, 1), (30, 28), (26, 40), (0, 17), (8, 24), (14, 4), (33, 27), (40, 36), (4, 13), (1, 33), (32, 36), (23, 4), (11, 20), (2, 25), (39, 11), (4, 37), (26, 16), (3, 33), (9, 40), (29, 17), (13, 36), (15, 9), (9, 30), (33, 35), (14, 40), (36, 2), (5, 20), (38, 9), (32, 13), (18, 36), (10, 3), (22, 10), (17, 19), (2, 27), (20, 17), (27, 3), (18, 25), (25, 12), (1, 4), (14, 15), (12, 39), (34, 34), (16, 24), (30, 16), (36, 30), (35, 32), (5, 25), (31, 9), (14, 29), (28, 4), (4, 36), (32, 16), (29, 39), (20, 32), (36, 18), (12, 4), (27, 22), (40, 31), (28, 35), (11, 0), (8, 19), (36, 28), (0, 12), (24, 1), (8, 10), (13, 9), (13, 0), (25, 35), (1, 18), (8, 9), (13, 15), (24, 26), (11, 12), (12, 3), (8, 28), (36, 21), (35, 13), (23, 25), (29, 34), (12, 8), (24, 35), (7, 29), (9, 13), (14, 9), (28, 16), (16, 18), (27, 2), (4, 31), (3, 34), (18, 9), (29, 18), (33, 18), (13, 29), (10, 27), (19, 26), (27, 23), (24, 7), (5, 10), (35, 21), (31, 30), (39, 39), (2, 4), (26, 29), (23, 37), (36, 15), (10, 34), (14, 26), (22, 13), (11, 1), (16, 36), (14, 12), (31, 21), (37, 34), (7, 4), (30, 12), (40, 5), (8, 26), (29, 13), (6, 24), (35, 23), (6, 20), (38, 38), (1, 34), (34, 9), (14, 21), (26, 39), (38, 12), (4, 9), (12, 37), (22, 17), (40, 26), (35, 0), (22, 1), (30, 1), (14, 35), (2, 14), (3, 18), (11, 9), (19, 13)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (45, 3), (28, 31), (18, 28), (29, 0), (1, 37), (28, 29), (17, 36), (35, 23), (14, 31), (43, 26), (8, 17), (6, 21), (0, 10), (5, 20), (8, 23), (32, 20), (10, 30), (3, 16), (42, 39), (20, 0), (19, 0), (31, 12), (34, 34), (4, 26), (21, 15), (40, 37), (34, 36), (44, 38), (12, 3), (21, 27), (43, 17), (26, 36), (7, 29), (24, 14), (19, 27), (0, 25), (15, 2), (1, 36), (5, 39), (6, 35), (23, 22), (35, 31), (5, 4), (38, 4), (35, 34), (40, 28), (8, 1), (21, 0), (18, 10), (29, 5), (14, 23), (2, 34), (31, 16), (9, 4), (20, 27), (10, 1), (37, 18), (34, 30), (29, 20), (16, 9), (12, 19), (42, 12), (43, 4), (13, 4), (33, 40), (0, 27), (12, 15), (1, 22), (43, 21), (42, 29), (26, 10), (2, 4), (10, 7), (10, 31), (39, 14), (40, 2), (32, 17), (40, 14), (36, 11), (45, 25), (45, 33), (37, 6), (39, 39), (1, 11), (35, 16), (35, 19), (33, 33), (3, 2), (7, 24), (31, 11), (40, 22), (30, 21), (28, 21), (31, 2), (5, 11), (20, 11), (32, 16), (14, 0), (23, 29), (41, 22), (26, 16), (44, 25), (46, 11), (9, 29), (0, 11), (2, 37), (21, 2), (30, 34), (5, 33), (30, 0), (25, 32), (39, 23), (36, 35), (31, 30), (22, 6), (15, 1), (40, 26), (36, 7), (27, 22), (10, 12), (10, 20), (8, 26), (23, 15), (8, 18), (27, 4), (33, 2), (10, 25), (8, 22), (12, 5), (2, 17), (41, 30), (43, 25), (29, 30), (4, 19), (38, 13), (9, 28), (29, 15), (5, 22), (34, 22), (28, 33), (40, 38), (1, 0), (14, 34), (24, 1), (7, 10), (33, 3), (31, 20), (21, 29), (33, 6), (22, 11), (30, 30), (43, 39), (8, 15), (24, 28), (10, 32), (16, 33), (9, 21), (2, 16), (43, 38), (23, 18), (44, 6), (34, 31), (39, 2), (23, 8), (15, 35), (0, 39), (41, 23), (39, 40), (25, 20), (13, 24), (19, 37), (5, 24), (43, 20), (23, 39), (4, 1), (0, 19), (45, 10), (38, 34), (12, 38), (7, 38), (1, 27), (12, 40), (7, 5), (27, 39), (40, 40), (16, 12), (41, 3), (38, 24), (29, 12), (5, 13), (46, 16), (34, 23), (0, 13), (9, 1), (1, 23), (26, 14), (28, 35), (37, 33), (23, 2), (42, 36), (21, 38), (27, 33), (30, 35), (34, 38), (28, 8), (1, 35), (39, 34), (8, 19), (6, 31), (22, 28), (2, 33), (29, 32), (24, 9), (45, 27), (28, 14), (41, 24), (40, 36), (43, 22), (22, 26), (28, 9), (6, 2), (42, 26), (15, 0), (41, 9), (35, 1), (0, 22), (42, 24), (42, 22), (33, 22), (0, 23), (43, 6), (1, 21), (40, 31), (26, 23), (20, 25), (1, 15), (10, 38), (13, 23), (36, 14), (17, 27), (3, 15), (35, 33), (9, 39), (7, 30), (21, 9), (23, 21), (21, 39), (35, 35), (33, 28), (26, 27), (27, 7), (0, 20), (14, 20), (7, 28), (16, 34), (9, 14), (29, 36), (14, 25), (17, 33), (24, 21), (20, 17), (32, 13), (23, 14), (12, 13), (15, 36), (22, 31), (43, 24), (40, 4), (14, 22), (35, 2), (34, 10), (14, 14), (5, 23), (40, 8), (23, 13), (1, 9), (31, 37), (22, 30), (37, 36), (24, 15), (15, 28), (19, 9), (4, 33), (4, 30), (21, 24), (36, 12), (45, 15), (42, 23), (12, 26), (0, 26), (7, 17), (36, 21), (11, 10), (18, 9), (39, 0), (15, 9), (8, 12), (0, 14), (45, 4), (8, 13), (31, 35), (0, 15), (0, 40), (45, 14), (6, 8), (14, 9), (4, 6), (27, 15), (31, 31), (35, 13), (18, 21), (4, 8), (22, 8), (6, 22), (12, 7), (12, 33), (20, 35), (46, 14), (46, 27), (44, 36), (19, 32), (31, 40), (23, 0), (23, 40), (19, 19), (9, 24), (42, 2), (9, 20), (32, 31), (13, 39), (27, 40), (3, 35), (20, 32), (33, 24), (32, 40), (14, 15), (10, 29), (18, 32), (23, 24), (27, 18), (35, 12), (6, 34)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 44x46 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 45), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 45), (20, 45), (32, 19), (30, 39), (4, 20), (36, 45), (30, 7), (22, 15), (42, 0), (4, 3), (23, 29), (19, 26), (39, 20), (41, 26), (21, 14), (1, 27), (39, 13), (29, 40), (12, 1), (26, 31), (33, 20), (0, 32), (10, 38), (5, 36), (8, 35), (2, 13), (26, 29), (0, 27), (34, 35), (5, 25), (22, 25), (36, 4), (17, 30), (14, 43), (2, 40), (1, 9), (43, 31), (0, 17), (40, 14), (28, 38), (33, 11), (2, 7), (27, 27), (12, 21), (6, 30), (37, 30), (7, 37), (0, 11), (38, 26), (7, 8), (36, 36), (14, 30), (41, 31), (3, 30), (35, 26), (29, 14), (43, 22), (23, 26), (29, 2), (8, 39), (37, 31), (30, 1), (31, 15), (16, 36), (37, 39), (20, 5), (21, 41), (8, 27), (22, 23), (14, 17), (12, 34), (6, 1), (19, 13), (40, 15), (13, 26), (21, 9), (40, 0), (6, 0), (17, 44), (30, 30), (39, 15), (35, 42), (27, 12), (3, 18), (24, 33), (23, 15), (33, 5), (0, 9), (24, 14), (42, 29), (12, 22), (37, 40), (43, 38), (13, 21), (42, 17), (35, 4), (15, 31), (37, 44), (35, 3), (26, 22), (41, 8), (9, 20), (9, 4), (3, 41), (37, 33), (42, 18), (5, 13), (30, 21), (13, 16), (9, 5), (19, 3), (1, 33), (8, 13), (26, 43), (31, 44), (9, 30), (21, 13), (7, 9), (27, 41), (13, 2), (16, 1), (3, 15), (20, 36), (21, 26), (3, 0), (35, 9), (18, 23), (8, 9), (13, 1), (19, 7), (9, 16), (31, 28), (26, 44), (36, 15), (18, 35), (41, 18), (16, 29), (4, 41), (39, 16), (16, 3), (7, 0), (28, 20), (10, 2), (17, 34), (13, 0), (21, 45), (17, 18), (42, 6), (32, 3), (21, 39), (10, 20), (18, 45), (15, 27), (14, 21), (43, 14), (15, 23), (28, 23), (2, 4), (26, 42), (38, 41), (7, 2), (21, 24), (4, 27), (1, 12), (36, 31), (19, 9), (27, 18), (21, 19), (25, 21), (34, 4), (22, 22), (19, 31), (14, 32), (19, 28), (3, 19), (23, 44), (43, 32), (3, 38), (21, 44), (41, 45), (14, 12), (31, 2), (22, 12), (25, 43), (2, 26), (10, 30), (12, 39), (14, 26), (10, 6), (6, 3), (24, 8), (11, 23), (29, 3), (11, 29), (29, 11), (10, 45), (43, 17), (34, 6), (33, 22), (25, 2), (31, 8), (11, 27), (24, 36), (22, 44), (27, 9), (13, 36), (0, 28), (42, 8), (27, 11), (26, 45), (2, 12), (35, 8), (19, 22), (24, 45), (36, 39), (16, 25), (10, 44), (37, 21), (3, 28), (25, 7), (29, 32), (31, 37), (18, 33), (5, 38), (43, 1), (18, 18), (37, 11), (14, 1), (29, 43), (15, 26), (12, 8), (38, 39), (4, 29), (28, 10), (12, 11), (3, 21), (42, 23), (18, 1), (39, 6), (32, 32), (37, 38), (15, 13), (20, 1), (29, 1), (41, 36), (5, 22), (13, 30), (2, 21), (28, 26), (22, 18), (19, 21), (11, 12), (35, 16), (41, 27), (25, 29), (24, 16), (10, 37), (34, 15), (8, 16), (13, 40), (3, 10), (5, 7), (4, 43), (23, 45), (42, 35), (18, 29), (42, 20), (23, 42), (6, 21), (37, 43), (27, 24), (13, 41), (24, 22), (16, 24), (29, 30), (23, 11), (19, 11), (21, 40), (42, 26), (17, 22), (41, 32), (4, 14), (14, 31), (36, 27), (4, 42), (10, 22), (4, 10), (20, 18), (18, 44), (11, 26), (9, 24), (4, 37), (32, 23), (16, 4), (32, 27), (11, 20), (15, 39), (16, 41), (14, 25), (31, 41), (7, 35), (11, 33), (8, 8), (10, 21), (29, 27), (28, 37), (6, 6), (25, 4), (0, 35), (3, 17), (37, 13), (39, 39), (37, 6), (35, 37), (7, 10), (14, 16), (3, 42), (3, 40), (18, 17), (24, 42), (4, 25), (18, 5), (5, 11), (27, 7), (34, 25), (22, 26), (25, 39), (8, 20), (36, 30), (8, 15), (24, 17), (8, 29), (30, 20), (17, 29), (39, 29), (2, 17), (3, 13), (32, 11), (25, 14), (40, 40), (17, 33), (12, 40), (13, 9), (11, 16), (33, 2), (25, 28), (21, 10), (21, 22), (7, 23), (31, 29), (28, 33), (30, 3), (12, 25), (27, 23), (31, 13), (7, 3), (13, 5), (20, 22), (38, 16), (5, 14), (17, 20), (37, 24)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "In a 45x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (39, 10), (36, 8), (9, 37), (6, 13), (42, 12), (41, 35), (29, 21), (15, 17), (25, 34), (22, 