How to divide a 20-person event into one, two and three people?

For the above questions, if I ask: how to set up a competition system of 20 people, not only can the top three be decided absolutely fairly, but also the number of participants can be as small as possible.

If the number of players is not considered, there are 190 games in the round robin for 20 people. It is absolutely fair to rank them according to their distribution. In order to reduce the number of competitions, we have to adopt the elimination system. The timetable I set is as follows:

First, a group of five people were randomly selected to compete in four ABCD groups, and 1 and 2 were promoted to the top eight, and then 1, 2, 3 and 4 were decided by drawing lots according to the elimination rules. As long as 1 and 2 are not in the same group, this term is fair. If 1 and No.2 come from the same group, then No.3 in this group will be knocked out with the previously decided No.3, and the winner will be the final winner of No.3. In this way, each non-top three members will lose to three or two people, and at least 1 of these two people will lose to another 1, which is in line with the principle of fairness. (Of course, if there is an abnormal situation that Group A loses to Group D first and Group A wins first, it will be difficult to handle. )

According to the above competition system, in theory, the top three can be decided in up to 49 games (round robin 10*4, knockout 4+2+2, play-offs 1).