[guga42k]

>What definitely exists in Russia (or at least some big cities) is a system of free after-school classes, where you can go and learn how to solve olympiad-type math problems and become more interested in maths

And for people outside of big cities there were schools-by-correspondence famously running by Moscow State University for math and MIPT for math/physics. The setup was you were mailed a small booklet every month. You had to study the material, solve problems and sent solutions back. The solutions were graded and sent back to you. It was great on so many levels. First and the most important aspect it taught discipline and time management. The material was amazing when you were given gradual increase in complexity instead of sheer volume of simple problems or a few olympiad-level problems which can't be solved if you are not there yet.

[skeletal88]

I had that in Estonia as well, when I was in the gymnasium in 2002-03. I applied to the school for.. Exact sciences that was part of an university, for their informatics course. They sent me booklets with lessons and exercises and i sent my solutions, then received the next booklet with the results. I wasn't good at that, but it was interesting.