From a pile of 104 tokens two players pick up some tokens, alternating turns and obeying three rules:

1. First player is allowed to take any amount of tokens, but not all of them.
2. Next quantities are limited , allowing the player to take only a divisor of the quantity taken by his partner in the preceding move.
3. The player taking the last token wins.

Devise a winning strategy.

So it appears, at least when starting with 104, that whoever can leave a power of two first wins, as long as the opponent cannot immediately take the rest.

Posted by Steve Herman on 2011-01-21 16:33:25