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

This article is contributed by DANISH RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up


Article Tags :
Practice Tags :


3


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.