3. $333=9 \cdot 37=10 \cdot 33+3$. Therefore, the number of apartments in the entrance is less than 37 but more than 33. In this range, only 36 is divisible by 9. So, there are 36 apartments in the entrance, and 4 on each floor. Since $333=9 \cdot 36+2 \cdot 4+1$, apartment 333 is on the third floor.
3. Sasha invited Dima to visit, saying that he lives in entrance 10, apartment No. 333, but forgot to mention the floor. Approaching the building, Dima noticed that the building is nine-story. Which floor should he go to?