Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site pucc-i
Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!inuxc!pur-ee!CS-Mordred!Pucc-H:Pucc-I:ags
From: ags@pucc-i (Seaman)
Newsgroups: net.math,net.wanted
Subject: Round-robin scheduling without a computer.
Message-ID: <304@pucc-i>
Date: Tue, 5-Jun-84 09:43:57 EDT
Article-I.D.: pucc-i.304
Posted: Tue Jun  5 09:43:57 1984
Date-Received: Thu, 7-Jun-84 07:05:56 EDT
References: <373@tty3b.UUCP>
Organization: Purdue University Computing Center
Lines: 34

My face is red!  Last night I posted a method for round-robin scheduling
which involved using a backtracking program to find the appropriate first-
round pairings, plus a simple rotation to get the subsequent rounds.  The
method was correct, but unnecessarily complicated.  I have cancelled the
article, but it already had a pretty good head start.

After sleeping on the problem, I remembered something I knew 30 years ago:
the first-round pairings don't matter!  Here is how it works, with example
for N=22:

1) If you have an odd number of participants, add one called "BYE" to make
   it even.

2) Pair them off for the first round:

    1  2  3  4  5  6  7  8  9 10 11
   22 21 20 19 18 17 16 15 14 13 12

3) Hold one entry fixed (I'll use #22) and let the others rotate for
   subsequent rounds.  Second round is:

    2  3  4  5  6  7  8  9 10 11 12
   22  1 21 20 19 18 17 16 15 14 13

   and so on.

Throwing away my backtracking program,
-- 

Dave Seaman
..!pur-ee!pucc-i:ags

"Against people who give vent to their loquacity 
by extraneous bombastic circumlocution."