Players wanting to obtain first non-positIve integer to win
Source: Baltic Way 2011
November 6, 2011
combinatorics proposedcombinatorics
Problem Statement
Two persons play the following game with integers. The initial number is . The players move in turns. Each move consists of subtraction of an integer between and inclusive, or division by , rounding down to the closest integer when necessary. The player who first obtains a non-positive integer wins. Which player has a winning strategy?