41

TUNNEL WIRES*

illustration

Engineers have just dug a tunnel under the River Spoog, and Bob Truffles has laid four electric cables along the tunnel. Unfortunately, the four cables look absolutely identical, and there are so many twists and turns in them that it is now impossible to tell which is which. He could walk through the tunnel untwisting the cables, but Bob has thought of a better way of sorting them out: his plan is to join two cables together at one end of the tunnel, starting with A and B, and then at the other end see which two cables make a complete electrical circuit when he puts power through them. The first test he does will obviously only tell him that two cables are either ‘A and B’ or ‘B and A’. Using this method, how many trips along the tunnel does he need to make in order to label all four cables correctly?