A game of Nim (Posted on 2002-04-23)

	Submitted by levik
Rating: 3.8000 (10 votes)
Solution:	(Hide)
To win this game, a player must strive to leave the deck containing four cards for the other player. Then no matter how many cards the second player takes, the first player will win by taking the rest. (This doesn't work for 3 cards because the second player will just take them all, nor for 5 cards, because the second player will take one leaving the first player with 4.) So taking this a step further, a deck of 8 cards is also a winning deck for player one, since no matter what player two does, player one can make sure that the deck will contain four cards after his turn. In fact, the strategy is to make sure that the deck contains the number of cards that's a multiple of four after your turn. Player one can only use this strategy with the 54 card deck by taking two cards from it. All the other cards already contain a number of cards that's a multiple of four, and with these, the game can be won by the second player if he follows the strategy.

	Subject	Author	Date
	One way to do it?	Captain Paradox	2004-01-15 08:23:53
	This game	Alpha Tiger	2003-05-16 02:02:47
	Good Game	cges	2002-12-13 05:18:50