The Trainee Technician

Puzzle Level :- Very Hard

PUZZLE

           A 120 wire cable has been laid firmly underground between two telephone exchanges located 10km apart. Unfortunately after the cable was laid it was discovered to be the wrong type, the problem is the individual wires are not labelled. 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 labelling the wires.What is the shortest distance in kilometres you will need to walk to correctly identify and label each wire?

ANSWER

    20km

SOLUTION

        To solve this issue we need to group the wires at one end and go to second end and find the wires in each group with help of battery and light and label them.

Then again form groups by choosing one one wire from previous groups and then go to first end and label them based on their groups.

This is difficult to understand it in statements. so i will explain it in details with example.

For convenience let's assume there are only 6 wires instead of 120. Let's assume them as 1,2,3,4,5,6

Now group them as first group contains one and second group contains two etc...

(Here grouping means we tie the wires and tape them so that they can pass electricity)

{1} , {2,3}, {4,5,6}

and Label each wire with group number (X1,X2,X3 are groups )

{1}  => X1

{2,3} => X2

{4,5,6} => X3

Now go to other end. With battery and light find these groups.

suppose if we attach battery to wire-1 , No other wire will pass the electricity and light will be off

if we pass the current over 2  the current will pass through 2 and 3 similarly for 4,5,6.

This way we can find the group of each wire they belong to

Now label each wire in each group as below

X1 => {A1}

X2 => {A2, B2}

X3 => { A3, B3, C3}

Now group the wires at this second end (Y1,Y2,Y3 are new groups as second end)  by picking one wire from each first group (i.e X1, X2, X3)

{A1, A2, A3} => Y1

{B2, B3}  => Y2

{C3}  =>  Y3

Now go to first end of cable  and separate all wires and try to find the each wire's group(i.e Y1, Y2, Y3) using battery and light.

If the wire belongs to  Y1 group and previously it is in X1 group then label it as A1

similarly wire belong to Y1 and X2  groups is A2

Y1, X3 => A3

Y2, X2 => B2

Y2, X3 => B3

Y3, X3 => C3

This way we can label the wires correctly at both ends.

and we just travelled 20km in this case.

Similarly for 120 wire case we can first group wires as 1,2,3,4,5....etc  and solve the puzzle with similar approach.

--------------------------------END--------------------------