MathDB
A game with balls and boxes

Source: Turkey JBMO TST 2023 Day 1 P4

April 30, 2023
combinatorics

Problem Statement

Initially, Aslı distributes 10001000 balls to 3030 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?