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points of the plane have been colored by 2013 different colors

Source: 2013 Saudi Arabia Pre-TST 3.3

September 13, 2020
combinatoricsColoringcombinatorial geometry

Problem Statement

The points of the plane have been colored by 20132013 different colors. We say that a triangle △ABC\vartriangle ABC has the color XX if its three vertices A,B,CA,B,C has the color XX. Prove that there are in nitely many triangles with the same color and the same area.
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