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In 1973 Fraenkel discovered interesting sequences which split the positiveintegers. These sequences became famous, because of a related unsolvedconjecture. Here we construct combinatorial games, with `playable' rulesets,with these sequences constituting the winning positions for the second player.Keywords: Combinatorial game, Fraenkel's conjecture, Impartial game, Normalplay, Playability, Rational modulus, Splitting sequences

Playability and arbitrarily large rat games