RO-TST 2010 Problem 9

Let $n$ be an integer number greater than or equal to $2$ , and let $K$ be a closed convex set of area greater than or equal to $n$ , contained in the open square $(0, n) \times (0, n)$ . Prove that $K$ contains some point of the integral lattice $\mathbb{Z} \times \mathbb{Z}$ .

Marius Cavachi