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Guess my Number (Posted on 2004-12-20) Difficulty: 2 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionYes and knowMath Man2016-05-08 19:42:15
another solutionFroggie2005-03-24 11:41:30
easy oneravi2005-02-22 11:56:23
re: Another simpler solution?james2005-02-22 01:42:36
think i got itdev e.2005-02-07 02:40:19
re: K.I.S.S.3llis2005-01-13 13:57:47
the rude solutionerdos2005-01-01 20:11:52
re(5): Independent solutionPenny2004-12-27 15:09:35
re(4): Independent solutionHugo2004-12-27 12:12:58
re(3): Independent solutionPenny2004-12-27 09:16:15
re(2): Independent solutionAnna2004-12-26 23:31:07
re: Independent solutionAnna2004-12-26 23:03:29
Solutionre: Only answer.Ross2004-12-24 22:15:24
re: K.I.S.S.Captain Paradox2004-12-24 02:02:19
SolutionOnly answer.Vinnie2004-12-23 20:38:27
Solutioneeeeeeeeeeeeerrrrrrrrrrmegan2004-12-23 10:23:33
guess (possible solution)David2004-12-23 06:30:24
re: solution of sortsJuha S2004-12-22 20:27:38
solution of sortsJuha Salonen2004-12-22 19:45:52
re(4): Independent solutionTristan2004-12-21 17:41:00
Some Thoughtsre: Independent solutionDanny2004-12-21 15:30:09
re(3): Independent solutionFletch2004-12-21 09:19:07
re(2): Independent solutionTristan2004-12-21 05:41:02
re: Another simpler solution?Jer2004-12-20 18:53:29
SolutionAnother simpler solution?Erik O.2004-12-20 18:30:06
SolutionK.I.S.S.Penny2004-12-20 17:39:51
re: Alternate possibilityFletch2004-12-20 17:11:20
re: Independent solutionFletch2004-12-20 17:04:43
SolutionIndependent solutionTristan2004-12-20 16:28:09
SolutionAlternate possibilityPenny2004-12-20 12:28:25
SolutionImpossible solutionPenny2004-12-20 12:12:31
SolutionPossible solutionFederico Kereki2004-12-20 11:39:55
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