



 
John, With 10 players it takes 9 weeks for a player to play everybody else. You can do it like this: place dots 1, 2, ..., 9 equally spaced on a circle and dot 10 in the centre. The schedule for week k consists of the players matched by drawing a straight line segment from 10 to k, and between the players such that the straight line segment between them is perpendicular to the one from 10 to k. Unless I make a typing mistake, this gives you
The same method works for en even number of players. When there are an odd number it is similar but one has to sit out each week. Have fun.  


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