Puzzle | Find Number of matches

A Tournament of cricket is to played with 100 teams. How many matches needs to be played to get a winner considering all matches are knockouts and the winning team plays with the other winning team ?

Asked in : Exl (On campus selection interview)

Solution :-
1st round: We need two teams to play one match so in the,
1st round = 100/2 = 50 matches

2nd round : This time we have 50 teams in tournament now,
2nd round =50/2 = 25 matches

3rd round Now we have 25 teams
3rd round = 24/2 = 12 matches ( there are odd number of teams in the 3rd round, one team is left, and 3rd round will be held in between 24 teams)

4th round : Now we have 13 teams, another team is left and matches played will be
4th round – 12/2 = 6 matches

5th round : No of teams left are 7
5th round = 6/2 = 3 matches

6th round : No of teams left are 4
6th round = 4/2 = 2 matches

7th round : Finally, 2 teams are left. Match is played between them
7th round = 2/2 = 1 match

So, the total number of matches played = 50 + 25 + 12 + 6 + 3 + 2 + 1 = 99

Trick : Find the number of losers. It is the number of teams subtracted by the winning team = 99 losers
that’s why, number of matches played = 99

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