I play a Sudoku app on the phone pretty much everyday. Mastermind has many traits comparable to Sudoku.
Mastermind like Sudoku is a game of logic and deduction. The first time I played Mastermind I felt like an idiot. What kept me wanting to play more is that, by playing this game I feel that it will help me become a little smarter. That's exactly the reason why I play Sudoku so much! I want to become smarter.
My wife and I had a lot of fun playing Mastermind. We took turns being the code maker and the code breaker. She beat me every time, I was amazed at her intelligence and looking forward to upping mine. We both agree that it does have the same kind of charm as Battleship.
Highly recommended, it's a classic for a reason!