2023 IOQM/Problem 16
Problem
The sides of a convex hexagon 
are coloured red. Each of the diagonal of the hexagon is coloured red or blue. If N is the number of colourings suhch that every triangle 
, where 
has at least one red side, find the sum if the squares of digits of N.
Solution
Two triangle can be formed: 
and 
, which might or might not have red colouring, rest of the triangle will have at least 1 red colouring because they will be a part of the hexagon, eg: 
.
\textbf{I}:
