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Tag Game of Fifteen or 15 - popular puzzle invented in 1878 by Noah Chapman. It is a set of identical square tiles with applied numbers, enclosed in a square box. The length of the box four times the length of the side knuckles for a set of 15 elements (and three times for a set of 8 elements), respectively, in the box left blank one square field. Goal of the game - moving the knuckle of the box to achieve the ordering of numbers, it is desirable to making as little as possible moves.