Cutting the Holey Cake
RAY: My neighbor Joan decides to bake some brownies for her two little grandsons. She got one of those rectangular pans. Because these kids are really competitive, she knows she has to divide what she bakes right in half -- which is pretty easy to do if you've got a rectangular pan.
So, she bakes the brownies, takes them out and puts them on the cooling rack. Before she cuts it in half, however, her husband comes along and cuts a rectangle out of the middle, at random.
Imagine, now, you've got a rectangular cake, and he cuts a rectangle out of the middle. He wasn't even nice enough to cut it out of the corner! The cuts aren't even parallel to the sides of the original cake.
It's not touching an edge, but it could be, and it's not necessarily parallel to any of the sides.
She says, "What's this all about? How am I going to cut it in half now?"
He says, "Well, I guess you'll just have to bake more brownies, and I'll eat this."
She was bemoaning this to one of her girlfriends on the phone, and the girlfriend says, "I have a remedy for your dilemma."
Joan asks, "Does it involve rat poison?"
The girlfriend says, "No, I have a way that you can cut this cake in half and make sure that each of your grandchildren gets the same amount of brownie. In fact, I have two ways to do it. There's a hard way and an easy way."
Joan says, "Give me both ways."
So, here's the question. How can you, with one cut of the knife, cut the brownies in half?
Think you know? Drop Ray a note!
[ Car Talk Puzzler ]