### MEMO 2014 pojedinačno problem 2

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Avg: 6,0 We consider dissections of regular -gons into triangles by diagonals which do not intersect inside the -gon. A

Find all triangulable numbers.

*bicoloured triangulation*is such a dissection of an -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*triangulable*if every regular -gon has a bicoloured triangulation such that for each vertex of the -gon the number of black triangles of which is a vertex is greater that the number of white triangles of which is a vertex.Find all triangulable numbers.

Izvor: Srednjoeuropska matematička olimpijada 2014, pojedinačno natjecanje, problem 2