# Minimum Tournament Required

During a contest, I came up with a question:

What are the minimum number of tournaments needed to get the winner? A player is out when he loses two matches. Total players are 51. ( Assume Badminton )

I'm not sure how to solve it. Unfortunately, It is confusing me with combinations and permutations. Any suggestions? Thanks!

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Just to be 100% sure, does "tournament" = "match"? There's probably different interpretations of these terms in mathematics, sports, and everyday English. Also, are you after the minimum number of tournaments to guarantee a winner (regardless of the outcomes of individual matches)? – Douglas S. Stones Oct 23 '12 at 11:04
@DouglasS.Stones Here Tournaments simply means "A game or contest in which two persons compete with each other" . Dont take it too seriously .Keep it simple :) – Sharad Dixit Oct 26 '12 at 6:38

51 players, 1 winner: 50 needed to go out.

50 players out, 2 losses each, need: 100 losses.

100 losses means 100 games.

So, minimum is: 100 games.

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I agree. There might be 101 games if the eventual winner loses one. – Ross Millikan Jul 9 '12 at 15:21

95 matches required... if make a binary tree with 32 players competing, only 1 will remain in end with no loss yet while the rest have 1 loss each... if these 32 players wid 1 loss each are made to compete again, then only 1 with 1 loss will remain and rest will be eliminated from the contest... this process can be done wid any number of players by making proper trees and optimizing number of matches required... i'm not sure if am able to optimize it enough to give least number of matches or not !

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This contradicts the earlier answer by ypercube. In particular, 95 matches implies 95 losses, which is insufficient to cause 50 people to have lost at least twice each. – Douglas S. Stones Oct 23 '12 at 11:11