The Knockout Problem

Probability Level 2

A table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 100 players took part in that tournament.

How many matches were played?


The answer is 99.

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Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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2 solutions

Montesa Joy Rebao
Nov 13, 2014

the number of games is equal to

the number of players minus one

G= N - 1

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Because each game results in one loss (assuming no draws), and there needs to be 100 − 1 = 99 100-1=99 losses for one winner, hence 99 \boxed{99} games are to be played.

Jared Low - 6 years, 4 months ago

100 players play 50 matches => 50 players

50 players play 25 matches => 25 players

24 players play 12 matches and 1 player doesn't play => 12 + 1 = 13 players

12 players play 6 matches and 1 player doesn't play => 6 + 1 = 7 players

6 players play 3 matches and 1 player doesn't play => 3 + 1 = 4 players

4 players play 2 matches => 2 players

2 players play 1 matches => 0 players

So, there are 50+25+12+6+3+2+1 = 99 matches

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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