Open and Shut Every room in my house has an even number of doors. Prove that the house has an even number of exterior doors. SelectClick for Answer> Each door has two sides, so the total number of door sides is even. Since the number of door sides inside the house is even, the number on the exterior must be even as well. From L.A. Graham, Ingenious Mathematical Problems and Methods, 1959. December 7, 2009January 22, 2013 | Puzzles