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 itís 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, this is my first posting, sorry for errors in my english.
I believe that all twelve wires (And any number of wires) can be identified by making four trips (2 x cellar+ 2 * roof).
Go to the cellar and connect the wires two by two. Now you have 6 pairs of wire. Label them 1X and 1Y, 2X and 2Y,...
Go to the roof with battery and bulb. Identify all the pairs (Put the + from the battery to one wire, the - to the bulb and the other side of the bulb to the wire you are testing) and label them 1A, 1B for pair one and 2A, 2B for the second pair and so on. Connect 2A to 1B, 2B to 1C and so on, but do not connect 6B to 1A, leave them open. You now have one serie of wires all connected to each other, with two open ends. The serie is labeled 1A,1B, 2A, 2B,...
Go to the cellar again and open one of the connections. Take one of the wires and connect your battery and bulb at this wire, with the other side of the bulb you test all the wires at all the connections to see if any of these light your bulb. If so, you stop with this wire and start wioth another wire until you find one that does not give light when connected to whatever other wire. This wire will be one of the open ends at the roof. This wire is labeled 1A or 6B at the roof. Reconnect everything as it was before. You have now again a series of wires and you now which X or Y wire is the start (or end). Suppose it was 3X, Take then 3Y, use your light and bulb, and find out with which X or Y you get light (When all connections are open). If this is for example 5Y, then do the same procedure to the 5X wire. When continuing this way of workung, you will get a serie labelled 3X, 3Y, 5Y, 5X,... Now that you know the sequence of all the wires at the top and at the bottom, you should find out wether 1A = 3X and 1B = 3Y,... or that 6B = 3X, 6A = 3Y, 5B = 5Y,... This you do by connecting the + from the battery to 3X and connecting the - from the battery to all the others.
Go to the roof put the bulb to 1A and to another wire, if it gives no light, then 1A is connected to all the others, and the solution is 6B = 3X, 6A = 3Y, 5B = 5Y.
Sure more difficult to explain then to find out.