It's a Puzzlement

Two Fuses

by John P. Robertson

You have two fuses, each 12" long. Each fuse burns in exactly one hour, but does not necessarily burn at a uniform rate. Also, the two fuses do not necessarily burn at the same rate over corresponding segments. But a given segment on a given fuse burns in the same amount of time in either direction. How do you use these two fuses to time 15 minutes? Extra credit—how do you time 15 minutes using only one fuse?

Springs and Strings

The last puzzlement involved a weight suspended from a combination of springs and strings. The problem was to determine the final position of the weight after one of the strings was cut. Philip Heckman observes that, surprisingly, the final position of the weight is higher than the original position. In the initial position, the full weight is applied to each of the springs. After the string between the springs is cut, each spring supports only half the weight. Thus, each spring contracts to 5" length, and the weight winds up 26" from the ceiling.

Various solvers pointed out that the puzzle ignored the weight of the strings, the fact that under zero weight real springs would not contract to length zero, and some other items.

As presented in the puzzlement, the initial configuration seems to have only one equilibrium position. The position after the string is cut is not an equilibrium position for the initial position because now the distance between the springs is 16", while the string that was cut is only 10" long. I wonder whether there are any configurations that do have two, or more, equilibrium positions?

Solutions were also sent in by Chris Cooksey, Walter Fransen, and David Skurnick.