[Guest]

Hi,

Any answers......?.I found this puzzle very trick...any solutions for it...

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 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?

[bhramarraj]

20KM

[Guest]

How come?

[Guest]

how many wires are there? 120? if thats the case it would be 220km because youd have to walk to each end for each wire to connect the battery and the bulb and you wouldn't need to do it for the last wire because you'd know what type of wire it is hope this helps (and makes sense) :L

[Guest]

You need to walk 70 Km.

You actually need to walk D*ceil(log2(N)) Km, where D is the cable length, N the number of wires, and log2 the base 2 logarithm.

Here is the 1st step:

On one end, you split the wires into two groups, each consisting of 60 wires.

You label wires in the first group as "1" and wires in the second group as "0".

Then you short-circuit all wires in group "1", while taking care that all wires in group "0" don't touch each other.

You walk 10Km and go to the other end, and using the battery and the bulb you identify all wires that belong to group "1".

So you label each of them as either "1" or "0" depending on whether there is electric current or not.

Now, we have to move to step 2:

You split group "0" into two new groups. Label them "01" and "00", by just appending a one or a zero to the existing label.

Also, split group "1", ending up with two new groups with labels "11" and "10".

Then you short-circuit all wires from groups "01" and "11", getting again 60 wires in total.

Again, make sure that the others are not touching anything.

Time to walk again for a 2nd time to the other end.

Here you have to remove all short-circuits first, perform your continuity tests, and finally append a "1" or a "0" to each label.

You perform the same scheme again and again until all labels receive a unique binary number, which you use to identify them.

Each walk adds one extra bit of information to all labels. And you need at most 7 bit to describe any integer in the range 1...120.

So the answer is 7 walks, 10 Km each, or 70Km in total.

On each iteration, you should consider all wires with the same label as being members of the same group and split them into two new sub-groups, equally sized if possible. After labeling all the new sub-groups, you simply short-circuit only those wires with labels ending in "1".

Edited August 20, 2011 by plainglazed
fixed spoiler

[Guest]

You need to walk 70 Km.

You actually need to walk D*ceil(log2(N)) Km, where D is the cable length, N the number of wires, and log2 the base 2 logarithm.

Here is the 1st step:

On one end, you split the wires into two groups, each consisting of 60 wires.

You label wires in the first group as "1" and wires in the second group as "0".

Then you short-circuit all wires in group "1", while taking care that all wires in group "0" don't touch each other.

You walk 10Km and go to the other end, and using the battery and the bulb you identify all wires that belong to group "1".

So you label each of them as either "1" or "0" depending on whether there is electric current or not.

Now, we have to move to step 2:

You split group "0" into two new groups. Label them "01" and "00", by just appending a one or a zero to the existing label.

Also, split group "1", ending up with two new groups with labels "11" and "10".

Then you short-circuit all wires from groups "01" and "11", getting again 60 wires in total.

Again, make sure that the others are not touching anything.

Time to walk again for a 2nd time to the other end.

Here you have to remove all short-circuits first, perform your continuity tests, and finally append a "1" or a "0" to each label.

You perform the same scheme again and again until all labels receive a unique binary number, which you use to identify them.

Each walk adds one extra bit of information to all labels. And you need at most 7 bit to describe any integer in the range 1...120.

So the answer is 7 walks, 10 Km each, or 70Km in total.

On each iteration, you should consider all wires with the same label as being members of the same group and split them into two new sub-groups, equally sized if possible. After labeling all the new sub-groups, you simply short-circuit only those wires with labels ending in "1".

ah, information theory ftw! me likey.

[Guest]

30 km

1st go to one end say "A" and from 120 wires connect 2-2 wires and make 60 pairs

2nd Go back to the starting point say"B" and with battery and bring battery bulb and wire and see if circuit gets completed or not

3rd In case it doesn't attach battery to one wire and go back to point "A" detach the wire and try to complete the circuit if it does the 2nd wire in the pair is damaged

[Guest]

How big is the battery?

[Guest]

20km

1. beginning on side a, connect all but 4 wires into pairs. Of the remaining 4, 1 connects to the positive side of the battery, 2 connect to the negitive side of the battery, and one is left dead.
   
2. on side b, identify the positive wire and the two negative wires. (there will be 2 connections which will light the bulb. positive and each of the negative wires) Using these identify the pairs of wire (connect positive to a unknown wire, find the return current with a negative wire and you will have found a pair). Wire the pairs into one long wire (connecting pair 1 to pair 2 and so on). connect one of the negative wires to the dead wire.
   
