[Jprogramming] Set of combinations with each two sharing at most one element

[Raul Miller]

On 3/2/08, Zsbán Ambrus <ambrus at math.bme.hu> wrote:
> Twenty-four bikers, 'A' to 'X', participate in matches.  In every
> match, exactly four bikers compete.  No two bikers may compete in more
> than one matches.  How many matches can you organize this way?

A related question is "do these matches have a canonical form"?

I do not know the answer to this question, but I can transform that
38 match competition you posted to this equally valid 38 match set:

ABCD AEFG AHIJ AKLM ANOP AQRS ATUV BEKU BHQG BILW BNFV BRTJ BMXP EHCO
EIRP EQVX ETDL EJMS HKDF HNTS HRUX HLVP IKTX INCU IFOS IGMV KNQW KROV
KCJP NRGL NDJX QTCF QDMO QJLU RFMW TGOW CSXW DGSU

-- 
Raul