The electrician problem
You’re an electrician working at a mountain. There are N wires running from one side of the mountain to the other. The problem is that the wires are not labeled, so you just see N wire ends on each side of the mountain. Your job is to match these ends (say, by labeling the two ends of each
wire in the same way).
In order to figure out the matching, you can twist together wire ends, thus electrically connecting the wires. You can twist as many wire ends as you want, into as many clusters as you want, at the side of the mountain where you happen to be at the time. You can also untwist the wire ends at the side of the mountain where you’re at. You are equipped with an Ohm meter, which lets you test the connectivity of any pair of wires. (Actually, it’s an abstract Ohm meter, in that it only tells you whether or not two things are connected, not the exact resistance.)
You are not charged [no pun intended] for twisting, untwisting, and using the Ohm meter. You are only charged for each helicopter ride you make from one side of the mountain to the other. What is the best way to match the wires? (Oh, N>2, for there is no solution when N=2.)
Suppose that there are N wires.
If N is even: At the first end, connect pairs of wires together,
leaving two wires unconnected. Go to the other end. Find a pair of
connected wires, and number them #2 and #3. Find another pair and
label them #4 and #5. Repeat for all of the pairs, with the last pair
labeled #N-2 and #N-1. There remains two wires that are not connected
to each other. Label one of these #1 and the other #N. Connect #1 to
#2, #3 to #4, etc, leaving #N-1 and #N unconnected. Go back to the
first end. One of the originally unconnected wires still is
unconnected. Label it #N and label the other originally unconnected
wire #1. Now find the wire connected to #1 and label it #2. The wire
that originally was connected with new wire #2 can be labeled #3. The
wire that is now connected to the newly labeled #3 is #4. In this way,
all of the wires
can be identified on both ends in two trips (one round trip).
If N is odd: At the first end, connect pairs of wires together,
leaving one wire unconnected. Label it #1. Go to the other end. Find a
pair of connected wires, and number them #2 and #3. Find another pair
and label them #4 and #5. Repeat for all of the pairs, with the last
pair labeled #N-1 and #N. There remains one wire that is not connected
to any other wire. Label it #1. Connect #1 to #2, #3 to #4, etc,
leaving #N unconnected. Go back to the first end. Find the wire
connected to #1 and label it #2. The wire that originally was
connected with new wire #2 can be labeled #3. The wire that is now
connected to the newly labeled #3 is #4. In this way, all of the wires
can be identified on both ends in two trips (one round trip).
Your Answer
More puzzles to try-
Enemy in three letters
Synonyms of enemy in three letters ?Read More »Which family do you think is likely to have a girl ?
You along with your friend are standing in front of two houses. Each of those houses inhabits a family with ...Read More »Why didn’t they?
There was a train going along the track and a car coming along the road at a right angle to ...Read More »Never Falls
Iron roof, glass walls, burns and burns never falls!!!Read More »How can she threaten her students with the single detention so they all take the quiz?
A teacher decides to give a pop quiz one day but all of her students refuse to take the quiz ...Read More »Time Formula
Can you tell us the current time to see the below representation? 0 ========= B.Sc LLBRead More »Find The Letter
A B C D E F G H These are the letters given to you. Now you have to find ...Read More »Wise Woman riddle
A wealthy wise old woman feared that her son was lazy and as a result rather stupid. When the old ...Read More »When did the girls went for picnic puzzle
Sofia, Angelina & Emma went for a picnic. After a few days they forgot the date, day and month on ...Read More »Can be swallowed both way
What can be swallowed, but can also swallow you ?Read More »Right triangle with a 23
Find two positive integers that together with 23 are the lengths of a right triangle. Hint: There’s a simple technique that, ...Read More »Cheapest word processor riddle
Last week I bought a word processor small enough to fit in my pocket. It can write in any language ...Read More »Five digit number of which First and last digits are same riddle
I am thinking of a five digit number such that: First and last digits are same, their submission is an ...Read More »Two in a corner
Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?Read More »What is seen in the picture which made husband KILL her beautiful wife?
What is seen by the husband in the picture that made him MURDER his wife?Read More »Alphabet Puzzle
You can only use any letter once, what are the largest and smallest numbers that you could write down in ...Read More »Ranking The Students
In a class test the rank of five students are: Joe did not come second Julie did not come first ...Read More »Can you find that logic?
DEAD, BALL, FEAR, SHOP The above mentioned letters have been placed in that order using a logic. Can you find ...Read More »Let’s Play Chess
* You are playing with white and its ur turnRead More »Identify the correct statement.
Here are three answers: 1. Answer A 2. Answer A or B 3. Answer B or C There is only ...Read More »