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 Solution by Richard)

If test 1 is done in one location or the other, bridging the battery and bulb from the 12th wire to any of the others will not do anything as the other ends are not connected.  You might be assuming you can attach the - terminal of the battery in the basement and the positive end in the attic, but I'm sure that's not allowed as there's no identified wire extending from basement to attic.

Also, you state the 12th wire is identified in the first test.  How is this? Even if you attached a neg terminal to one wire in the attic and tested half the wires in the basement with the pos terminal, that wouldn't identify which corresponded to the 12th in the attic. By testing them all, you'd find which one matched the 12th in the attic, but nothing else.

 

 

Posted by Charlie on 2004-06-30 15:03:46