Rope Riddle
Posted by Rob Herman at August 6th, 2006
GenCon Indy is next weekend, and I’m going. Due to work considerations I’m driving down either Friday after work or Saturday.
This one kind of sneaks up on you. I’d read it three or four times and never had an answer. Then reader John Rhoadhouse posed it to me the other day, and somehow I got a solution in only a couple of minutes; in another minute, he had a different, more elegant solution that I suspect is actually the intended one.
So here you go. Consider a certain kind of rope. It has the following characteristics: If you light one end, it will burn up in exactly one hour. But the rate of burning may vary unpredictably; for instance, the first half of the rope may burn in 10 minutes and the second half take 50; or it may be divided into many different areas; and there’s no way to tell. The upshot of this is that you can’t measure and cut the rope to measure a fraction of an hour.
Given two of these ropes, how can you measure 45 minutes?
Are the ropes presumed to be identical and burn consistently from one use to the next? If not, I’m still working.
No, they are not.
Here is my solution, by the way. A more elegant one exists.
Light one of the ropes at both ends. When it finishes burning, 30 minutes will have elapsed. Then cut the second rope into two pieces and light both ends of each piece. One piece may burn up before the other. If it does, cut the remaining piece in half and light both new ends. By keeping it burning in four places in this way, the second rope is made to burn for 15 minutes.
There’s really not much to be done with these ropes except burning them, which doesn’t seem to leave a lot of options. After spending a good deal of time attempting to figure out a simple solution, my mind slowly drifted towards the fantastical, and I slipped into madness. Ideas included tieing the ropes in a sailors knot and burning it, or coating them with glue and creating a makeshift sundial. Or perhaps greating a terrible Rope Golem, who would then murder a clock-maker, and bring to me the spoils of his dark hunt. Thankfully, a few choice words from Rob made the tumblers of my mind click into place, and the solution appeared, clear as day.
Since rob spoiled one I will spoil the solution I came up with after hearing his. light both ends of the first rope and one end of the second (this may require the help of a friend or in abscence of a friend, someone who likes to light things on fire) when the first rope is completely burnt (30 minutes later) light the other end of the second rope. When the second rope is burnt 45 minutes will have passed.
I was given a similar riddle but asked to measure 15 minutes. How is this done? ( I still don’t know)
I think the second half of my solution to the riddle is an acceptable way to measure 15 minutes. You only need one rope.
I praise God for answering my prayers. God, you are so wonderful, majestic. Jesus Christ, I adore Your Sacred Heart.d
I got it. Burn one rope on both sides so it burns for thirty minutes. Also, burn the other rope on one side. After thirty minutes you will have one burnt up rope with the other one burning on one side. Light the remaining rope that is burning on one side so that is burning on both sides. When it is done, you have measured 45 minutes.