Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A two-player game is played with two piles of stones, with sizes m,n. On a player's turn, that player can remove any positive number of stones from one pile, or the same positive number of stones from each pile. A player loses when they are unable to take a stone. If 1≤m,n≤30, for how many of the 30×30=900 starting positions does the first player have a winning strategy?

share|improve this question
    
I.e., the winner takes the last stones. If there are the same number of stones on both piles, the next player can take all, so the strategy must be to keep them different and none empty (one pile empty means the other player can take it all). –  vonbrand Mar 23 '13 at 20:32
1  
This is known as Wythoff's game. It has a very interesting theory. –  MJD Mar 24 '13 at 13:38

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.