RAY: Hi, we're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to talk about cars, car repair and the...the answer to last week's Puzzler.
TOM: What was it?
RAY: Here it is. This is the second...
TOM: Oh! The string!
RAY: Yes.
TOM: Was it the string Puzzler?
RAY: Yes, this is the second in a string of string Puzzlers. We did the first string Puzzler back in the spring. That was the spring string, and here are the facts: You have two pieces of string that each take exactly an hour to burn, but their burn rates are not linear. So, one string may burn quickly for five minutes or 15 minutes, and then slowly for the next 10 minutes, and so on. But we know that after exactly an hour...
TOM: Both strings are gone.
RAY: If they're lit at one end, will be completely burned up.
TOM: Burned to a crisp. Mon dieu!
RAY: The spring string, the Bruce Springsteen Puzzler, was this: How could you measure a 15-minute period of time with this, knowing these things? That you have two strings.
TOM: Yeah.
RAY: Both of which will burn up in an hour if lit at one end, and all you had [was] these two strings and the cigarette lighter. You had a Zippo lighter or some such thing, OK? And the way you did that, you took the two strings and you light three ends at once, right?
TOM: It doesn't matter which three?
RAY: Any three ends.
TOM: Any three ends.
RAY: The first piece burns up entirely in half an hour, right? If it takes an hour to burn the whole thing, if you light it at both ends, it's gonna burn up in half an hour, OK? And because you've lit both ends, it had to burn up in a half an hour. The second piece burns for half an hour because it was lit at the same time as the other two ends.
TOM: Right.
RAY: OK? So, then you know there's half an hour's burn time left in the second string. You light that at the other end, and - voila--you've got 15 minutes, right?
TOM: Sure. I think I follow that.
RAY: Right.
TOM: Yeah, so what was this question this time?
RAY: So now the Puzzler was: How do you measure six minutes?
TOM: Six minutes!
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 one...now 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?
RAY: OK?
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. And for having his correct answer selected at random from among the thousands of correct answers that we received, Ed's gonna get a copy of our brand new CD about fathers and cars, the title of which is Why You Should Never Listen to Your Father When It Comes to Cars. Our kids actually suggested that title. God bless their rotten, black, little hides. So, congratulations, Ed, and enjoy the CD.
RAY: We'll have a new, I would say, semiautomotive...
TOM: Ah, quasi-automotive.
RAY: Semiautomotive Puzzler coming up in the third half of today's show, so stay tuned for that. In the meantime, you can call us and ask any question...
[ Car Talk Puzzler ]
