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December 2009

## Fun with fuses

You are given two fuses, each of which burns for exactly one minute. However, since the fuses are not of uniform thickness, they do not burn at a uniform rate along their lengths. How can you use the two fuses to measure 45 seconds?

## Solution

The trick to solving this puzzle is to consider lighting the fuses at both ends. We know they don't burn evenly, but by lighting a fuse at both ends it will burn twice as fast, and burn itself out in half the time.

So to start off with light fuse A at one end, and light fuse B at both ends. Fuse B will burn out after 30 seconds. Fuse A has now been burning for 30 seconds and so has 30 seconds left to burn, so at this point light the other end of Fuse A. Fuse A is now burning twice as fast, and will extinguish after a further 15 seconds (half the time it had left to burn). Therefore Fuse A has burned for 45 seconds in total.

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