11.2

Part of 2021 Ukraine National Mathematical Olympiad

Problems(1)

3 vertices from n into n-gon, are sidelengths of a triangle

Source: 2021 Ukraine NMO 11.2

Find all natural numbers

n \ge 3

for which in an arbitrary

n

-gon one can choose

3

vertices dividing its boundary into three parts, the lengths of which can be the lengths of the sides of some triangle.
(Fedir Yudin)

combinatorial geometrycombinatoricsgeometry