Let P be a convex polygon, and let n \geq 3 be a positive integer. On each side of P, erect a regular n-gon that shares that side of P, and is outside P. If none of the interiors of these regular n-gons overlap, we call P n-good.
(a) Find the largest value of n such that every convex polygon is n-good.
(b) Find the smallest value of n such that no convex polygon is n-good.