Problem #PRU-100329

Problems Set theory and logic Algorithm Theory Game Theory Winning and loosing positions

Problem

The March Hare and the Dormouse also decided to play a game. They made two piles of matches on the table. The first pile contains 7 matches, and the second one 8. The March Hare set the rules: the players divide a pile into two piles in turns, i.e. the first player divides one of the piles into two, then the second player divides one of the piles on the table into two, then the first player divides one of the piles into two and so on. The loser is the one who cannot not find a pile to divide. The March Hare starts the game. Can the March Hare play in such a way that he always wins?