String Puzzler, Number B

The Puzzler

RAY: Six minutes. I'll make it easier. A minute, anything.

TOM: Oh.

RAY: Well, it has a completely different answer.

TOM: Oh, I knew it! I knew when you were being so generous, I said, "Gee, you want to give such a big hint?" And little did I know that the big hint was a big red herring. I should have known you wouldn't be so generous.

RAY: I didn't even give a hint, did I?

TOM: Well, you repeated how the old one was done! That was unnecessary because you were trying to lead everyone down the wrong track.

RAY: Oh.

TOM: And now you just admitted that.

RAY: That was awfully sneaky of me, wasn't it?

TOM: Yeah, it was very sneaky.

RAY: Well, here's what you do.

TOM: Here's what you do, yeah?

RAY: You take the Zippo lighter and you tie it to pay attention!

TOM: Tie it to a doorknob?

RAY: To a doorknob and to one of your incisors!

TOM: Pull the string and it opens the door, and there's the clock right there in the other room. Is that it?

RAY: Not quite. But close. You tie one end of the string to the Zippo lighter.

TOM: Yeah.

RAY: OK? And you might not realize it, but you have constructed a pendulum.

TOM: Oh, man.

RAY: You then take the lighter, and you'll light the other string at both ends.

TOM: Not the one that you just tied to the...?

RAY: No.

TOM: No, the other one?


TOM: You light it at both ends?

RAY: You light it 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.

TOM: Right.

RAY: And what you do while the string is burning...

TOM: You count pendulum swings.

RAY: You count pendulum swings, and of course, everyone knows that a pendulum's cycle is independent of its amplitude. That's why pendula were so popular in clock use.

TOM: Yes.

RAY: 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...

TOM: The other end.

RAY: And then back to point A?

TOM: Remains the same.

RAY: Remains the same.

TOM: A little-known fact about pendulums.

RAY: 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...

TOM: You flunked 801?

RAY: I don't understand it.

TOM: Was that covered in 801?

RAY: 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.

TOM: Yeah.

RAY: Therefore, if I divide this by five...

TOM: Which will be six minutes.

RAY: Which will be six minutes.

TOM: 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?

RAY: You count to six minutes.

TOM: Oh, man.

RAY: So you can count any amount of time.

TOM: Anything. Six minutes was a red herring as well.

RAY: Right.

TOM: See, if you had said, "How could you count up to anything?"...

RAY: Well, I considered...

TOM: No, that would have been too easy.

RAY: I was considering having the string tied to a red herring.

TOM: These Puzzlers are getting really, really interesting. Oh, man, the winner is Ed Krystlemeyer, from Mt. View, Wyoming.

[ Car Talk Puzzler ]

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