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MathNet 2006 — Part 02 Question 7

Math Olympiad Vault · MathNet 2006 — Part 02

Question 7

On a gridded board of $10$ rows by $500$ columns, starting with the lower left square and following the model suggested by the figure, Joaquín painted $2006$ squares black.
Question illustration
Then Agustina painted the squares that had two or more neighboring black squares blue. How many squares did Agustina paint?

Note: Two squares are neighbors if they have a common side.