I've been waiting for this one for a while. Ghost Trick: Phantom Detective is a title that won accolades on the Nintendo DS last year, and it's now arrived on iOS in a universal version (that's free to download to boot). The idea is that you're a ghostly "phantom detective" who must solve his own murder. You can't directly interact with the living, but you can mess with inanimate objects in their world. So move objects around and try to change the fate of other dead people. It sounds morbid, but there's a fun sense of humor and style that keep it entertaining. The first two chapters are free to play through, and you