[Retros] How many times could a Diagram be repeated during a legal game?

[raosorio at fibertel.com.ar]

Hi,

I want to share here something which is my mind from some years ago.
Let's define "Diagram" just as a board showing pieces on it, i.e., no matter
at all anything regarding the right's status, not even who's to move.

Questions:

a) How many times could a Diagram  be repeated during a legal game?

b) How many single moves are needed to show these repetitions starting 
     from a proper Diagram and knowing who's to move?  (following the retro
     conventions)

I have the advantage to have headquarters at the Argentine Chess Club so I
have the opportunity to test this type of things with very  skilfull master lever
players. It's remarkable how  far are they to accept the the answer to a).

I will post my own answers in few days but it would be interesting to have
some interaction first (of course I could be missing something).

Best,
Roberto Osorio