MEMO 2014 pojedinačno problem 2

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24. rujna 2014.
We consider dissections of regular n-gons into n - 2 triangles by n - 3 diagonals which do not intersect inside the n-gon. A bicoloured triangulation is such a dissection of an n-gon in which each triangle is coloured black or white and any two triangles which share an edge have different colours. We call a positive interger n \geq 4 triangulable if every regular n-gon has a bicoloured triangulation such that for each vertex A of the n-gon the number of black triangles of which A is a vertex is greater that the number of white triangles of which A is a vertex.
Find all triangulable numbers.
Izvor: Srednjoeuropska matematička olimpijada 2014, pojedinačno natjecanje, problem 2