String Puzzler, Number B

Oct 23, 1999

RAY: Ha! We're back! You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to discuss cars, car repair and, uh, the new Puzzler. Now, as promised, this is the second in a series of two...

TOM: Yeah. Of the string Puzzlers.

RAY: Of string Puzzlers. You may remember...

TOM: You might refer to it as "string theory," almost.

RAY: You could.

TOM: You could.

RAY: Yeah. You could.

TOM: And will the story here be spellbinding, as you promised?

RAY: Riveting.

TOM: Riveting?

RAY: Like blue jeans.

TOM: Riveting.

RAY: Not really. You may remember the other Puzzler in the spring regarding string.

TOM: Two pieces of string, you burn something.

RAY: There you go.

TOM: Time goes by, half an hour.

RAY: 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.

TOM: Right.


TOM: But at an unpredictable rate.

RAY: At an unpredictable, nonlinear 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.

TOM: Gotcha.

RAY: OK? 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.

TOM: Three?

RAY: Yes.

TOM: It's only got two ends. It's one piece of string.

RAY: No, you have two pieces of string.

TOM: Two pieces of string. Got it.

RAY: The first piece burns up in half an hour, OK?

TOM: Because it's lighting from both ends.

RAY: Both ends, OK. 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.

TOM: Boom. And that's 15 minutes.

RAY: And there you go, OK?

TOM: That's good.

RAY: That's good, yeah. And a lot of people got the answer to that.

TOM: Sure.


TOM: And I like it too.

RAY: So, now you're armed with the same two pieces of string.

TOM: Yeah.

RAY: Your Zippo lighter.

TOM: Yeah.


TOM: Yeah.

RAY: And that's it. And the question is: How do you measure six minutes?

TOM: Six minutes?

RAY: Yeah. In other words, I want you to tell me...

TOM: You might be cooking an egg, and that would be important.

RAY: How could you tell me, OK, boom! Right now, six minutes has elapsed from the...right? OK?


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.

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