Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 9/17/84; site mhuxt.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!js2j
From: js2j@mhuxt.UUCP (sonntag)
Newsgroups: net.puzzle
Subject: Re: How to win a bottle of Champagne
Message-ID: <890@mhuxt.UUCP>
Date: Tue, 28-May-85 10:56:11 EDT
Article-I.D.: mhuxt.890
Posted: Tue May 28 10:56:11 1985
Date-Received: Thu, 30-May-85 02:28:50 EDT
References: <179@ubvax.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 42

>    There once were two brothers herding a flock of
> sheep. One day, they decided to sell them all in
> the market. Each beast was sold for as many dollars
> as sheep there originally were in the herd.

    The total amount of money was a square number, then.

> The total amount of money was in $10 bills, plus
> less than $10 in $1 bills. The elder brother proceded
> to share it. He took a $10 bill, then gave one to
> his brother, then took one again, and so on till
> he turned out taking the last $10 bill ; 

     There were an odd # of $10 bills plus change.

> he then
> gave all of the $1 bills to the youngster, who burst
> out : "Hey, but you've got #@% dollars more than I have ".
> 
> How about now working out what he really said ?

     The amount of money they had was a square number with an odd
digit in the 10's place.  Searching the numbers less than 10 exhaustively,
we find that 4 and 6 are the only numbers which, when squared, yield
such numbers.  The numbers greater than 10 can all be written as N=10*a+b,
where a and b are integers less than 10.  When squared,     
N^2=100*a^2+20*a*b+b^2.  Notice that the first two terms of this
expression have an *even* number of tens.  The only way N^2 can have an
odd digit in the 10's place is if b^2 has an odd digit there.  Thus the
number of sheep (and the price of the sheep) must be in the following
sequence: 4,6,14,16,24,26,34,36...   Happily, the square of any number
in this series ends in the same digit, 6, which is the number of $1 bills
which the younger brother receives in lieu of a tenner.  So what he really
said was "Hey, but you've got *four* dollars more than I have!"

    Now where's my champagne?

*** REPLACE THIS LINE WITH YOUR MESSAGE ***
-- 
Jeff Sonntag
ihnp4!mhuxt!js2j
    "You can be in my dream if I can be in yours." - Dylan