Math CentralQuandaries & Queries


Question from Roland:

We have a golf tournament, 12 players, three rounds. We want to pair so that we have pairings with as few duplications as possible.

Hi Roland,

There is actually 161 ways you could pair golfers for a single round of golf. A combination is a group chosen from a set (or larger group) where the order of when the individual members of group does not matter. A permutation is a group chosen where the order does matter. For example: How many ways can 1st, 2nd and 3rd place in a race be awarded from a group of 10 runners? Since for pairings in a golf tournament order does not matter, so I will use combinations. (For example: Player 1 vs Player 12 is the same as Player 12 vs Player 1).
For the first pair, you choose 2 golfers from a group of 12. For the next pair, you choose 2 golfers from a group of 10 (because 2 are already in a pair). The next pair, you choose 2 golfers from a group of 8... you get the idea. Add all the combinations together for the total number of combinations.


For more information on combinations check out

The easiest way to create pairs for 3 rounds of golf is create two rows, numbers 1-6 on the top row and 7-12 on the bottom row. Keep the top row fixed and rotate the bottom row one to the left for each round. Using this method you could add up to 3 more rounds of golf.


For a more complicated golf tournament structure with groups of 4 check out:


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