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Slight edit for clarity. Instead of people eliminated in the first round we could also count the number of games played in the first round.
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Epiousios
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Another famous approach is to count the $2$-player games to determine a winner among $2^{n+1}$ people. It's $2^{n+1}-1$, the number of people to eliminate. It's also $2^n$ people eliminated in the first round, halving each round until we reach the final.

Another famous approach is to count the $2$-player games to determine a winner among $2^{n+1}$ people. It's $2^{n+1}-1$, the number of people to eliminate. It's also $2^n$ people in the first round, halving each round until we reach the final.

Another famous approach is to count the $2$-player games to determine a winner among $2^{n+1}$ people. It's $2^{n+1}-1$, the number of people to eliminate. It's also $2^n$ people eliminated in the first round, halving each round until we reach the final.

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J.G.
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Another famous approach is to count the $2$-player games to determine a winner among $2^{n+1}$ people. It's $2^{n+1}-1$, the number of people to eliminate. It's also $2^n$ people in the first round, halving each round until we reach the final.