10.5. There are two piles of stones, one with 15 stones and the other with 20. Two players play the following game: they take turns, and on each turn, they can take any number of stones, but only from one pile. The player who cannot make a move loses. Who wins with correct play?
10.5. Answer: First. Solution. We will describe the winning strategy for the first player. On the first move, he takes 5 stones from the pile that has 20 stones. Thus, after his move, each pile has 15 stones. With each subsequent move, the first player should take the same number of stones as the second player, but from the other pile, i.e., after each move by the first player, the two piles will have the same number of stones. This means that the first player always has a move, i.e., the second player loses.