Bluffing Androids

Evan

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Mar 6, 2008, 1:19:30 PM3/6/08

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Nine androids sat around a table playing Texas Hold 'Em. During a
random shuffle,
a single card flew out of the deck landing face up. Each android made
the following comment:

#1: The card is a diamond or a heart.
#2: Only two androids at this table ever tell the truth.
#3: The card is a Jack or a King.
#4: The card is a 4 or a spade.
#5: Android #7 never lies.
#6: The card is a face card.
#7. The card is not a King or a Queen.
#8: The card is a club or a spade.
#9: The card is a club or a diamond.

Suddenly all of the androids' stack buffers overflowed. What card were
they looking at?

(In other words, what card causes a contradiction? It's not the joker.)

Nick Wedd

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Mar 6, 2008, 5:27:48 PM3/6/08

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In message
<ad20176d-13aa-4945...@v3g2000hsc.googlegroups.com>, Evan
<evan_on...@yahoo.com> writes

The facts, as given, are consistent with any of the 52 cards. I guess
that the intended answer is the queen of hearts.

Nick
--
Nick Wedd ni...@maproom.co.uk

Evan

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Mar 6, 2008, 5:59:13 PM3/6/08

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Yes, the queen of hearts was the intended answer, and darn, I think I
see your point.
Oh well, I'll tweak it some more. Thanks for playing.

Evan

On Mar 6, 2:27 pm, Nick Wedd <n...@maproom.co.uk> wrote:
> In message
> <ad20176d-13aa-4945-b131-40b920a13...@v3g2000hsc.googlegroups.com>, Evan
> <evan_on_use...@yahoo.com> writes
[snipped]

>
> The facts, as given, are consistent with any of the 52 cards. I guess
> that the intended answer is the queen of hearts.
>
> Nick
> --

> Nick Wedd n...@maproom.co.uk- Hide quoted text -
>
> - Show quoted text -

Dan Hoey

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Mar 11, 2008, 1:30:40 PM3/11/08

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Evan wrote:
> Yes, the queen of hearts was the intended answer, and darn, I think I
> see your point. Oh well, I'll tweak it some more. Thanks for
> playing.
>
> Evan

I think the problem is the addition of quantifiers extending beyond the
present case. To be properly self-referential, Android 2 should say
"Only two androids at this table are telling the truth" and Android 5
should say "Android 7 is not lying." You might as well have Android 7
say "The card is not a King, Queen, or Joker" so you don't need to
mention it later. I think that makes the puzzle kosher.

The problem of overquantification messes up the Liar Paradox, such as
when Epimenides (a Cretan) said "All Cretans are liars." Not a paradox
if true (since Epimenides might be a liar, telling the truth for a
change) nor if false (since the non-lying Cretans might not include
Epimenides.

Dan Hoey
hao...@aol.com

Ed Murphy

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Mar 16, 2008, 2:22:05 AM3/16/08

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Dan Hoey wrote:

> Evan wrote:
>> Yes, the queen of hearts was the intended answer, and darn, I think I
>> see your point. Oh well, I'll tweak it some more. Thanks for
>> playing.
>>
>> Evan
>
> I think the problem is the addition of quantifiers extending beyond the
> present case. To be properly self-referential, Android 2 should say
> "Only two androids at this table are telling the truth" and Android 5
> should say "Android 7 is not lying." You might as well have Android 7
> say "The card is not a King, Queen, or Joker" so you don't need to
> mention it later. I think that makes the puzzle kosher.

Yes. Here's a full solution of the revised puzzle:

If the card is a 4, then #4, #5, and #7 told the truth.
J #3, #5, #6, and #7
Q #6
K #3 and #6
Otherwise #5 and #7

If the card is a C, then #8 and #9 told the truth.
D #1 and #9
H #1
S #4 and #8

The only way to create a contradiction is to have exactly two androids
other than #2 telling the truth, which forces the Queen of Hearts.