Problems(1)
The game Boddle uses eight cards numbered 6,11,12,14,24,47,54, and n, where 0≤n≤56. An integer D is announced, and players try to obtain two cards, which are not necessarily distinct, such that one of their differences (positive or negative) is congruent to D modulo 57. For example, if D=27, then the pair 24 and 54 would work because 24−54≡27 mod 57. Compute n such that this task is always possible for all D. number theory