ARO 2011 11-6
Source:
May 6, 2011
combinatorics proposedcombinatoricsgame
Problem Statement
There are more than stones on the table. Peter and Vasya play a game, Peter starts. Each turn, a player can take any prime number less than stones, or any multiple of stones, or stone. Prove that Peter always can take the last stone (regardless of Vasya's strategy).S Berlov