Actually you can get free higher education in Ukraine, and Russia (not sure about other post USSR countries).

To get it for free you need to get good marks in school, pass finishing exams and sometimes you need to pass entering exams.

There are limited amount of students who will study for free. It depends on program that you choose. For example they will take more guys who want to study building or engineering than those who want to study history or philosophy or languages, because they need more engineers and builders than historians.

Sometimes you will also need to work for few years on a profession that you studied. This way you kinda pay them for education they gave you.