In 1973 Fraenkel discovered interesting sequences, dubbed the rat sequences (rat for rational numbers), that partition the positive integers. These sequences became famous, because of a related unsolved conjecture. Here we construct nim-type combinatorial games, called the rat games, for which these sequences constitute the losing positions for the current player. We define a notion of playability for classes of heap games and show that the rat games are playable. Moreover, we find new definitions of the rat sequences, including a variation of the classical mex-rule.
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