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Question from Caroline, a teacher:

I couldn't find a similar question, hopefully there isn't one!

I have a softball team of 18 people (7 girls and 11 boys), but am limiting each game to 13 players (6 girls and 7 boys). The season is 10 games long. How do I create a rotating schedule which allows members to play evenly? I tried separating the boys and girls to create rotation for each but I got confused. Some are unable to attend all games but for the simplicity of a rotation schedule can you please help?


Strictly, you can't. There are 13x10 = 130 spots, 18 does not divide this. Similarly, 7 does not divide the 60 spots you wish to reserve for girls, nor 11 the 70 spots reserved for boys.

The best you can do is have 4 girls miss 1 game and 3 miss 2; while 7 boys miss 4 games and 4 miss 3.




For the girls, number them 1 through 7, and then sit out girl, 1, then 2, ..., then 7, then 1, then 2, ..., then 6. Girls 1 though 6 each miss 2 games. Girl 7 misses 1 game.

For the boys, number them 1 though 11, and then sit out boys 1,2,3,4, then 5,6,7,8, then 9, 10,11,1, then 2,3,4,5, and so on. No one sits out 2 weeks in a row. Three of the 4 players who are out in a particular week play in both of the next 2 weeks. Not all boys will get the same number of games, but the difference in games played is at most 1, and that's the best possible.

I hope this helps.


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