4. There are 17 button-lamps arranged in a circle. Initially, all the lamps are on. With one press of a button, the state of the pressed button-lamp and its neighbors changes (from on to off and vice versa). Is it possible to turn off all the button-lamps with such operations?
Solution. After seventeen single presses on each button-lamp, they will all change their state three times, which means they will not be lit. Answer: possible.

Criteria. Any correct solution: 7 points.

The correct pressing algorithm is indicated, but it is not justified why it leads to the goal: 6 points.

It is stated that each button needs to be pressed no more than once, and the order of pressing does not matter: 1 point.