21.9*. In the park, there are 10000 trees planted in a square grid pattern (100 rows of 100 trees each). What is the maximum number of trees that can be cut down so that the following condition is met: if you stand on any stump, you will not see any other stump? (The trees can be considered thin enough.)
21.9. Let's divide the trees into 2500 quartets, as shown in Fig. 21.3. In each such quartet, no more than one tree can be cut down. On the other hand, all the trees growing in the upper left corners of the squares formed by our quartets of trees can be cut down. Therefore, the maximum number of trees that can be cut down is 2500.