in reply to Re^2: Unique Combos with Math::Combinatorics (fair 5)
in thread Unique Combos with Math::Combinatorics

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

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)

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

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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

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    - tye        

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