alt Hacker NewsCompetition. Nobody in the US cares about school math/physics/... olympiads. But they are/were a big deal in schools in the xUSSR.
There also was no centralized test system (like SAT) up until early 2000-s. People had to go and sit on entrance exams in each university where they wanted to apply. But winners of olympiads got automatic admission into good universities.
In addition, social sciences were a minefield in the USSR, especially subjects like political science or history. And hard sciences were safe.
For entrance exams though... At least in Poland, we had them as well. They were corrupt.
Cheating was rampant, and a very common way for getting admitted was paying professors from that uni for tutoring - who would train them on the type of tasks they would do at that uni.
And it prevented you from attending unis far away a lot of time due to time contraints.