The Mad Hatter poured Alice another cup of tea and set the teapot down.
"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 unbirthday 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 yesorno question, that's all"
Alice thought for a moment, then smiled, knowing exactly what to ask.
What question should Alice ask?
(In reply to
Independent solution by Tristan)
Alice puts her right hand behind her back. She asks, "Is the number four less than the number of fingers up on my right hand, or is it a two?" (This question is asked as a yesorno question, not a whichisit question.)
If the number is 3, the March Hare will say, "No." If the number is a 2, he will say, "Yes." If it is a 1, he will say "I don't know."
I don't think that he can know the answer to any of them if he doesn't know how many fingers she is holding up. If the number is 2 then it could be yes or no depending on how many fingers she has up. Yes if she's holding up 4. No if it's anything else. If the number is 3 and she is holding up 4 fingers or less then the answer is no. But if she's holding up 5 fingers then it's yes.

Posted by Danny
on 20041221 15:30:09 