28), (26, 0), (4, 36), (39, 13), (19, 25), (13, 10), (1, 31), (9, 22), (13, 27), (2, 39), (31, 10), (33, 14), (40, 19), (19, 10), (5, 1), (35, 30), (19, 12), (24, 10), (8, 23), (8, 17), (9, 14), (28, 37), (30, 32), (21, 28), (26, 1), (9, 19), (7, 37), (15, 21), (32, 4), (2, 28), (33, 36), (27, 37), (28, 19), (13, 19), (20, 36), (20, 4), (8, 9), (43, 8), (18, 12), (3, 28), (14, 38), (8, 29), (23, 4), (28, 8), (14, 31), (36, 38), (29, 7), (29, 34), (29, 16), (36, 39), (29, 8), (40, 10), (14, 40), (13, 29), (1, 1), (4, 15), (41, 3), (21, 11), (36, 27), (14, 27), (19, 5), (11, 17), (13, 24), (29, 28), (16, 37), (26, 35), (0, 32), (27, 24), (22, 7), (13, 36), (16, 8), (32, 29), (31, 16), (3, 34), (0, 37), (20, 9), (1, 32), (40, 35), (6, 34), (30, 21), (33, 37), (30, 11), (2, 5), (20, 10), (17, 8), (40, 26), (10, 22), (12, 19), (12, 32), (36, 11), (12, 17), (7, 14), (13, 32), (26, 12), (2, 16), (34, 21), (31, 13), (19, 20), (13, 8), (20, 2), (38, 5), (5, 25), (5, 0), (9, 5), (26, 8), (18, 16), (29, 27), (18, 27), (17, 3), (20, 25), (6, 2), (27, 5), (25, 37), (12, 16), (6, 3), (10, 4), (26, 21), (9, 2), (9, 33), (43, 34), (3, 35), (22, 25), (30, 18), (5, 26), (37, 6), (30, 40), (41, 1), (3, 37), (35, 18), (20, 8), (18, 8), (30, 30), (37, 0), (18, 4), (4, 29), (4, 19), (43, 33), (34, 36), (36, 16), (12, 29), (18, 38), (2, 33), (38, 9), (32, 22), (13, 5), (4, 20), (17, 18), (26, 6), (7, 36), (8, 28), (34, 40), (41, 10), (18, 33), (32, 37), (22, 36), (28, 20), (27, 40), (7, 19), (21, 0), (11, 11), (6, 17), (12, 24), (0, 21), (2, 30), (27, 12), (3, 5), (12, 14), (35, 10), (16, 23), (6, 15), (13, 14), (28, 40), (36, 30), (11, 5), (28, 6), (23, 31), (38, 35), (13, 12), (18, 31), (9, 38), (14, 26), (25, 28), (26, 4), (23, 37), (21, 16), (27, 4), (35, 13), (3, 6), (23, 18), (27, 14), (4, 2), (14, 33), (19, 11), (5, 4), (6, 16), (40, 12), (1, 19), (40, 21), (35, 34), (7, 31), (37, 29), (27, 35), (15, 5), (2, 8), (35, 3), (34, 8), (17, 0), (4, 3), (32, 30), (40, 38), (24, 27), (26, 17), (18, 40), (20, 15), (13, 16), (19, 8), (43, 2), (7, 6), (41, 15), (9, 13), (16, 33), (1, 29), (29, 0), (32, 2), (19, 29), (37, 27), (13, 15), (14, 5), (21, 32), (15, 37), (21, 18), (27, 34), (43, 17), (29, 23), (41, 21), (19, 1), (23, 14), (3, 31)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 44x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 33), (14, 2), (8, 30), (20, 17), (14, 4), (36, 0), (39, 35), (24, 27), (43, 35), (1, 5), (26, 1), (43, 38), (34, 4), (32, 21), (28, 7), (10, 30), (17, 34), (20, 13), (11, 35), (6, 29), (7, 41), (17, 7), (0, 32), (22, 14), (35, 10), (19, 17), (7, 6), (4, 33), (9, 1), (33, 25), (18, 22), (9, 38), (22, 38), (2, 6), (14, 11), (28, 10), (0, 12), (35, 4), (31, 18), (30, 32), (32, 2), (15, 13), (37, 35), (23, 26), (28, 34), (1, 8), (42, 27), (2, 20), (38, 16), (40, 29), (35, 19), (33, 0), (30, 34), (13, 31), (16, 26), (16, 2), (12, 20), (31, 41), (34, 41), (35, 38), (36, 26), (35, 24), (19, 34), (5, 29), (9, 6), (5, 13), (7, 20), (14, 28), (34, 0), (34, 13), (4, 20), (21, 26), (19, 29), (34, 27), (16, 25), (21, 27), (16, 13), (26, 19), (7, 30), (14, 14), (26, 6), (3, 0), (19, 7), (2, 19), (3, 16), (36, 39), (29, 38), (37, 40), (33, 24), (16, 0), (7, 9), (8, 16), (35, 35), (34, 29), (7, 36), (25, 36), (16, 29), (1, 11), (26, 39), (22, 34), (14, 15), (32, 19), (32, 7), (18, 10), (25, 22), (35, 41), (9, 30), (38, 25), (33, 19), (31, 35), (39, 32), (15, 24), (13, 4), (34, 14), (1, 29), (38, 1), (5, 27), (0, 14), (25, 26), (20, 10), (30, 31), (15, 32), (36, 30), (5, 22), (4, 6), (30, 28), (23, 3), (28, 2), (35, 20), (13, 21), (24, 13), (30, 9), (15, 5), (39, 10), (2, 41), (39, 15), (28, 20), (34, 11), (13, 38), (7, 34), (0, 17), (13, 9), (1, 17), (39, 12), (28, 24), (5, 36), (38, 38), (12, 15), (2, 23), (6, 2), (6, 35), (43, 6), (8, 37), (38, 35), (11, 17), (38, 4), (7, 17), (29, 33), (2, 33), (39, 37), (38, 36), (9, 27), (28, 18), (29, 1), (0, 36), (10, 6), (35, 31), (11, 0), (33, 32), (20, 30), (14, 41), (3, 12), (20, 41), (42, 26), (22, 1), (27, 11), (7, 23), (21, 16), (4, 29), (17, 25), (4, 2), (41, 30), (32, 4), (13, 39), (5, 40), (10, 20), (8, 28), (8, 24), (12, 21), (43, 40), (24, 23), (36, 12), (12, 27), (33, 7), (43, 36), (7, 1), (6, 39), (39, 5), (29, 40), (43, 22), (23, 31), (18, 25), (9, 34), (36, 11), (41, 2), (6, 25), (38, 33), (8, 6), (17, 13), (9, 23), (25, 35), (20, 19), (40, 8), (15, 29), (16, 23), (6, 28), (13, 0), (19, 40), (19, 26), (12, 7), (40, 0), (39, 21), (31, 28), (1, 30), (26, 4), (8, 1), (23, 5), (29, 18), (5, 4), (12, 2), (18, 3), (37, 22), (31, 29), (39, 27), (37, 13), (26, 29), (41, 15), (34, 18), (42, 8), (13, 26), (0, 26), (1, 15), (34, 22), (6, 11), (30, 25), (7, 18), (35, 26), (35, 32), (32, 40), (21, 35), (19, 10), (37, 5), (4, 11), (14, 34), (6, 30), (40, 38), (34, 36), (24, 38), (32, 1), (28, 32), (26, 37), (9, 10), (7, 38), (34, 30), (25, 14), (18, 35), (24, 3), (29, 19), (43, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 42x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (25, 36), (8, 7), (8, 30), (20, 13), (32, 22), (13, 4), (28, 10), (27, 35), (19, 40), (39, 26), (25, 20), (39, 35), (2, 34), (30, 31), (31, 21), (22, 34), (17, 32), (6, 33), (23, 21), (33, 18), (30, 27), (35, 27), (15, 29), (8, 23), (23, 6), (22, 0), (41, 19), (3, 7), (6, 35), (41, 17), (31, 9), (11, 19), (18, 15), (12, 1), (17, 0), (3, 3), (4, 6), (1, 39), (15, 24), (26, 6), (30, 28), (25, 41), (25, 16), (29, 20), (4, 31), (29, 37), (1, 4), (4, 27), (2, 21), (36, 10), (1, 27), (22, 26), (32, 11), (10, 28), (25, 6), (3, 12), (3, 14), (5, 33), (12, 36), (1, 37), (2, 41), (8, 24), (22, 41), (40, 10), (0, 38), (29, 39), (37, 25), (30, 23), (18, 29), (16, 40), (37, 33), (30, 19), (33, 3), (11, 16), (14, 27), (33, 1), (23, 39), (26, 4), (10, 14), (11, 36), (40, 9), (17, 21), (11, 11), (32, 24), (27, 1), (13, 18), (26, 18), (33, 4), (33, 23), (18, 40), (10, 7), (32, 17), (19, 6), (37, 35), (2, 25), (12, 20), (26, 10), (7, 17), (31, 23), (27, 20), (10, 35), (41, 14), (23, 25), (6, 40), (18, 22), (1, 8), (35, 37), (7, 16), (24, 18), (3, 11), (0, 33), (21, 33), (37, 12), (25, 7), (15, 9), (20, 39), (29, 28), (13, 1), (28, 22), (28, 5), (9, 28), (34, 27), (30, 25), (19, 17), (23, 29), (19, 36), (9, 25), (36, 31), (37, 21), (34, 13), (26, 33), (5, 20), (30, 0), (20, 32), (13, 23), (8, 41), (19, 35), (18, 41), (7, 21), (41, 3), (11, 23), (22, 37), (9, 11), (17, 33), (13, 28), (8, 4), (5, 38), (27, 39), (26, 11), (3, 8), (38, 38), (34, 18), (17, 3), (1, 7), (27, 26), (23, 17), (35, 14), (5, 6), (23, 38), (6, 3), (32, 18), (13, 15), (16, 28), (34, 40), (0, 2), (10, 21), (24, 17), (29, 11), (22, 22), (3, 28), (15, 21), (31, 20), (9, 18), (25, 27), (13, 14), (32, 12), (33, 7), (33, 6), (26, 40), (28, 21), (17, 31), (7, 11), (14, 5), (6, 16), (11, 37), (30, 9), (36, 11), (40, 0), (11, 7), (0, 4), (21, 13), (4, 36), (14, 38), (0, 14), (33, 17), (5, 8), (24, 13), (9, 22), (7, 19), (18, 28), (36, 16), (25, 4), (28, 34), (13, 13), (37, 0), (27, 11), (38, 19), (30, 10), (16, 5), (21, 16), (30, 24), (34, 38), (27, 25), (41, 30), (26, 25), (17, 2), (24, 40), (38, 14), (39, 11), (0, 40), (15, 26), (40, 23), (32, 4), (9, 31), (8, 1), (4, 33), (36, 26), (2, 8), (36, 33), (22, 17), (20, 5), (22, 40), (33, 27), (7, 34), (37, 15), (38, 22), (34, 26), (38, 30), (31, 31), (2, 3), (24, 27), (16, 36), (3, 0), (10, 32), (6, 38), (32, 21), (34, 0), (15, 27), (13, 39), (1, 0), (26, 14), (14, 19), (15, 23), (39, 37), (23, 2), (20, 9), (17, 29), (9, 23), (9, 2), (11, 35), (31, 11), (38, 1), (23, 34), (22, 36), (38, 26), (0, 26), (13, 38), (14, 22), (33, 16), (8, 18), (0, 41), (21, 22), (36, 28), (10, 11), (31, 30), (9, 13), (2, 38), (22, 8), (38, 32), (10, 17), (25, 34), (5, 36), (27, 38), (17, 26), (32, 1), (32, 2), (19, 33), (31, 39), (17, 15), (11, 41), (35, 24), (22, 28), (31, 27)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 43x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (3, 38), (7, 29), (0, 36), (1, 24), (14, 25), (16, 26), (7, 21), (17, 21), (42, 6), (20, 33), (31, 10), (1, 26), (9, 25), (5, 15), (42, 26), (40, 12), (32, 4), (2, 27), (27, 38), (26, 28), (29, 18), (19, 15), (13, 26), (39, 16), (11, 21), (12, 20), (23, 13), (14, 13), (0, 38), (30, 39), (0, 18), (30, 25), (15, 2), (31, 18), (20, 9), (23, 19), (40, 5), (29, 8), (23, 14), (19, 21), (22, 8), (22, 7), (29, 16), (4, 15), (34, 19), (17, 17), (18, 18), (28, 38), (8, 17), (21, 22), (30, 31), (29, 33), (40, 30), (32, 24), (13, 32), (38, 14), (34, 