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# How many rounds will be there …

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How many rounds will be there in a knockout of (a) 10 teams and (b) 13 teams?

Mr Thunder 1 day, 7 hours ago

In a knockout tournament, the number of rounds can be determined by finding the smallest $$r$$ such that $$2^r \geq n$$, where $$n$$ is the number of teams. Let's calculate for each case: **(a) 10 teams:** To determine the number of rounds $$r$$: $2^r \geq 10$ Let's find the smallest $$r$$ where $$2^r \geq 10$$: - $$2^3 = 8$$ (not enough) - $$2^4 = 16$$ (sufficient) So, $$r = 4$$ rounds are needed for 10 teams in a knockout tournament. **(b) 13 teams:** To determine the number of rounds $$r$$: $2^r \geq 13$ Let's find the smallest $$r$$ where $$2^r \geq 13$$: - $$2^3 = 8$$ (not enough) - $$2^4 = 16$$ (sufficient) So, $$r = 4$$ rounds are needed for 13 teams in a knockout tournament. Therefore, in both cases: - For 10 teams, there will be $$\boxed{4}$$ rounds. - For 13 teams, there will also be $$\boxed{4}$$ rounds.

Asti Singh 2 weeks, 4 days ago

4

Dhon Molsom 2 weeks, 6 days ago

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