MathDB
2player game blowing up a balloon

Source: China Northern MO 2014 p8 CNMO

May 5, 2024
combinatoricsgamewinning strategy

Problem Statement

Two people, AA and BB, play the game of blowing up a balloon. The balloon will explode only when the volume of the balloon V>2014V>2014 mL. AA blows in 11 mL first, and then they takes turns blowing. It is agreed that the gas blown by each person must not be less than the gas blown by the other party last time and should not be more than twice the amount of gas the other party blew last time. The agreement is that the person who blows up the balloon loses. Who has a winning strategy ? Briefly explain it. (Do not consider the change in volume caused by the change in tension when the balloon is inflated).