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The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and more) is a sliding puzzle. It has 15 square tiles numbered 1 to 15 in a frame that is 4 tile positions high and 4 tile positions wide, with one unoccupied position.
As a famous example of the sliding puzzle, it can be proved that the 15 puzzle can be represented by the alternating group, [2] because the combinations of the 15 puzzle can be generated by 3-cycles. In fact, any n × m {\displaystyle n\times m} sliding puzzle with square tiles of equal size can be represented by A n m − 1 {\displaystyle A ...
There are many confusing and conflicting claims, and several countries claim to be the ultimate origin of this game. One game—lacking the 5 × 4 design of Pennant, Klotski, and Chinese models but a likely inspiration—is the 19th century 15-puzzle, where fifteen wooden squares had to be rearranged. It is suggested that unless a 19th-century ...
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English: 15-puzzle, a sliding tile puzzle game. It consists of 15 numbered interlocking tiles in a box. The tiles cannot be removed from the box, but since there is one tile missing, they can be slid to different positions. The object of the game is to restore the numbered tiles to consecutive order as shown, from an initial random order.
An equable polyomino must be made from an even number of squares; every even number greater than 15 is possible. For instance, the 16-omino in the form of a 4 × 4 square and the 18-omino in the form of a 3 × 6 rectangle are both equable. For polyominoes with 15 squares or fewer, the perimeter always exceeds the area. [30]