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MathNet 2007-part-02 — 187 problems (EN–VI) Question 104

Math Olympiad Vault · MathNet 2007-part-02 — 187 problems (EN–VI)

Question 104

We have a square grid of $19 \times 19$. We call a rectangle **good** if its edges are all along the border of small squares. What is the smallest $n$ with the following property?

Property: If $9$ small squares are removed from the grid, we can divide remaining area into $n$ or less number of good rectangles.