Match Math

Feb 27, 1999

RAY: 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 the new Puzzler.

TOM: I'm excited! I'm really looking forward to this!

RAY: Oh, shut up!

TOM: Well you made it sound like such a big deal.

RAY: I didn't. I have two pairs of Puzzlers. Each pair is related, but not to the other pair. So, I have two Puzzlers that are similar, and I have another two Puzzlers coming up in the next few weeks that are also similar.

TOM: So you like to use these, like, sequentially? The similar ones?

RAY: Nonsequentially.

TOM: All non?

RAY: Yeah. Whatever case makes...

TOM: Or chronologically.

RAY: Or nonchronologically. And the beauty of these Puzzlers is their brevity. As opposed to last week's.

TOM: And their autonomy, I suppose.

RAY: Yes, they are autonomous.

TOM: And their relatedness.

RAY: And their relatedness.

TOM: In another sense.

RAY: The first one is arithmetic, and I used this on the staff last week.

TOM: Oh, man!

RAY: And they gave us the second one.

TOM: I do remember this!

RAY: All right. Go and get a bunch of matchsticks. We'll wait. Okay. Time's up. A little piece of paper and a pen, with which you can represent matchsticks. The numerator of this fraction is going to be Roman numerals, okay? And the Roman numeral is 23, which is two Xs...


RAY: Right.

TOM: And so you can see these being made up of matches. Two matches making up...

RAY: Anyway, there are a bunch of matchsticks, and make your line. And then the denominator is going to be 7 in Roman numerals, which is V-I-I. And then an equals sign--it's a little equation--equals 2, which is represented by two matchsticks, two vertical matchsticks, I-I. Okay? Roman numeral 23, X-X-I-I-I, over Roman numeral 7, which is V-I-I, equals 2, which is I-I, capital. Obviously, this equation is wrong.

TOM: Right. It's close!

RAY: It's close enough! What the heck.

TOM: For them, it is close enough.

RAY: Your challenge is to move one matchstick and make the equation correct. Now, you cannot turn it in, you cannot take one matchstick, for example, and make it 22 over 7 does not equal 3.

TOM: That was my pretty quick solution.

RAY: Yeah, that's bogus. That's completely bogus. So, an unequal sign is not allowed.

TOM: So, the question is, How can you move one matchstick and make this into an actual equation?

RAY: There you go. Now, if you think you...

TOM: Equation! Equality! So to speak.

RAY: Yes.

TOM: And, by the way, one of the issues that came up, if I take one of the matchsticks away from the X, I will be left with a sort of diagonal-facing line...

RAY: That's bogus. That isn't...

TOM: And that means...

RAY: Nothing.

TOM: No, you can't do that.

RAY: Right. The answer.

TOM: No, you can't do that!

RAY: You can't!

TOM: You can't do that.


RAY: OK? So, how can you move one matchstick to make the equation correct? Now, we're going to get a bunch of people to go, "Aw, man, this is bogus!" But...tough!

TOM: Well, that's what Puzzlers are all about! If the answer was simple and straight forward, it wouldn't be a puzzlement, now would it?

RAY: No, it would be a third-grade math problem.

TOM: It would be a third-grade math problem, exactly! These are brain-stretchers, man! I mean, so people who are going to complain: we don't want to hear it!

RAY: Exactly!

TOM: It's the very nature of puzzlement.

RAY: And I think the solution is elegant. You are going to take one away from the numerator.

TOM: Yeah, so, instead of saying 23, it's going to be 22.

RAY: And now you have 22 over 7, and with that one matchstick that you removed, a number should jump into your head.

TOM: Yes!

RAY: Because 22 over 7 equals pi, and you're going to put that matchstick that you've removed from the numerator atop the 2 on the right side of the equation, and --

TOM: Oh, man!

RAY: Although it isn't quite accurate, you're going to make the symbol for pi, thus making the equation correct, and I think it's pretty --

TOM: I mean, everyone has used that approximation. I use it all the time in my calculations!

RAY: Yes.

TOM: I don't like to write out 3.14159... and all those other digits. I just use 22 sevenths, and I'm sure everyone else does too, whether they'll admit it or not.

RAY: Who's our winner this week?

TOM: Shut up. The winner is Laura Leonard from Charleston, South Carolina.

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