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MathNet 2011 Question 63

Math Olympiad Vault · MathNet 2011

Question 63

A grid of points has $10$ rows and $10$ columns. Each point is coloured red or blue. Neighbouring points in the same row or column are joined by a segment of their common colour if they have the same colour, and by a green segment otherwise. There are $52$ red points: $2$ at corners, another $16$ on the boundary, and the remaining red points in the interior.
Question illustration
There are $98$ green segments. Find the number of blue segments.