A total of 129 players entered a singleelimination handball

A total of 129 players entered a single-elimination handball tournament. In the first round of play, the top seeded player received a bye and the remaining 128 players played in 64 matches. Thus, 65 players entered the second round of play. How many matches must be played to determine the tournament champion?

Solution

A total of 129 players entered a single-elimination handball tournament. In the first round of play, the top seeded player received a bye and the remaining 128 players played in 64 matches. Thus, 65 players entered the second round of play. How many matches must be played to determine the champion.
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Before 1st round: 129 or 64 games
Before 2nd round: 129-(128/2) = 129-64 = 65 or 32 games
Before 3rd round: 65-32 = 33 or 16 games
Before 4th round: 33-16 = 17 or 8 games
Before 5th round: 17-8 = 9 or 4 games
Before 6th round: 9-4 = 5 or 2 games
Before 7th round: 5-2 = 3
Now they need 3 games to determine a champ
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64 + 32 + 16 + 8 + 4 + 2 + 3 = 129 games