Thanks Ian. I am also curious about close solutions for the number of players between 22 and 33.

For instance, according to the schoolgirl problem, 18 does not meet the "perfect" requirements of 6n+3, but for a total of 18 players you can complete 8 rounds and only be missing one opponent. Here is the table:

{"day 1: ", "ABC", "DEF", "GHI", "ahf", "dbi", "gec"}

{"day 2: ", "Abc", "Def", "Ghi", "aHF", "dBI", "gEC"}

{"day 3: ", "abC", "deF", "ghI", "AHf", "DBi", "GEc"}

{"day 4: ", "aBc", "dEf", "gHi", "AhF", "DbI", "GeC"}

{"day 5: ", "ADG", "BEH", "CFI", "aei", "bfg", "cdh"}

{"day 6: ", "Adg", "Beh", "Cfi", "aEI", "bFG", "cDH"}

{"day 7: ", "adG", "beH", "cfI", "AEi", "BFg", "CDh"}

{"day 8: ", "aDg", "bEh", "cFi", "AeI", "BfG", "CdH"}

The only pairs that don't play together are Aa, Bb, Cc, Dd, etc. So I would consider that a very close solution.

The same is true for 24 players. You can complete 10 normal rounds and in the last round have 6 foursomes play to make everything "perfect". See below:

{"day 1: ", "ABC", "DEF", "GHI", "JKL", "MNO", "PQR", "STU", "VWX"}

{"day 2: ", "JOT", "ESB", "API", "DML", "HCV", "QWN", "FKU", "GRX"}

{"day 3: ", "DVK", "SFO", "JQI", "EHL", "PTG", "WRC", "BMU", "ANX"}

{"day 4: ", "EGM", "FBV", "DWI", "SPL", "QKA", "RNT", "OHU", "JCX"}

{"day 5: ", "SAH", "BOG", "ERI", "FQL", "WMJ", "NCK", "VPU", "DTX"}

{"day 6: ", "FJP", "OVA", "SNI", "BWL", "RHD", "CTM", "GQU", "EKX"}

{"day 7: ", "BDQ", "VGJ", "FCI", "ORL", "NPE", "TKH", "AWU", "SMX"}

{"day 8: ", "OEW", "GAD", "BTI", "VNL", "CQS", "KMP", "JRU", "FHX"}

{"day 9: ", "VSR", "AJE", "OKI", "GCL", "TWF", "MHQ", "DNU", "BPX"}

{"day 10: ", "GFN", "JDS", "VMI", "ATL", "KRB", "HPW", "ECU", "OQX"}

{"day 11: ", "AFMR", "BNHJ", "CPOD", "EQVT", "GKSW", "IXUL", , }

So here is my question. I'd like to create tables for an upcoming tournament. I suspect that there will be between 22 and 33 players show up and I need to be prepared ahead of time to just fill in the blanks. It appears that there are better solutions that exist for plugging in teams rather than just creating a bye.

For instance, on game day if I have 26 players show up, is there a better or closer solution that exists rather than using the 27 player table and just making one of the players a BYE? The thing that helps me is it is unlikely that all rounds will be completed, so an odd round like I have shown above will not affect anything. I know ahead of time that we will not complete all the rounds for a "perfect" solution. What I am interested in is that we complete at least say 8 rounds with "perfect" threesomes and no repeats.