There are twelve wires that run from your cellar to your roof. Unfortunately on their journey they could be randomly mixed up, so you can't tell which cellar wire-end corresponds to which roof wire-end. You have a battery and a light bulb, and you can temporarily twist wires together. You can also travel from the cellar to the roof and back again any number of times. Thus you can construct circuits and test the wires at either end in order to deduce what is going on. But it’s a long way to the roof. So, starting at the bottom, what is the minimum number of journeys you have to make, in order to work out exactly which wire-end in the cellar corresponds with which wire-end on the roof?

Two. Take all but one wire out, and label them using any method possible. Take the remaining 11 to the attic and run them down (assuming you can't push a wire 30 or so feet). So, you've now got 11 labeled wires heading from cellar to attic, and one unlabeled which by defintion is also uniquely identified.

Not only does this prevent confusion, it also saves the time thinking about a logical solution. Additionally, at the expense of pulling the wires out, you save two trips. And you'll never have to perform this again.

Hey, it never said anything about removing and replacing the wires.

Posted by Eric on 2004-06-30 14:53:04