3. An accident has occurred in the reactor of a research spacecraft, and toxic substances are leaking from it. All corridors between rooms are equipped with airtight doors, but there is no time to close individual doors. However, the captain can still give the command "Close $N$ doors," after which the ship's artificial intelligence will close $N$ random doors. What is the smallest $N$ so that the entire crew can be guaranteed to survive in the lounge?
Solution. There are a total of 23 corridors on the spaceship. If no more than 21 doors are closed, then the corridors between the reactor and the right engine, and between the right engine and the lounge, may remain open, which means the crew will be in danger. Therefore, at least 22 doors must be closed.

Criteria. Correct answer without justification - 0 points. Error in counting the number of corridors - 4 points.

![](https://cdn.mathpix.com/cropped/2024_05_06_3eae483af5a465c21e29g-1.jpg?height=783&width=482&top_left_y=1616&top_left_x=1438)