24), (42, 17), (35, 3), (9, 24), (22, 11), (18, 37), (25, 15), (3, 22), (18, 26), (8, 35), (14, 36), (9, 31), (2, 39), (1, 5), (20, 0), (33, 8), (14, 34), (14, 17), (1, 22), (32, 25), (3, 3), (24, 34), (26, 34), (24, 27), (20, 10), (33, 39), (28, 6), (20, 11), (26, 29), (11, 32), (8, 27), (30, 30), (29, 5), (42, 18), (27, 18), (34, 33), (15, 14), (5, 1), (17, 36), (4, 24), (4, 38), (5, 16), (13, 27), (12, 30), (9, 14), (39, 36), (15, 35), (27, 24), (23, 25), (9, 18), (2, 21), (11, 4), (12, 31), (21, 34), (2, 6), (17, 25), (13, 34), (19, 11), (19, 1), (29, 12), (6, 24), (37, 33), (3, 4), (16, 23), (0, 10), (21, 37), (11, 12), (36, 24), (27, 26), (2, 8), (5, 22), (20, 36), (21, 18), (33, 9), (31, 27), (11, 34), (15, 9), (22, 26), (3, 21), (39, 2), (15, 13), (0, 16), (22, 6), (18, 39), (42, 13), (19, 35), (23, 33), (18, 33), (33, 27), (5, 31), (10, 2), (37, 30), (39, 3), (27, 31), (22, 25), (41, 24), (42, 32), (24, 14), (37, 2), (0, 28), (32, 34), (20, 29), (31, 33), (12, 39), (39, 5), (2, 35), (17, 39), (17, 30), (28, 35), (0, 34), (21, 14), (16, 31), (12, 21), (23, 32), (19, 37), (8, 4), (4, 34), (26, 2), (5, 9), (23, 16), (20, 7), (36, 12), (31, 30), (14, 9), (11, 7), (8, 18), (31, 39), (19, 22), (5, 19), (23, 10), (37, 29), (14, 39), (40, 32), (5, 4), (9, 13), (22, 37), (41, 11), (38, 8), (38, 30), (24, 23), (7, 39), (32, 20), (1, 31), (27, 20), (14, 23), (5, 10), (36, 26), (1, 17), (33, 14), (1, 29), (22, 32), (3, 13), (32, 38), (25, 28), (33, 19), (21, 2), (4, 5), (9, 4), (38, 39), (31, 7), (39, 9), (1, 11), (11, 17), (28, 9), (1, 35), (17, 33), (15, 17), (36, 20), (37, 7), (40, 6), (0, 20), (28, 32), (29, 31), (22, 2), (30, 19), (41, 27), (11, 25), (16, 14), (34, 38), (6, 7), (0, 12), (3, 30), (23, 0), (34, 18), (23, 24), (1, 8), (2, 3), (15, 3), (12, 1), (6, 17), (23, 23), (28, 20), (5, 5), (21, 12), (16, 39), (8, 13), (15, 10), (6, 28), (7, 20), (31, 14), (28, 18), (16, 12), (40, 38), (5, 21), (8, 39), (23, 1), (36, 35), (11, 18), (22, 15), (16, 20), (9, 7), (0, 14), (24, 19), (36, 11), (12, 12), (40, 8), (13, 24), (20, 2), (33, 32), (16, 16), (33, 36), (34, 11), (8, 14), (9, 12), (4, 19), (22, 23), (22, 30), (35, 36), (3, 34), (25, 18), (16, 27), (27, 29), (26, 3), (38, 19), (13, 6), (39, 27), (13, 23), (9, 28), (21, 39), (41, 23), (37, 23), (13, 7), (5, 8), (5, 32), (8, 2), (19, 34), (15, 18), (12, 34), (10, 38), (10, 36)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 46x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (37, 21), (17, 38), (7, 2), (29, 40), (10, 36), (7, 20), (41, 3), (28, 4), (31, 27), (5, 33), (33, 17), (24, 34), (29, 18), (25, 28), (10, 35), (15, 2), (43, 39), (35, 4), (14, 16), (33, 28), (7, 43), (5, 20), (8, 4), (24, 2), (19, 26), (5, 2), (26, 21), (21, 19), (16, 28), (35, 23), (27, 19), (37, 27), (29, 2), (38, 12), (29, 12), (28, 30), (25, 43), (39, 11), (30, 0), (26, 30), (7, 37), (38, 31), (25, 24), (37, 8), (19, 43), (8, 39), (30, 40), (2, 0), (44, 8), (27, 37), (31, 39), (25, 37), (19, 9), (19, 14), (8, 0), (22, 17), (21, 26), (39, 16), (45, 16), (32, 32), (3, 25), (19, 8), (21, 27), (15, 18), (1, 15), (8, 13), (40, 34), (5, 40), (37, 43), (38, 11), (18, 28), (17, 19), (0, 24), (36, 1), (35, 0), (12, 16), (24, 40), (43, 2), (10, 32), (18, 19), (34, 27), (15, 3), (10, 27), (13, 39), (13, 33), (42, 28), (41, 18), (8, 2), (44, 0), (19, 18), (41, 16), (2, 19), (44, 31), (33, 40), (12, 20), (26, 9), (5, 27), (17, 16), (6, 43), (37, 18), (16, 30), (1, 33), (9, 10), (2, 17), (22, 20), (26, 11), (3, 8), (16, 29), (35, 7), (39, 35), (6, 30), (26, 13), (44, 28), (34, 34), (26, 17), (5, 11), (7, 29), (29, 30), (30, 14), (44, 36), (38, 13), (45, 3), (20, 14), (23, 25), (27, 24), (26, 8), (5, 9), (20, 33), (37, 15), (28, 40), (30, 13), (12, 12), (6, 35), (32, 42), (24, 6), (36, 18), (21, 28), (4, 19), (19, 21), (16, 15), (31, 9), (2, 12), (24, 3), (12, 17), (36, 3), (41, 34), (25, 39), (10, 10), (2, 25), (6, 34), (0, 9), (43, 24), (26, 25), (8, 22), (15, 14), (41, 28), (30, 30), (4, 23), (45, 28), (23, 11), (43, 29), (37, 20), (39, 4), (37, 5), (24, 17), (39, 26), (36, 42), (32, 18), (40, 8), (2, 10), (25, 38), (38, 6), (25, 18), (33, 31), (16, 11), (0, 38), (25, 31), (5, 16), (30, 19), (35, 30), (13, 24), (18, 9), (1, 23), (9, 29), (16, 26), (3, 13), (27, 1), (43, 14), (27, 4), (26, 0), (41, 39), (9, 5), (13, 36), (20, 10), (23, 32), (45, 11), (12, 40), (42, 18), (16, 13), (39, 8), (43, 18), (22, 14), (30, 23), (30, 4), (26, 29), (30, 29), (31, 22), (44, 39), (31, 41), (14, 24), (20, 1), (16, 18), (33, 8), (17, 5), (15, 26), (20, 8), (41, 10), (22, 7), (29, 39), (0, 19), (4, 38), (43, 43), (14, 5), (32, 10), (6, 23), (17, 37), (34, 21), (24, 39), (14, 1), (4, 16), (0, 34), (2, 35), (1, 17), (18, 25), (0, 5), (12, 4), (9, 14), (18, 41), (8, 42), (18, 12), (2, 21), (7, 36), (23, 19), (37, 10), (38, 0), (18, 42), (24, 22), (14, 28), (31, 23), (18, 0)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x45 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 44), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (0, 35), (23, 41), (0, 31), (21, 8), (36, 42), (31, 8), (8, 29), (24, 38), (31, 33), (34, 30), (13, 18), (0, 11), (27, 40), (36, 33), (10, 34), (9, 10), (6, 32), (7, 35), (20, 28), (7, 38), (17, 34), (8, 14), (9, 39), (41, 11), (2, 22), (1, 34), (16, 24), (5, 42), (45, 0), (4, 36), (28, 2), (46, 35), (30, 31), (29, 11), (45, 20), (16, 31), (18, 15), (8, 23), (13, 34), (4, 2), (42, 21), (2, 20), (42, 14), (14, 16), (38, 15), (27, 30), (1, 1), (42, 2), (35, 37), (5, 19), (5, 29), (45, 1), (6, 39), (1, 7), (1, 6), (5, 28), (43, 44), (36, 18), (20, 31), (11, 42), (38, 27), (26, 41), (8, 17), (44, 6), (33, 40), (28, 11), (37, 25), (32, 1), (28, 38), (33, 17), (46, 0), (34, 13), (39, 5), (33, 27), (20, 33), (42, 38), (43, 29), (2, 13), (26, 2), (46, 2), (36, 28), (33, 9), (23, 23), (3, 44), (30, 18), (22, 16), (30, 42), (27, 10), (19, 29), (32, 37), (31, 15), (37, 36), (25, 32), (3, 0), (44, 42), (31, 36), (21, 23), (43, 4), (30, 39), (28, 32), (15, 19), (32, 31), (24, 1), (32, 0), (3, 20), (20, 25), (10, 23), (4, 30), (24, 11), (41, 38), (1, 23), (35, 22), (16, 40), (20, 5), (17, 29), (27, 32), (29, 36), (29, 22), (17, 12), (44, 26), (7, 34), (11, 41), (44, 23), (34, 33), (2, 8), (6, 35), (15, 8), (15, 35), (15, 23), (4, 7), (39, 41), (31, 35), (30, 27), (27, 17), (9, 8), (41, 2), (42, 15), (9, 34), (2, 36), (36, 38), (14, 41), (21, 0), (21, 4), (39, 15), (39, 20), (42, 29), (19, 2), (30, 9), (46, 29), (25, 24), (18, 21), (34, 9), (9, 29), (4, 34), (18, 18), (43, 40), (22, 39), (7, 28), (4, 33), (8, 28), (31, 40), (21, 9), (27, 35), (8, 10), (37, 13), (4, 28), (5, 43), (16, 6), (13, 29), (36, 17), (36, 23), (0, 20), (6, 16), (25, 12), (42, 6), (8, 41), (40, 19), (14, 22), (8, 35), (28, 25), (21, 35), (13, 23), (2, 27), (8, 7), (24, 12), (7, 30), (26, 5), (11, 36), (24, 43), (8, 43), (26, 8), (44, 31), (37, 10), (20, 30), (17, 4), (15, 40), (45, 42), (39, 28), (29, 10), (10, 17), (12, 23), (41, 28), (7, 40), (28, 7), (13, 32), (10, 16), (43, 28), (17, 18), (19, 23), (7, 27), (15, 17), (45, 22), (14, 12), (26, 44), (2, 33), (44, 15), (29, 13), (19, 11), (14, 1), (19, 16), (28, 9), (1, 12), (27, 19), (36, 20), (22, 32), (32, 41), (41, 44), (21, 13), (34, 12), (33, 41), (16, 16), (31, 2), (0, 9), (11, 10), (30, 41), (21, 36), (26, 37), (10, 28), (4, 0), (20, 39), (9, 13), (29, 44), (10, 13), (8, 11), (4, 8), (46, 36), (20, 8), (29, 42), (14, 28), (24, 21), (24, 7), (22, 42), (25, 14), (35, 15), (40, 5), (43, 21), (37, 37), (39, 8), (29, 19), (21, 39), (41, 12), (16, 26), (12, 11), (46, 23), (46, 17), (12, 0), (42, 35), (44, 40), (31, 38), (37, 3), (22, 9), (35, 40), (36, 43), (34, 36), (2, 32), (25, 22), (32, 44), (25, 27), (45, 29), (41, 22), (27, 38), (24, 42), (14, 0), (14, 18), (30, 2), (21, 38), (6, 40), (32, 42), (39, 22), (44, 16), (18, 1), (13, 7), (19, 27), (10, 12), (36, 25), (3, 3)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 49x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (34, 17), (29, 4), (24, 14), (0, 21), (27, 0), (46, 19), (34, 13), (36, 30), (43, 17), (16, 9), (41, 0), (16, 15), (26, 32), (16, 3), (48, 30), (11, 11), (33, 7), (14, 4), (28, 28), (29, 22), (25, 19), (31, 11), (12, 8), (32, 5), (4, 18), (1, 1), (22, 11), (8, 7), (5, 24), (37, 33), (36, 9), (28, 37), (11, 26), (24, 12), (46, 15), (43, 39), (13, 28), (13, 25), (1, 29), (2, 30), (43, 0), (26, 34), (21, 0), (19, 37), (29, 14), (27, 15), (4, 4), (31, 0), (19, 4), (42, 38), (36, 4), (33, 37), (3, 