A tennis tournament has 85 participants. Players who lose a game are immediately eliminated; players who win a game keep playing. Still, the organizers have a lot of choices to make. They could give a first round bye to some players so that after the first round there are 26 = 64 players and no more bye are needed. Or they could give even a second round bye to the best players, or possibly even a third round bye to the very best ones. What is the best strategy for the organizers if they want to choose the winner of the tournament using as few games as possible?

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Answered: A tennis tournament has 85…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A tennis tournament has 85 participants. Players who lose a game are immediately eliminated; players who win a game keep playing. Still, the organizers have a lot of choices to make. They could give a first round bye to some players so that after the first round there are 2⁶ = 64 players and no more bye are needed. Or they could give even a second round bye to the best players, or possibly even a third round bye to the very best ones. What is the best strategy for the organizers if they want to choose the winner of the tournament using as few games as possible?

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