# Burning two fuses of variable length [duplicate]

This is an alteration (not a duplicate) of either the "Two Fuses burn for 45 minutes" or Burning ropes as timers questions. The fuses in my question are not identical and the answer(s) to the other questions are not identical to the answer I've accepted. In this scenario:

• I have two fuses of varying length.
• The fuses are not made of the same material.
• Each fuse does not burn at the same rate as the other.
• A fuse does not necessarily burn at the same rate throughout.
• Each fuse burns for 30 minutes.
• Folding one of the fuses in half does not guarantee that it'll burn twice as fast as the burn rate is not uniform.

How do I time 45 minutes by burning fuses?

• Duplicate doesn't mean exactly the same, it means same solution... Which in this case it is... Mar 28, 2017 at 14:03
• That's not how I define "duplicate": exactly like the original question Mar 28, 2017 at 14:05
• A dictionary is all fine and dandy, but this is the definition that matters Mar 28, 2017 at 14:14
• That's all very well, but it doesn't define what is considered to be a duplicate question/answer, only why and how questions are marked as duplicate. Mar 28, 2017 at 14:22
• Your only argument for how they're different is that the fuses are not identical. However that is completely irrelevant to your solution as you have stated: "Each fuse burns for 30 minutes". Regardless of how varied the fuses are, how different the burn rate is, it will always burn for 30 minutes. That makes any of the accepted solutions from the other duplicate puzzles, applicable to your question. Mar 28, 2017 at 14:41

## 2 Answers

Light one at both ends.
when it is burned out 15 minutes have passed.
Light the other fuse and wait 30 minutes.
Total: 15 + 30 = 45 minutes.

Additional reasoning.

you are going to say that lighting one at both ends does not ensure it will burn out in 15 minutes. I say, if you build such a fuse I'll buy you 10 beers.

• I don't think he can argue it won't burn in 15 minutes as it states that it will burn in 30 minutes, regardless of burning speeds.. Although I'm tempted by the beer offer to try and figure a way out ;) Mar 28, 2017 at 13:51

It's the same answer as the other question you linked to, just half the times for everything.

Folding one in half and lighting it together to get half the time (15 min), and letting the other burn normally (30 min). Together you'll get 45 minutes.

• The burn rate isn't uniform; there's no guarantee that it'll take half the time to burn half the length. Mar 28, 2017 at 13:52
• Folding it in half means that it burns at the rate of the fastest-burning part. It could take 15 minutes to burn 30% of the way and 10 minutes to burn the remaining 20%. Mar 28, 2017 at 13:59
• Whether you fold it in half or not really doesn't alter the fact that you've lit both ends and it burns in 15 minutes Mar 28, 2017 at 14:07
• We seem to be hung up on the halving part. So, let us say the fuse is laid out circularly, where both ends are simultaneously lit. The burn time will still be 15 minutes, regardless of the speed of the arcs. Mar 28, 2017 at 14:30
• ^ That works too.. I was just trying to pull from the other question's answer to show they work the same way. Mar 28, 2017 at 14:31