4), (41, 30), (41, 1), (29, 19), (43, 23), (43, 24), (3, 25), (40, 38), (39, 22), (7, 25), (7, 33), (25, 3), (16, 10), (28, 31), (31, 9), (37, 4), (35, 9), (11, 7), (37, 29), (16, 11), (7, 16), (29, 12), (25, 28), (42, 25), (35, 39), (14, 37), (45, 7), (16, 5), (15, 15), (12, 17), (14, 10), (0, 18), (4, 29), (38, 13), (32, 27), (20, 8), (20, 34), (22, 5), (13, 15), (14, 0), (43, 27), (42, 26), (2, 15), (43, 25), (6, 26), (12, 30), (45, 23), (11, 28), (5, 19), (42, 32), (11, 14), (0, 8), (45, 19), (8, 0), (9, 3), (17, 15), (25, 35), (21, 17), (6, 38), (8, 3), (40, 10), (3, 26), (3, 20), (3, 17), (27, 29), (45, 6), (5, 12), (21, 29), (18, 1), (30, 24), (12, 34), (34, 35), (27, 39), (47, 16), (2, 23), (5, 36), (28, 32), (24, 33), (39, 9), (3, 1), (37, 3), (39, 10), (27, 33), (34, 19), (17, 3), (25, 25), (24, 34), (39, 8), (19, 8), (16, 27), (11, 0), (41, 5), (34, 6), (24, 10), (28, 25), (18, 18), (10, 9), (10, 37), (2, 27), (46, 21), (47, 3), (47, 2), (11, 32), (28, 20), (3, 33), (37, 9), (0, 22), (20, 17), (26, 28), (36, 7), (44, 5), (46, 20), (29, 33), (12, 10), (37, 15), (47, 15), (36, 27), (15, 26), (19, 3), (42, 27), (24, 11), (26, 20), (18, 36), (33, 20), (1, 24), (1, 10), (34, 24), (14, 27), (23, 33), (10, 0), (26, 1), (25, 7), (8, 34), (11, 24), (16, 28), (45, 32), (32, 33), (22, 35), (48, 26), (12, 5), (27, 11), (48, 33), (24, 38), (18, 2), (42, 33), (43, 16), (47, 36), (20, 37), (37, 38), (6, 15), (16, 39), (10, 18), (26, 35), (27, 36), (12, 1), (23, 16), (12, 31), (37, 20), (29, 36), (32, 2), (36, 36), (9, 26), (22, 38), (25, 16), (13, 5), (4, 10), (34, 11), (29, 5), (19, 12), (24, 3), (23, 3), (7, 39), (25, 23), (21, 18), (12, 22), (35, 17), (30, 17), (45, 14), (1, 27), (28, 34), (10, 2), (23, 13), (27, 9), (9, 13), (33, 0), (23, 8), (38, 31), (17, 19), (15, 39), (46, 31), (9, 16), (29, 7), (21, 11), (14, 1), (8, 10), (10, 36), (21, 23), (4, 37), (45, 0), (24, 6), (11, 39), (0, 7), (18, 35), (29, 3), (26, 8), (35, 26), (14, 6), (4, 17), (18, 15), (7, 37), (1, 5), (2, 34), (22, 33), (0, 26), (40, 33), (14, 32), (22, 4), (4, 5), (0, 20), (7, 12), (32, 36), (25, 1), (11, 35), (31, 27), (24, 9), (8, 12), (2, 0), (4, 16), (48, 10), (2, 38), (6, 37), (26, 13), (24, 15), (19, 26), (0, 17), (9, 5), (15, 9), (23, 12), (48, 36), (7, 26), (30, 33), (8, 38), (44, 18), (36, 0), (35, 30), (4, 13), (39, 1), (27, 37), (23, 10), (5, 5), (0, 9), (34, 28), (17, 28), (29, 8), (42, 5), (48, 2), (16, 21), (27, 38), (8, 32), (34, 27), (14, 33), (38, 32), (46, 26), (46, 22), (2, 11), (3, 31), (19, 16), (17, 8), (24, 28), (21, 2), (12, 18), (8, 16), (30, 15)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 44x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (43, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (10, 24), (23, 5), (13, 28), (28, 29), (39, 17), (3, 0), (17, 1), (43, 9), (11, 40), (19, 5), (23, 8), (40, 9), (12, 3), (21, 9), (36, 41), (21, 23), (43, 7), (29, 15), (4, 24), (25, 18), (5, 26), (27, 3), (14, 32), (33, 13), (24, 26), (23, 3), (12, 35), (40, 16), (4, 16), (15, 2), (14, 26), (28, 16), (3, 7), (22, 35), (42, 4), (40, 3), (28, 39), (31, 14), (9, 43), (10, 26), (35, 3), (18, 43), (43, 16), (17, 11), (13, 38), (11, 29), (9, 18), (15, 37), (18, 0), (16, 2), (34, 13), (32, 0), (31, 43), (18, 2), (37, 13), (16, 32), (17, 22), (9, 42), (15, 19), (24, 34), (6, 10), (3, 8), (29, 38), (33, 23), (0, 24), (37, 32), (7, 42), (13, 20), (17, 16), (6, 24), (2, 8), (37, 17), (9, 2), (22, 38), (5, 18), (22, 32), (16, 23), (19, 16), (8, 6), (20, 23), (41, 43), (16, 0), (12, 15), (35, 17), (38, 12), (15, 23), (40, 23), (30, 36), (7, 39), (11, 20), (10, 33), (40, 17), (33, 2), (18, 37), (37, 21), (4, 4), (36, 38), (23, 2), (10, 22), (14, 19), (18, 15), (32, 33), (17, 35), (38, 10), (24, 21), (13, 13), (20, 41), (17, 34), (31, 38), (39, 7), (19, 13), (12, 31), (38, 38), (28, 42), (30, 31), (5, 14), (26, 35), (33, 27), (39, 27), (42, 24), (30, 27), (43, 19), (21, 39), (18, 14), (24, 6), (36, 13), (13, 32), (15, 43), (24, 35), (1, 37), (17, 29), (39, 0), (12, 43), (29, 21), (10, 1), (27, 18), (24, 2), (9, 13), (2, 11), (42, 7), (26, 10), (36, 8), (23, 29), (10, 15), (29, 19), (7, 40), (5, 30), (5, 34), (26, 18), (41, 40), (35, 22), (29, 10), (40, 12), (22, 34), (25, 13), (18, 35), (7, 29), (4, 3), (14, 31), (19, 8), (26, 2), (25, 9), (30, 8), (34, 3), (42, 31), (5, 28), (22, 14), (10, 23), (16, 3), (0, 20), (3, 18), (28, 1), (35, 6), (18, 34), (34, 42), (27, 1), (37, 3), (31, 32), (15, 20), (43, 1), (1, 27), (21, 26), (24, 40), (21, 19), (15, 29), (14, 8), (25, 20), (9, 38), (24, 32), (29, 20), (8, 0), (7, 0), (37, 1), (34, 21), (38, 9), (42, 28), (9, 17), (8, 25), (20, 8), (20, 35), (10, 40), (20, 42), (7, 26), (8, 29), (15, 9), (16, 17), (32, 11), (29, 27), (36, 37), (43, 14), (12, 27), (1, 28), (29, 30), (40, 34), (6, 33), (33, 36), (9, 5), (40, 4), (17, 0), (3, 21), (31, 39), (25, 36), (13, 42), (23, 42), (24, 13), (16, 43), (24, 9), (22, 36), (21, 16), (29, 14), (29, 37), (42, 1), (20, 19), (34, 5), (27, 31), (39, 33), (30, 1), (22, 5), (38, 39), (40, 33), (33, 30), (36, 10), (8, 42), (12, 2), (2, 26), (35, 30), (43, 10), (8, 38), (34, 10), (40, 22), (25, 15), (28, 0), (19, 20), (36, 29), (3, 34), (26, 37), (19, 7), (35, 12), (38, 32), (43, 22), (23, 40), (28, 19), (32, 39), (34, 19), (9, 11), (5, 8), (39, 43), (17, 38), (15, 5), (31, 25), (41, 5), (41, 34), (31, 21), (3, 2), (25, 29), (38, 22)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 45x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (32, 10), (40, 12), (20, 28), (28, 33), (16, 36), (11, 28), (25, 18), (5, 29), (27, 5), (12, 13), (38, 18), (15, 3), (6, 34), (1, 0), (2, 37), (38, 36), (26, 19), (15, 0), (35, 16), (24, 37), (22, 35), (23, 17), (13, 23), (25, 37), (27, 10), (24, 6), (24, 28), (14, 30), (17, 17), (37, 7), (19, 6), (8, 7), (13, 17), (15, 30), (15, 16), (37, 8), (16, 0), (14, 11), (12, 17), (4, 26), (29, 37), (20, 11), (23, 25), (43, 6), (39, 13), (23, 14), (13, 33), (28, 4), (18, 2), (35, 14), (9, 14), (4, 30), (10, 27), (25, 0), (15, 38), (5, 9), (31, 23), (25, 7), (26, 10), (16, 14), (41, 27), (26, 33), (35, 11), (20, 34), (42, 37), (44, 20), (23, 16), (1, 5), (29, 9), (21, 26), (40, 23), (15, 18), (15, 24), (35, 18), (34, 28), (24, 23), (6, 31), (1, 34), (3, 17), (9, 19), (25, 19), (10, 36), (31, 31), (37, 27), (42, 27), (3, 39), (27, 22), (29, 8), (34, 17), (2, 2), (28, 11), (6, 29), (17, 1), (40, 32), (22, 39), (31, 5), (31, 39), (18, 3), (28, 0), (35, 30), (33, 25), (19, 4), (39, 36), (1, 21), (27, 6), (38, 27), (7, 18), (19, 19), (17, 29), (32, 35), (38, 22), (1, 18), (9, 22), (25, 21), (5, 14), (6, 20), (28, 30), (27, 27), (18, 9), (19, 28), (14, 35), (19, 17), (26, 38), (38, 14), (10, 18), (38, 33), (19, 24), (21, 1), (39, 3), (20, 4), (29, 7), (18, 15), (4, 11), (2, 31), (44, 33), (9, 0), (29, 6), (27, 0), (39, 14), (44, 10), (22, 21), (27, 7), (13, 25), (22, 38), (29, 0), (17, 26), (33, 18), (15, 39), (31, 36), (22, 32), (33, 23), (9, 10), (15, 13), (28, 9), (6, 4), (8, 25), (40, 0), (21, 23), (12, 9), (33, 6), (30, 12), (3, 24), (21, 2), (14, 12), (13, 2), (9, 11), (0, 37), (42, 12), (35, 9), (23, 6), (26, 21), (14, 22), (3, 22), (17, 5), (33, 32), (28, 28), (14, 19), (34, 39), (9, 26), (5, 4), (17, 38), (32, 38), (4, 32), (31, 7), (38, 23), (2, 26), (1, 30), (1, 8), (19, 35), (3, 31), (38, 24), (23, 31), (31, 21), (30, 19), (20, 24), (30, 8), (18, 27), (34, 27), (27, 2), (36, 12), (2, 4), (37, 32), (27, 32), (19, 12), (16, 23), (5, 12), (38, 17), (34, 6), (41, 36), (10, 6), (17, 32), (2, 3), (6, 1), (21, 33), (18, 36), (15, 20), (43, 5), (26, 14), (4, 21), (35, 2), (14, 32), (13, 7), (29, 36), (33, 12), (5, 0), (26, 20), (12, 33), (36, 38), (6, 15), (36, 31), (30, 24), (11, 16), (26, 12), (14, 2), (13, 0), (12, 18), (10, 31), (31, 20), (1, 19), (32, 24), (8, 32), (43, 10), (23, 35), (3, 38), (31, 19), (42, 14), (37, 12), (34, 24), (11, 10), (14, 3), (15, 1), (9, 30), (38, 4), (30, 32), (15, 23), (44, 25), (1, 17), (44, 13), (8, 24), (40, 35), (10, 29), (22, 7), (41, 12), (8, 1), (31, 1), (33, 4), (0, 7), (42, 33), (6, 13), (28, 10), (20, 25), (30, 31), (16, 35), (39, 8), (35, 25), (38, 39), (30, 5), (25, 16), (44, 18), (4, 14), (24, 27), (19, 10), (21, 16), (42, 11), (33, 10), (44, 26), (0, 19), (39, 0), (2, 28), (33, 31), (17, 18), (7, 15), (38, 11), (8, 5), (12, 8), (33, 17), (3, 9), (10, 7), (19, 20), (4, 19), (13, 26), (7, 38), (24, 1), (29, 26), (16, 19), (24, 9), (16, 28), (39, 12), (0, 12), (16, 16), (27, 20), (28, 