37th Swedish 1997 Problem 4 A and B play a game as follows. Each throws a dice. Suppose A gets x and B gets y. If x and y have the same parity, then A wins. If not, then they make a list of all two digit numbers ab ≤ xy with 1 ≤ a, b ≤ 6. Then they take turns (starting with A) replacing two numbers on the list by their (non-negative) difference. When just one number remains, it is compared to x. If it has the same parity A wins, otherwise B wins. Find the probability that A wins.