It's a Puzzlement

Exact Ranking

by John P. Robertson

David Bickerstaff had the following puzzle published in the American Math-ematical Monthly in 1961. It is based on an actual incident. He asked the editor of a college magazine to tell him the exact ranking of the five top placers in a contest. The editor declined but offered to pass judgment on his guesses. His first guess was A-B-C-D-E. He was informed that he was most skillful at being wrong, as he had each person out of her true position and not one in his ranking followed her immediate predecessor. He then asked if it were D-A-E-C-B. Now he was told that he had two in the correct position and two correctly following her immediate predecessor. David was then able to determine the correct ranking. What is it?

Two Fuses

The puzzle involved two fuses. Each would burn in exactly one hour, but not necessarily uniformly, and the two did not necessarily burn at the same rate over corresponding segments. The question was how to time 15 minutes. For extra credit an additional problem was to time 15 minutes using just one fuse.

Abbe Bensimon's solution to the first problem was to light one fuse at both ends, and the second one at one end. When the first fuse burns out, light the second end of the second fuse. From this point until the second fuse burns out will be 15 minutes. For the second problem she suggests lighting both ends of one fuse, and, at the same time, lighting that fuse somewhere in the middle. When one segment burns out, light the remaining one in the middle. By keeping four ends burning in this way, the one fuse will burn out in fifteen minutes.

Steve Fallon, Leigh Halliwell, Greg Hansen, Noel Hehr, Michael Lewis, Orin Linden, Doug McKenzie, Dave Skurnick, and Anthony Yau also submitted solutions.

Springs and Strings

A number of solvers were not listed in the last issue. They are Jason Israel, Paul Ivanovskis, Ignace Kuchazik, Aaron Schindler, and John Soutar.