Draw a line through every wall of this five-room floor plan without lifting your pen
A floor plan shows five rooms, with walls separating them and the outside. Starting anywhere, can you draw one continuous line that crosses each wall exactly once, without lifting your pen or retracing a line? Martin Gardner called this one of the oldest topological puzzles still in circulation.
Reveal the answer
It can't be done. Three of the rooms (plus the outside) have an odd number of walls, and a region with an odd number of walls must be where the line starts or ends, since the line can only pass through a region an even number of times otherwise. A single line has only two endpoints, but the puzzle needs at least three, so no solution exists, a clean example of using parity to prove something is impossible, not just hard.