Pollywogs!

I find that when I have a problem or a question, simply writing it in the form of a question, or exploring it in writing by trying to describe what I am thinking will help me either figure it out myself or at least understand better what is going on:

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?

If you light both ends of one rope, it will burn in exactly a 1/2 hour. Thus, burn one rope from both ends and the other rope from only one end. Once the one rope (which is burning from both ends) finally burns out (and you know a 1/2 hour has elapsed), you also know that the other rope (which is buring from only one end) has exactly 1/2 hour left to burn. Since you only want 45 minutes, light the second end of the rope. This remaining piece will burn in 15 minutes. Thus, totaling 45 minutes.

I didn't think this was possible until I began writing out why it was impossible until I was confronted with the fact that not only was it possible, it made perfect sense.  Just reading it over initially, my mind didn't make 'the connection'.  I'm glad I took the time to understand it, it was more enjoyable than not figuring it out and saying 'oh that is fucking retarded'…