22), (3, 32), (15, 4), (19, 18), (43, 21), (27, 17), (5, 21), (27, 14), (0, 24), (33, 20), (0, 23), (18, 19), (40, 2), (4, 7), (6, 7), (12, 4), (43, 23), (36, 19), (42, 3), (23, 4), (16, 25), (29, 3), (24, 4), (33, 11), (19, 37), (42, 23), (31, 33), (3, 30), (8, 9), (44, 11), (37, 0), (4, 20), (2, 24), (2, 1), (13, 27), (14, 28), (24, 11), (26, 30), (43, 33), (6, 11), (11, 8), (28, 20)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "In a 41x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (38, 33), (39, 7), (12, 36), (9, 24), (18, 26), (13, 30), (27, 16), (21, 12), (29, 38), (14, 25), (4, 39), (33, 20), (23, 34), (28, 22), (6, 1), (27, 43), (4, 27), (32, 11), (7, 20), (25, 35), (31, 45), (6, 43), (8, 27), (22, 24), (33, 13), (7, 0), (21, 4), (37, 34), (32, 9), (19, 4), (19, 32), (31, 41), (10, 44), (20, 13), (2, 2), (10, 45), (5, 19), (21, 6), (40, 39), (18, 40), (7, 38), (13, 36), (5, 13), (38, 46), (17, 14), (33, 38), (34, 42), (32, 37), (30, 36), (32, 32), (24, 4), (31, 16), (25, 18), (7, 18), (9, 14), (37, 23), (20, 47), (35, 41), (26, 19), (4, 37), (25, 41), (22, 18), (21, 8), (37, 30), (13, 40), (28, 30), (0, 30), (9, 36), (17, 24), (36, 45), (14, 30), (10, 8), (19, 13), (14, 19), (14, 15), (30, 17), (23, 48), (37, 40), (36, 23), (26, 2), (21, 44), (15, 27), (22, 2), (8, 24), (35, 5), (20, 9), (17, 0), (34, 2), (12, 31), (20, 27), (21, 32), (23, 46), (6, 9), (22, 6), (34, 4), (28, 9), (30, 29), (22, 23), (16, 0), (27, 46), (10, 0), (10, 11), (4, 18), (9, 37), (15, 21), (36, 46), (14, 47), (11, 30), (31, 23), (26, 13), (33, 29), (23, 29), (39, 25), (18, 34), (10, 26), (18, 23), (1, 45), (38, 37), (37, 7), (5, 38), (22, 15), (6, 24), (18, 16), (12, 15), (3, 15), (7, 48), (33, 31), (30, 32), (6, 29), (24, 13), (34, 1), (39, 37), (1, 38), (17, 30), (11, 46), (11, 4), (31, 26), (22, 40), (7, 45), (10, 41), (15, 14), (7, 23), (19, 39), (5, 17), (40, 16), (39, 13), (15, 19), (14, 45), (14, 41), (18, 42), (21, 39), (22, 16), (1, 8), (37, 13), (24, 16), (36, 44), (39, 16), (17, 37), (23, 20), (12, 25), (29, 20), (13, 2), (13, 38), (25, 2), (25, 48), (4, 36), (33, 25), (19, 46), (4, 33), (15, 35), (12, 19), (8, 29), (15, 20), (4, 44), (3, 5), (12, 37), (26, 38), (32, 48), (12, 24), (16, 47), (7, 10), (28, 11), (0, 4), (32, 34), (23, 25), (28, 17), (11, 32), (5, 40), (40, 10), (35, 23), (37, 0), (33, 46), (28, 4), (3, 0), (16, 46), (11, 34), (7, 25), (36, 32), (27, 10), (12, 14), (10, 47), (36, 7), (28, 15), (10, 2), (39, 42), (32, 22), (34, 39), (5, 8), (32, 42), (27, 38), (39, 17), (11, 0), (31, 5), (13, 17), (9, 15), (18, 39), (24, 8), (12, 48), (20, 32), (21, 14), (39, 40), (38, 9), (36, 36), (25, 36), (28, 2), (30, 34), (23, 47), (36, 28), (34, 15), (10, 36), (7, 26), (21, 2), (33, 33), (22, 4), (14, 6), (16, 6), (2, 41), (31, 20), (38, 15), (38, 45), (8, 1), (24, 15), (27, 32), (35, 11)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 47x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (40, 23), (45, 41), (12, 15), (5, 19), (45, 21), (14, 10), (1, 1), (19, 20), (34, 41), (39, 8), (32, 37), (20, 9), (2, 11), (43, 35), (28, 34), (17, 14), (2, 2), (24, 26), (30, 34), (3, 7), (37, 6), (21, 27), (35, 29), (38, 17), (25, 10), (17, 33), (27, 42), (12, 2), (23, 12), (31, 4), (1, 22), (23, 19), (31, 5), (27, 16), (14, 24), (27, 32), (36, 1), (28, 37), (43, 29), (34, 38), (27, 10), (32, 38), (23, 7), (31, 15), (9, 36), (29, 32), (4, 20), (4, 35), (16, 15), (6, 30), (24, 33), (24, 1), (22, 6), (1, 9), (32, 17), (11, 26), (23, 25), (38, 10), (22, 36), (2, 24), (29, 16), (37, 3), (38, 4), (27, 41), (6, 20), (6, 18), (25, 19), (31, 12), (26, 40), (20, 19), (35, 28), (14, 29), (34, 9), (10, 14), (41, 25), (46, 27), (13, 32), (16, 6), (42, 20), (11, 3), (22, 27), (33, 10), (6, 3), (9, 3), (40, 2), (7, 15), (43, 17), (42, 1), (9, 32), (17, 13), (1, 28), (45, 26), (3, 33), (12, 29), (20, 18), (15, 19), (27, 34), (9, 24), (34, 40), (1, 31), (44, 30), (26, 10), (18, 34), (41, 4), (11, 28), (4, 24), (41, 32), (27, 9), (18, 25), (39, 4), (18, 27), (7, 32), (27, 21), (30, 4), (22, 34), (26, 36), (21, 23), (9, 6), (29, 30), (19, 16), (42, 40), (1, 4), (0, 19), (7, 31), (18, 16), (22, 19), (39, 27), (28, 38), (34, 34), (23, 36), (14, 22), (34, 20), (36, 38), (21, 24), (26, 28), (28, 40), (24, 41), (32, 2), (43, 19), (6, 5), (5, 9), (30, 28), (7, 27), (39, 17), (4, 5), (0, 22), (10, 34), (25, 34), (20, 31), (2, 35), (38, 41), (16, 36), (45, 31), (30, 40), (40, 18), (46, 32), (42, 26), (0, 37), (31, 29), (19, 6), (35, 35), (13, 34), (13, 28), (3, 23), (30, 27), (30, 39), (19, 13), (34, 1), (45, 13), (16, 9), (10, 2), (3, 4), (31, 17), (37, 30), (26, 15), (4, 16), (4, 14), (9, 7), (10, 23), (32, 39), (33, 32), (11, 5), (42, 22), (14, 4), (38, 28), (46, 31), (18, 4), (27, 17), (18, 2), (10, 26), (6, 29), (13, 24), (14, 25), (37, 39), (20, 17), (37, 9), (35, 41), (46, 6), (7, 35), (37, 22), (18, 19), (19, 32), (32, 14), (29, 1), (37, 12), (35, 40), (13, 7), (41, 9), (25, 33), (35, 12), (24, 4), (21, 7), (34, 14), (0, 11), (39, 14), (45, 38), (17, 24), (38, 34), (38, 8), (10, 10), (33, 2), (24, 2), (42, 42), (7, 19), (22, 26), (14, 9), (26, 9), (12, 7), (29, 27), (33, 36), (2, 39), (36, 10), (26, 26), (14, 42), (26, 21), (36, 9), (16, 16), (30, 20), (4, 1), (27, 30), (26, 22), (17, 41), (41, 37), (8, 37), (4, 7), (29, 40), (42, 7), (12, 22), (39, 31), (10, 6), (33, 37), (13, 29), (45, 33), (33, 35)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "In a 47x47 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (46, 46), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (42, 6), (37, 29), (0, 45), (40, 8), (36, 42), (29, 11), (43, 13), (4, 27), (13, 42), (27, 15), (22, 13), (7, 12), (0, 25), (28, 12), (36, 19), (36, 2), (20, 29), (38, 1), (20, 44), (24, 41), (0, 7), (5, 46), (22, 19), (16, 21), (25, 11), (13, 8), (3, 31), (30, 37), (4, 31), (18, 5), (9, 38), (25, 46), (20, 10), (39, 13), (11, 43), (9, 9), (43, 26), (17, 33), (34, 29), (34, 5), (2, 7), (32, 2), (45, 1), (23, 5), (33, 21), (1, 12), (28, 42), (46, 4), (33, 40), (45, 29), (37, 22), (29, 38), (25, 15), (23, 22), (0, 23), (33, 7), (28, 23), (35, 16), (34, 34), (15, 3), (44, 34), (40, 32), (11, 35), (23, 20), (1, 45), (25, 44), (38, 16), (12, 13), (0, 46), (44, 8), (33, 13), (24, 38), (27, 3), (35, 43), (25, 33), (28, 6), (15, 45), (21, 6), (43, 16), (1, 19), (17, 20), (13, 23), (41, 46), (42, 25), (12, 30), (41, 25), (45, 19), (46, 14), (28, 35), (37, 34), (32, 18), (35, 4), (8, 22), (39, 46), (41, 7), (9, 32), (27, 25), (30, 6), (32, 14), (31, 27), (22, 37), (29, 14), (35, 8), (31, 13), (23, 7), (11, 8), (7, 44), (8, 17), (21, 39), (9, 43), (16, 38), (0, 40), (1, 6), (46, 33), (38, 24), (28, 4), (8, 44), (28, 1), (18, 3), (5, 25), (0, 24), (6, 24), (0, 3), (37, 3), (6, 32), (26, 29), (43, 12), (3, 45), (5, 43), (12, 0), (2, 19), (34, 3), (12, 22), (10, 45), (21, 43), (25, 6), (41, 12), (33, 28), (34, 10), (43, 35), (42, 21), (3, 39), (15, 26), (24, 0), (8, 20), (13, 26), (35, 25), (33, 27), (23, 38), (10, 36), (42, 39), (35, 45), (35, 15), (26, 38), (28, 13), (46, 1), (46, 30), (14, 0), (18, 32), (27, 44), (21, 37), (40, 28), (25, 24), (0, 34), (30, 7), (19, 3), (33, 39), (13, 28), (10, 1), (34, 42), (44, 15), (30, 34), (15, 46), (17, 36), (15, 38), (13, 1), (1, 10), (0, 20), (12, 27), (12, 21), (0, 35), (37, 35), (14, 6), (1, 43), (41, 33), (2, 44), (29, 15), (3, 40), (28, 2), (26, 43), (16, 23), (10, 3), (31, 6), (28, 36), (24, 3), (11, 30), (2, 25), (23, 16), (10, 7), (39, 5), (5, 17), (27, 33), (24, 26), (24, 11), (24, 32), (10, 5), (41, 19), (38, 41), (28, 27), (7, 41), (20, 43), (31, 34), (29, 17), (43, 5), (9, 15), (22, 43), (11, 21), (18, 22), (17, 18), (25, 19), (39, 25), (9, 34), (5, 41), (14, 3), (16, 11), (17, 31), (14, 28), (42, 22), (28, 39), (41, 43), (27, 9), (12, 15), (38, 36), (5, 31), (16, 15), (46, 19), (26, 4), (4, 23), (34, 20), (45, 23), (19, 45), (38, 31), (32, 32), (32, 45), (5, 39), (33, 23), (12, 36), (39, 27), (8, 23), (17, 43), (0, 28), (33, 42), (4, 1), (25, 25), (35, 33), (4, 9), (46, 0), (21, 41), (36, 24), (34, 40), (27, 26), (5, 13), (27, 8), (28, 40), (16, 6), (37, 9), (22, 28), (44, 30), (6, 3), (35, 6), (41, 24), (40, 30), (20, 38), (4, 3), (16, 2), (32, 21), (27, 16), (36, 3), (36, 9), (17, 4), (19, 0), (12, 12), (37, 20), (40, 17), (9, 17), (19, 28), (0, 10), (31, 42), (2, 40), (16, 41), (17, 10), (2, 2), (14, 36), (26, 3), (15, 31), (32, 40), (5, 11), (8, 10), (37, 21), (39, 10), (29, 3), (7, 20), (30, 13), (40, 4), (34, 