Mathematic Mistake

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.

[ Car Talk Puzzler ]