Problem #26

You are given three stacks of cards having a cards, b cards, and c cards respectively. At each turn, you are allowed to remove 3 cards from one of the stacks, but you must add 1 card to each of the other stacks. For example, using ordered triples to denote the number of cards in each stack, a possible sequence of moves is (3,1,4) to (0,2,5) to (1,3,2) to (2,0,3) to (3,1,0) to (0,2,1) at which point the process terminates. Give a (relatively) simple rule for determining, given a, b, and c, what the final outcome will be.