5. The city center is a rectangle measuring $5 \times 8$ km, consisting of 40 blocks, each $1 \times 1$ km, with boundaries formed by streets that create 54 intersections. What is the minimum number of police officers needed to be placed at the intersections so that any intersection can be reached by at least one police officer driving no more than 2 km along the city streets?

Answer: 6 police officers.
Solution. Evaluation. Consider the intersections on the boundary. There are 26 in total. Each police officer can control no more than 5 intersections (if he is on the boundary, then exactly 5, if he is inside the city, then no more than 3 on each side and no more than 5 in the corner). Therefore, at least 6 police officers are needed.

Example (see fig).

![](https://cdn.mathpix.com/cropped/2024_05_06_c70926c617437423699dg-2.jpg?height=369&width=603&top_left_y=2140&top_left_x=218)

Criteria. If the solution is incorrect - 0 points.

If only an example is constructed - 2 points.

If only the evaluation is proven - 4 points.

If the correct solution (both example and evaluation) - 7 points.