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Article #2531

Re: Dividing apples

#2531
From: C.M. Hicks
Date: Tue, 26 Jan 1993 11:47
26 lines
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bcash@crchh410.BNR.CA (Brian Cash) writes:

><SPOILER>  (maybe...)

>Is it 351?  I figured it this way:

I think so, and I worked it the same way. I'm now trying to find a general
solution for dividing Q apples among P people - I'll post if I find one.

>Call the number of apples given to person 1 N, person 2 X, and person 3 Y.
>Now if N = 25, then X and Y must both equal 0. (1 solution)
>If N = 24, then {X=1,Y=0} and {X=0, Y=1} are valid. (2 solutions)
>If N = 23, then {X=1, Y=1}, {X=0, Y=2}, {X=2, Y=0} are valid. (3 solutions)
>If N = 22, then there are 4 solutions.
>If N = 21, then there are 5 solutions.
>...
>If N = 0, then there are 26 solutions (run X from 0 to 25 and Y is
>forced to a value).  
>So the total number is 1+2+3+4+...+26 or 351.

Christopher Hicks
--
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 Christopher Hicks    |    If it doesn't fit...
 cmh@uk.ac.cam.eng    |                        ...you need a bigger hammer.
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Path: arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!agate!doc.ic.ac.uk!uknet!cam-eng!cmh
From: cmh@eng.cam.ac.uk (C.M. Hicks)
Newsgroups: rec.puzzles
Subject: Re: Dividing apples
Message-ID: <1993Jan26.114740.11328@eng.cam.ac.uk>
Date: 26 Jan 93 11:47:40 GMT
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