Does Mary have a winning strategy?
Source: Tournament of Towns Spring 2003 - Senior A-Level - Problem 5
June 15, 2011
modular arithmeticcombinatorics unsolvedcombinatorics
Problem Statement
Prior to the game John selects an integer greater than .Then Mary calls out an integer greater than . If John's integer is divisible by , then Mary wins. Otherwise, John subtracts from his number and the game continues (with the new number). Mary is not allowed to call out any number twice. When John's number becomes negative, Mary loses. Does Mary have a winning strategy?