Underground Cable - One Puzzle a Day - Puzzle Buddies

Puzzle:

There is an underground cable in which there are 10 wires, no two wires being connected in any way. The two ends of the cable are 5 miles apart. Sad thing is the wires are all of the same color, material and width and are not labeled. You cannot figure out which wire at one end corresponds to which wire at the other end by looking at them.

You have been given the job to label all the wires at both the ends. Armed with only a battery and a bulb and assuming that you are standing at one of the ends, how many total miles will you have to walk to finish your job? (Don't ask why you don't have a car!)

Will the number change if there are 20 wires?

Solution:

Call the end of the cable that you are at as X. Label one wire A. Join two wires together and label both of them B. Join three wires together and label each of them C. Join the remaining four wires together and label each of them D.

Now go to the other end Y. With the battery and the bulb you can easily find out which wires are joined together and label them as A, B, C or D accordingly.

Now join together one wire from each of the groups and label each of them as 1. Join one wire from each of the groups B, C and D and label them as 2. Join one wire each from C and D and label them as 3. Label the remaining wire from D as 4. We now have the following labels at Y end of the cable: A1, B1, C1, D1, B2, C2, D2, C3, D3 and D4.

Now go to the other end X. Find out the wires joined together and label them as 1, 2, 3 or 4 respectively. We had previously labeled wires as A, B, C or D at end X. So, we now have the labels A1, B1, C1, D1, B2, C2, D2, C3, D3 and D4 at end X too.

It is easy to verify that similarly labeled wires at the two ends are one and the same.

Thus, you had to make only one trip, walking 10 miles. This logic can be applied to any number of wires and the walking distance remains the same.