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MathNet 2022-part-04 — 197 problems (EN–VI) Question 123

Math Olympiad Vault · MathNet 2022-part-04 — 197 problems (EN–VI)

Question 123

A convex $s$-gon is divided into $q$ quadrilaterals, $b$ of which are not convex. Prove that
$$
q \geq b + \frac{s-2}{2}.
$$