Fuses

A very nice puzzle from Problem Solving by Thomas DeFranco and Charles Vinsonhaler.

Puzzle

You have two fuses, each twelve inches 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? (You are allowed as much time to prepare as you wish.)

Extension

How do you time 15 minutes using only one fuse?

Help

Hint

Given one fuse, can you think of a way to time exactly 30 minutes?

Solution

Take one of the fuses, fuse 1, and bend it so that it forms a loop. Take the other fuse, fuse 2, and place it so that one end touches both ends of fuse 1. Light this area where all three ends meet. Then fuse 1 will finish burning in exactly 30 minutes, at which time fuse 2 has another 30 minutes remaining. Thus we should light the other end of fuse 2 at this time. From this point on it will take 15 minutes for what remains of fuse 2 to finish burning.

References

Problem Solving by Thomas DeFranco and Charles Vinsonhaler.