http://ferrao.org/numeri/ is an elegant puzzle game based on Slitherlink (similar to Sudoku and Kakuro).
Your goal is to draw a single loop line that makes every cell valid. A cell is valid (white) when the number of line segments around it matches the displayed value. Touching a cell toggles all the line segments around the same cell.
The simplicity of the rules and interface allow you to focus on the puzzle challenge.
I'm sure you will like it. The majority of my usability tests with new users resulted in addiction.
You can find it in the apple store.
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