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You've been dealt five cards from a standard deck, and you wish to communicate the exact contents of your hand. The catch is that you're only allowed to make utterances of the form "I have an $X$" or "I don't have any $X$s", where $X$ is the name of a rank. How many such statements do you need to convey what's in your hand, and what's the simplest protocol you can use?

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    What exactly is "the exact contents of your hand"? If you can only mention ranks, you can't differentiate between suits, so "the exact contents of your hand" can't include information about the suits? Also, you can't differentiate between having three queens and two kings and having three kings and two queens when all you can say is whether you do or don't have any queens and kings? Ah -- or are you looking for how to use these utterances as a code unrelated to their English meaning?2012-11-02
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    @joriki: Yes, you can predesign a protocol under which the choice (and order) of statements should be interpreted. The protocol might be easier to remember, though, if the statements are *somewhat* related to their English meaning.2012-11-02
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    It is a rather different problem if all your statements need to be true.2012-11-02
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    @Ross: Yes, that's what I thought at first :-)2012-11-02
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    @Ross: I'd be interested in the answer for that case, too.2012-11-02
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    @joriki: Now I see, not so much. It just means you can only make $13$ different statements instead of $26$, so now you need at least $6$. Since the actual log is about $5.76$ you don't have much freedom to waste codes, so the encoding will probably be much more complicated.2012-11-02
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    @Ross: Ah, I see. Interesting. I confused being true with being said to convey its truth :-)2012-11-02
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    @joriki: In a sense, that is the point of asking for the simplest protocol-to our human brains a statement with the purpose of conveying its truth is simpler.2012-11-02

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