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?

1. Twist together wires in basement in pairs except for two. Label pairs A - E. The two that are unpaired should be hooked up to the battery terminals.
2. Go to roof. Identify the two that are currently connected to battery by testing ends with light bulb. Label these 2 and 2'.
3. Next, connect 2 to another wire end (label 2.5) and find its partner wire from below. You label this wire 3.
4.-7. Continue this process until you have 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7 identified. (Draw a picture if you are having trouble imagining this)
8. Leaving wires connected on roof (2-2.5, 3-3.5, etc.) and two loose ends (2' and 7), return to basement, unhook battery, and take battery to roof. Connect to loose ends 2' and 7. (The roof is now essentially set up the same way as the basement was to start: five pairs and a battery pair)
9. Return to basement with lightbulb (you have now made two complete trips).
10. Untwist pairs A-E but maintain labels. Find 2' and 7 by testing lose ends with lightbulb (you know which is which because 7 will have a letter label and 2' will not). Now you know 2 by default, because you knew which two wires were 2 and 2' and have identified 2'. You also know 6.5 by default, because you know 7-6.5 were twisted together initially (perhaps as pair A).
11. Next you use 6.5 and the light bulb to find 6. Now you know 5.5 by default (was paired with 6 at start). Continue this pattern until you have identified all wires!
Done in two trips total.

Posted by Sara on 2004-07-17 08:15:47