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- Ricky X. F. Chen added an answer:The maximum number of cycles of the product of a given permutation and a n-cycle?

#### About Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).

I found this problem without comments in a french exercise book of 1982, now out of print : {\em 1932 exercices de mathématiques} by Luc Moisotte, ISBN 2-04-015483-3.