Problem 11.1. Masha lives in apartment No. 290, which is located in the 4th entrance of a 17-story building. On which floor does Masha live? (The number of apartments is the same in all entrances of the building on all 17 floors; apartment numbers start from 1.$)$
# Answer: 7.

Solution. Let $x$ be the number of apartments per floor, then there are $17 x$ apartments in each entrance. Thus, in the first three entrances, there are $51 x$ apartments, and in the first four $68 x$.

If $x \geqslant 6$, then in the first three entrances there are at least 306 apartments, so apartment No. 290 cannot be located in the fourth entrance. And if $x \leqslant 4$, then in the first four entrances there will be no more than 272 apartments, which again means that apartment No. 290 cannot be located in the fourth entrance. The only remaining option is when $x=5$.

Then in the first three entrances, there are 255 apartments, and apartment No. 290 is the 35th in the fourth entrance, i.e., it is located on the 7th floor.