Conundrum: Nim, Part I
Tuesday, May 20th, 2008Iachimo likes to hang out at the local tavern, drawing in tourists to play a game of Nim. You don’t like Iachimo. You don’t like him at all. You think he’s a huckster and a con man. You’d like nothing better than to beat him at his own game. You want to beat him at Nim.
In Nim, two opponents take turns drawing from several piles of coins. On your turn, you may remove as many coins as you like from any one pile. The winner is the one who takes the last coin and leaves his opponent without a move. The coins themselves are not on the line, but Iachimo likes to make the game more interesting with a modest wager.
As you enter the tavern, you notice that Iachimo is set up for business. He has stacked five piles of coins, numbered 1, 2, 3, 4, and 5. Each pile has the same number of coins as the pile number: 1, 2, 3, 4, and 5. He sees you coming and amiably offers you a friendly wager which you quickly accept.
“I’ll go first,” you smile, and before Iachimo can object, you make your move.
What’s your first move? What’s your strategy for winning?
UPDATE: The solution is posted in the comments.