ten thousand matches and a bowl, 2 player game
Source: 2024 Austrian Regional Competition For Advanced Students p3
March 26, 2024
combinatoricsnumber theory
Problem Statement
On a table, we have ten thousand matches, two of which are inside a bowl. Anna and Bernd play the following game: They alternate taking turns and Anna begins. A turn consists of counting the matches in the bowl, choosing a proper divisor of this number and adding matches to the bowl. The game ends when more than matches are in the bowl. The person who played the last turn wins. Prove that Anna can win independently of how Bernd plays.(Richard Henner)