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 that 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?
15 comments:
Testing The wire with the battery and light bulb. hooks battery up goes to other end of wire which is 10km labels what ever wire made the light bulb turn. goes back to the other side which is another 10km unhooks the battery labels it plugs it in, and the other wire. Now walks another distance of 10km to get all the cables properly installed. which = 30 km.
for 120 wires, a lot!
1,160km put together, but 10km each of the 58 times -- for a pair of wires each time.
you will need to do it again for 58 times to identify each individual wires.
so 2,320km all in all. but the shortest distance you have to walk will still be 10km each time.
20 Km
hmmmm... Let's say, as a trainee technician, I run this idea by my boss: We can connect a bulb to one end of a wire, set this up on a table of sorts, and walk 10km to the other side. I can now touch the battery to each wire and see whether or not the battery lights up. When it does light up, I can label it and attach the battery to another wire. I can label this wire right here, and walk to the other side, and attach the bulb to other wires to see if they light up.
Basically, I start on side A to attach the battery to a random wire (#1), walk 10km to the other side and test wires with a battery to see which wire correctly powers the bulb, and, when I find the correct wire, label it #1. Then, I change the wire the battery is on, label it #2, walk back 10 km, and find which wire correctly powers the bulb.
10kmX120wires=120 km
Quite a workout! And it probably won't be accomplished all in one night :P
I think my boss would approve, right? :D
5km- fold the cable in half
30 km. The secret is to attach ends of wires together in bundles that include different numbers of wires, ranging in size from 1-15 wires. Using that technique, you should be able to narrow down which wire ends correspond with each other in two iterations.
So the steps would like like this: label then attach wire ends into bundles. Walk 10 km. Test. Make new, different bundles at the opposite end. Walk 10 km back. Disconnect previous wire bundles and test again to determine which ends go with which. Now walk 10 km back to correctly label the wires at the far end.
Pair off the 120 wires into 60 pairs at one end of the cable. Walk 10 kms to the other end of the cable. Use the battery and light bulb to identify each pair (the bulb will light up when a connected pair of wires are chosen and connected to the battery and light bulb). So, distance walked is 10 kms.
20km
you assemble 10 group of 11 and one of 10 at one place, identify each wire and group
go on the other side
test identify the groups
take one in each group, do the same, 10 group of 11 and one of 10
you are sure to have different groups
identify the wires and the groups.
return to the starting place
identify
now you have approximately one kind of tag of 11 groups and another kind of tag of eleven groups, 11 x 11 = 121
combine the two tags and you have each wire identified.
groups
1,2,3,4,5,6,7,8,9,10,11
41,42,43,44,45,46,47,48,49,50,51
wires
141,142,143
1151,1152,1153
the real answer is this one, instead, the 11 groups don,t work because you don,t know the precise group at the other end.
the good answer is groups, of quantity in numerical order, like a pyramide.
group 1 = one wire #1
group 2 = two wires #2,3
group 3 = three wires #4,5,6
and after you identify at one end
#1 to #120 for the wires
and 1 to 15 for the groups
at the other end
find the groups
1 to 15
1 to 120 for the wires
make groups as if it was a triangle
and you turn 60 degrees
15 different groups
wire 1 group one goes in group 15
wire 2 and 3, group 2 goes in group 14 and 15, respectivly
go to starting and identify the groups adding to what is already there.
wire #1 is identiffied
wire #2 goes from group 2 to group 15, you know wich wire change from group 2 to group 15, then you know it's wire 2.
wire #10 goes from group 4 to group 12
best would be to make a matrix of 12 *10... 12 wires in one group and 10 grps......
first make group of 12 wires at one end n connect battery... go to other end n identify these twelve and make 1 grp...in this way make 12 grps now ... from each grp take first wire n attach battery at other end identify first wire of each grp .. similarly all wires can be determined.......
If the wires are not wrapped in a non-conductive material, you do not need to attach the battery and the lightbulb to the ends. Any part of the metal will do as it all conducts electricity. As a result, you can stand in one location and connect the bulb and the battery to the wire a small enough distance from each other so that you can reach both of them without walking.
Therefore, the smallest distance in kilometers needed to walk in order to test the wires is 0.
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the shortest distance to label each wire is 10 km
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