MathDB

Axel and Berta play the following games: On a board are a number of positive integers. One move consists of a player exchanging a number

x

on the board for two positive integers y and

z

(not necessarily different), such that

y + z = x

. The game ends when the numbers on the board are relatively coprime in pairs. The player who made the last move has then lost the game. At the beginning of the game, only the number

2015

is on the board. The two players make do their moves in turn and Berta begins. One of the players has a winning strategy. Who, and why?

Problem Statement