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DE-BUNDESWETTBEWERB 2022 Problem 6

    On a table lie 2022 matches and a regular dice that has the number aa 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 aa can Moritz force Max to lose?

    Dataset text AI-MO AoPS. Quoted with source.

    Official text: Bundeswettbewerb Mathematik 2022 official paper, page 2.

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