[ Inequalities. Case Analysis ] [Examples and Counterexamples. Constructions]

Authors: Golenisheva-Kumuzova T.I., Gurvich V.M., Kozhevnikov P.A., Yatsenko I.V.

There was not enough space for building a typical house. The architect changed the project: removed two entrances and added three floors. As a result, the number of apartments increased. He was pleased and decided to remove two more entrances and add three more floors.

Could the number of apartments have become even less than in the original project? (In each entrance, there is the same number of floors and the same number of apartments on all floors in all entrances.)

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Let's say the original project had 5 entrances, 2 floors, and one apartment on each floor. Then there were 10 apartments. After the project was changed, it became 3 entrances and 5 floors - 15 apartments, and after the second change - 1 entrance and 8 floors - 8 apartments.

## Answer

It could.