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While giving byes on 4 quarter based knockout basis tournament for 21 teams, 1 quarter will have 3 byes but with that there is difficulty having proper pairing of the matches.

So, How can I draw a fixture of knockout tournament for 21 teams using the quarter method with the stipulations I present?

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If I understand this question correctly you would like three brackets of five and one bracket of six. With the winner of each bracket having a spot in the semi finals. Here is what it looks like: 21 Team Tournament

If the teams are ranked 1-21 then it should be easy to find the pairings. If the teams are not ranked, then draw names out of a hat for the tournament slots.

Now if you have them seeded you would want the four highest seeds to have the possibility of meeting up in the two semi final games. Using the PDF for the 21 team tournament the match ups should be (the number corresponds to the game number on the sheet):

 1. 16 vs 17 
 2. 13 vs 20
 3. 12 vs 21
 4. 15 vs 18
 5. 14 vs 19 
 6. 8 vs 9
 7. 7 vs 10
 8. 6 vs 11
 9. 1 vs winner of game 1
 10. 5 vs winner of game 2
 11. 4 vs winner of game 3
 12. 2 vs winner of game 4
 13. 3 vs winner of game 5

From there on out the winners will play according to the bracket.

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    It is really even simpler - just go to the next power of 2...in this case a 32 team bracket. Put your 21 teams in slots 1-21, and erase all the slots that are empty of teams. What is left is your tournament. – Oldcat Sep 4 '14 at 20:30

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