7), (0, 13), (31, 32), (45, 4), (1, 18), (44, 28), (31, 18), (2, 0), (45, 17), (20, 12), (1, 26), (18, 30), (36, 12), (36, 23), (45, 41), (4, 2), (42, 12), (28, 10), (22, 18), (30, 5), (21, 24), (14, 17), (9, 30), (22, 26), (0, 4), (2, 37), (42, 30), (9, 45), (20, 22), (9, 8), (21, 35), (38, 35), (44, 38), (2, 16), (8, 0), (6, 16), (38, 23), (1, 15), (19, 1), (13, 36), (30, 35), (29, 43), (35, 3), (23, 33), (5, 36), (10, 29), (26, 30), (12, 3), (6, 0), (13, 35), (9, 10), (16, 1), (18, 14), (26, 46), (22, 6), (29, 19), (25, 29), (1, 44), (8, 32), (20, 39), (2, 21), (16, 37), (17, 35), (36, 21), (30, 29), (6, 13), (30, 28), (21, 18)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "In a 49x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (48, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (21, 17), (4, 22), (39, 7), (0, 19), (28, 14), (19, 8), (8, 13), (9, 16), (29, 27), (25, 12), (7, 35), (44, 37), (5, 17), (33, 15), (30, 12), (25, 9), (47, 24), (2, 23), (12, 20), (8, 6), (27, 17), (45, 24), (13, 35), (38, 16), (37, 24), (14, 18), (37, 17), (14, 8), (45, 28), (32, 28), (14, 34), (30, 6), (29, 10), (22, 19), (26, 34), (10, 27), (22, 14), (34, 40), (4, 29), (11, 19), (34, 37), (28, 38), (22, 20), (3, 16), (14, 16), (9, 18), (28, 16), (37, 32), (39, 40), (14, 10), (24, 15), (0, 14), (47, 15), (25, 13), (29, 5), (46, 27), (28, 23), (36, 29), (7, 32), (17, 24), (41, 28), (30, 17), (6, 30), (45, 8), (7, 29), (6, 12), (13, 12), (31, 12), (28, 20), (10, 39), (28, 30), (11, 31), (21, 37), (12, 30), (22, 38), (6, 4), (32, 8), (30, 20), (32, 20), (24, 13), (25, 27), (3, 23), (36, 16), (13, 6), (20, 5), (38, 23), (21, 5), (36, 35), (8, 7), (11, 30), (35, 1), (45, 26), (32, 34), (27, 20), (36, 1), (0, 1), (35, 36), (8, 29), (40, 28), (29, 24), (0, 25), (27, 16), (26, 16), (39, 36), (20, 19), (41, 8), (1, 33), (3, 24), (6, 15), (18, 36), (18, 30), (9, 7), (10, 4), (32, 1), (30, 41), (38, 32), (37, 34), (37, 16), (48, 39), (8, 22), (23, 10), (30, 24), (12, 21), (10, 31), (21, 8), (24, 34), (3, 26), (48, 2), (12, 17), (44, 38), (19, 9), (45, 18), (28, 15), (36, 14), (25, 28), (22, 16), (33, 13), (45, 30), (20, 0), (10, 36), (15, 23), (42, 31), (27, 1), (18, 40), (2, 33), (23, 0), (36, 34), (18, 29), (2, 31), (27, 19), (37, 18), (10, 16), (46, 21), (4, 41), (23, 14), (13, 38), (15, 39), (33, 39), (15, 20), (35, 31), (36, 5), (28, 17), (9, 15), (36, 8), (5, 14), (41, 0), (41, 11), (8, 31), (48, 28), (8, 10), (47, 7), (12, 22), (30, 23), (14, 32), (37, 10), (37, 9), (21, 3), (40, 12), (1, 31), (6, 25), (38, 22), (3, 0), (19, 36), (41, 29), (2, 19), (16, 2), (24, 23), (44, 39), (48, 15), (4, 38), (45, 19), (47, 31), (46, 11), (41, 38), (26, 41), (19, 28), (21, 16), (43, 40), (27, 9), (23, 22), (33, 17), (12, 1), (13, 5), (19, 3), (18, 20), (4, 31), (27, 41), (5, 28), (42, 6), (32, 30), (7, 41), (18, 39), (10, 3), (34, 18), (0, 13), (15, 15), (34, 32), (36, 25), (27, 10), (11, 12), (29, 22), (12, 2), (45, 1), (20, 28), (0, 7), (13, 23), (26, 20), (6, 27), (22, 35), (44, 28), (25, 4), (8, 0), (44, 29), (7, 20), (10, 20), (8, 34), (12, 34), (5, 1), (13, 29), (0, 4), (39, 4), (13, 14), (35, 37), (24, 36), (18, 18), (15, 4), (39, 16), (46, 15), (12, 29), (47, 10), (5, 13), (42, 9), (44, 33), (15, 5), (43, 17), (3, 1), (16, 1), (29, 41), (42, 2), (43, 21), (25, 39), (16, 8), (23, 15), (7, 9), (38, 25), (47, 20), (35, 25), (47, 22), (7, 4), (8, 36), (3, 27), (14, 23), (38, 3), (19, 30), (16, 20), (44, 14), (8, 2), (41, 26), (48, 13), (10, 28), (44, 36), (23, 31), (23, 23), (24, 8), (18, 4), (32, 24), (9, 28), (18, 3), (9, 38), (46, 28), (6, 40), (30, 32), (45, 23), (48, 32), (4, 18), (39, 5), (42, 39), (44, 35), (1, 26), (45, 15), (34, 33), (19, 4), (9, 3), (35, 16), (25, 21), (21, 36), (43, 15), (8, 39), (40, 38), (40, 36), (1, 18), (16, 36), (38, 38), (18, 9), (37, 3), (6, 17), (39, 2), (21, 12), (47, 9), (35, 32), (33, 1), (8, 35), (40, 35), (32, 33), (43, 30), (6, 10), (19, 33), (26, 27), (7, 8), (2, 18), (7, 22), (19, 34), (36, 36), (14, 29), (0, 12), (37, 23), (33, 16), (39, 32), (13, 21), (4, 2), (24, 32), (27, 35), (27, 8), (24, 26), (5, 41)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 43x44 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (42, 43), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (29, 33), (19, 18), (36, 21), (7, 24), (7, 23), (2, 3), (16, 42), (12, 4), (26, 15), (36, 2), (12, 14), (21, 16), (5, 43), (12, 15), (24, 0), (11, 1), (40, 18), (22, 3), (5, 24), (19, 11), (24, 2), (12, 28), (33, 28), (1, 36), (33, 18), (26, 25), (32, 23), (31, 34), (11, 42), (41, 33), (40, 40), (15, 31), (33, 15), (6, 13), (22, 29), (25, 43), (0, 34), (25, 14), (26, 6), (35, 0), (10, 43), (13, 3), (25, 3), (28, 3), (16, 12), (31, 4), (5, 6), (38, 11), (3, 13), (6, 14), (21, 29), (3, 10), (33, 39), (10, 40), (38, 30), (39, 18), (20, 27), (37, 1), (20, 8), (18, 28), (36, 20), (32, 1), (13, 29), (8, 32), (3, 33), (15, 26), (26, 18), (28, 33), (25, 27), (42, 29), (9, 17), (29, 11), (0, 3), (12, 31), (21, 28), (33, 31), (19, 12), (7, 8), (13, 26), (17, 11), (3, 3), (24, 16), (0, 5), (24, 4), (21, 21), (31, 2), (42, 41), (7, 41), (34, 12), (0, 33), (13, 39), (9, 33), (4, 29), (35, 1), (23, 6), (34, 30), (1, 4), (21, 26), (34, 10), (42, 14), (18, 9), (27, 40), (28, 37), (39, 34), (12, 3), (27, 13), (20, 18), (39, 10), (23, 27), (27, 1), (21, 9), (4, 9), (17, 31), (34, 20), (38, 21), (32, 5), (1, 20), (3, 17), (27, 31), (1, 35), (7, 3), (35, 25), (9, 21), (8, 7), (38, 15), (39, 32), (29, 25), (0, 23), (31, 16), (40, 26), (29, 6), (42, 5), (12, 12), (21, 40), (38, 34), (7, 33), (15, 43), (29, 16), (6, 15), (4, 12), (16, 24), (40, 34), (30, 27), (28, 5), (0, 9), (39, 21), (2, 16), (34, 26), (6, 2), (6, 28), (18, 2), (17, 39), (39, 22), (5, 12), (2, 20), (13, 43), (41, 36), (3, 9), (40, 7), (1, 33), (19, 8), (37, 16), (9, 14), (31, 27), (2, 27), (20, 22), (27, 28), (19, 14), (40, 5), (30, 17), (19, 0), (8, 33), (24, 28), (21, 1), (22, 15), (6, 5), (39, 30), (12, 7), (24, 3), (6, 0), (17, 37), (29, 26), (14, 22), (40, 3), (42, 15), (6, 34), (35, 28), (7, 21), (24, 12), (18, 8), (39, 39), (22, 0), (37, 35), (2, 14), (18, 10), (24, 17), (12, 33), (15, 30), (5, 13), (12, 22), (33, 5), (5, 21), (24, 1), (0, 18), (8, 23), (2, 34), (11, 38), (15, 5), (37, 29), (7, 32), (40, 35), (28, 2), (10, 35), (3, 27), (0, 31), (10, 13), (34, 32), (35, 27), (2, 38), (6, 41), (33, 37), (2, 15), (4, 17), (23, 23), (8, 1), (19, 1), (36, 32), (1, 18), (35, 10), (14, 27), (30, 22), (11, 37), (5, 34), (30, 0), (36, 37), (39, 4), (25, 19), (4, 5), (25, 20), (34, 39), (15, 27), (40, 28), (15, 28), (0, 2), (22, 27), (17, 17), (10, 38), (0, 11), (39, 5), (24, 13), (31, 32), (14, 5), (20, 35), (26, 0), (34, 18), (34, 17), (3, 22), (0, 36), (40, 32), (11, 34), (19, 2), (22, 37), (16, 9), (20, 6), (20, 16), (36, 41), (34, 15), (8, 10), (23, 10), (18, 4), (10, 28), (20, 14), (3, 30), (24, 32), (13, 0), (25, 32), (38, 9), (19, 6), (32, 36), (24, 36), (26, 31), (36, 28), (7, 40), (32, 16), (35, 29), (1, 41), (2, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (31, 39), (24, 23), (37, 7), (33, 14), (37, 19), (37, 11), (9, 24), (29, 20), (2, 0), (45, 27), (45, 18), (3, 8), (38, 37), (4, 19), (22, 28), (1, 14), (35, 17), (14, 19), (29, 35), (22, 22), (37, 33), (16, 30), (5, 4), (24, 38), (17, 32), (28, 1), (18, 6), (38, 34), (35, 39), (47, 7), (15, 4), (43, 32), (24, 34), (16, 13), (39, 5), (19, 36), (31, 28), (4, 34), (15, 11), (39, 13), (11, 25), (37, 36), (18, 5), (45, 11), (46, 8), (35, 25), (17, 1), (32, 35), (33, 37), (13, 15), (6, 21), (9, 18), (5, 12), (34, 22), (20, 24), (5, 28), (24, 7), (20, 25), (46, 11), (7, 19), (23, 29), (39, 27), (14, 30), (42, 30), (36, 10), (43, 23), (3, 21), (3, 36), (23, 12), (21, 15), (33, 5), (3, 9), (42, 13), (10, 19), (35, 24), (5, 17), (2, 17), (34, 13), (13, 36), (18, 9), (38, 32), (31, 17), (30, 6), (9, 8), (1, 11), (27, 21), (13, 14), (36, 3), (29, 21), (26, 37), (30, 19), (29, 29), (12, 6), (27, 15), (21, 8), (32, 6), (21, 34), (41, 20), (22, 36), (47, 29), (35, 35), (22, 4), (46, 15), (34, 3), (35, 31), (43, 33), (34, 6), (0, 18), (46, 22), (27, 4), (3, 3), (23, 6), (34, 20), (35, 9), (1, 12), (19, 29), (39, 30), (42, 34), (21, 3), (25, 4), (24, 16), (21, 31), (44, 30), (4, 1), (45, 26), (2, 2), (44, 21), (38, 15), (18, 22), (21, 22), (47, 28), (24, 26), (32, 32), (23, 33), (6, 26), (13, 37), (8, 32), (13, 12), (37, 26), (23, 2), (9, 38), (23, 0), (10, 33), (37, 8), (2, 24), (33, 39), (22, 2), (28, 18), (45, 