Amazon have just posted another free app for the Kindle. It’s called Grid Detective, and it’s a logic puzzle type of a game.
You start each level with a set of clues. Your goal is to deduce the solution based on the apparently unrelated clues. There are 10 Easy, 10 Moderate, and 10 Hard puzzles in the app, and the easy ones look difficult to me.
On a related note, I’ve also added this app to the page which lists free Kindle apps.