All edges and all diagonals of regular hexagon A1A2A3A4A5A6 are colored blue or red such that each triangle AjAkAm,1≤j<k<m≤6 has at least one red edge. Let Rk be the number of red segments AkAj,(j=k). Prove the inequality
k=1∑6(2Rk−7)2≤54. inequalitiescombinatorics unsolvedcombinatoricsIMO Longlist