"May I please have one of those biscuits?" asked Alice rather timedly, rather taken aback by the sight of her present company.

"A biscuit?? Oh, I don't know. Those are the March Hare's special un-birthday biscuits, don't you know. Can she have a biscuit, March ?" asked the Hatter.

"A biscuit?? One of mine? Hurmph. Ok, I'm thinking of an integer from one to three (inclusive). If you get it, you can have a biscuit. If not, I'm afraid you'll just have to leave" said the March Hare, leaning back.

"Oh goodness, I don't know" said Alice worriedly. "Couldn't I just get a hint?"

"Oh, all right..." the March Hare sighed. "You get to ask me one yes-or-no question, that's all"

Alice thought for a moment, then smiled, knowing exactly what to ask.

What question should Alice ask?

Alice asks: "Is n, the number you are thinking of, an odd number for which there are nonzero integers x, y and z such that x^n + y^n = z^n ?"

(ref: Fermat's last theorem)

If he is thinking of 1, he will answer "Yes"

If he is thinking of 2, he will answer "No"

If he is thinking of 3, he will scratch his head and say "I don't have the foggiest idea...."  

Edited on December 20, 2004, 12:18 pm

Posted by Penny on 2004-12-20 12:12:31