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# 15 Puzzle

The 15 Puzzle is a square tablet containing 15 smaller square tiles labeled with the integers 1 to 15, set so that only one square may be moved at a time into the only available empty square by a move up or down or left or right (but never diagonally). The goal of the puzzle is to take a puzzle in an unsorted initial state, such as

7 | 8 | 1 | |

2 | 3 | 4 | 5 |

6 | 9 | 10 | 11 |

12 | 13 | 14 | 15 |

and set each tile in its proper order.

1 | 2 | 3 | 4 |

5 | 6 | 7 | 8 |

9 | 10 | 11 | 12 |

13 | 14 | 15 |

The puzzle was invented by Noyes Chapman, who also created a famously unsolvable version with 14 and 15 switched. His original idea was to construct a puzzle with 16 tiles that would be moved to form a magic square with 34 as its magic constant. The 15 Puzzle was initially made of wood; today they are almost always made of plastic. Darling calls it “the Rubik’s cube of its day.”

# References

- 1 D. Darling, “15 Puzzle” in The Universal Book of Mathematics: From Abracadabra To Zeno’s paradoxes. Hoboken, New Jersey: Wiley (2004)

## Mathematics Subject Classification

91A24*no label found*00A08

*no label found*

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