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JBMO TST Moldova Problem 3

Source: JBMO TST Moldova Problem 3

October 13, 2020
combinatoricsregular polygon

Problem Statement

Let there be a regular polygon of nn sides with center OO. Determine the highest possible number of vertices kk (k≥3)(k \geq 3), which can be coloured in green, such that OO is strictly outside of any triangle with 33 vertices coloured green. Determine this kk for a)n=2019a) n=2019 ; b)n=2020b) n=2020.
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