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From: thorp@mmlai.UUCP (John Thorp)
Newsgroups: comp.ai
Subject: Re: Beyond Mr.P & Mr.S.
Message-ID: <144@mmlai.UUCP>
Date: Fri, 4-Sep-87 00:28:52 EDT
Article-I.D.: mmlai.144
Posted: Fri Sep  4 00:28:52 1987
Date-Received: Sun, 6-Sep-87 08:13:24 EDT
References: <668@xn.LL.MIT.EDU> <1064@homxc.UUCP> <1065@homxc.UUCP> <1111@homxc.UUCP>
Organization: Martin Marietta Labs, Baltimore, MD
Lines: 70
Summary: The End?


Before this gets out of hand...

	It seems the trick to seeing the solution is to realize the
	YOU are a third party to the dialog.  Just because the author
	has choosen not to give the house number in the problem
	DOES NOT mean the saleaman does not know the house number.
	For a matter of fact, the salesman can observe the house number.
	His response of "no I can not tell you the age of your daughters"
	leeds us to one of two conclusions:

		1) the solution is not unique for the house number he
		   is observing. [.ie (1,6,6) (2,2,9)]

		   NOTE: The only house number to produce more
			 than one solution is 36, so this must be
			 the house.

	or	2) He is incapable of solving the problem for the given
		   house number. [.ie "I can't solve this problem!"]

	We all know that salesmen will do anything for a sale,
	even correctly solve math problems :-), so option 2 can
	not be the case.

	If the house number had provided a unique solution [ie. (1,2,10)],
	then the salesman would have responded with the proper triple
	and been done with it.

	If you follow the above, then the final paragraph by the housewife
	selects which of the TWO possible solutions is the correct one.
	(there exists an oldest daughter, singular) -> (2,2,9)

	Remember: The key is you, the reader, are an observer not a
		  participant.


> In article <1238@pdn.UUCP>, colin@pdn.UUCP (Colin Kendall) writes:
> > In article <1295@houdi.UUCP>, marty1@houdi.UUCP (M.BRILLIANT) writes:
> > 
> > 	"mother:   OK, you're right, I made it tough on you, but I have to go
> > 	now and drive my oldest daughter to her piano lesson."
> > 
> > If the ages of the daughters are 1, 2, and 10, she has an oldest
> > daughter. The various solvers seem to have made the 
> > assumption that the other two daughters are the same age.
>
 			  | Its not up to YOU to choose a house number the 
 			  | salesman can see it himself.
			 VV
> So the house number is 20, and the solution is
> unique.  Why didn't the salesman reply
> immediately?  He missed the quick kill because the information
> was insufficient at first.  Only after the quote above did he have
> enough info.
	HE had enough info all along.  If he had responded with (1,2,10)
	The housewife would have looked at him, looked at the number (36)
	and slammed the door.

	I hope this helped !


	comp.ai maybe...
	rec.puzzles yes!

-- 
John Thorp @ Martin Marietta Labs / Artificial Intelligence Department

ARPA: thorp@mmlai.uu.net
UUCP: {uunet, super, hopkins!jhunix} !mmlai!thorp