# 15 Puzzle

The 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)
Title 15 Puzzle 15Puzzle 2013-03-22 16:46:21 2013-03-22 16:46:21 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Definition msc 91A24 msc 00A08 Fifteen Puzzle Game of Fifteen