Re: hmmm...check this, Mr P

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Posted by Brad Paul on October 23, 2002 at 22:32:47:

In Reply to: hmmm...check this, Mr P posted by Denis Borris on October 23, 2002 at 20:17:31:

: Why not this way:

: : Tim, who knew Ted's numbers, said "My total now could be 29 minimum or 48
: : maximum."
: i1 + e1 = 29
: i2 + c2 = 48

: : Tom, who knew Tim's numbers, said "My total now could be 27 minimum or 72
: : maximum."
: o1 + i1 = 27
: o2 + i2 = 72
: :
: : Ted, who knew Tom's numbers, said "My total now could be 12 minimum or 62
: : maximum".
: e1 + o1 = 12
: e2 + o2 = 62

: Solving those gives:

: i1 = 22
: i2 = 29*
: o1= 05
: o2= 43*
: e1= 07
: e2= 19*
: * same as yours
I think there are three possibilities of interpreting the question:

1) When they say "My total now could be y minimum or x maximum." it
is because they could have gotten ether of their neighbors cards. i.e
their full statement should have been:
"Given I kept the card I did: My total now could be y minimum or x maximum."
This was my interpretation because the problem said A knows B's cards.

2) When they say "My total now could be y minimum or x maximum." it is
because they could have given ether one of their cards away. i.e
their full statement should have been:
"Given I got the card I did: My total now could be y minimum or x maximum."

3) Or a combination of 1 and 2 where out of all four possible card
combinations they make their statement about min and max. This is the
one you did.

However, seeing what you did I now prefer interpretation number 3)

I like what you have done with the die problem. I still want a way to
generate the full thing analytically. I have now decided that is the
same question as "What is the multiplicity function for a magnetic
dipole with (2j+1) levels" This type of question is addressed in
statistical mechanics texts. However in statistical mechanics there
are easier ways at getting to the thermodynamical properties than
finding the multiplicity function. The Perl script that I ran to post
those probabilities has now ran for a few days and are converging on
your numbers.

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Thank you Mr B and Mr P..... Jerry 22:58:12 10/23/02 (0)

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: : Why not this way: : : : Tim, who knew Ted's numbers, said "My total now could be 29 minimum or 48 : : : maximum." : : i1 + e1 = 29 : : i2 + c2 = 48 : : : Tom, who knew Tim's numbers, said "My total now could be 27 minimum or 72 : : : maximum." : : o1 + i1 = 27 : : o2 + i2 = 72 : : : : : : Ted, who knew Tom's numbers, said "My total now could be 12 minimum or 62 : : : maximum". : : e1 + o1 = 12 : : e2 + o2 = 62 : : Solving those gives: : : i1 = 22 : : i2 = 29* : : o1= 05 : : o2= 43* : : e1= 07 : : e2= 19* : : * same as yours : I think there are three possibilities of interpreting the question: : 1) When they say "My total now could be y minimum or x maximum." it : is because they could have gotten ether of their neighbors cards. i.e : their full statement should have been: : "Given I kept the card I did: My total now could be y minimum or x maximum." : This was my interpretation because the problem said A knows B's cards. : 2) When they say "My total now could be y minimum or x maximum." it is : because they could have given ether one of their cards away. i.e : their full statement should have been: : "Given I got the card I did: My total now could be y minimum or x maximum." : 3) Or a combination of 1 and 2 where out of all four possible card : combinations they make their statement about min and max. This is the : one you did. : However, seeing what you did I now prefer interpretation number 3) : I like what you have done with the die problem. I still want a way to : generate the full thing analytically. I have now decided that is the : same question as "What is the multiplicity function for a magnetic : dipole with (2j+1) levels" This type of question is addressed in : statistical mechanics texts. However in statistical mechanics there : are easier ways at getting to the thermodynamical properties than : finding the multiplicity function. The Perl script that I ran to post : those probabilities has now ran for a few days and are converging on : your numbers.

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