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?

Right - the key to this is that there are THREE conditions: +ve, -ve and not connected.

Assumptions: not allowed to short battery (connect + to - directly)

In basement, attach 1-4 to +ve, 5-8 to -ve and leave 9-12 disconnected. Take bulb with you and
GO UP.

In roof, find a combination of wires that will light the bulb. Start with one and try all others until it lights. if none light, mark your first wire group C and take next.
When you get a light, mark one wire A and the other B. Find all other Bs (will light bulb). Then connect a B and find all other As (will light bulb).
Mark them A1 to A4, B1 to B4, C1 to C4.
Group C are wires 9-12.
Connect C1 to A1, A2, and A3.
Connect C2 to B1 and B2.
Connect C3 to B3.
Note that there no short in this combination.

Take the bulb with you and
GO DOWN (journey 2).

In basement, disentangle all wires and disconnect from battery. Connect battery + to bulb +, then Bulb - to one of 9-12.
Then connect any of 1-8 to battery - to make circuit.

Find which of wire 9-12 lights 3 others. This identifies precisely C1 and which group A attaches to (1-4 or 5-8). Assume that group A is 1-4. A4 will not light - this identifies it exactly. Assume it is wire 4.
Move to another C wire: if it lights two it is C2. If it lights 1, it is c3 and you have identified B3. B4 will not light and is identified. C4 lights nothing.

We have now identified C1,2,3,4; A4, B3,B4 exactly.
Assume A4 = 4, B3 = 7, B4 = 8, C1-4 = 9-12 in that order.

Now disconnect everything and reconnect:
9 to 1 and 5
10 to 2 and 6
11 to 3

Take bulb and BAttery and
GO UP (Journey 3)

In roof:
Untangle/disconnect all wires.
Same connection process as in basement:
C1 is known, therefore A1 and B1 (as we can distinguish between groups A & B) can be found
Similarly for C2 and hence A2 and B2.
C3 identifies A3

And we're done...

Technically, you now need to disconnect all in roof and

GO DOWN (journey 4)

to disconnect everything in the basement before anything can be used....

Not bad eh?

Posted by Hew BG on 2004-07-15 11:31:34