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From: hopp@nbs-amrf.UUCP (Ted Hopp)
Newsgroups: net.puzzle
Subject: Re: [A "logic puzzle"] (Solution)
Message-ID: <117@nbs-amrf.UUCP>
Date: Wed, 29-Jan-86 10:47:55 EST
Article-I.D.: nbs-amrf.117
Posted: Wed Jan 29 10:47:55 1986
Date-Received: Sat, 1-Feb-86 03:45:39 EST
References: <292@watdragon.UUCP>
Distribution: net
Organization: National Bureau of Standards
Lines: 50

> This is a puzzle which someone told me the other day. I have no solution as
> yet - perhaps some of you creative types can come up with one.
> 
> 	Two friends are walking down the street. One says to the other "Do
>         you have any children?". The other replies "Yes - three sons".
>  
>         The first asks "How old are they?", to which the second replies
> 
> 		"The sum of their ages is thirteen, the product of their ages
> 		 is as old as you are. The oldest weighs 61 pounds."
> 
> 	How old are the three sons? For that matter how old is the friend?
> 	And what does the eldest weight have to do with anything???
> 
>                          Alec Saunders - University of Waterloo CS.
> 	P.S. No discussions of weight and mass please - assume common usage.

Let's examine the clues.  The trick, of course, is to recognize a clue
for what it is.

	"Three sons"
	"The sum of their ages is thirteen"

From this, we know the ages are a partition of 13 into three positive integers.
There are fourteen partitions (ignoring permuations).  I won't bother listing
them here.

	"the product of their ages is as old as you are"

This doesn't tell us much yet, except that the friend now knows this.

	"The oldest weighs 61 pounds"

Aha!  This gives it all away.  There are two vital clues here, neither of
which has to do with weight.

The first clue is: knowing the sum AND the product of the ages isn't enough
information (at least in the world of logic puzzles), otherwise this new
information wouldn't have been offered.  Well, we can form the product
of each of the partitions of 13, and we find that the only partitions that
do not have unique products are (1,6,6) and (2,2,9), both of which multiply
to 36.  (Therefore, the friend is 36 years old.)

The second clue is: there is an oldest son.  The solution, then is (2,2,9).

As a check, 61 pounds is a reasonable weight for a 9-year old boy.

-- 

Ted Hopp	{seismo,umcp-cs}!nbs-amrf!hopp