The sliding block puzzle was invented in the 1880s with the fifteen puzzle which simply had the numbers 1-15 on the blocks. My homage to this form of puzzle is the eight puzzle which is remarkably similar in concept but only uses 8 blocks which is a much more sensible prototype. You could also put any kind of picture you want on the top of the blocks.
Each block is made up of 3 different layers, the middle layer is shifted right and up slightly to form an overlapping section with the block next to it. Where the tiles overlap the surfaces have been engraved, this reduces the thickness of the material and makes it slide easily in the gaps. The edge of the puzzle also have 3 layers which is staggered in a similar fashion. The edge is backed like the other tray puzzles and this stops the pieces from falling out of the middle. The edge is a single solid piece, because of this the last row of blocks has to be glued into place inside the puzzle so be careful not to spread the glue outside the block or it won't slide correctly.
Because this puzzle is just a series of blocks it could be expanded to any dimension and size you requires. I made this from 3mm poplar ply wood which makes it very easy to have a deep engrave. (svg here)