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."