# Answer to riddle #17: One Minute Inhomogeneous Fuse

17. You have a string-like fuse that burns in exactly one minute. The fuse is inhomogeneous, and it may burn slowly at first, then quickly, then slowly, and so on. You have a box of matches, and no watch. How do you measure exactly 30 seconds?

If you had 2 fuses could you measure 45 seconds?

If you had 2 fuses could you measure 45 seconds?

This is one is fairly simple if you can do it, and difficult if you can't...

Before reading the answer can I interest you in a clue?

Answer first:

The fuse will extinguish after half a minute. A one minute fuse is necessarily made up of two 30 second fuses. The problem is that because the fuse is inhomogeneous we can't know where the halfway point in time is. By lighting the fuse at both ends when the flames meet, both ends have necessarily been burning for 30 seconds. Obviously we are assuming that the fuse burns at the same speed in either direction. Which is perfectly reasonable in my opinion.

We can do to that 30 seconds fuse what we did to the one minute fuse, that is to say, burn it at both ends. Joining that all together the answer is to light fuse #1 at both ends, and fuse #2 at one end. After 30 seconds fuse #1 will burn out. Immediately after fuse #1 burns out light the second end of fuse #2. 15 seconds later after a total of 45 seconds fuse #2 will extinguish.

It's worth noting that this technique could be extended further. Trivially with 3 fuses we could time 52.5 seconds. If we can extinguish fuses too we could actually make a fuse of any length we require.

Answer first:

**Light the fuse at both ends!!!!**

The fuse will extinguish after half a minute. A one minute fuse is necessarily made up of two 30 second fuses. The problem is that because the fuse is inhomogeneous we can't know where the halfway point in time is. By lighting the fuse at both ends when the flames meet, both ends have necessarily been burning for 30 seconds. Obviously we are assuming that the fuse burns at the same speed in either direction. Which is perfectly reasonable in my opinion.

## Two Fuses, 45 seconds

This question is an extension of the first. We have now worked out how to time 30 seconds. If you burn a 1 minute fuse for 30 seconds you will effectively make a 30 second fuse.We can do to that 30 seconds fuse what we did to the one minute fuse, that is to say, burn it at both ends. Joining that all together the answer is to light fuse #1 at both ends, and fuse #2 at one end. After 30 seconds fuse #1 will burn out. Immediately after fuse #1 burns out light the second end of fuse #2. 15 seconds later after a total of 45 seconds fuse #2 will extinguish.

It's worth noting that this technique could be extended further. Trivially with 3 fuses we could time 52.5 seconds. If we can extinguish fuses too we could actually make a fuse of any length we require.

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