[net.math] Need help finding algorithm

stevev@tekchips.UUCP (06/04/84)

>    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

arr@tty3b.UUCP (10-7-83"Andy R. 94130) (06/16/84)

I hope you don't think my request trivial but here goes.

    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.  Since I am a programmer at heart I decided to make
a "quick" program to print the schedule for "N" players.
Well I'm stuck!!!  It aint such an easy task.  The only
way I could get a working program is to make it totally
a trial-and-error/iterative type job.  This takes a while
to run if the "N" is large; especially if I'm using a PC.
    I am bound-and-determined to find a better way!!!
I just can't believe something that is so conceptually
simple can be so hard to program.
    If anyone out there in NETland can help I will be
forever grateful!!!  If I don't find a solution my wife
is going to leave me and I will be sent to a loony bin
mumbling..."But there has got to be a better way...."



From the ever active terminal of 
				Andy Rolfe
				ATT Teletype Corp.
				312-982-3202
				ihnp4!tty3b!arr

   THANKS IN ADVANCE FOR ANY EFFORTS!!!