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 itís 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?
It seems that most people, except perhaps Leigh, misunderstand the basic electrical circuit. You have 2 ends, or poles, on the battery, and 2 on the lightbulb as well. So you can't just "hook up 6 wires to the battery", unless you connect some to the positive and some to the negative. Then you have to determine which ones are which, which is what I like about Leigh's solution. However, with no other restrictions in the description, here's a great solution (like the colored lights):
Give a friend (who you bribed with beer to help you) one of two walkie-talkies or cell phones, and the battery, and send him/her to the cellar. You go to the roof with the light bulb. He/she hooks up 2 wires to the battery; you find which ones are hot. Then your friend switches one of the wires and you find which 2 are now hot, and the one that was hot in both is #2, the remaining one is #3 and the first is #1. You both then switch to 2 new wires and repeat the process 3 more times to identify all wire ends.
CURIOSITY: I might understand if the wires were in the attic, or more likely the second floor, but why are there 12 wires on the roof?