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Creating 4 Foursomes
One afternoon at Euler Golf Club in Newton, New York, the head pro received a phone call with an unusual request. It seems that a prominent member of the club, Bartholomew Stockman, wanted to entertain twelve clients at the club over a four day period. Mr. Stockman and three of his company’s financial advisors would also play. In order for Stockman and the advisors to get to know each client, Mr. Stockman wanted the sixteen players to play in four foursomes each day with one adviser per foursome. In addition, Mr. Stockman wanted each client to play with each other client. This meant that no one would play with another person twice. The head pro said this would be no problem and he would make sure the outing would go smoothly.
Later that day, the head pro turned to his first assistant, Smiley Edwards, and tasked him with creating the foursome sheets for each of the four days. When Smiley received the list of names from Mr. Stockman’s office, he began dividing the names into groups of four. The groupings for the first two days came easily. However, Smiley had trouble not repeating names for the third and fourth days. Despite his determined efforts, he couldn’t make it work.
Afraid that he would look stupid to his boss, he turned to Archie Meadese, a high schooler who did odd jobs around the pro shop. The sharp young man said that he would do it if he were paid 50 cents for each player, each day. Not thinking that 50 cents sounded like much, Smiley agreed. Two days later, Archie gave the completed tee sheets to Smiley. This is how the clever teenager figured it out.
First, he assigned numbers 1 through 4 to Mr. Stockman and his three executives and numbers 5 through 16 to each client. He listed them as follows:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16.
Then he grouped the numbers by rows, creating foursomes:
Day 1
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16.
Next he grouped the numbers by columns:
Day 2
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16.
In contemplating Day 3, he saw that so far the groups had all used numbers from the same row or the same column. This meant each new foursome would have to use numbers from different rows and columns. For simplicity’s sake, he decided to start with the numbers on the diagonals for Golfer 1 and Golfer 4:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16.
Now eight numbers remained. Still understanding that the numbers for Golfer 2 and Golfer 3 would have to come from different rows and columns, he grouped Golfers 2 and 3 like this:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16.
Therefore the tee sheet looked as follows for the third round:
Day 3
1 6 11 16
2 5 12 15
3 8 9 14
4 7 10 13.
Organizing the foursomes for the fourth day, came easily for Archie. Starting with Golfer 1, he made a list of the six players Golfer 1 still had not played with. Predictably, they turned out to be from different rows and columns. He did the same with Golfers 2, 3, and 4. His lists looked like this:
1: 7, 8, 10, 12, 14, 15
2: 7, 8, 9, 11, 13, 16
3: 5, 6, 10, 12, 13, 16
4: 5, 6, 9, 11, 14, 15
Careful not to repeat numbers, Archie filled out the foursomes.
Day 4
1 7 10 14
2 8 9 13
3 5 12 16
4 6 11 15
When the four days of golf were over, Bartholomew Stockman thanked the head pro. “Everything went great. I was really impressed with how well you created the foursomes. I tried my hand at figuring it out initially but I just got confused. You must be good with numbers.”
The pro raised his palms to fend off the compliment. “Oh, no, no. Not me. Smiley handled it.” Mr. Stockman then turned to the first assistant. “My, Smiley. I didn’t know you were so smart. Thank you for your efforts.” Smiley smiled reluctantly as he shook hands with the impressed member.
Smiley Edwards was glad that Archie Meadese made him look good, but he wasn’t so sure it was worth the $32 he owed the clever lad.