2 [ Inequalities problems. Case analysis ]

Sasha invited Petya to visit, saying that he lives in the 10th entrance in apartment No. 333, but forgot to mention the floor. Approaching the building, Petya noticed that the building is nine-story. Which floor should he go to? (The number of apartments on each floor is the same, apartment numbers in the building start from one.)

#
If there are no more than three apartments on a floor, then in ten entrances, there will be no more than $10 \cdot 9 \cdot 3=270$ apartments, which means apartment № 333 will not be in the 10th entrance. If there are no fewer than five apartments on a floor, then already in nine entrances, there will be no fewer than $9 \cdot 9 \cdot 5=405$ apartments, which means Sasha's apartment will not be in the 10th entrance. Therefore, there are 4 apartments on each floor, and in the first nine entrances, there are $9 \cdot 9 \cdot 4=324$ apartments. Then in the 10th entrance, the apartments start from 325. On the second floor, they will start from 329, and on the third floor, from 333. Thus, Petya needs to go up to the third floor.

## Answer

To the 3rd floor.