3. on side a again, first identify which negative wire is connected to the dead wire (we now know 4 wires absolutely). Working from negative to positive, deconstruct the circuit that you built. you want to find the pair that, when broken, you can light the bulb only by connecting one side of it to the to the light and the positive side of the battery. reconnect this pair (its wires being identified) and find the next one (here you would be able to light the bulb by connecting either the first pair, or one disconnected end to bulb and the positive end of the battery). Repeat this process until all wires have been identified.
   

[Guest]

30 km

1st go to one end say "A" and from 120 wires connect 2-2 wires and make 60 pairs

2nd Go back to the starting point say"B" and with battery and bring battery bulb and wire and see if circuit gets completed or not

3rd In case it doesn't attach battery to one wire and go back to point "A" detach the wire and try to complete the circuit if it does the 2nd wire in the pair is damaged

SORRY GUYS I MADE A SILLY MISTAKE

my answer is 20 km my procedure is same but there was a big mistake

let say you are standing at point "A"

now at "A"make 60 pairs of 2-2 wires

now travel 10 km to point "B"

at point "B" with the help of wire and battery see if all the circuit gets completed or not in case no

say in the case of wire 5 and 6

then again attach 4 and 5 and move to the point "a"(10km)and detach wire 5 and 6 and now with the pair of wire 4 and 5 try to complete the circuit

if the bulb lights then the damaged wire id 6 and if not then it's 5

Edited August 21, 2011 by optimus prime

[Guest]

20km

1. beginning on side a, connect all but 4 wires into pairs. Of the remaining 4, 1 connects to the positive side of the battery, 2 connect to the negitive side of the battery, and one is left dead.
   
2. on side b, identify the positive wire and the two negative wires. (there will be 2 connections which will light the bulb. positive and each of the negative wires) Using these identify the pairs of wire (connect positive to a unknown wire, find the return current with a negative wire and you will have found a pair). Wire the pairs into one long wire (connecting pair 1 to pair 2 and so on). connect one of the negative wires to the dead wire.
   
3. on side a again, first identify which negative wire is connected to the dead wire (we now know 4 wires absolutely). Working from negative to positive, deconstruct the circuit that you built. you want to find the pair that, when broken, you can light the bulb only by connecting one side of it to the to the light and the positive side of the battery. reconnect this pair (its wires being identified) and find the next one (here you would be able to light the bulb by connecting either the first pair, or one disconnected end to bulb and the positive end of the battery). Repeat this process until all wires have been identified.
   

I like your solution but for one minor problem:

now you must trudge back to end B to disconnect the wires and complete the labeling, This makes 30 KM. Of course your boss probably needs you to be at the end A so you will need to walk another 10KM. Assuming you are a regular jogger, this has taken a minimum of 3 hours (for the 30KM, or if walked at a fast pace 5hours. Your boss should have given you an assistant in which case, with the aid of a cell phone, your assistant keeps the battery at end A, you walk to end B. Now the task can be accomplished with only one trip, requiring only 1/3 of the time, or 2/3 man hours,.

Edited August 21, 2011 by thoughtfulfellow

[Guest]

I like your solution but for one minor problem:

now you must trudge back to end B to disconnect the wires and complete the labeling, This makes 30 KM. Of course your boss probably needs you to be at the end A so you will need to walk another 10KM. Assuming you are a regular jogger, this has taken a minimum of 3 hours (for the 30KM, or if walked at a fast pace 5hours. Your boss should have given you an assistant in which case, with the aid of a cell phone, your assistant keeps the battery at end A, you walk to end B. Now the task can be accomplished with only one trip, requiring only 1/3 of the time, or 2/3 man hours,.

a nice thought but,

You don't actually need the third trip even to preform labeling. when you are on side b, label the wires as follows. the first pair of wires in the first pair 1a and 1b. Repeat this process until all wires are labeled. Back on side A, you can label the wires the same way. The real problem is that you might need 2 batteries, as the first battery will might drain while you walk back from side B to side A. If this is an issue, you should still be able to accomplish the task in 30 km. And yes, the assistant is defiantly a good idea, you don't even really need a cell phone. You wouldn't even need a cell phone, as most any phone could be used with the cables (assuming there isn't too much noise).

