European Mathematical Cup 2016 senior division problem 2
Source:
December 31, 2016
combinatorics
Problem Statement
For two positive integers and , Ivica and Marica play the following game: Given two piles of
and cookies, on each turn a player takes cookies from one of the piles, of which he eats and puts of
them on the other pile. Number is arbitrary in every move. Players take turns alternatively, with Ivica going
first. The player who cannot make a move, loses. Assuming both players play perfectly, determine all pairs of
numbers for which Marica has a winning strategy.Proposed by Petar Orlić