Fifteen puzzle

The fifteen puzzle is a game in which 15 of the 16 squares of a 4x4 frame are filled with numbered sliding pieces, leaving one space in which to slide on piece at a time. The object is to slide the 15 pieces into numerical order.

The 'hook' in the fifteen puzzle is that there are two distinct sets of positions which can be assembled from the pieces, depending on parity, and there is no way of moving between them using the allowed moves, as they preserve parity. This allowed its inventor Sam Loyd to offer a large prize which could never be claimed, fuelling the popularity of the game.

For larger versions of the fifteen puzzle, the problem of finding a solution is easy. The problem of finding the shortest solution is NP-Complete.

External links:

• Article explaining parity in the fifteen puzzle (http://www.cut-the-knot.com/pythagoras/fifteen)