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?

Leigh you shortcut your battery when making the n1p1 connection, but as there are a number of ways to make the connections on the roof, this can easily be avoided.

Now, could somebody check this, it is combination of Leighs solution with mine and (If it is correct) would allow any number of wires to be tested in one complete roundtrip.

Label your wires 1 to 12.  In the cellar connect 1 to the + battery and 2 and 3.  Make pairs (4,5...6,7...8,9...10,11) leave 12 alone

Go to the roof and use your bulb to find a wire that gives light with two others.  This is wire 1, the two others are 2 and 3 (label them X and Y), though you don't know which is which.  Use 1 and 2 or 3 to look for the pairs, label them A,B...H.  There is one wire left (12)

Now connect X  to A, B to C, D to E, F to G, H to 12 and go to the cellar.  Disconnect your battery.  You connect 12 to the battery, start opening a pair and test the wires if it lights, you open all other connections.  If the bulb still lights, you have identified H.  Connect your battery to H and using the same technique identify G.  Continue doing so until you reach X.  Y is the wire from the original 2,3 pair.  And you already knew 1.  

 

Posted by Hugo on 2004-07-21 08:11:15