8.5. In a city, there are 10 streets parallel to each other and 10 others intersect them at right angles. What is the minimum number of turns a closed route can have, passing through all intersections?
8.5. Answer. 20.

It is easy to provide an example with 20 turns. We will prove that fewer than 20 turns are not possible. Consider 10 streets of a certain direction. If the route passes through each of them, then there are already at least two turns of the route on each of them, and the proof is complete. If there is a street that the route does not pass through at all, then it must pass through all ten perpendicular streets. We can apply the same reasoning to them.