Round Robin Tournament Scheduling
Schedules - You must register to Post and Download => Requests => Topic started by: pitchman on September 16, 2013, 07:20:48 AM
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Need help figuring out a schedule for a pitch league I run. The league runs for 10 weeks and I want it so that every player plays the least amount of time on another player's table. So if there are 24 players and there are 4 players per table each week for 10 week then no player should be on the same table with another player for the first 7 weeks with the 7th week having only 1 previous player having played on that table. Thanks in advance.
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I can offer a schedule like this:
R1 (5 23 11 12)
R1 (6 21 2 1)
R1 (24 13 9 4)
R1 (10 8 19 16)
R1 (17 15 18 14)
R1 (22 7 3 20)
R2 (24 7 16 10)
R2 (14 8 21 11)
R2 (6 17 20 23)
R2 (1 19 3 15)
R2 (9 22 5 2)
R2 (12 13 18 4)
R3 (3 4 23 14)
R3 (10 6 12 15)
R3 (18 19 22 21)
R3 (2 20 16 9)
R3 (5 11 7 13)
R3 (8 1 24 17)
R4 (5 13 10 3)
R4 (20 14 8 18)
R4 (4 12 24 21)
R4 (23 22 1 16)
R4 (11 9 6 15)
R4 (2 17 19 7)
R5 (23 15 13 17)
R5 (22 10 4 20)
R5 (18 16 11 6)
R5 (8 3 12 2)
R5 (19 5 14 24)
R5 (21 1 7 9)
R6 (7 23 8 6)
R6 (13 9 20 19)
R6 (3 24 2 18)
R6 (15 5 4 21)
R6 (1 11 17 10)
R6 (12 16 14 22)
R7 (14 1 12 7)
R7 (16 17 21 3)
R7 (15 20 5 8)
R7 (22 24 13 6)
R7 (19 4 11 2)
R7 (9 10 23 18)
R8 (2 14 6 5)
R8 (7 16 15 4)
R8 (1 18 8 13)
R8 (23 3 22 11)
R8 (10 21 20 24)
R8 (17 19 9 12)
R9 (4 22 17 8)
R9 (14 3 10 9)
R9 (15 2 24 23)
R9 (6 7 18 19)
R9 (20 12 1 5)
R9 (11 21 13 16)
R10 (13 2 10 14)
R10 (3 6 4 1)
R10 (16 18 17 5)
R10 (21 12 23 19)
R10 (11 20 7 24)
R10 (8 9 15 22)
Where each pair of players meets at a table either once or twice. However it will not have the property that the first 7 weeks have all pairs unique. You might be able to construct such a schedule by hand, so start with the 24 golfer schedule here (http://www.mathpuzzle.com/MAA/54-Golf%20Tournaments/mathgames_08_14_07.html) and then write down the 8 triples such as AQI which don't occur, these will form the basis of rounds 8 to 10, you would then need to plug the gaps so as not to introduce any other pairings more than once.
I am not sure I have understood what you mean by '1 previous player'.
PS note that the golf schedule I linked to has an error on day 6, the first E should be a G.
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The '1 previous player' is that in the 7th round of play you will have to have one of the players that was on your table in the prior 6 weeks be on your table again. The table you just sent will have in round 1 and 2 players 10 & 16 on the same table. I was hoping to have no one on the same table for the first 6 weeks. You've done this for me in the past with 28 players and it work out wonderfully.
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28 players and 9 rounds is special, in the sense that a fully balanced schedule is possible, so it is a simple matter to add a 10th round. Unfortunately 24 players and 10 rounds presents more difficulty. It is possible to go 7 rounds (not 6) without having pairs of players sit together twice, this is the golf schedule that I have linked to above, but adding a further three rounds to this unbalanced schedule is a challenging problem, which is why I chose an easier option above.
I am still unsure about the format of play at a table, do you play as 4 individuals, or are you playing 2 against 2?
For anyone else interested, here is a link to the previous thread on this subject.