A dice game
Source: German Bundeswettbewerb 2022, Round 2, Problem 2
September 14, 2022
combinatorics
Problem Statement
On a table lie 2022 matches and a regular dice that has the number on top. Now Max and Moritz play the following game:
Alternately, they take away matches according to the following rule, where Max begins: The player to make a move rolls the dice over one of its edges and then takes a way as many matches as the top number shows. The player that cannot make legal move after some number of moves loses.
For which can Moritz force Max to lose?