Kapuila
Kapuila is a different kind of App combining a fun game with logic and memory exercises.
You get 3 games in one:
Memory: Test and train your short term memory.
Logic: Test and train your ability to solve logical puzzles.
You can also play a version alternating between the two kind of puzzles.
There are 3 individual leaderboards for the different games all integrated with Apples Gaming center so that you can compare score with other players.