The sum of A and B can have no carry. If we assume A ≠ B ≠ C, then you can have ...
... (A, B, C) ∈ {(1, 2, 3), (2, 1, 3), (1, 3, 4), (3, 1, 4), (1, 4, 5), (4, 1, 5), (1, 5, 6), (5, 1, 6), (1, 6, 7), (6, 1, 7), (1, 7, 8), (7, 1, 8), (1, 8, 9), (8, 1, 9), (2, 3, 5), (3, 2, 5), (2, 4, 6), (4, 2, 6), (2, 5, 7), (5, 2, 7), (2, 6, 8), (6, 2, 8), (2, 7, 9), (7, 2, 9), (3, 4, 7), (4, 3, 7), (3, 5, 8), (5, 3, 8), (3, 6, 9), (6, 3, 9), (4, 5, 9), (5, 4, 9)}
