Question 53
Fedir and Mykhailo have three piles of stones: the first contains $100$ stones, the second $101$, the third $102$. They are playing a game with the following rules: they move in turns, in his turn a player chooses any two piles of stones, containing, say, $a$ and $b$ stones correspondingly, and takes from each of them the number of stones equal to the greatest common divisor of numbers $a$ and $b$. The winner is the player, after whose move some pile becomes empty for the first time. Who wins if Fedir moves first, and both try to win?