  In this paper, we proposed an interesting problem that might be classified
into enumerative combinatorics. Featuring a distinctive two-fold dependence
upon the sequences' terms, our problem can be really difficult, which calls for
novel approaches to work it out for any given pair $(m,n)$. Complete or partial
solutions for $m=2, 3$ with smaller $n$'s are listed. Moreover, we have proved
the necessary condition for $p(m,n) \neq 0$ and suggested an elegant asymptotic
formula for $p(2,n)$. In addition, several challenging conjectures are
provided, together with concise comments.
