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5

Part of 2012 Swedish Mathematical Competition

Problems(1)

3 vertrices have same color, also isosceles, when 3 colors for 13-gon

Source: 2012 Swedish Mathematical Competition p5

4/30/2021
The vertices of a regular 1313-gon are colored in three different colors. Show that there are three vertices which have the same color and are also the vertices of an isosceles triangle.
combinatorial geometryColoringisosceles