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Author Topic: Can you solve this logic puzzle?  (Read 606 times)

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Offline anoni

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Can you solve this logic puzzle?
« on: December 11, 2016, 08:34:31 AM »
Hi there furs! This is for the more logical ones of you, I have a logic puzzle that a friend and I came up with that uses concepts in game theory. So see if you can solve it!


The puzzle:


  We have a game, in this game we use a standard deck of playing cards. We then have two people, a tester and a guesser. The tester draws two cards from the deck, the guessers goal is to guess the suit of at least ONE of the cards, he only gets one guess and he must be absolutely sure of the suit before he guesses.


  The guesser also has the ability to ask as many yes or no questions as he wants, but here's the trick! When the guesser asks a yes or no question, the tester considers the question for one card and in his head answers it, then he considers the question for the other card, and in his head answers it. He then picks the any of those two answers he wants and tells you that answer. The tester is trying to fool the guesser and make the guesser lose.


  The question is will the guesser win every time or is there a scenario where the tester can always win? Assume the guesser and tester are perfectly logical and rational and the tester is trying to make the guesser lose.


  So here is an example. Suppose the Tester has a clubs card and a hearts card. The guesser asks "Do you have a clubs?". The tester first asks the question for the clubs card, is the clubs a clubs, yes it is! The tester then asks the question for the hearts card, is the hearts a clubs? No! He thus can choose to say either yes or no, an intelligent tester will say no :P


  If however the tester has two clubs cards and the guesser asks "Is your card a clubs?". The tester first goes to his first clubs card, is the clubs a clubs? Yes. He then goes to his second clubs card, is that clubs a clubs? Yes. So he can pick an answer that's either yes or yes, so he's forced to say yes and the guesser wins.


  The guesser can ask any yes or no questions, however some questions don't make any sense to the tester. For example, suppose you ask "Do you have a clubs and a hearts?", and suppose the tester does in fact have a clubs and a hearts. He first looks at his hearts card and asks "Is the hearts card a club and a hearts?" No. He then looks at his clubs card and says "Is the clubs card a hearts and a clubs?" No. So he says no.


  If you ask "Is this card specifically a hearts?" The tester goes to the hearts, "Is this card specifically a hearts?" yes. The tester goes to the clubs "Is this card specifically a hearts?" No. He can choose to say yes or no. Basically, he only asks the question as if he only has one card, and asks the question twice, so if you ask a question that involves BOTH the card, you're unlikely going to get a satisfactory answer.


  Generally the best questions you can ask are questions of the form "Do you have a hearts OR a clubs?" As this question makes sense with one card, and if he has two different cards he is forced to say yes for at least one suit combination, you can then increase and say "Do you have a hearts OR a clubs OR a spade" etc. There are four suits. Good luck!
« Last Edit: December 11, 2016, 08:36:26 AM by anoni »
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Re: Can you solve this logic puzzle?
« Reply #1 on: December 18, 2016, 04:23:11 PM »
There are 10 combinations of suits HH, DD, CC, SS, HD, HC, HS, DC, DS, SC (Note CS, for example, doesn't count as a different combination to SC for these purposes.  When the order does matter it is called a permutation).
 
So the Guesser asks:
 
Is the card a heart?
Is the card a diamond?
Is the card a club?
Is the card a spade?
 
If the answer is yes to any of these then the Guesser guesses that suit. If not then,
 
Is the card either a heart or a diamond?
Is the card either a heart or a club?
Is the card either a heart or a spade?
Is the card either a diamond or a club?
Is the card either a diamond or a spade?
Is the card either a spade or a club?
 
The Tester must answer yes to at least one of these options, namely the one which lists the suits of both cards. 
 
The Tester must answer yes at least once to these 6 questions and must answer no at least three times, but may answer yes or no to four of the six.
 
If the Tester answers yes only once then you know the suits of both cards and may guess.
 
If the Tester answers yes twice then one suit will be present in both of the combinations, guess that suit.
If the Tester answers yes five times out of six then the cards are of the two suits different to the two suits which get the no answer.
 
If the Tester answers yes four times the two no answers will cover three suits, guess the fourth suit.
 
If the Tester answers yes three times then there are 6 combinations of pairs.  Two combinations have a suit present in all three pairs, guess that suit. Two combinations will have two suits which are present twice and two suits which are present once each, guess either of the suits present twice. Two combinations have three suits present twice and one suit not present.


So this is where I'm stuck.  From here you have a 2/3 chance to guess correctly, but I can't think of a way to get a definitive answer if the Tester answers yes three times. At least assuming that the Tester will be consistent when asked the same questions again.  Otherwise if you had two rounds of three yes answers which had both of the combinations that have a suit absent then you know both absent suits which tells you which two are present of course.


I will probably come back to this when my head is clear.  UGH! I hate to leave it when so many of the possible scenarios are solved! XD

 

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