Second player can win in infinitely many starting positions
Source: Baltic Way 1995
October 8, 2011
combinatorics proposedcombinatorics
Problem Statement
Consider the following two person game. A number of pebbles are situated on the table. Two players make their moves alternately. A move consists of taking off the table pebbles where is the square of any positive integer. The player who is unable to make a move loses. Prove that there are infinitely many initial situations in which the second player can win no matter how his opponent plays.