28), (41, 14), (28, 32), (39, 9), (1, 2), (6, 19), (1, 9), (2, 33), (6, 2), (12, 11), (40, 16), (11, 37), (20, 7), (10, 14), (39, 28), (33, 34), (30, 18), (8, 37), (21, 37), (11, 14), (12, 10), (36, 20), (47, 30), (33, 24), (11, 0), (12, 2), (47, 14), (30, 12), (16, 8), (0, 16), (43, 13), (3, 17), (28, 14), (42, 1), (12, 15), (24, 30), (5, 29), (40, 31), (26, 11), (7, 28), (19, 9), (4, 31), (32, 21), (32, 1), (26, 30), (16, 20), (44, 29), (26, 36), (17, 12), (24, 33), (5, 1), (32, 13), (8, 13), (38, 18), (0, 31), (36, 4), (20, 9), (8, 20), (6, 28), (11, 4), (2, 14), (10, 3), (26, 3), (19, 28), (8, 11), (20, 22), (2, 25), (15, 28), (29, 10), (45, 6), (7, 21), (31, 12), (34, 16), (32, 31), (25, 13), (14, 2), (1, 4), (19, 20), (7, 11), (22, 21), (43, 22), (19, 16), (38, 4), (37, 31), (39, 21), (28, 25), (45, 3), (46, 39), (23, 20), (28, 21), (40, 12), (7, 31), (45, 14), (39, 23), (12, 0), (14, 20), (21, 19), (25, 16), (23, 17), (9, 30), (47, 16), (21, 28), (25, 28), (12, 29), (38, 10), (41, 29), (5, 15), (2, 28), (23, 16), (42, 26), (5, 27), (25, 35), (37, 3), (12, 35), (13, 27), (25, 39), (31, 34), (38, 36), (42, 25), (14, 17), (30, 0), (27, 2), (47, 18), (21, 0), (2, 26), (29, 31), (38, 12), (43, 3), (36, 39), (37, 14), (11, 35), (27, 20), (34, 18), (38, 30), (20, 33), (35, 3), (13, 7), (8, 4), (28, 15), (15, 14), (12, 21), (37, 37), (1, 8), (7, 2), (44, 18), (36, 17), (43, 35), (41, 10), (4, 5)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 41x42 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (40, 41), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (12, 15), (40, 17), (3, 17), (3, 12), (35, 40), (23, 37), (4, 13), (24, 40), (36, 8), (37, 36), (18, 34), (2, 13), (8, 5), (5, 6), (39, 41), (24, 19), (17, 13), (32, 26), (11, 10), (24, 4), (10, 26), (12, 23), (6, 33), (35, 9), (23, 35), (37, 4), (18, 28), (8, 39), (27, 31), (11, 7), (5, 35), (31, 1), (18, 17), (22, 13), (3, 34), (8, 18), (20, 14), (20, 32), (20, 37), (33, 9), (35, 1), (31, 3), (14, 1), (7, 22), (34, 14), (20, 20), (31, 9), (4, 21), (18, 32), (3, 22), (29, 27), (10, 8), (23, 20), (35, 24), (34, 35), (31, 25), (9, 19), (35, 39), (27, 5), (28, 31), (26, 15), (27, 15), (29, 3), (13, 28), (7, 1), (39, 32), (15, 40), (2, 3), (30, 9), (6, 3), (7, 14), (1, 1), (24, 2), (16, 2), (34, 2), (0, 34), (31, 6), (6, 5), (32, 18), (10, 19), (33, 13), (22, 18), (26, 32), (34, 36), (18, 15), (9, 22), (9, 26), (33, 26), (34, 32), (6, 39), (39, 3), (35, 14), (19, 22), (24, 16), (2, 0), (3, 20), (5, 31), (24, 36), (2, 18), (7, 4), (9, 21), (6, 31), (2, 38), (26, 28), (8, 33), (17, 18), (30, 11), (5, 11), (12, 18), (14, 20), (10, 10), (4, 28), (20, 7), (19, 35), (36, 6), (22, 40), (16, 33), (0, 8), (2, 30), (4, 35), (13, 0), (11, 33), (28, 37), (32, 36), (26, 40), (21, 12), (33, 18), (11, 5), (12, 9), (5, 27), (18, 35), (37, 28), (15, 35), (5, 39), (3, 29), (1, 39), (10, 14), (1, 3), (18, 24), (5, 29), (13, 10), (40, 32), (31, 4), (1, 15), (10, 5), (4, 31), (38, 15), (25, 0), (17, 30), (14, 4), (40, 21), (20, 16), (14, 25), (30, 4), (2, 15), (36, 1), (27, 33), (38, 10), (19, 11), (11, 2), (12, 28), (18, 13), (38, 21), (16, 5), (16, 7), (28, 8), (22, 6), (25, 6), (16, 8), (18, 12), (40, 9), (8, 35), (40, 37), (6, 35), (38, 6), (33, 30), (28, 39), (12, 7), (38, 24), (0, 37), (19, 40), (21, 23), (18, 20), (12, 38), (31, 36), (11, 40), (30, 14), (14, 39), (36, 18), (13, 41), (1, 26), (32, 35), (7, 38), (15, 8), (30, 13), (36, 29)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "In a 48x40 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (47, 39), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (27, 3), (5, 10), (19, 6), (42, 19), (36, 20), (39, 22), (32, 23), (0, 26), (3, 25), (21, 11), (39, 24), (41, 9), (4, 30), (16, 35), (34, 0), (36, 1), (27, 2), (27, 14), (28, 16), (21, 30), (40, 39), (12, 4), (20, 23), (38, 19), (28, 38), (11, 34), (21, 0), (33, 21), (39, 1), (10, 20), (28, 26), (25, 17), (28, 1), (0, 37), (12, 17), (44, 12), (40, 32), (30, 9), (35, 23), (14, 11), (36, 21), (26, 18), (20, 6), (41, 19), (38, 31), (40, 19), (7, 11), (42, 13), (34, 11), (26, 10), (43, 1), (16, 10), (8, 0), (46, 22), (19, 20), (17, 5), (26, 28), (5, 24), (16, 11), (9, 39), (46, 32), (35, 33), (11, 25), (12, 30), (19, 25), (22, 20), (2, 26), (30, 27), (43, 4), (16, 37), (16, 18), (13, 9), (33, 29), (19, 38), (40, 14), (15, 14), (13, 7), (17, 22), (18, 21), (44, 14), (45, 7), (3, 12), (8, 15), (35, 35), (3, 1), (6, 4), (9, 26), (21, 27), (40, 35), (21, 39), (40, 36), (11, 13), (1, 17), (44, 29), (15, 38), (26, 21), (33, 37), (9, 6), (45, 8), (23, 14), (38, 9), (16, 36), (24, 31), (19, 23), (0, 24), (31, 14), (17, 39), (7, 30), (17, 23), (46, 1), (4, 0), (29, 38), (39, 14), (8, 31), (40, 0), (24, 26), (38, 21), (15, 18), (29, 30), (28, 12), (28, 0), (30, 14), (16, 29), (14, 15), (43, 9), (13, 38), (27, 18), (32, 5), (37, 1), (20, 20), (8, 35), (26, 13), (28, 9), (16, 30), (14, 13), (29, 16), (42, 35), (1, 21), (3, 35), (14, 2), (39, 33), (8, 23), (9, 0), (11, 11), (26, 11), (8, 18), (8, 21), (8, 10), (26, 6), (11, 0), (24, 12), (7, 12), (0, 31), (24, 34), (10, 15), (26, 37), (27, 22), (0, 20), (16, 9), (9, 12), (47, 10), (43, 8), (6, 5), (25, 13), (28, 11), (10, 12), (39, 15), (45, 37), (15, 22), (31, 17), (4, 38), (25, 19), (47, 6), (39, 3), (23, 26), (12, 2), (47, 22), (31, 39), (4, 11), (28, 20), (46, 13), (40, 27), (0, 28), (35, 25), (41, 0), (21, 12), (36, 34), (21, 19), (44, 22), (39, 8), (18, 10), (1, 10), (16, 12), (17, 18), (40, 4), (11, 16), (10, 11), (22, 11), (29, 21), (21, 18), (43, 11), (18, 9), (37, 22), (47, 34), (20, 33), (20, 7), (12, 18), (1, 1), (6, 0), (18, 16), (24, 36), (23, 37), (26, 23), (40, 23), (2, 21), (37, 8), (38, 39), (36, 2), (19, 15), (32, 37), (25, 6), (32, 10), (3, 30), (34, 23), (37, 26), (32, 16), (23, 13), (9, 33), (47, 16), (17, 33), (11, 19), (4, 3), (30, 23), (16, 15), (16, 20), (16, 39), (42, 7), (5, 0), (7, 27), (24, 14), (5, 17), (27, 20), (40, 21), (42, 4), (42, 24), (32, 3), (1, 33), (7, 0), (29, 2), (2, 17), (5, 2), (20, 15), (24, 4), (3, 31), (14, 25), (2, 28), (21, 25), (38, 7), (31, 3), (16, 16), (37, 17), (14, 38), (2, 16), (21, 34), (6, 9), (29, 37), (31, 15), (20, 32), (26, 39), (35, 8), (46, 5), (14, 5), (47, 35), (33, 30), (1, 36), (37, 16), (13, 33), (23, 12), (22, 13), (2, 12), (11, 15), (20, 8), (14, 12), (9, 5), (41, 20), (5, 8), (12, 29), (9, 14), (35, 32), (30, 7), (21, 16), (30, 21), (21, 24), (46, 25), (46, 11), (20, 35), (15, 28), (39, 39), (34, 3), (1, 38), (27, 13), (28, 31), (43, 26), (22, 22), (10, 35), (18, 26), (14, 3), (15, 19), (31, 36), (10, 23), (6, 24), (8, 1), (17, 11), (6, 37), (29, 17), (27, 21), (26, 16), (47, 32), (41, 10), (39, 36), (2, 36), (11, 26), (44, 3), (23, 4), (23, 29), (30, 32), (5, 29), (33, 38), (16, 6), (44, 30), (31, 11), (36, 38), (23, 9), (37, 31), (0, 39), (45, 6), (44, 26), (46, 34), (5, 28), (29, 10), (39, 37), (7, 24), (1, 2), (23, 23), (15, 37), (44, 24), (41, 34), (9, 15), (6, 8), (36, 33), (28, 17), (40, 18), (34, 10), (6, 22), (2, 19), (13, 36), (41, 2), (26, 27), (7, 19), (29, 39), (17, 15), (10, 18), (41, 14), (31, 23), (7, 10), (3, 0), (3, 28), (11, 31), (32, 14), (44, 38), (6, 1), (23, 16), (33, 2), (42, 37)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "In a 45x43 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (44, 42), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (4, 23), (10, 26), (19, 20), (21, 34), (22, 31), (27, 13), (17, 3), (31, 11), (22, 23), (31, 29), (34, 26), (15, 41), (4, 3), (0, 34), (2, 16), (7, 34), (0, 16), (38, 40), (35, 8), (0, 28), (43, 28), (23, 29), (40, 16), (0, 27), (17, 16), (1, 28), (43, 26), (25, 42), (43, 2), (17, 2), (41, 40), (22, 38), (41, 7), (11, 20), (37, 27), (25, 5), (5, 32), (44, 17), (24, 29), (31, 13), (26, 13), (17, 6), (16, 22), (25, 8), (11, 5), (36, 14), (16, 18), (9, 26), (43, 14), (7, 40), (3, 37), (29, 42), (1, 8), (10, 7), (1, 18), (3, 32), (28, 22), (17, 34), (5, 17), (40, 0), (3, 13), (15, 8), (27, 30), (29, 5), (10, 16), (19, 11), (20, 36), (40, 21), (6, 41), (26, 8), (26, 0), (17, 25), (3, 12), (36, 39), (36, 0), (11, 41), (28, 30), (14, 4), (23, 17), (9, 28), (17, 38), (8, 1), (26, 39), (37, 0), (7, 6), (9, 15), (27, 2), (14, 23), (38, 14), (3, 19), (35, 38), (25, 41), (0, 36), (40, 33), (6, 13), (37, 9), (37, 21), (2, 12), (1, 14), (40, 41), (19, 35), (29, 3), (24, 6), (0, 37), (11, 18), (22, 35), (2, 32), (35, 28), (8, 34), (22, 37), (24, 16), (34, 9), (32, 40), (27, 37), (32, 39), (20, 