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From: lewisd@homxc.UUCP (D.LEWIS)
Newsgroups: comp.ai
Subject: Re: Beyond Mr.P & Mr.S.
Message-ID: <1065@homxc.UUCP>
Date: Mon, 31-Aug-87 16:35:04 EDT
Article-I.D.: homxc.1065
Posted: Mon Aug 31 16:35:04 1987
Date-Received: Fri, 4-Sep-87 07:23:21 EDT
References: <668@xn.LL.MIT.EDU> <1064@homxc.UUCP>
Organization: AT&T Bell Laboratories, Holmdel
Lines: 55
Summary: whooops. Mr. P and Mr. S corollary revisited

In article <1064@homxc.UUCP>, lewisd@homxc.UUCP (D.LEWIS) writes:
> In article <668@xn.LL.MIT.EDU>, vanhove@XN.LL.MIT.EDU (Patrick Van Hove) writes:
> > 
> > I had a somewhat different story of the same type.
> > 
> > mother: Before you go any further, I just want to see if you are really
> > 	as much >mister-smart< as you pretend. Let's see. 
> > 	My husband noticed a while ago that since the last birthday, 
> > 	the product of the ages of my three daughters is exactly 
> > 	the number on our house. If I add that the sum of their ages
> > 	is 13, can you figure out how old they are?
> > 
> >  (Note: 
> >   	integer ages;
> > 	integer house-numbers;)
> (edited - mother refers to "oldest daughter") 
> > salesman:
> > 	Your oldest daughter? Well then, I think I know the answer now:
> > 	their ages are >CENSORED<, >CENSORED< and >CENSORED<.
> > 
> 

I wrote:
> The key is noticing that there must be only a single answer of the
> form n,n,n+p for ages.  The solution, then is in listing out the possibilities:
>   n n n+p  product
>   ================
>   1 1 11   11
>   2 2 9    36
>   3 3 7    42
>   4 4 5    80
>   5 5 3    75
>   6 6 1    36
> So, because the salesman couldn't tell the difference immediately but was
> able to after he was told that there was a single oldest daughter, we
> know that the house number is 36 and that the daughters are 2, 2, and 9.

Aside from the fact that I can't multiply 3,3,and 7 correctly,
I erred in the solution.  It is true that the key is in realizing
that the salesman can come up with two or more answers -- an answer
being x,y,z such that x+y+z=13 and all such pairs have the same
product or set of products -- but that when he is told that the oldest
daughter is not a twin the answer is unique.

It turns out that there are only 14 possibilities.  Of these, only
two pairs have the same value -- the two mentioned above.  And then
2,2,9 is deducible. 

Sorry for the goof.  I'm beating this into the ground. 


-- 

David B. Lewis    {ihnp4!}homxc!lewisd
201-615-5306 Eastern Time, Days.