If you enjoy Sudoku then chances are you will really love Kakuro.
All it takes to play Kakuro is a knowledge of elementary arithmetic (addition and subtraction), a little analysis, and some dedication. Like Sudoku no digit may appear twice in any row or column of contiguous cells. Unlike Sudoku all the cells in a row or column must also add up to a specified value.
This game has an introductory help screen to get you started and 58 puzzles for you to play. Future versions of this game will allow you to download extra puzzles when you wish.
Also, if you are really stuck, this game allows cheating by allowing you to see any errors you have made or, if things are really bad, to see the answers. But don't do it. It is much more satisfying to figure it out on your own.
All these puzzles are guaranteed to be solvable without guessing (though not necessarily easy). All puzzles have unique solutions.
1.10: Added the ability to move to the next puzzle in a book after completing the current puzzle. Just navigate back to the initial screen and you will be presented with an option to go to the next puzzle. This will work after you select your next puzzle (it won't work if you upgrade with a puzzle in play).
1.09: Fixed a bug where a message stayed on the screen after the puzzle was dismissed.