There is a terrific book by Jerry Slocum and Dic Sonneveld titled "The Fifteen Puzzle" (check it out here), which details the rise of the game's popularity in the 1880s  ad the many iterations that have been produced over the years since.  (It also details a bunch of variations on solving it, the most  basic being sliding the tiles to put them in order from 1-15.) In it is pictured one set that looks a very much like this one, which they speculate might pre-date the 1880s craze for it. I'm really not sure this one is that old, but this is very lovely, with what appear to be handwritten numbers on the recessed wood tiles, all held in a hinged box, which appears to me to be birds eye walnut veneer with marquetry detail around the edge.  Terrific on the desk or coffee table for procrastinating or amusing guests!

 4 1/2" x 4 1/2" x 7/8". Very good condition, with light wear and aging to top, as pictured.