Quandaries
and Queries
To Whom It May Concern:
I have a golf outing fast approaching and I’m having a problem matching the golfers so that everyone plays a round of golf with every other golfer in the group.
My problem is this: I have 16 golfers playing 5 rounds of golf. I would like a different foursome for every round of golf, that is each round (5 total) an individual is playing with 3 other players he hasn’t played with as of yet. Can you crunch the numbers and get back to me?
The way I see it, we have 20 combinations (5 rounds x 4 golfers) with numbers 1 thru 16.
Hi Bob,
This type of scheduling problem usually doesn't have a nice answer. The fact that you have 16 golfers is extremely fortunate since there is a solutiion in this situation.
Here are the four foursomes for each of the five rounds. The golfers are numbered 0 to 15.
Round1
{0, 4, 8, 12}, {1, 5, 9, 13}, {2, 6, 10, 14}, {3, 7, 11, 15}
Round2
{0, 5, 10, 15}, {1, 4, 11, 14}, {2, 7, 8, 13}, {3, 6, 9, 12}
Round3
{0, 6, 11, 13}, {1, 7, 10, 12}, {2, 4, 9, 15}, {3, 5, 8, 14}
Round4
{0, 7, 9, 14}, {1, 6, 8, 15}, {2, 5, 11, 12}, {3, 4, 10, 13}
Round5
{0, 1, 2, 3}, {5, 4, 7, 6}, {10, 11, 8, 9}, {15, 14, 13, 12}
Chris