Matchstick Mathematics Number 3-E

Jun 26, 1999

RAY: Hi, we're back, and 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. This is another of the very famous "matchstick" puzzles.

TOM: Ah, in a long series, the "matchstick puzzle" series.

RAY: Very long series. Most of the kids are out of school or close to being out of school. I thought that before their minds get too dull, this would be a good little puzzle to just keep them going a little longer, maybe.

TOM: So is that a hint, kids?

RAY: Everything is a hint.

TOM: Everything is a hint. From the time you say the word "Puzzler," and maybe even prior to that, every word is a hint.

RAY: All right, get a bunch of matches, matchsticks--wooden matches preferably.

TOM: Or toothpicks.

RAY: Or toothpicks.

TOM: You don't want kids playing with matches.

RAY: Matches. We don't need no stinking matches!

TOM: I've seen it coming a mile.

RAY: Get a bunch of toothpicks and make the following equation with Roman numerals: XI, that's 11, with matchsticks or toothpicks, plus I, then an equals sign (=) X. So you have XI plus I...

TOM: Eleven plus one.

RAY: Eleven plus one equals ten.

TOM: That's not right.

RAY: That's not right and the question very simply is: What is the fewest number of matches you can move to get an equation that is correct? You can't throw away any matches.

TOM: You gotta move one or two, three.

RAY: I asked what's the fewest number.

TOM: Fewest number.

RAY: Fewest number you can move. I want to give a hint.

TOM: Wait a minute, I have a question. Can you use the plus sign or the equals sign as well?

RAY: Well, for example, you can take the vertical piece of the plus sign and take it away so you would have 11 minus 1 equals 10, but what would you do with the thing you took away? Stick it in your ear? You've got to use them all.

TOM: Oh, I would put it on top of the equals sign.

RAY: Oh, that's bogus. That's absolutely bogus.

TOM: Then it would be 11 minus 1 absolutely equals 10.

RAY: I will give you the hint.

TOM: So you could do that. You can move those things around as long as you don't lose any.

RAY: I presented this to my son the other day, my younger son, and he looked at it for a minute. We had it set up on the kitchen table.

TOM: With matches or toothpicks?

RAY: Cigars.

TOM: Cubans?

RAY: Yeah, he leaves the room, and as soon as he re-enters, he has the answer.

RAY: Of course, I obfuscated. As you'll soon find out.

TOM: But the basic question was, how...what is the least number of matches you can? Is that the question?

RAY: Yes, the smallest number of matches.

TOM: Yeah, yeah.

RAY: OK. And the hint that I gave is that when I presented this to my younger son, Andrew, the other day, he got the answer after he had left the room and returned.

TOM: That's brilliant. I thought that was brilliant.

RAY: A brilliant, brilliant hint.

TOM: A brilliant hint. That's what I'm saying. I thought that was a brilliant hint--after I knew the answer, of course.

RAY: As he stood there at my side and looked at the equation, he said, "Gee, I don't know, Dad." He said, "I can certainly move a match and make the thing correct," he said. And I told him, "Well, you don't have to move any matches." Wow. And he walked out of the room bewildered, and when he came back...

TOM: Was he just bewildered or was he going, "Stupid jerk." He mumbled.

RAY: But when he came back he had the answer, because if you walk around to the other side of the table and look at the equation...

TOM: You see it upside down.

RAY: You see it as X equals I plus IX.

TOM: Man.

RAY: And you have to move no matches to make the equation correct. Who's our winner this week, Tommy?

TOM: Wow. How would I know, I've been so spellbound here I haven't even looked. Here it is. The winner is Jim Shaughnessy from Troy, New York.

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