LabPixie’s Flood-It! [App Store] is a free ad-supported game that can offer you a surprisingly fun challenge.
The developer summarizes the gameplay:
Flood It! is a simple yet addictive strategy game in which you have to flood the whole game board with one color in less than the allowed steps. You start from the top left corner and progress by selecting one of the colored balls on the left. When you change your current area color, every adjacent square with the same color also changes, that way you can flood other areas on the board. Select from 3 sizes of the board and try to flood-it in the least amount of steps!
The basic game, of course, has been done before in Flash as well as in the App Store, but this is a free and well implemented version of the game.
App Store Link: Flood-It!, Free