Hello, we have twenty golfers and four rounds of golf. We would like to figure out how to make foursomes so that each golfer plays with as many different golfers as possible. Thank you for your time.

Mona

Hi Monica,

Number the golfers from 1 to 20 and arrange them in 5 rows and 4 columns as below.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The rows give the foursomes for the first round, so the first foursome is 1, 2, 3 and 4 the second is 5, 6, 7 and 8, and so on.

For round two shift the second column down one row, wrapping the 18 to the top, shift the third column down two rows wrapping the 19 and 15 to the top and shift the fourth column down three rows wrapping the 20, 16 and 12 to the top. This gives

 1 18 15 12 5 2 19 16 9 6 3 20 13 10 7 4 17 14 11 8

The rows give the foursomes for the second round, so the first foursome is 1, 18, 15 and 12 the second is 5, 2, 19 and 16, and so on.

For round three again shift the second column down one row, wrapping the 14 to the top, shift the third column down two rows wrapping the 11 and 7 to the top and shift the fourth column down three rows wrapping the 8, 4 and 20 to the top. The rows give the foursomes for the third round.

Repeat the procedure for round four.

Penny