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There exists a monochromatic isosceles trapezium ABCD

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February 18, 2011
geometrytrapezoidceiling functioncombinatorics proposedcombinatorics

Problem Statement

Let P1P_1 be a regular nn-gon, where n∈Nn\in\mathbb{N}. We construct P2P_2 as the regular nn-gon whose vertices are the midpoints of the edges of P1P_1. Continuing analogously, we obtain regular nn-gons P3,P4,…,PmP_3,P_4,\ldots ,P_m. For m≥n2−n+1m\ge n^2-n+1, find the maximum number kk such that for any colouring of vertices of P1,…,PmP_1,\ldots ,P_m in kk colours there exists an isosceles trapezium ABCDABCD whose vertices A,B,C,DA,B,C,D have the same colour.
Radu Ignat
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