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From: stevev@tekchips.UUCP
Newsgroups: net.math
Subject: Re: Need help finding algorithm
Message-ID: <839@tekchips.UUCP>
Date: Mon, 4-Jun-84 12:31:36 EDT
Article-I.D.: tekchips.839
Posted: Mon Jun  4 12:31:36 1984
Date-Received: Wed, 6-Jun-84 06:36:56 EDT
Organization: Tektronix, Beaverton OR
Lines: 27

>    I was asked to create a schedule for opponent play in
>a league.  There were 22 members in the league and they
>wanted each player to play every other player once, with
>no player playing more than once a week.  That meant that
>it would be a 21 week schedule with 11 two person games a
>week. ...

A simple schedule for 2n players in 2n-1 weeks may be found by placing
the players names in two rows of n entries.  The players in the same column
play each other the first week.  For the next week, rotate all players
(say clockwise) except the player in the top/left position (who stays where
he is).  For the week after that, perform the same rotation, etc.  A
five-week six-player schedule, for example is as follows:

Week 1:		Week 2:		Week 3:		Week 4:		Week 5:
  1 2 3		  1 6 2		  1 5 6		  1 4 5		  1 3 4
  6 5 4		  5 4 3		  4 3 2		  3 2 6		  2 6 5

The rotation is such that 2 is always in the position that 3 was in the
previous week, 3 in 4's last position ... 6 in 2's last position, etc.
For the first week, 1 plays 6, 2 plays 5, 3 plays 4; the second week
1 plays 5, 6 plays 4 and 2 plays 3, etc.

		Steve Vegdahl
		Tektronix, Inc.
		Beaverton, OR