Ryan Morlok’s Blog

Suppose you are wiring a surround sound speaker system.  The room’s dimensions are a bit strange:  3 meters tall, 4 meters wide, and 27 meters long (ok, this is a huge room).  You’re in the process of wiring the rear center channel (point A in the diagram below) which is located 2 meters from each wall and 1 meter from the ceiling.  This needs to be connected to the amplifier on the opposite wall (point B) which is 2 meters from each wall and 1 meter off the ground.

Click to enlarge

Speaker wire is incredibly expensive, and you’re trying to find the shortest possible length you can use. The only rule is that the wire must be directly attached (touching) a surface at all times (a wall, the floor, or the ceiling). You cannot leave the wire dangling by cutting through the space of the room.

An obvious (but non-optimal) solution would be to go from the speaker straight up the wall across the ceiling, and down the opposing wall to the amplifier. This would give a length of 30 meters (1+27+2=30). What is the shortest possible path connecting the two points and how much speaker wire must be used?

Special thanks again to Mikhail for the question. Those crazy Russians are full of good brain teasers. Also thanks to Ben Cirillo for drawing up the diagram in the *real* autocad.