A game with balls and boxes
Source: Turkey JBMO TST 2023 Day 1 P4
April 30, 2023
combinatorics
Problem Statement
Initially, Aslı distributes balls to boxes as she wishes. After that, Aslı and Zehra make alternated moves which consists of taking a ball in any wanted box starting with Aslı. One who takes the last ball from any box takes that box to herself. What is the maximum number of boxes can Aslı guarantee to take herself regardless of Zehra's moves?