Answer: Tuesday Teaser #27
1. You have only one such rope. How will you measure 30 minutes?
For this problem, simply burn the rope from both ends. It will then burn twice as quickly as usual and hence will take 30 minutes to burn through.
2. You have two such ropes. How will you measure 45 minutes?
For this problem, burn the first rope from both ends, and at the same time light one end of the second rope. When the first rope burns out, half an hour will have past and the second rope will have 30 minutes left to burn. At this point, light the other end of the second rope so that it burns through twice as fast, leaving a total of 45 minutes.
3. You have only one such rope. How will you measure 15 minutes?
For this problem, we need to light the rope from “four ends” so that it burns through four times faster. The question is where to get the extra two ends from. My suggestion would be to cut the rope into four pieces and light one end of each of them. Then when the first rope finishes, cut a piece from one of the other ropes and light one end of that. This process would then be repeated until all of the rope had burnt through. By burning it from four ends throughout, you would then have measured 15 minutes. The mathematician in me doesn’t particularly like this solution as it theoretically relies on an infinite number of cuts, but in practice it would seem to work very well.
