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?

(In reply to understandable solution by Steve)

OK! 

I was dwelling on this, then (warning, here comes a bad pun, not to mention a cliche) the light came on!

Even though my anwer seems to show solid logical thought, it is not technically accurate.  Two pieces of information are vital to this problem.

1: batteries have  positive and negative terminals, both of which must be in the circuit.

2: If I gang 3 wires on the + and three on the - terminal, there is no way of figuring out which is which using a light bulb!  Clever solution coming soon!

Posted by Steve on 2004-07-09 07:33:40