If 20 teams are participated in knockout tournament when how many match will be conducted
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Answer:
In a knockout tournament, there is only one unbeaten team/ individual, i.e the eventual winner. Therefore, the rest of the participants have to loose in order to have one winner. Therefore, in a knockout tournament of 100 teams, there needs to be 99 games, each game eliminating one participant such that we are left with the winner after 99 games.
The games will have to organised in the following manner:
Round 1 - 28 players get a bye, i.e. straight entry to round 2 and 72 players play 36 matches in which 36 win and progress to the next round.
Round 2 - no of participants 64 (28 with direct entry to round 2 and 36 that won in round 1), no of matches 32
Round 3 - 32 participants play in 16 matches, 16 progress to next round
Round 4 - 16 participants play in 8 matches, 8 progress to next round
Round 5 - 8 participants play in 4 matches, 4 progress to next round
Round 6 - 4 participants play 2 matches, 2 progress to next round/ finals.
Finals - 2 participants play 1 match and the winner is determined.
Total number of matches - 36+32+16+8+4+2+1=99
The readon why 28 players get straight to round 2 is because we want to bring the no of participants in a round to 2^n form. If we had 50 matches between 100 participants, we would have 50 going through to next round and 25 matches between them in round 2 and 25 moving to round 3. Now we can have 12 matches between 24 participants and no opponent for the 25th participant. This is the reason we want to keep the no of participants to a 2^n form.
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