Golf Problem
I have 12 golfers who golf in Foursomes.
We are golfing for 4 days.
If I mark each player with a letter.
a,b,c,d,e,f,g,h,i,j,k,l.
I need to find a calulation so everyone plays with each other at least once.
Thank you for trying
Carlton2772
1 Answer
The number of ways you can choose 2 players out of 12 players is
\[{12\choose 2}=\frac{12!}{10!2!}=66.\]
So there is going to be a total of $66=4\times 16+2$ games. So you can arrange 16 games for three days and 18 games for one day.
You can have 3 groups of 4 each day, so the 4 players in a group only play with each other. Then in the first day there will be
\[3\times{4\choose 2}=18\]
games. Then you arrange 16 games for the remaining 3 days.
Poincare
133
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