7.5. In a row, there are 20 free chairs. From time to time, a person approaches and sits on one of the free chairs, at which point one of their neighbors, if any, immediately stands up and leaves (the two of them do not sit together). What is the maximum number of chairs that can be occupied?
Answer: 19.

Note that all chairs cannot be occupied, otherwise, when the 20th person sat down, no one would leave, and the neighboring chair would be occupied. We will show how 19 chairs can be occupied. The first person takes the first chair, the next person takes the third chair, the third person takes the second chair, and the third person leaves. Then the next person takes the fourth chair, the next takes the third chair, and the fourth person leaves, and so on. By such operations, the first 19 chairs can be filled.

Remarks. The algorithm is provided for occupying 19 chairs without proving maximality - 5 points.