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?

Hi to you all.  I've been contemplation the problem for some time and I think I got it figured out.  This is my first post here and I hope my english is good enough explain what I think might be a possible solution.  Also, I'm no electrical engineer so... well, here goes.

One trip to the roof should be enough.  Starting on the cellar, twist wires together this way: Wire alone (labelled 1), Group of 2 wires together (Group B), 3 wires together (group C) and 4 wires together (group D).  Then, go up to the roof and circuit test.  You should have the 1, B, C and D groups sorted out.  Then do the following:

Tie wire 1 to wire from group C (label it 2) and from D (label it 3)

Tie one wire from B (4), C (5), D (6) together

Tie one wire from B (7) and C (8) together

Tie one wire from C (9) and D (10) together

Next, go back downstairs, undo the connections and circuit test them.  The wire B that closes the circuit with wire 1 is number 2, and the wire C that does the trick is number 3.  Find out group BCD and you've got 4,5 and 6 respectively.  B and C? 7 and 8.  And finally C and D which should be 9 and 10 respectively...

Hope no one gets short circuited on the way...

Posted by Marcelo on 2004-07-04 13:52:55