September 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?

*This puzzle was taken from Norman Do's regular Puzzle Corner column for the Gazette of the Australian Mathematical Society. Why not try your hand at the problems in the latest Puzzle
Corner?*

If you are stumped by last issue's puzzle, here is the solution.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

## Comments

## I have an alternate solution

Bend one of the fuses so the two ends are touching at the center point of itself, then light the center of that fuse, and one end of the other fuse. When the bent fuse has burned completely, you have 3 quarters of an hour remaining on the other fuse.

This works because lighting the center of the fuse is like cutting it in half, doubling it's burning time, just like lighting both ends at once. If both ends are lit, in addition to the center, the total burning time is reduced to one quarter of it's original time.

## Correction to last post

Sorry, I found this puzzle on another website that didn't have the ability to comment, and that version was using hours instead of minutes

## Problem with alternate solution

The offered alternative solution only works if the fuses burn at a constant speed. The questions says we can't assume this.

## FUSES SOLUTION

LIGHT ONE FUSE AT BOTH ENDS AND AT THE SAME TIME LIGHT THE OTHER AT ONE END

THE TIMING STARTS NOW

AFTER 30 SECONDS THE FUSE THAT WAS LIT AT BOTH ENDS WILL HAVE PASSED AWAY !

AT THIS INSTANCE LIGHT THE OTHER FUSE AT THE END THAT IS STILL INTACT

WHEN THIS HAS DIED ANOTHER 15 SECONDS WILL HAVE GONE

45 IN TOTAL

## Assumption

"AFTER 30 SECONDS THE FUSE THAT WAS LIT AT BOTH ENDS WILL HAVE PASSED AWAY !"

How do you know that. Burning speed is not constant.