Subject:
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Re: King, Queen & Jack
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Newsgroups:
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lugnet.off-topic.fun
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Date:
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Fri, 22 Dec 2000 07:28:15 GMT
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Viewed:
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172 times
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In lugnet.off-topic.fun, Geoffrey Hyde writes:
> Thanks, Shiri - I think I got it right the first time. The statement I
> figured could possibly be true was most likely to have been correct, and
> after you posted, I think it is.
In your 1st post, you seem to think that it is a matter of probability, when
in fact, it's not, as Shiri pointed out (quite correctly). Let's examine
closely. (Don't read if for some reason you're still figuring it out)
> Only one of the following statements about a particular hand of cards is true:
Alright. There are to be three statements about a hand of cards. Let's call
them 1, 2, and 3. (I peeked at how many there were)
> a. There is a king in the hand, or an ace, or both.
Ah. So, statement 1 is made up of two sub-statements:
A: There is a king in the hand
B: There is an ace in the hand
And the resulting statement 1:
A OR B OR (A AND B)
> b. There is a queen in the hand, or an ace, or both.
Again, statement 2 is made up of two sub-statements:
C: There is a queen in the hand
B: There is an ace in the hand
(notice that B has already been declared above as a sub-statement)
And the resulting statement 2:
C OR B OR (C AND B)
> c. There is a jack in the hand, or a ten, or both.
Statement 3 is ALSO made up of two sub-statements:
D: There is a jack in the hand
E: There is a ten in the hand
And the resulting statement 3:
D OR E OR (D AND E)
So, if only ONE statement of 1, 2, and 3 is true, the others MUST be false,
as stated.
Let's assume #1 is true. That means that either A or B being true (or both)
will make statement #1 true. Hence, we can say little about A or B yet. BUT,
because ONLY one statement is true, we KNOW that statements 2 & 3 are false.
Now look at statement 2. If either C or B were true, it would make statement
#2 true! So obviously, both C and B MUST be false. Similarly, D and E MUST
also be false. Hence, a truth table:
A B C D E
T F F F F
But what if #2 is true instead? Well, by the same logic, we find:
A B C D E
F F T F F
And what if #3 is true? We'd get:
A B C D E
F F F ? ?
And we'd know that one of D or E must be true, and possibly both.
So, now as to the question:
> Q. Is it possible that there is an ace in the hand?
Let's see... that was statement B. And going back to our little truth
tables, if #1 is true, B is false. If #2 is true, B is false. And if #3 is
true, B is false again. Hence, there can NOT be an ace in the hand if "Only
one of the ... statements ... is true".
Perhaps you misread Scott's post, but he worded the question without flaw as
far as I can see.
DaveE
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Message is in Reply To:
 | | Re: King, Queen & Jack
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| Thanks, Shiri - I think I got it right the first time. The statement I figured could possibly be true was most likely to have been correct, and after you posted, I think it is. -- Cheers ... Geoffrey Hyde Shiri Dori <shirid@hotmail.com> wrote in (...) (24 years ago, 22-Dec-00, to lugnet.off-topic.fun)
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