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## Rope burning logic problem

Last week, Abbas Raza of 3 Quarks Daily posed a list of logic problems to the site’s readers. I’d seen some of these problems before and I didn’t have the time to work through the unfamiliar ones, but my favorite was the very first question:

You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: if you light one end of the rope, it will take exactly one hour to burn all the way to the other end. But it doesn’t have to burn at a uniform rate. In other words, half the rope may burn in the first five minutes, and then the other half would take 55 minutes. The rate at which the two ropes burn is not necessarily the same, so the second rope will also take an hour to burn from one end to the other, but may do it at some varying rate, which is not necessarily the same as the one for the first rope. Now you are asked to measure a period of 45 minutes. How will you do it?

For those in the US, this is a little something to keep the conversation at the holiday dinner table interesting. I’ll post the answer here this weekend…good luck.

Update: Alright, here’s the answer. Light both ends of rope A and one end of rope B. After 30 minutes, rope A will be completely burned up and there will be 30 minutes of rope B left. Light the other end of rope B; it will burn up in 15 minutes. Total time elapsed since starting the ropes on fire: 45 minutes.