It’s not even about math, although it’s not as simple as it might seem.
How to play 15 Puzzle
The name of this puzzle comes from the fact that there are 15 sliding tiles set in a 4×4 square and also because you must arrange them in ascending or descending order. Since there are 16 slots and only 15 tiles, that leaves you with an empty slot so you can slide the pieces around.
The numbers on the tiles go from 1 to 15. You can start by placing the the target number, 15, in the upper left corner and place the tiles in descending order or you can start with 1 and work your way up.
You might think it’s child’s play, but the fact is that many mathematicians have analyzed the puzzle. They came up with the startling conclusion that depending on the way the tiles are arranged at the beginning half of the initial positions are impossible to solve no matter how many moves you make. This has to do with terms like invariant, parity of the permutation of the 16 tiles, which sure don’t sound like much fun. If you ever find such a toy in a shop it will probably be solved, just as Rubik cubes are sold, which means that no matter how much you scramble the tiles you will always be able to arrange the tiles in order. So don’t try to excuse yourself by saying it’s probably one of the unsolvable configurations.
History of the 15 Puzzle
Today, a Canadian postmaster named Noyes Palmer Chapman is credited with inventing the 15 puzzle in 1874. His original design was passed from hand to hand until it reached Boston, where the first commercial 15 puzzles were manufactured in 1879. The odd thing is that following the 1880s craze with the 15 puzzle, the famous American chess player and puzzle inventor Sam Loyd claimed that he had created the popular toy.
Another famous American chess player, world champion Bobby Fischer was a fan of the 15 puzzle and his personal record was solving the puzzle in 25 seconds, a feat he demonstrated on a popular TV show.