Question 64
Assume the dimensions of an answer sheet to be $297 \text{ mm}$ by $210 \text{ mm}$. Suppose that your pen leaks and makes some non-intersecting ink stains on the answer sheet. It turns out that the area of each ink stain does not exceed $1 \text{ mm}^2$. Moreover, any line parallel to an edge of the answer sheet intersects at most one ink stain. Prove that the total area of the ink stains is at most $253.5 \text{ mm}^2$. (You may assume a stain is a connected piece.)