# Good \(n\)-gons

**Discrete Mathematics**Level 5

Consider a convex \(2015\)-gon \(P\). An \(n\)-gon with all its vertices among those of \(P\) is called good if it doesn't share any edge in common with \(P\). Let the number of such \(n\)-gons be \(N_n\).

Find the digit sum of \(N_{20}+N_{15}\).

**Note 1 :** All numbers are expressed in base \(10\). You may need a CAS to find the digit sum.

**Note 2 :** Try this easier variant first.

**Looking forward to see different solutions :)**