I have a problem which is a variation of the Sports League Scheduling
Problem. This problem pertains specifically to a tennis league at my
own sports club. Each winter, the pro puts out a blank sheet of paper
for people to sign up for tennis leagues. From year to year, the
number of people who sign up fluctuates; however, the number of tennis
courts available stays the same at 4 courts. For my particular
problem, lets say that 12 people sign up for the league (this is a
singles league) so each week, 4 people will have byes and 8 will play.
Can anyone come up with an algorithm which allows each player to play
each other player 1 time only and also deals out a fair number of bye
weeks to each player? Assume the league runs until every player has
played every other player once. If anybody can come up with such an
algorithm, would it scale well to years when a different number of
players signed up?

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