35), (12, 10), (1, 0), (33, 9), (37, 17), (10, 30), (1, 9), (1, 15), (19, 12), (31, 36), (19, 28), (4, 29), (17, 36), (14, 1), (11, 39), (44, 34), (29, 7), (38, 37), (41, 10), (34, 24), (1, 13), (27, 38), (0, 2), (3, 10), (40, 18), (17, 31), (38, 11), (41, 32), (31, 28), (42, 32), (27, 28), (1, 19), (36, 8), (20, 25), (24, 17), (23, 12), (39, 24), (23, 30), (35, 25), (33, 16), (8, 39), (27, 8), (28, 1), (30, 18), (6, 5), (2, 17), (5, 12), (24, 15), (42, 27), (28, 17), (16, 27), (12, 13), (0, 6), (28, 28), (40, 20), (37, 5), (43, 32), (34, 6), (5, 1), (27, 6), (32, 25), (14, 25), (2, 18), (41, 33), (15, 39), (16, 17), (5, 40), (40, 27), (32, 23), (43, 17), (25, 23), (9, 1), (1, 36), (34, 12), (5, 0), (42, 4), (14, 18), (10, 38), (5, 31), (13, 16), (1, 41), (8, 8), (22, 0), (5, 30), (43, 7), (17, 23), (29, 23), (12, 30), (25, 29), (5, 20), (14, 22), (29, 19), (37, 14), (10, 5), (34, 25), (41, 35), (0, 30), (36, 3), (30, 15), (38, 39), (26, 28), (0, 10), (35, 40), (0, 3), (7, 39), (40, 36), (10, 9), (9, 32), (19, 40), (7, 41), (10, 8), (18, 36), (30, 2), (16, 4), (41, 41), (24, 11), (12, 29), (1, 24), (11, 35), (0, 22), (44, 19), (33, 21), (44, 14), (12, 1), (23, 9), (13, 30), (21, 36), (8, 14), (8, 19), (35, 15), (27, 4), (33, 37), (21, 25), (9, 17), (14, 32), (32, 11), (20, 4), (34, 19), (24, 4), (20, 8), (11, 30), (6, 27), (24, 20), (32, 22), (40, 39)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "In a 42x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (33, 32), (33, 38), (26, 33), (4, 6), (16, 23), (13, 35), (21, 8), (37, 39), (10, 15), (24, 15), (40, 25), (39, 24), (33, 31), (1, 16), (31, 26), (8, 27), (8, 12), (0, 2), (3, 1), (19, 37), (38, 25), (0, 40), (23, 10), (36, 18), (19, 29), (35, 15), (20, 28), (7, 40), (6, 19), (3, 20), (40, 31), (40, 14), (12, 21), (41, 4), (5, 24), (35, 33), (32, 28), (21, 16), (1, 11), (15, 27), (40, 8), (21, 32), (26, 19), (33, 15), (39, 40), (30, 9), (31, 17), (18, 4), (40, 20), (13, 8), (15, 35), (6, 3), (39, 39), (18, 22), (17, 28), (34, 40), (30, 34), (34, 18), (0, 34), (29, 22), (33, 14), (16, 13), (4, 13), (32, 17), (38, 1), (18, 0), (30, 26), (0, 37), (1, 21), (11, 37), (0, 8), (31, 39), (40, 30), (20, 18), (10, 35), (27, 8), (14, 5), (5, 13), (22, 32), (25, 26), (23, 25), (3, 2), (5, 34), (12, 1), (2, 28), (29, 24), (2, 21), (21, 26), (6, 14), (31, 21), (10, 7), (1, 28), (21, 23), (18, 12), (5, 40), (11, 20), (25, 30), (29, 29), (34, 20), (22, 38), (10, 26), (26, 12), (9, 7), (3, 25), (34, 9), (12, 6), (31, 5), (41, 15), (17, 10), (6, 21), (1, 27), (39, 31), (1, 32), (35, 7), (8, 37), (8, 30), (29, 37), (32, 13), (11, 25), (11, 32), (41, 37), (35, 14), (24, 22), (39, 12), (28, 40), (34, 25), (17, 36), (20, 40), (22, 6), (13, 7), (21, 35), (14, 25), (9, 6), (8, 38), (10, 14), (34, 30), (41, 25), (5, 3), (35, 27), (7, 31), (28, 2), (17, 2), (17, 30), (14, 9), (2, 13), (7, 32), (10, 24), (38, 4), (4, 25), (16, 10), (20, 30), (30, 21), (9, 2), (20, 13), (25, 31), (38, 29), (2, 4), (19, 13), (28, 32), (17, 27), (15, 15), (24, 19), (28, 13), (1, 18), (3, 35), (38, 31), (21, 17), (2, 12), (9, 18), (32, 22), (29, 16), (33, 35), (18, 36), (16, 5), (1, 4), (38, 30), (39, 35), (2, 26), (29, 34), (38, 34), (0, 36), (38, 36), (34, 28), (15, 4), (4, 10), (27, 30), (15, 13), (41, 34), (8, 39), (21, 36), (36, 20), (27, 0), (5, 36), (13, 26), (36, 25), (24, 18), (39, 9), (26, 23), (27, 2), (25, 13), (41, 38), (24, 8), (14, 30), (24, 6), (14, 21), (17, 29), (38, 18), (30, 33), (34, 15), (5, 28), (30, 39), (25, 22), (14, 0), (38, 33), (2, 2), (7, 13), (23, 32), (23, 40), (28, 29), (26, 10), (20, 31), (26, 15), (6, 9), (14, 15), (34, 23), (4, 4), (29, 7), (7, 12), (11, 18), (34, 27), (28, 17), (39, 20), (38, 5), (15, 33), (25, 17), (41, 3), (20, 14), (9, 16), (20, 32), (3, 11), (10, 19), (37, 28), (31, 14)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "In a 46x41 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (45, 40), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (30, 18), (1, 29), (15, 12), (0, 32), (17, 29), (7, 15), (37, 17), (45, 35), (38, 38), (44, 29), (28, 23), (36, 9), (18, 19), (24, 20), (23, 36), (19, 2), (15, 29), (9, 8), (5, 6), (26, 30), (5, 12), (17, 1), (38, 19), (0, 39), (29, 31), (38, 11), (30, 28), (29, 8), (42, 9), (45, 37), (18, 30), (35, 38), (33, 26), (6, 11), (21, 10), (19, 39), (30, 35), (38, 35), (22, 19), (9, 32), (43, 18), (43, 3), (12, 21), (27, 20), (31, 19), (40, 17), (10, 24), (19, 11), (23, 13), (4, 32), (45, 16), (38, 32), (26, 29), (5, 18), (45, 26), (16, 14), (12, 30), (18, 2), (26, 17), (13, 13), (38, 30), (44, 16), (17, 34), (20, 12), (7, 33), (44, 32), (30, 16), (33, 35), (30, 12), (21, 30), (29, 30), (5, 34), (44, 22), (35, 9), (10, 4), (7, 11), (26, 25), (31, 3), (25, 38), (29, 2), (39, 37), (44, 6), (43, 12), (37, 29), (9, 28), (38, 3), (5, 9), (9, 14), (37, 35), (11, 31), (18, 32), (36, 23), (42, 28), (42, 15), (27, 13), (14, 26), (28, 6), (4, 34), (28, 8), (5, 25), (37, 13), (23, 29), (39, 6), (20, 36), (40, 37), (17, 40), (26, 28), (4, 20), (35, 4), (20, 5), (23, 22), (12, 33), (3, 20), (17, 3), (22, 25), (6, 6), (27, 16), (30, 15), (39, 14), (0, 6), (13, 29), (31, 32), (35, 22), (24, 8), (33, 40), (23, 10), (18, 11), (34, 31), (22, 33), (10, 23), (37, 23), (26, 0), (31, 18), (32, 8), (24, 7), (7, 37), (25, 31), (43, 4), (29, 16), (30, 20), (40, 33), (42, 11), (21, 24), (40, 23), (4, 0), (23, 40), (17, 13), (35, 31), (39, 39), (26, 34), (3, 22), (28, 15), (0, 4), (42, 20), (44, 1), (10, 16), (22, 2), (6, 20), (26, 2), (0, 5), (37, 27), (44, 9), (9, 29), (16, 27), (13, 11), (32, 27), (18, 15), (1, 17), (22, 22), (6, 10), (36, 33), (10, 10), (10, 35), (27, 3), (16, 16), (6, 38), (38, 29), (24, 24), (3, 7), (31, 30), (0, 14), (10, 13), (8, 10), (42, 23), (16, 20), (19, 36), (17, 14), (32, 23), (29, 11), (2, 16), (40, 35), (32, 15), (6, 21), (16, 15), (32, 1), (22, 35), (19, 14), (40, 30), (25, 39), (29, 5), (21, 27), (12, 8), (37, 4), (45, 4), (30, 38), (9, 11), (45, 31), (1, 26)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "In a 42x49 grid, what is the fewest number of steps it takes to get from the bottom left (0, 0) to the top right (41, 48), provided you can move right or up by any number of cells (like a chess rook) at each step, subject to the constraint that you cannot move through the following cells: (20, 30), (26, 36), (29, 3), (30, 27), (2, 36), (0, 44), (32, 30), (21, 37), (10, 10), (24, 22), (7, 28), (21, 11), (40, 4), (19, 8), (9, 0), (4, 12), (22, 24), (23, 40), (1, 3), (38, 9), (3, 21), (17, 48), (1, 33), (9, 39), (10, 15), (6, 33), (38, 36), (12, 1), (20, 15), (31, 4), (14, 42), (12, 9), (20, 23), (2, 31), (32, 14), (7, 12), (23, 13), (9, 22), (40, 47), (3, 3), (20, 3), (4, 23), (15, 6), (38, 2), (21, 21), (5, 40), (34, 33), (12, 11), (11, 8), (8, 34), (23, 21), (18, 23), (26, 17), (23, 48), (15, 37), (31, 17), (28, 28), (37, 32), (32, 45), (4, 36), (20, 20), (27, 3), (19, 38), (26, 24), (1, 48), (35, 43), (4, 41), (30, 14), (37, 5), (23, 22), (6, 13), (0, 34), (35, 27), (38, 5), (33, 7), (33, 34), (25, 2), (17, 30), (11, 43), (14, 48), (12, 5), (28, 7), (23, 1), (20, 25), (0, 28), (2, 12), (24, 11), (5, 13), (21, 26), (1, 16), (35, 7), (15, 4), (28, 41), (35, 14), (27, 29), (33, 1), (35, 34), (38, 14), (2, 41), (6, 44), (0, 23), (11, 40), (9, 26), (37, 9), (21, 16), (29, 4), (1, 25), (25, 17), (30, 28), (39, 7), (28, 40), (28, 36), (4, 29), (33, 13), (39, 5), (4, 30), (19, 29), (14, 22), (2, 39), (32, 0), (5, 29), (11, 37), (16, 1), (24, 13), (35, 3), (32, 27), (22, 5), (4, 26), (15, 0), (22, 46), (2, 11), (11, 42), (8, 42), (19, 3), (28, 39), (41, 6), (41, 45), (29, 45), (4, 38), (28, 11), (33, 17), (11, 45), (21, 42), (36, 27), (31, 30), (33, 46), (2, 13), (5, 23), (31, 3), (26, 23), (18, 10), (17, 44), (17, 27), (33, 41), (6, 12), (29, 8), (4, 25), (34, 25), (28, 22), (30, 34), (16, 24), (22, 44), (26, 43), (21, 12), (8, 30), (27, 5), (35, 16), (8, 20), (28, 1), (4, 11), (18, 36), (16, 5), (29, 18), (27, 13), (8, 5), (34, 14), (7, 9), (15, 39), (37, 42), (20, 37), (5, 37), (35, 12), (17, 38), (9, 9), (25, 7), (37, 38), (41, 1), (1, 45), (15, 17), (41, 11), (41, 26), (8, 19), (26, 2), (28, 45), (8, 45), (32, 17), (40, 20), (6, 23), (36, 47), (1, 11), (2, 43), (19, 34), (13, 31), (30, 3), (18, 8), (14, 34), (29, 48), (30, 38), (38, 19), (19, 12), (11, 21), (18, 45), (11, 3), (30, 13), (15, 33), (40, 10)? If it's impossible, answer with -1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}