# You have 2 fuses and a lighter. When each fuse is lit, it takes exactly one hour to burn from one end to the other. You can assume that both of the fuses are identical.

# Using only those 2 fuses and the lighter, how would you measure a period of exactly 45 minutes?

When you first think about this puzzle (it may even be called a riddle), it may seem impossible to find a solution. But, there must be an answer since someone is asking this question. What do we have and what do we know? We have 2 fuses, a lighter, and we know each fuse takes one hour to burn. It seems like all we can do is measure one hour, since we can’t make any other assumptions. So, this means we must really try to think creatively, because there is something here that we are missing.

## Thinking “outside the box”

What if we start the flame from the middle of a fuse? Would that allow us to measure half an hour? Actually, no it would not, because we can not assume that half of the **length** of the fuse would burn in half an hour – it may just be that 1/10th of the length of the fuse take 50 minutes to burn and the other 9/10ths of the fuse takes 10 minutes to burn. So, starting the flame in the middle of the fuse is not a valid option.

What would happen if we burn a fuse from both sides? That sounds interesting. Well, what would happen is that the fuse would burn out in just 30 minutes – this is because the fuse would be burning from both sides and the flames would burn until they meet each other and extinguish after exactly 30 minutes. Well, that sounds very useful – because we can now measure 30 minutes!

## We made an extra assumption here – that the fuses burn at a uniform rate

We want to make a little side note here: we are assuming that the burn rate is uniform – meaning that burning 1/4th of the fuse from one end will take exactly the same amount of time as burning 1/4th of the fuse from the other end of the fuse. It could potentially take 1 minute to burn the first 9/10th of the rope and 59 minutes to burn just the last 1/10th of the rope if the burn rate were not uniform. This was not an assumption stated in the problem, but it is important, and if you ever do encounter this question in an interview it is an assumption you should probably make whether the interviewer states it or not (some interviewers are bad enough to just ask this question without really understanding) because there really would be no solution to this problem if we did not assume the burn rate was uniform. Anyways, that is our little side note, please carry on and read the entire solution below.

Now that we can measure 30 minutes, how could we measure 15 minutes more to get 45 minutes total? Well, can we use the idea of burning a fuse from both sides to measure that extra 15 minutes? That sounds like it has potential – what if we burn fuse # 1 from both ends, and we burn fuse #2 from only one end. Then, after 30 minutes has passed, we can burn the other end of fuse #2. Fuse #2 would finish burning in 15 minutes because it has already has 30 minutes worth of time burned from it, but it is also burning from both ends – so that cuts the burning time in half. And 30 + 15 would give us 45 minutes – so we finally have an answer!

## 2 Ropes 45 Minutes

You may also see a variation of this puzzle being asked with ropes instead of fuses. But, keep in mind that the answer is exactly the same as the one we gave above whether you are dealing with ropes or fuses.