Puzzler Answer: Mathematic Mistake

RAY: Everyone, almost everyone remembers from his or her days in school the Pythagorean Theorem. A squared, plus B squared, equals C squared the sides of a right triangle and C is the hypotenuse. We all know that there are certain numbers that work for this formula, like 3, 4, 5, 5, 12, and 13, one, one square is square of 2 da, da, da. Now many hundreds of years ago, a French mathematician by the name of Fermet declared that this formula only works for squares. Are you a square? It works. If you take the integers A, B, C and you take them for the third, fourth, fifth power or whatever, it doesn't work. For example, there are no integers for which A cube plus B cube equals C cube he says. He writes this in a paper and says by the way, I have a neat little proof, but I didn't have room to write it in the margin. But trust me. And that's why that theorem is now known as Fermut ?? joke. Anyway, as luck would have it, a young mathematician issues a statement that Fermut is wrong, and he has the numbers to prove it. He calls a press conference. He says I have three numbers to prove Fermut is wrong, and I will give you the numbers first and then I will give you the powers. He wants to build the drama you know next week. The numbers he says are 91 is A, B is 56, and C is 121.

TOM: And he's claiming that at some power, A to the N plus B to the N is going to equal C to the N.

RAY: There you go.

TOM: Got it.

RAY: It just so happens that at this press conference there are some science reporters, and one of the reporters has his 10-year old kid with him. And the kid very sheepishly raises his hand and stands up and says I hate to disagree with you sir, but you're wrong. The question is how did the kid know that this mathematician couldn't dispute Fermut with these three numbers, and the numbers were 91, 56, and 121.

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 and for having her correct answer chosen at random this week, Donna Marie! Donna Marie Markey from Albany New York!

RAY: Gets a new washer and dryer!

TOM: Almost. She will get one one hundredth of a washer and dryer. She will get a $25 gift certificate to the Car Talk Shameless Commerce Division.