0809.3: Solution

Solutions Page for Logic Puzzle #3: Wires

 The winners of the third logic puzzle contest are:

Matt Eichenfield '09 and Brendan Conway '09

The Puzzler's solution:

1. Arbitrarily, we’ll start on the south side. Choose one wire, and label it #1. Pair up all other wires, leaving wire #1 unconnected. Label each pair, but not with numbers. Pairs of letters, e.g. AA, AB, AC...BA, BB, BC.... will provide enough labels.
2. Travel to the north side.
3. Determine the lone, unconnected wire by attaching the voltage source to each wire in turn, until you find one that does not electrify any other wire. Label it #1.
4. Pick any other wire, label it #2.
5. Find the wire to which #2 is connected. Label it #3.
6. Repeat steps 4 and 5, increasing the label numbers by twos, until all wires are numbered.
7. Connect #1 to #2, #3, to #4, and so on, leaving #501 unconnected. Notice that all the wires are now connected, so that if you send electricity through #1, it will pass through all the wires.
8. Travel to the south side.
9. Disconnect all connections, but leave the letter labels in place.
10. Send electricity through wire #1. Wire #2 will now be live. Label it #2.
11. Find the wire which had previously been paired with Wire #2. Label it #3.
12. Repeat steps 10 and 11, increasing label numbers by twos, until all wires are numbered.

Note, this solution only works for odd numbers of wires, since it requires us, at step 3, to determine the lone, unconnected wire. To use this method to label 502 wires, I would need an extra trip to determine a starting point.


Peter Rabinowitz's even better solution, which works for 502 wires as well as for 501:

I’ll do it in two trips--regardless of the number of wires. I begin by connecting pairs of wires on side A. If I have one extra wire, fine. I can label that with the last number, whatever it is.

I then go to side B. I can now reconstruct all the pairs, because I can send voltage through a wire and--assuming that I have the right kind of voltage detection equipment--see what other wire it comes through. (I can also figure out which is the wire that doesn’t have a connection at the other side). I now number all of my wires on side B. Arbitrarily choosing one wire as wire 1, I assign its pair number 2. I then aribitrarily choose a wire as 3 and assign its pair the number 4. And so on. I then connect 2 to 3 and 4 to 5. I now have, in effect, a single long wire (and perhaps a short wire that I know is the last, extra wire). I attach the voltage source to point 1 and go back to the other side.

On side A, I disconnect all the pairs (but remember how they were paired). There will now be evidence of an electrical charge only at the end of the first wire. When I find that wire (which I can now label 1), I reconnect it to its pair (which will be wire 2). I then see where the voltage is coming to, and that will be wire 3. I continue the process until I have found the entire route.