# Underground wire correction optimization Puzzle

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A 120 wire cable has been laid firmly underground between two telephone exchanges located 10 km apart.
Unfortunately after the cable was laid it was discovered to be the wrong type, the problem is the individual wires are not labeled. There is no visual way of knowing which wire is which and thus connections at either end is not immediately possible.

You are a trainee technician and your boss has asked you to identify and label the wires at both ends without ripping it all up. You have no transport and only a battery and light bulb to test continuity. You do have tape and pen for labeling the wires.

What is the shortest distance in kilometers you will need to walk to correctly identify and label each wire?

SherlockHolmes Expert Asked on 17th February 2016 in

He will go till the start of 119th cable testing every oneand test it and las t one will be checked by telephone exchange

Yodha Expert Answered on 19th February 2016.

Puzzle is asking the shortest distance in km

on 22nd February 2016.

on 22nd February 2016.

Explanation-
Suppose two exchanges be A and B
We have 120 Cables
So,
We start at A ,
Connect wires in group of 1, 2, 3… 15
Now,
walk to the other exchange B(10 Km), and using the battery and bulb, identify the groups 1 to 15.

Then number the wires as:
wire 1 in group 1,
wire 2 and 3 in group 2,
wire 4, 5 and 6 in group 3 and so on…

Then connect the first wire from each group to wire 1, second wire from each group to wire 2, third wire from each group to wire 3 and so on…

Travel back to the first exchange i.e. A(another 10 Km) and
Number each of the wires as follows:
Number group 1 wire as 1.
Then from each group, identify the wire connected to wire 1 and no. them as the first wire in the groups i.e. 2,4,7…
Similarly, from each group identify the wire connected to wire 2…

And Hence we’ll have all the wire correctly numbered, by traveling just 20km.

SherlockHolmes Expert Answered on 23rd February 2016.

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