circle problem

[Rick Shepherd]

That's the same configuration I independently found.  Although I haven't
taken the time to think through the generalization, it's easy to see that
there are a large number of configurations (all permutations of the q blue
and r red balls in the q+r remaining fixed locations) which will solve it
once the locations of the p black balls are determined and fixed for the
pair (p+q+r, k).

The original statement of this problem closely resembles a problem which, if
I recall correctly, is called the Josephus Problem (every 10th person
removed, which relates to the word "decimate", as I was reminded by my son,
who's studying Latin now.).

Rick Shepherd

----- Original Message -----
From: "Brian L. Galebach" <briang at SEGmail.com>
To: <seqfan at ext.jussieu.fr>
Cc: <briang at ProbabilitySports.com>
Sent: Monday, November 18, 2002 10:40 AM
Subject: RE: circle problem


> Perhaps I am missing something, but this seems fairly straightforward to
me.
>
> Start with 30 Ms.  Count forward past 8 Ms and change the 9th to W.
> Continue the process, wrapping back to the start of the string when
> necessary, until 15 Ms have been changed to Ws.
>
> I get MMMMWWWWWMMWMMMWMWWMMWWWMWWMMW.
>
> -Brian Galebach
>
> -----Original Message-----
> From: murthy amarnath [mailto:amarnath_murthy at yahoo.com]
> Sent: Saturday, November 16, 2002 8:14 AM
> To: seqfan at ext.jussieu.fr
> Subject:
>
>
>  To all,
> Can some one solve this problem.
>
> There are 15 males and 15 females. They are to be
> arranged in a circle choosing a predecided starting
> point. Go on choosing every 9'th person and take
> him/her out of the circle instantly. Continue doing so
> till 15 persons are out of the circle.
> The question is how to arrange them so that only
> (all)females are out.
>
>
> Generalize.
> Let there be p  black  balls , q blue balls and  r
> red balls. How to arrange so that   all black balls
> are removed if one goes on removing every  k'th ball
> as  above.
> thanks
> regards
> amarnath
>
> __________________________________________________
> Do you Yahoo!?
> Yahoo! Web Hosting - Let the expert host your site
> http://webhosting.yahoo.com