The Knockout Tournament

 In a classic ‘knockout’ tournament, each entrant plays a match against a single opponent, and the winner goes through to the next round. This continues until there is just one person left - the Champion !

The process of organising the competition is simple if there 8 entrants :

 

 If there are only 6 entrants, the situation is a little more complicated, and the organizer has to arrange for some entrants to get ‘byes’ into the second round: (see C and D below ) 

 

 

The Problem :

 6 entrants needed 3 rounds and a total of 5 matches to be played. There were 2 ‘byes’.

 How many rounds, and how many matches in total, need to be played if there were 25 entrants instead ?  How many ‘byes’ will be given in the first round ?

Draw up a possible match ‘tree’ for this tournament.

 What would be the requirements for a tournament with 100 entrants ?

Open the File as a Word Document

 

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Last modified: June 18, 2007