The 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. I'm ten to the N. What occurred to me was C is 121 no matter what you do that. Any power is going to end in a one. 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.
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 ]