Sliding Puzzle
32 games
Description
Nothing leaves the board. Everything just has to end up somewhere else, and there's no way round that - which is exactly why a sliding puzzle feels so good when it finally gives.
Unblock It 3D is the classic shape of it: one piece needs to reach the exit and everything else is in the way. Unblock it Atlantis is the same idea dressed for somewhere else entirely. Sort Tiles turns it into an organising problem rather than an escape, and Arrow Slide Puzzle fixes which way each piece can travel, which tightens things up considerably once you're a few moves in.
There are 32 free games here, all in the browser with nothing to install, and most of them will happily sit half-solved in a tab while you go and think about something else.
If you want more of the same thinking, Logic games is the tag to follow, and Brain games is the wider shelf.