Question 159
A convex $n$-gon is drawn on the blackboard, $n \ge 4$. Paint each its vertex black or white. Say that a diagonal is *multicolor* if its endpoints are of different colors. We say that the painting is *good* if one can partition the $n$-gon into triangles by drawing some multicolor diagonals sharing no internal points. Find the number of good paintings.
(S. Berlov)
(S. Berlov)