Help to write the R-code, please

Task:
A family of sets of letters is given. Find K for which one can
construct a
set consisting of K letters, each of them belonging to exactly K sets
of a
given family.

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PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Do this. It warns you that this list is not for homework help, nor is it a do-my-work-for-me forum.

Sent from my phone. Please excuse my brevity.