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IOQM 2023-24 P-16

Source:

September 3, 2023

Problem Statement

The six sides of a convex hexagon A1A2A3A4A5A6A_1 A_2 A_3 A_4 A_5 A_6 are colored red. Each of the diagonals of the hexagon is colored either red or blue. If NN is the number of colorings such that every triangle AiAjAkA_i A_j A_k, where 1≤i<j<k≤61 \leq i<j<k \leq 6, has at least one red side, find the sum of the squares of the digits of NN.
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