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Omni-MATH / We consider dissections of regular n-gons into n−2 triangles by n−3 diagonals which do not intersect inside the n-gon. A [i]bicoloured triangulation[/i] is such a dissection of an …

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We consider dissections of regular nn-gons into n−2n - 2 triangles by n−3n - 3 diagonals which do not intersect inside the nn-gon. A [i]bicoloured triangulation[/i] is such a dissection of an nn-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 integer n≥4n \ge 4 [i]triangulable[/i] if every regular nn-gon has a bicoloured triangulation such that for each vertex AA of the nn-gon the number of black triangles of which AA is a vertex is greater than the number of white triangles of which AA is a vertex. Find all triangulable numbers.
Plain-text mathematical notation (without MathML)
We consider dissections of regular n-gons into n−2 triangles by n−3 diagonals which do not intersect inside the n-gon. A [i]bicoloured triangulation[/i] 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 integer n≥4 [i]triangulable[/i] 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 than the number of white triangles of which A is a vertex.

Find all triangulable numbers.
Original LaTeX notation
We consider dissections of regular $n$-gons into $n - 2$ triangles by $n - 3$ diagonals which do not intersect inside the $n$-gon. A [i]bicoloured triangulation[/i] 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 integer $n \ge 4$ [i]triangulable[/i] 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 than the number of white triangles of which $A$ is a vertex.

Find all triangulable numbers.

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task_id
d800a609-6999-5752-b7b7-23119d228e22
task_key
test--d800a609-6999-5752-b7b7-23119d228e22
task_revision_id
1
config / split
/ test

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