If you're into mind-benders, pay attention. What we've got here is Magic Cuts, a game born not only from the desire to make you furiously scratch your head, but also an academic paper about "dissecting planar shapes into two identical parts."
What results is an enjoyable romp, dragging lines about to slice shapes up into their identical halves. There's a whole plethora of things to halve, and some will definitely challenge you. The result is a seemingly simple game that's both fun and elegant.
Other than that, there's not much to say. It's free in the Market, so get out there and start slicing. QR code and download links are after the break.