2. Let $A B C D$ be a square of side 4. Determine the largest positive integer $k$ with the following property: For an arbitrary arrangement of $k$ points strictly inside square $A B C D$, one can always find a square of side 1 , entirely contained in square $A B C D$ (with sides not necessarily parallel to the sides of square $A B C D$ ), whose strict interior contains none of the $k$ given points.

(Bojan Bašić)