Question 21
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 $d$ of this number and adding $d$ matches to the bowl. The game ends when more than 2024 matches are in the bowl. The person who played the last turn wins.
Prove that Anna can win independently of how Bernd plays.
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 $d$ of this number and adding $d$ matches to the bowl. The game ends when more than 2024 matches are in the bowl. The person who played the last turn wins.
Prove that Anna can win independently of how Bernd plays.