Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 1 - Problem Solving and Critical Thinking - 1.3 Problem Solving - Exercise Set 1.3 - Page 39: 40

Answer

7 games need to be played to determine the tournament winner.

Work Step by Step

Eight teams are competing in the tournament. Any team that loses a game is eliminated. This means that after 1 game, there is 1 less potential winner. We have the real winner when there's exactly 1 potential winner left, or rather when all the other teams are eliminated. We have 8 teams, therefore for there to be 1 left, we need to eliminate $8-1=7$ teams. To eliminate 7 teams in this tournament, there has to be exactly 7 games. 7 games need to be played to determine the tournament winner.
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