The Fifteen Puzzle
The 15-puzzle consists of a 4-by-4 grid with tile numbered $1$ to $15$ placed in the grid. The object of this puzzle is to randomly arrange the tiles on the grid, and then by sliding tiles around one tries to return all tiles to their home positions.
In the 1880's most of the nation was fascinated by this puzzle. When arbitrarily placing the 15 tiles into the box, attempts to solve the puzzle seemed to end up in one of two places: either the puzzle was solved, or all tiles were solved with the exception of tiles 14 and 15, these ones were switched. Think you can find a way to switch tiles 14 and 15?