Two children must split a pie. They are gluttons and each prefers to eat as much of the pie as they can. The parent tells one child to cut the pie into two pieces and then allows the other child to choose which pie to eat. The first child can divide the pie into any multiple of tenths (for example, splitting it into pieces that are 1/10 and 9/10 of the pie, or 2/10 and 8/10, and so forth). Show that there is a unique backward induction solution to this game.