Open and Shut

Posted in Puzzles by Greg Ross on December 7th, 2009

Every room in my house has an even number of doors.

Prove that the house has an even number of exterior doors.

	Select Click 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.

Futility Closet