Mathematic Mistake

Nov 21, 1998

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 noticed you didn't make any promises about the puzzler like it's scintillating, exciting, automotive, folkloric, brilliant!

RAY: I didn't really know which puzzler I was going to use.

TOM: OK.

RAY: Did I do the one with the poison wine glass?

TOM: Not!

RAY: Not recently. Here it is.

TOM: Oh, you have one!

RAY: Well, yes I do. Of course I have a puzzler!

TOM: All right.

RAY: Everyone, almost everyone remembers from his or her days in school the Pythagorean Theorem.

TOM: Yes.

RAY: A squared, plus B squared, equals C squared. And there are numbers like three, four and five; five, 12, 13 which satisfy that little equation.

TOM: Yeah.

RAY: And many hundreds of years ago a French mathematician by the name of Fermat said, this only works for squares. He said, if you take A, B, and C, integers A, B, and C...

TOM: Yes.

RAY: And there are some A squared plus B squared that will equal C squared, and we believe that. We know we have verification of it.

TOM: Yeah, we got real numbers that fit it.

RAY: We got real numbers that work.

TOM: Right.

RAY: He said, if it isn't squared but it's something else like cubes or to the fourth power or to the fifth power --

TOM: Forget it!

RAY: It doesn't work. So, for example, there is no A cubed plus B cubed, which equals C cubed.

TOM: That's what he said!

RAY: There is no A to the fourth plus B to the fourth that equals C to the fourth. As luck would have it, a young mathematician issues a statement that he has three numbers which prove Fermat's theorem is incorrect. He calls a press conference. Now, he doesn't want to divulge everything right away. He wants to dramatize, build a little bit, does he not?

TOM: Gonna give them one number.

RAY: He gives them all three numbers. He doesn't tell the power.

TOM: Ah!

RAY: He's going to give them A, B, and C. Here are the numbers, you ready?

TOM: Oh, I got to write this down.

RAY: A equals 91.

TOM: Yeah.

RAY: B equals 56.

TOM: I know the answer already.

RAY: Wait a minute!

TOM: Yeah, I'm gonna tell you what C equals.

RAY: I'm gonna tell you!

TOM: I'm gonna tell you what it is!

RAY: Go ahead.

TOM: A 147.

RAY: Wrong. C equals 121. So, it just so happens that at this little impromptu press conference, there are all these science reporters from all the po-dunky little newspapers that are around this town. And one of the guys, one of the reporters has his 10-year-old kid with him, because this happens to be a holiday. He's off from school. And the kid very sheepishly stands up and raises his hand, and he said, I hate to disagree with you, sir, but you're wrong. The question is, how did he know?

TOM: That the guy couldn't possibly --

RAY: That he couldn't dispute Fermat with these numbers.

TOM: With these three numbers.

Answer: 

TOM: Well, you know as I was driving home last week, the answer came to me in a flash.

RAY: Are you ten?

TOM: And I'm more than ten. I'm ten to a power.

RAY: Yes, you are.

TOM: I'm ten to the N.

RAY: Well, yeah, almost everyone is ten to some power.

TOM: Well, what occurred to me was C is 121 no matter what you do that. Any power is going to end in a one.

RAY: There you go.

TOM: And no matter what you do to the other ones, you can't make them come out to add up to one. You can't do it.

RAY: There you go. And that's exactly what the kid saw. He said 91 to the Nth power is going to end in one.

TOM: That's going to end in a one also.

RAY: Fifty-six to the Nth power is going to end in six. Six plus one has not to equal seven.

TOM: Not one.

RAY: The one's digit is going to be a seven. So the one's digit of the 121 to the Nth power has got to be seven and it can't be.

TOM: It can't be.

RAY: Who's our winner this week?

TOM: The winner is Mrs. Donna Marie Markey. Wow, she gave us a whole name like that. Donna Marie Markey from Albany, New York.

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