Round Robin Tournament Scheduling

8 golfers

Lee Perriam · 2 · 4845

Lee Perriam

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on: April 19, 2006, 01:00:58 PM
I have 8 golfers playing four rounds of golf. How do I schedule the golf such that each player plays with everyone at least once and the number of repeats is minimised?


Ian Wakeling

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Reply #1 on: April 21, 2006, 02:04:32 AM
Lee,

You don't say how you would like to arrange the players for each round.  If you want foursomes then the situation is ugly, you will have to have a few pairs of players that play together in three out of the four rounds.  For example see my response to a similar request.

An alternative comes from considering how to schedule 9 players. Here the most natural thing to do is to play three threesomes in each round like this,

Round 1: (5 4 2)  (1 3 8)  (7 9 6)
Round 2: (1 2 7)  (4 8 6)  (3 5 9)
Round 3: (6 1 5)  (3 7 4)  (8 9 2)
Round 4: (2 6 3)  (5 8 7)  (9 4 1)


This is an analog of Richard's Social square since every player plays with every other exactly once.  Now remove the 9th player from the schedule to give

Round 1: (5 4 2)  (1 3 8)  (7 6)
Round 2: (1 2 7)  (4 8 6)  (3 5)
Round 3: (6 1 5)  (3 7 4)  (8 2)
Round 4: (2 6 3)  (5 8 7)  (4 1)


These mixed rounds of two threesomes and a pair are the only way to shedule the 8 players so that they all play together exactly once.

Ian.