YouDunnit: a game that travels backwards in time

Over on Play This Thing! Greg Costikyan reviews YouDunnit, a difficult-to-play but incredibly clever game based on levels that go back in time and challenge you not to violate causality:
The basic setup is this: You murdered someone, in locked-room detective story-like fashion, and the detective has shown up to investigate. He's asking everyone their stories. If you catches you out in an inconsistency -- or if you somehow permit everyone else to establish a clear alibi -- you're screwed.

The actual gameplay involves a series of "levels" that are a hour in the past, two hours in the past, three hours in the past, and so on. If you do anything in a level that "violates causality," you are "caught in a lie." Thus, for example, if you give someone a cat in hour -1, and fail to pick up the cat in a previous hour, you lose. You have to keep track of the events that occur, and make sure things remain consistent.