IMO 1982 LL CZS21

Origin: CZS

Problem

All edges and all diagonals of regular hexagon A1A2A3A4A5A6 are colored blue or red such that each triangle AjAkAm, 1 \leqj < k < m \leq6 has at least one red edge. Let Rk be the number of red segments AkAj, (j ̸= k). Prove the inequality  k=1 (2Rk −7)2 \leq54.