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 Guess my Number (Posted on 2004-12-20)
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?

 Submitted by Sam Rating: 3.7647 (17 votes) Solution: (Hide) There are several possible solutions. In general, the object of Alice's question should be to turn a binary question (yes-or-no) into a tertiary question (yes, no or "I don't know"). There are numerous questions of this type, of which my favorite is "I'm thinking of a number between two and three. Is my number higher than yours?" If the hare says yes, his number is one, if he says no, his number is three, and if he says that he doesn't know, his number is two. Federico Kereki also offered an alternative solution: Alice's aim is not to guess the Hare's number but to win a biscuit. In which case, a possible question would be "Is it the case that either 'no' is the answer to this question or you will give me a biscuit?" The Hare can't say "no", as this would be lying (because the first half of the "or" would be true) yet if he says "yes" he will be forced to give Alice a biscuit (the first half of the "or" would be false, so he'd have to make the other half true). These answers, of course, rely on the Hare being truthful.

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 Subject Author Date Yes and know Math Man 2016-05-08 19:42:15 another solution Froggie 2005-03-24 11:41:30 easy one ravi 2005-02-22 11:56:23 re: Another simpler solution? james 2005-02-22 01:42:36 think i got it dev e. 2005-02-07 02:40:19 re: K.I.S.S. 3llis 2005-01-13 13:57:47 the rude solution erdos 2005-01-01 20:11:52 re(5): Independent solution Penny 2004-12-27 15:09:35 re(4): Independent solution Hugo 2004-12-27 12:12:58 re(3): Independent solution Penny 2004-12-27 09:16:15 re(2): Independent solution Anna 2004-12-26 23:31:07 re: Independent solution Anna 2004-12-26 23:03:29 re: Only answer. Ross 2004-12-24 22:15:24 re: K.I.S.S. Captain Paradox 2004-12-24 02:02:19 Only answer. Vinnie 2004-12-23 20:38:27 eeeeeeeeeeeeerrrrrrrrrr megan 2004-12-23 10:23:33 guess (possible solution) David 2004-12-23 06:30:24 re: solution of sorts Juha S 2004-12-22 20:27:38 solution of sorts Juha Salonen 2004-12-22 19:45:52 re(4): Independent solution Tristan 2004-12-21 17:41:00 re: Independent solution Danny 2004-12-21 15:30:09 re(3): Independent solution Fletch 2004-12-21 09:19:07 re(2): Independent solution Tristan 2004-12-21 05:41:02 re: Another simpler solution? Jer 2004-12-20 18:53:29 Another simpler solution? Erik O. 2004-12-20 18:30:06 K.I.S.S. Penny 2004-12-20 17:39:51 re: Alternate possibility Fletch 2004-12-20 17:11:20 re: Independent solution Fletch 2004-12-20 17:04:43 Independent solution Tristan 2004-12-20 16:28:09 Alternate possibility Penny 2004-12-20 12:28:25 Impossible solution Penny 2004-12-20 12:12:31 Possible solution Federico Kereki 2004-12-20 11:39:55

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