24 player pitch league

[pitchman]

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.

[Ian Wakeling]

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 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.

[pitchman]

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.

[Ian Wakeling]

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.