Let the vertices of a regular 72-gon be colored red, blue, and green in equal parts. Show that there are 4 vertices of each color such that the resulting monochromatic quadrilaterals formed are congruent to each other.

Tiana Hill

Tiana Hill

Answered question

2022-10-07

Let the vertices of a regular 72-gon be colored red, blue, and green in equal parts. Show that there are 4 vertices of each color such that the resulting monochromatic quadrilaterals formed are congruent to each other.

Answer & Explanation

Samantha Braun

Samantha Braun

Beginner2022-10-08Added 9 answers

A circle is divided into 432 congruent arcs by 432 points. The points are colored in four colors such that some 108 points are colored Red, some 108 points are colored Green, some 108 points are colored Blue, and the remaining 108 points are colored Yellow. Prove that one can choose three points of each color in such a way that the four triangles formed by the chosen points of the same color are congruent.

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