Island Networks

The minimum number of round trips is one. More surprisingly, one round trip could be used to label any number of wires.

Here's how:

Label the wires 0,1,2,3...9.

Connect the wires into the following groups: {0} {1,2} {3,4,5} {6,7,8,9}. So wire 0 is left alone, and wires 6,7,8,9 are all connected.

Paddle to the island. Using the light buld and battery as a circuit detector, begin testing the wires to see which ones can pair into a complete circuit. One of the wires won't complete a circuit at all; this is wire 0. Label it "A".

Two of the wires will complete a circuit with each other, and no other wires; these are {1,2}. Note that you don't know which is which, but label them "B" and "C".

Three wires will complete circuits with two other wires. These are {3,4,5}; label them "D", "E", and "F".

The last four wires will each complete a circuit with the remaining others. Label them "G", "H", "I", and "J".

Now group the wires as follows: {A,C,F,J} {B,E,I} {D,H} {G}. Note that none of the wires are in the same groups that they are at the other end.

Paddle back, and disconnect the original wires. Using the same method as before, test the wires to determine groupings: For example, if the wire you numbered "8" now completes a circuit with two other wires, it must be in group {B,E,I}. The only one of that set that was originally connected to the {6,7,8,9} group is I. So 8 connects to I. If, on the other hand, "8" completes a circuit with just one other wire it must be connected to "D" or "H". But we know "8" originally was connected to "G", "H", "I", and "J". So it must be "H".

This system not only allows you to test all ten wires in a single round trip, it works with an unlimited number of wires. Connect the wires in to groups of 1,2,3,4,5... etc. If you have left over wires (for example if you started with 17, then there would be 2 left over wires) one of our forum visitors, JRR, came up with a clever little solution: you can group leftovers together. This means you'll have two groups of the same size. But you can discriminate these two groups by leaving one terminal of the battery connected to one of them when you head for the island, and the other terminal connected to wire "0" (the single solo wire).

Wait, you think, won't I need the battery for the tests? Nope. Once you've figured out which is wire "0" and which is the same-size group, you can use wire 0 and one of the strays to substitute as your battery.