Let it Slide is one of the brainiest games I've posted to date.
The idea is very simple, and far from original: You get a board with pieces arranged in a particular pattern; you have to slide those around until you get the special piece into its target location.
It's not even about finding out where the target location is - you can just hover over "dim tiles" and instantly see where you're supposed to bring the special piece. But getting it there is a whole different story.
There are five tutorial levels, which I strongly recommend you do. Then there are twenty "beginner" levels, but that's really a misnomer. If those are the beginner levels, I don't want to know what the intermediate and advanced levels look like!
Every time you finish a level you get a score based on how many clicks it took you - each level has a "par" (the minimum number of clicks it could be completed in), and your performance is compared to that gold standard. Because it's such a brainy game, getting it right is quite satisfying. I was downright proud of myself when I managed to finish a few levels. All in all, quite recommended, especially if you've got a few minutes of quiet. It might actually help you focus better later on.