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an isosceles triangle

Source: Nordic 2019, P4

April 7, 2019
graph theorygeometry

Problem Statement

Let nn be an integer with n≥3n\geq 3 and assume that 2n2n vertices of a regular (4n+1)−(4n + 1)-gon are coloured. Show that there must exist three of the coloured vertices forming an isosceles triangle.
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