John,

One less week than the total number of players is always needed. For example, if there are 12 players then each player has to play 11 others. That takes 11 weeks.

Try this to get the schedule. I'll describe it for 12 but it works for any even number of players. Put 11 dots, numbered 1, 2, ..., 11, (roughly) equally spaced around the outside of the circle. Put a twelfth dot, numbered 12, in the centre of the circle. To get the schedule for week number k, draw a line through 12 and k, and then draw all of the lines through pairs of points on the circle that would be perpendicular to it. There should be 6 lines in total, including the one through 12 and k. Each line goes through a pair of points, and those are the players who meet that week.

For example, in week 1, 12 plays 1; 11 plays 2; 10 plays 3; 9 plays 4; 8 plays 5; and 7 plays 6. In week 2, 12 plays 2; 1 plays 3; 11 plays 4; 10 plays 5; 9 plays 6; ands 8 plays 7. If you draw the picture and do these two examples, then you'll see how things work.

Good luck!
--Victoria