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What's the difference between a math league and a competition?
Generally speaking, the league refers to round robin, for example, in a certain period of time or a certain number of games, points are calculated according to the outcome. Finally, the ranking is calculated by points.

Generally speaking, the competition is a knockout system, according to a certain number of times (it may also be a game of winning or losing, which depends on who gets the highest score), or the players catch each other and kill each other.

As far as football is concerned, the league generally refers to a season (a year or a quarter), and each team scores points according to the outcome, and finally depends on the results of each team.

The competition is similar to the cup, and it is eliminated by groups. Only one team wins in the final elimination, even if it is the champion.

However, in a math contest, sometimes it may just be a different name. It depends on the specific situation. Generally, competitions are selected from the lower level. If there are several regions or schools, they are generally leagues.