game for two with piles of coins, 2010 totally, winning strategy
Source: Dutch NMO 2010 p5
September 6, 2019
gamecombinatoricsgame strategycoinswinning strategy
Problem Statement
Amber and Brian are playing a game using coins. Throughout the game, the coins are divided into a number of piles of at least 1 coin each. A move consists of choosing one or more piles and dividing each of them into two smaller piles. (So piles consisting of only coin cannot be chosen.)
Initially, there is only one pile containing all coins. Amber and Brian alternatingly take turns to make a move, starting with Amber. The winner is the one achieving the situation where all piles have only one coin.
Show that Amber can win the game, no matter which moves Brian makes.