Jun 29, 2019
As promised, this is the second in a series of two string Puzzlers. You may remember the other Puzzler, with two pieces of string and a lighter.
Again, you have two pieces of string, and each of them will, if you light one end, will burn up in an hour's period of time, but at an unpredictable, non-linear rate.
So you can't say, "OK, look, I'm going to cut the thing in half and light one piece of it, and that's going to burn up in half an hour." All you know is that from beginning to end, the burn time is an hour. And the old Puzzler was: How could you measure a 15-minute period of time? And you did so by lighting three ends at once. The first piece burns up in half an hour.
The second piece burns for, obviously, half an hour, because it's, what? Lit at the same time as the other two ends. And then what you do is, you light the fourth end as soon as the first two flame-fronts have met. That's 15 minutes.
So, now you're armed with the same two pieces of string, your Zippo lighter, and that's it. And the question is: How do you measure six minutes?
RAY: Here's what you do. You tie one end of the string to the Zippo lighter. And you might not realize it, but you have constructed a pendulum.
You then take the lighter, and you'll light the other string at both ends and you immediately set the pendulum a-swinging, as they say, and you know it's going to take 30 minutes for that string to burn up. And what you do while the string is burning, you count pendulum swings.
Of course, everyone knows that a pendulum's cycle is independent of its amplitude. That's why pendula were so popular in clock use. Because as the pendulum seemed to slow down, it really didn't slow down. As the amplitude of the cycle decreased, the time it took for it to swing from point A all the way to point B on the other side and then back to point A remains the same. A little-known fact about pendulums.
Well, it's only true if the arc is small. If it gets too big, then there are other mathematics that get involved. Much too complex for me to explain here because I don't understand it. So, you count the number of swings, and when the thing has burned up completely, you say, "Ha. It took 30 minutes for--" let's pick a nice number like 300 swings of the pendulum.
Thirty divided by five, so 300 divided by five is 60 swings of a pendulum, and so you set it a-swinging again, and you count up to? Six minutes.