hello, my name is steve and i am writing you guys this email as a last resort for figuring out a random schedule for my fantasy football league. i am not a teacher or student, and i consider this to be a fairly complex triganomotry type question so ill say it's a secondary level.

here's the rub... i am in a ten(10) team league, split evenly into two five team divisions. we play a thirteen(13) game schedule and would like to play each team in your own division twice, and each team in the other division once. according to my rudimentary mathematics that equals 13 games. a good schedule should look somthing like this: team 1-5 = division 1 team 6-10 = division 2 team 1 should play teams 2-5 twice and teams 6-10 once.

thanks in advance for insight you can offer

humbly yours
steve



Hi Steve,

This has nothing to do with trigonometry; it is graph colouring; not too complex, but not completely elementary either:

For two divisions of 6 teams, this would give you 16 matches, and there are some results that would give you the 16 week schedule right away. However for odd divisions, one of the result breaks down, and I have to do a bit of work. Here is one possible schedule:

week 1 : (1-2) (3-4) (6-7) (8-9) (5-10)
week 2 : (2-3) (4-5) (7-8) (9-10) (1-6)
week 3 : (3-4) (5-1) (8-9) (10-6) (2-7)
week 4 : (4-5) (1-2) (9-10) (6-7) (3-8)
week 5 : (5-1) (2-3) (10-6) (7-8) (4-9)
 
week 6 : (1-3) (2-4) (7-9) (8-10) (5-6)
week 7 : (2-4) (3-5) (8-10) (9-6) (1-7)
week 8 : (3-5) (4-1) (9-6) (10-7) (2-8)
week 9 : (4-1) (5-2) (10-7) (6-8) (3-9)
week 10 : (5-2) (1-3) (6-8) (7-9) (4-10)
 
week 11 : (1-8) (2-9) (3-10) (4-6) (5-7)
week 12 : (1-9) (2-10) (3-6) (4-7) (5-8)
week 13 : (1-10) (2-6) (3-7) (4-8) (5-9)

It is not the only possible solution; anyway, you may want to intertwine the weeks 1 to 5 with the weeks 6 to 10, to avoid having two teams playing each other on consecutive weeks.

Claude

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