An electrician is faced with the following annoying dilemma. In the basement of a three-storey house he finds, bunched together in a hole in the wall, the exposed ends of eleven wires, but he has no way of knowing which end above belongs to which end below. His problem is to match ends.
To accomplish his task, he may do one of two things:
- · Short circuit the wires at either end by twisting the ends together in any manner he chooses.
- · Test for continuity of a closed circuit by means of a “continuity tester”, consisting of a battery and a bell. The bell rings when the instrument is connected to two ends of a continuous unbroken circuit.
Not wishing to exhaust himself with needless stair climbing and having a passionate interest in operations research, the electrician sat down on the top floor with a paper and pencil and soon devised the most efficient method of labelling the wires. What was his method?
On the top floor, the electrician shorted five pairs of wires by twisting them together, leaving the last wire free. Then he walked to the basement and identified the lower ends of the shorted pairs by means of his continuity tester. He labelled the bottom ends of the first shorted pair A1 and A2 respectively, the ends of the second shorted pair B1 and B2 respectively, the ends of the third shorted pair C1 and C2 respectively, the ends of the fourth shorted pair D1 and D2 respectively, the ends of the fifth shorted pair E1 and E2 respectively and the unpaired end he labelled F. He shorted the bottom ends of the wires by leaving A1 free, connecting A2 to B1, B2 to C1, C2 to D1, D2 to E1, and E2 to F.
Back on the top floor, he removed all the shorts but left the pairs twisted together at insulated portions so that the pairs were still identifiable. He then checked for continuity between the free wire, which he knew to be the upper end of F and some other wire. When he found the other wire he was at once able to label it E2 and identify its mate as E1. He next tested for contintuity between E1 and another end which when found could be marked D2 and its mate D1. Continuing in this fashion, the remaining ends were easily identified.