The goal is to trace a line with your pencil across each edge on the box only once without crossing the vertices or picking your pencil up.

Note that this "box" contains 16 unique "edges".

Prove why this is an impossible task regardless of where you first place your pencil.

Imagine the drawing represents a five-room house; consider the space around the house as a sixth room. Think each edge as a wall with a door. The upper corner rooms have 4 doors each; the other three rooms in the house, 5 doors each; and there are 9 door leading to the outside.<p>If you start in a room with an odd number of doors, you will end your tour outside that room, and viceversa. If there are more than two rooms with an odd number of doors, no matter where you start, you won't be able to finish your tour.<p>HOWEVER!! This is only valid if the house is on a plane. If it's not, the tour COULD be managed... can anybody here see how?

Posted by e.g. on 2005-04-06 17:51:48