I'm trying to prove that this problem is in NP:
Given $n$ dices, there are at least $m$ ways of rolling a given value $y$.
Theoretically I need to argue that there is an efficient verifier for Problem $X$. In other words, describe a verifier such that for any yes instance of $X$, there exists a certificate that the verifier will accept, and for any no instance of $X$, no such certificate exists. The running time of the verifier (and hence the size of the certificate) must be polynomial. Typically, a solution to the given problem is a sufficient certificate.
So in other words, I need to solve this problem algorithmically, correct? Any idea how I could implement this?