This app was mentioned in 3 comments, with an average of 3.33 upvotes
If I can direct you to the classic classics, Sudoku and a Rubik's Cube are like the bread and butter of logic games.
But don't buy an actual Rubik's Cube. Rubik's brand is actually kind of shit. Like the everyman's brand, they're only good for learning, and they tend to stick.
On Android I use Andoku 2. It has 5 game modes and 8 difficulties, with 150 boards for each difficulty and mode. ~6000 frigging puzzles. Has configurable ads, you can pick banner during puzzle or fullscreen interstial ads.
Edit: it's also free
As a frequent player of Sudoku I recommend Andoku 2 or 3 Free. I prefer 2 for the way it does pencil entries.
Contains fullscreen ads but only after you finish a puzzle or exit a menu. Sometimes. Fullscreen ads can be swapped with banner during game via options.
Edit: forgot to mention that this has multiple difficulties and pause/save functions. Includes standard, hyper, percent, diagonal, colour, and fuck-you-I'm-a-jigsaw-puzzle editions of Sudoku.
Comes with 8 difficulties and the easiest I've solved in less than 5 minutes.
How do you feel about Sudoku? I shared Andoku 2 in this thread already. Sudoku doesn't have to be convoluted and bacon turning, it has multiple difficulties and the easiest I've solved in like 5 minutes.
Contains fullscreen ads but only after you finish a puzzle. Sometimes.
Screenshots https://imgur.com/a/LepfW