How many rounds will be there …

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.

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