MathDB

M2551

Part of Kvant 2019

Problems(1)

Polygon partitioned into triangles by multicoloured diagonals

Source: Kvant Magazine No. 3 2019 M2551

3/14/2023
The vertices of a convex polygon with n⩾4n\geqslant 4 sides are coloured with black and white. A diagonal is called multicoloured if its vertices have different colours. A colouring of the vertices is good if the polygon can be partitioned into triangles by using only multicoloured diagonals which do not intersect in the interior of the polygon. Find the number of good colourings.
Proposed by S. Berlov
combinatoricsKvant