Cutting the Holey Cake
RAY: Here's the answer. The hard way is to take your knife, and holding it parallel to the cooling rack that the brownie is sitting on, slice the brownies that way. One kid's going to get the top half of the brownie and the other kid is going to get the bottom half. I don't like that solution because the top half and the bottom half are not truly equal.
And here's the other solution. If you take a rectangle, how would you find the center of a rectangle? You would draw diagonals and you would find the center.
Any line drawn through the center of a rectangle, that's not a diagonal, also cuts the rectangle in half. So if you were to draw a line through the center of the big rectangle and it went through the center of the hole, then you would cut the brownie into exactly two, equal pieces.
So what you do is find the center of the little rectangle that her husband cut out, by making two diagonals, then you draw two diagonals for the big piece of the brownie.
It makes no difference where the other rectangle is, if you connect the two centers with a straight line, and continue right through to the edges. You will have cut the brownie in half. Do we have a winner?
TOM: We do! The winner is Jim Loftus, from Cambridge, MA. Congratulations, Jim!
[ Car Talk Puzzler ]