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 re: Solution? by Charlie)

Ops...  Should've paid more attention...OK, let's see if this still works:

Divide, twist and label the wires into 5 groups the following way:

Group 1 - 1 wire

Group B - 3 wires

Groups C - 4 wires

Group X - 2 wires

Another group X - 2 wires

Make sure that you can distinguish the groups.

Go up to the roof and circuit test them.  You should be able to identify all groups except for the 2Xs.  OK, so far?

Now, twist and label the wires the following way (label number in parenthesis)

1 + X (2) + C (3)

X (the pair that connects to the previous X - 4) + B (5) + C(6)

B (7) + C (8)

X (from the other pair - 9) + B (10)

X (that connected to the previous one - 11) + C (12)

Go downstairs, untwist all of them and test them again.  The X that is circuited with one is number 2, the same goes for the C - number three.  By testing all wires you should get the groups together, and from the letter, you should be able to identify the number.

It sounds ok... hope it works...

 

Cheers

Posted by Marcelo on 2004-07-06 06:17:35