Re^2: Unique Combos with Math::Combinatorics (fair 5)

Trimming your original 30 teams more fairly, it is pretty easy to come up with a fair arrangement where each player gets to play on 5 teams. For example:

AGMS BIKR CFNQ DHLP EJOT UVWX
AHOQ AKPU ALTW ANRV BCDE BHTU
BJPX BLQV CHMW CIPV CJSU DGOR
DINX DJKQ EGNW EHKS EIMU FGIJ
FLRX FMTV FOSW GKTX LMNO PQRS
[download]

I strongly doubt that such can be broken into "rounds", however.

- tye

Comment on Re^2: Unique Combos with Math::Combinatorics (fair 5) Download Code

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Re^3: Unique Combos with Math::Combinatorics (fair 5) by ambrus (Abbot) on Mar 02, 2008 at 16:23 UTC
The 30 lines of the affine plane certainly can be broken to 6 rounds or parallel lines. ( `ABCDE FGHIJ KLMNO PQRST UVWXY AFKPU AGMSY AHOQX AILTW AJNRV BFOSW BGLQV BHNTU BIKRY BJMPX CFNQY CGKTX CHMRW CIOPV CJLSU DFMTV DGORU DHLPY DINSX DJKQW EFLRX EGNPW EHKSV EIMQU EJOTY` [download] ) Update: yeah, the example is wrong, but the statement is still true. Uh. `ABCDE FGHIJ KLMNO PQRST UVWXY AFKPU BGLQV CHMRW DINSX EJOTY AGMSY BHNTU CIOPV DJKQW EFLRX AHOQX BIKRY CJLSU DFMTV EGNPW AILTW BJMPX CFNQY DGORU EHKSV AJNRV BFOSW CGKTX DHLPY EIMQU` [download]	[reply] [d/l] [select]
Re^4: Unique Combos with Math::Combinatorics (fair 5) by tye (Sage) on Mar 03, 2008 at 17:20 UTC
If you use one line to "factor out" extra members from teams from other lines, then you can get 5 fair rounds: `_BCDE FGHI_ KLM_O PQ_ST UVWX. > AJNR. A_KPU _GLQV CHMR_ DIN_X EJOT. > FBWS. AGMS. BHN_U _IOPV DJ_QW EFLR_ > .TCKX AHO_X BIKR. CJLS_ DF_TV _GNPW > Q.UME AI_TW BJM_X CFNQ. _GORU E_KSV > LP.DH ajnrV bfOsw cGktx dhlp. eImqu BCDE FGHI KLMO PQST UVWX AJNR AKPU GLQV CHMR DINX EJOT FBWS AGMS BHNU IOPV DJQW EFLR TCKX AHOX BIKR CJLS DFTV GNPW QUME AITW BJMX CFNQ GORU EKSV LPDH` [download] - tye	[reply] [d/l]