[Guest]

a nice thought but,

You don't actually need the third trip even to preform labeling. when you are on side b, label the wires as follows. the first pair of wires in the first pair 1a and 1b. Repeat this process until all wires are labeled. Back on side A, you can label the wires the same way. The real problem is that you might need 2 batteries, as the first battery will might drain while you walk back from side B to side A. If this is an issue, you should still be able to accomplish the task in 30 km. And yes, the assistant is defiantly a good idea, you don't even really need a cell phone. You wouldn't even need a cell phone, as most any phone could be used with the cables (assuming there isn't too much noise).

I realized later that my explanation of the need for the third trip was insufficient.

You have not identified which pair is which on side B. So you will need to reconstruct your circuit, connect battery to the one end of the circuit and to one of the known wires from previous trip that was not connected at other end. Then return to B and repeat the process to identify which pair is which and label wires. My apologies for omitting this part of the explaination

[Guest]

the answer must be 20 km

[bhramarraj]

How come?

Make groups of wires--1wire, 2wires, 3wires,4wires,......, 14wires, 15wires. Note that they total to 120wires.

Now it is easy, walk 10km to other Telephone exchange, identify these 15groups with the help of continuity tester. and then proceed as under:

Put label no 1 on the Single wire of 1rst group.

Put label no.2 & 3 on two wires of the 2nd group.

Put label no 4, 5, & 6 on three wires of the 3rd group.....and so on.

After marking each wire as above, short wire no.1,2,4,7,11.... i.e. first wire of each of the 15 groups;

Then short wire no.3,5, 8,12... i.e. 2nd wire of each remaining 14 groups;

Then short wire no 6,9,13,18.... i.e. 3rd wire of each remaining groups; and so on....

After completing above task, walk again 10km to the first telephone exchange, and segregate the wires with the help of continuity tester as under:

Mark wire no 1 of single wire of group 1. Test continuity of this wire with wires of all other groups, and mark these wires as no 2,4,7,11,....,79,92,106.

Mark remaining wire of 2nd group as wire no 3.

Test continuity of the wire no 3, with wires of all remaining groups and mark those wires as no 5,8,12,.....,80,93,107.

Similar procedure will be repeated with other wires to segregate all wires numbered up to 120.

[bhramarraj]

Make groups of wires--1wire, 2wires, 3wires,4wires,......, 14wires, 15wires. Note that they total to 120wires. Now it is easy, walk 10km to other Telephone exchange, identify these 15groups with the help of continuity tester. and then proceed as under: Put label no 1 on the Single wire of 1rst group. Put label no.2 & 3 on two wires of the 2nd group. Put label no 4, 5, & 6 on three wires of the 3rd group.....and so on. After marking each wire as above, short wire no.1,2,4,7,11.... i.e. first wire of each of the 15 groups; Then short wire no.3,5, 8,12... i.e. 2nd wire of each remaining 14 groups; Then short wire no 6,9,13,18.... i.e. 3rd wire of each remaining groups; and so on.... After completing above task, walk again 10km to the first telephone exchange, and segregate the wires with the help of continuity tester as under: Mark wire no 1 of single wire of group 1. Test continuity of this wire with wires of all other groups, and mark these wires as no 2,4,7,11,....,79,92,106. Mark remaining wire of 2nd group as wire no 3. Test continuity of the wire no 3, with wires of all remaining groups and mark those wires as no 5,8,12,.....,80,93,107. Similar procedure will be repeated with other wires to segregate all wires numbered up to 120.

Sachin, am I right?

[Guest]

Sachin, am I right?

Your method definitely works! very clever.

[fabpig]

Loved this puzzle and the solutions given by Lt_Storm and bhramarraj.

bhrammaraj's solution works - as required - for this puzzle and anytime number of wires = (n+1)n/2. I'm guessing he's hit on the required solution purely by the fact that the number of wires is 120.

Lt_Storm., just a slight mod to your step 3. When you've established which pair is no. 1, no need to reconnect them. Live wire is 1A, dead wire is 1B. Then attach 1B to to positive to discover where 2A is.....and so on. Or is that what you said and I misunderstood?

Edited September 4, 2011 by fabpig

[wolfgang]

10 Km...

If he was at point A....he should join all the 120 ends together, then h`ll move 10 Km to the other end,,and He`ll check which wire gives no elecetricity with all others,and it is the damaged one.

[fabpig]

I think you're taking your lead from Optimus Prime who seemed to think there was a damaged wire, too. Unless I've misread the OP, there is no damaged wire.