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MathNet 2026 — Part 11 Question 7

Math Olympiad Vault · MathNet 2026 — Part 11

Question 7

Some squares of a $n \times n$ table $(n\gt 2)$ are black, the rest are white. In every white square we write the number of all the black squares having at least one common vertex with it. Find the maximum possible sum of all these numbers.

The answer is $3 n^{2}-5 n+2$.