### The Magnus-Derek game in groups

*Dániel Gerbner*

#### Abstract

The Magnus-Derek game (also called the maximal variant of the vector game),
introduced by Nedev and Muthukrishnan is the following: a token is moved around a table with
$n$ positions. In each round of the game Magnus chooses a number and then Derek chooses a
direction (clockwise or counterclockwise), and the token moves that many positions into that
direction. The goal of Magnus is to maximize the number of positions visited, the goal of
Derek is the opposite. In the minimal variant of the game the goals of the two players are
exchanged: Magnus wants to minimize the number of positions visited and Derek wants the
opposite. Here we introduce a generalization of these games: the token is moved in a group,
Magnus chooses an element of the group and Derek decides if the current position is multiplied
or divided by that element.

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