March 21st, 2010, 04:32 AM  #1 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Need help with boolean logics
There are 3 hats and 2 magicians. 1 magician is truthful the other tell lies. H1,H2 and H3 where Hi is "hat i with rabbit" Assume H1 v H2 v H3 is true and only one hat is with rabbit. Can asks one or two questions to the magicians but not the same magician if you asking two questions. Also need to prove the strategy for getting the right hat. 
March 21st, 2010, 09:04 AM  #2 
Senior Member Joined: Nov 2008 Posts: 199 Thanks: 0  Re: Need help with boolean logics
If you ask the question 'which hat would the other magician say the rabbit was in?' to either magician then the answer that they give will be a hat that definitely does not have the rabbit in (assuming they both know where it is and that they both know that the other always lies/tells the truth). So ask that question to each in turn and you'll eliminate the two hats that don't contain the rabbit.

March 21st, 2010, 03:45 PM  #3  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Need help with boolean logics Quote:
 
March 21st, 2010, 04:27 PM  #4 
Senior Member Joined: Nov 2008 Posts: 199 Thanks: 0  Re: Need help with boolean logics
Ah yes. Good thinking.

March 21st, 2010, 05:13 PM  #5 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Re: Need help with boolean logics
I understand your idea as much but how do I put it in logic equation? I'm completely new to this subject and finding it confusing. Any guide would be appreciated. 
March 23rd, 2010, 04:49 AM  #6 
Senior Member Joined: Nov 2008 Posts: 199 Thanks: 0  Re: Need help with boolean logics
I'm not sure exactly what you mean by a logic equation. p.s. Do you know which magician is the liar before you ask the questions? 
March 23rd, 2010, 05:37 AM  #7 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Re: Need help with boolean logics
No, we don't know which is telling lies

March 24th, 2010, 04:32 AM  #8 
Senior Member Joined: Nov 2008 Posts: 199 Thanks: 0  Re: Need help with boolean logics
Well, I'm not sure I can help you. I thought there might be a way of asking questions (with the second possibly depending on the answer to the first) such that the possible combinations of answers specify the hat uniquely but I could find it.

March 26th, 2010, 04:48 PM  #9 
Member Joined: Mar 2010 Posts: 32 Thanks: 0  Re: Need help with boolean logics
You seem to have had the answer and then given up. What's wrong with: Ask M1 if M2 would say yes if you asked him if there's a rabbit in H1. If he says, "no", there's a rabbit in H1, so you know. Otherwise ask M2 if M1 would say yes if you asked him if there's a rabbit in H2. If he says, "no", there's a rabbit in H2, so you know. Otherwise there's a rabbit in H3. 
March 27th, 2010, 04:03 AM  #10 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Re: Need help with boolean logics
So assume they all false right? What if H1 no and H2 no? means both H1 and H2 has rabbit? Is that even possible? 

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