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There is some issue with question I think, it's clearly given "Only one team emerges victorious in each round, while the other three teams face elimination.", so in a round only 4 teams participate? If that's a case, then there are 1024 teams and if we divide them in group of 4, there will be 256 contests and each contests will have 4 teams with one eventual winner, and based on the quoted definition, we should count this 256 rounds. Should have been written like in every round teams are divided in groups of 4 and each group will have one winner.
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