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