Sorry, this doesn't work when n is one less than a triangular number. I think a third trip is needed for this case. Franklin T. Adams-Watters -----Original Message----- From: franktaw@netscape.net Start at one end, and connect a group of 15 wires, a group of 14, ..., down to 1 single wire not connected to anything. Go to the other end, and you can determine which group each wire is in by how many other wires it is connected to. Now, take one wire from each group, and connect them in a group of 15. This exhausts the group of 1; take one from each remaining group for a group of 14, ..., with one final wire unconnected. Go back to start, and again identify the groups by size. Now each wire at each end is identified with a unique pair of numbers a,b in the range 1 to 15 (with a+b>=15). This gives us a solution in 2 trips any time n is triangular. In general, n = k(k+1)/2 + r, with k>1 and 0<=r<=k, we can identify groups of 2 through k, plus a group of r+1 unconnected wires, and get a similar labelling in 2 trips. This leaves the cases n=1, which is already solved, and n=2, which as noted is unsolvable (unless we have 10 miles of patch wire and a team of attack dogs to keep off the electrical vandals). (Actually, there is another potential solution for 2 wires: connect one of them to ground at one end. We should be able to get a small current though ground for this wire. Whether this will light the bulb sufficiently to be visible is another question.) Franklin T. Adams-Watters -----Original Message----- From: Michael Kleber <michael.kleber@gmail.com> A week or two ago I heard for the first time the following enjoyable brain teaser: --------- A company has just buried a 10-mile-long cable containing 120 individual wires. Unfortunately, the project was overseen by a summer intern, and the sad result is that the wires are entirely unlabelled. Your job is to fix this mess: label each wire with the same name on both ends. The tools you have available are (1) a battery, (2) a lightbulb, and (3) an unlimited amount of patch cord. And (4) your feet, and no other form of transportation. You start at one end of the cable, and can do as much as you want there, but then you need to walk down to the other end and repeat. In how few trips down the length of the cable can you label the wires? --------- I have a second problem for follow-up, but I can only present it to people who have solved the first problem (for general n, of course, not just n=120). So tune in tomorrow for my tale of the ups and downs in solving this one, and perhaps help me out of my end state (down). --Michael Kleber p.s.: An interesting observation is that with n=2 the problem is unsolvable; there is no way to tell the two wires apart. -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun