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 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?
(In reply to re(3): Independent solution
First of all, Alice's question is equivalent to "I am thinking of an integer between 0 and 1. Is your number my number or a two?" This equivalent doesn't have so many pedantic problems, and I hope it is clearer. My original question is just as good, but I use this equivalent for clarity.
No, I do not want to be pedantic. Arguing about diction, thumbs, and fingers is quite a waste of time.
You seem to be confusing the number of fingers Alice has behind her back with the number of fingers up behind her back. She may have five fingers, but she doesn't need to hold all five up. She could make a fist, for example.
You, too have misread the solution. Taking my equivalent statement, I'll go through why each of the March Hare's answers is what it is.
If the number is 3, the March Hare knows his number is neither a 2 nor Alice's number (a 1 or 0). The answer is NO.
If the number is 2, the March Hare knows his number is a 2, but not the same as Alice's number. Note that the answer to a question in "Is A or B true?" form is only NO when both A and B are false. The answer here is YES.
If the number is 1, the March Hare knows the number is not a two. The answer depends on whether it is equal to Alice's number. But he doesn't know Alice's number. His answer is I DON'T KNOW.
Edited on December 21, 2004, 5:55 pm
Posted by Tristan
on 2004-12-21 17:41:00