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- Some notes on disjunctive short sum: polychromatic nimPublication . Carvalho, Alda; Santos, Carlos Pereira dospolychromatic nim is a version of the classic game nim, played with colored stones, in which each pile has stones of a single color, and the player who successfully extinguishes a color wins the game. This game is closely related to the concept of short rule, the ending condition that states that a disjunctive sum ends as soon as any one of the components ends. Here, we discuss that rule, namely when applied to impartial games, and prove that the Grundy-values of polychromatic nim present an arithmetic-periodic behavior.