This game was invented by Noyes Chapman in 1880. It was the 15 number game which is sometimes wrongly credited to Sam Lloyd.
My parents loved these and would get one occasionally. They were a lot of fun, especially for a kid on a long drive. Sliding Piece Puzzles (Recreations in Mathematics) by Edward Hordern is the definitive book on this mathematical game.
For more information on these games read this Wikipedia entry.