A game of
nim is played with one pile of 30 tokens. The two player takes turns taking tokens off the pile. Whoever takes the last token wins.
To make the game a little more interesting, the rules have been changes slightly:
A player may take 1, 3, 4, or 5 tokens but not 2.
What is the best starting move and what is the general strategy?
(In reply to
re(3): Solution - Generalized! by nikki)
Yes, you were quite coherent. You laid out your thought process clearly. So clear, in fact, that even I understood it. What I find exceptional is the way you made the leap to
"If R>M/2, then the strategy is to take coins such that you leave you opponent with X coins such that X mod R = 0."
I wish I hadn't read that line. I would have liked to ponder it for a while and come to my own conclusion. But thank you Nikki and Brian. I really enjoy what I've learned from this puzzle.
re(4): Solution - Generalized!
