35 team knockout fixture

35 teams: 29 byes, 6 teams play Round I, 34 matches over 6 rounds.

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How the 35 team fixture is drawn

Upper half and lower half

35 is odd, so the upper half gets (35 + 1) ÷ 2 = 18 teams (Teams 1–18) and the lower half gets (35 − 1) ÷ 2 = 17 teams (Teams 19–35).

Byes

Byes = next power of 2 − number of teams = 64 − 35 = 29. 29 is odd, so the upper half gets (29 − 1) ÷ 2 = 14 byes and the lower half gets (29 + 1) ÷ 2 = 15 byes.

Which teams get the byes, and why

The textbook places byes in this order: the 1st bye to the last team of the lower half, the 2nd to the first team of the upper half, the 3rd to the first team of the lower half and the 4th to the last team of the upper half. The remaining byes follow the same pattern, moving inward. For 35 teams:

  1. Team 35 — last team of the lower half
  2. Team 1 — first team of the upper half
  3. Team 19 — first team of the lower half
  4. Team 18 — last team of the upper half
  5. Team 34 — 2nd-last team of the lower half
  6. Team 2 — 2nd team of the upper half
  7. Team 20 — 2nd team of the lower half
  8. Team 17 — 2nd-last team of the upper half
  9. Team 33 — 3rd-last team of the lower half
  10. Team 3 — 3rd team of the upper half
  11. Team 21 — 3rd team of the lower half
  12. Team 16 — 3rd-last team of the upper half
  13. Team 32 — 4th-last team of the lower half
  14. Team 4 — 4th team of the upper half
  15. Team 22 — 4th team of the lower half
  16. Team 15 — 4th-last team of the upper half
  17. Team 31 — 5th-last team of the lower half
  18. Team 5 — 5th team of the upper half
  19. Team 23 — 5th team of the lower half
  20. Team 14 — 5th-last team of the upper half
  21. Team 30 — 6th-last team of the lower half
  22. Team 6 — 6th team of the upper half
  23. Team 24 — 6th team of the lower half
  24. Team 13 — 6th-last team of the upper half
  25. Team 29 — 7th-last team of the lower half
  26. Team 7 — 7th team of the upper half
  27. Team 25 — 7th team of the lower half
  28. Team 12 — 7th-last team of the upper half
  29. Team 28 — 8th-last team of the lower half

Teams with a bye do not play Round I. They go straight to Round II.

Round I and total matches

35 − 29 = 6 teams play Round I in 3 matches:

  • Match 1: Team 8 vs Team 9
  • Match 2: Team 10 vs Team 11
  • Match 3: Team 26 vs Team 27

Total number of matches = number of teams − 1 = 35 − 1 = 34 (not including a third-place match). There are 6 rounds, because 64 = 2 × 2 × 2 × 2 × 2 × 2 — worked out from the textbook illustrations, not a textbook formula.

Print or save as PDF

Tap “Print fixture (A4)” and choose “Save as PDF” as the printer to get a 35 team knockout fixture PDF. The bracket prints on 2 A4 pages (upper half, then lower half) in portrait.

Questions

How many byes are there in a 35 team knockout fixture?

Byes = next power of 2 − number of teams = 64 − 35 = 29. 29 is odd, so the upper half gets (29 − 1) ÷ 2 = 14 byes and the lower half gets (29 + 1) ÷ 2 = 15 byes. The byes go, in order, to teams 35, 1, 19, 18, 34, 2, 20, 17, 33, 3, 21, 16, 32, 4, 22, 15, 31, 5, 23, 14, 30, 6, 24, 13, 29, 7, 25, 12 and 28. These teams do not play Round I and go straight to Round II.

How many matches and rounds are there for 35 teams?

Total number of matches = number of teams − 1 = 35 − 1 = 34, not including a third-place match. There are 6 rounds, because 64 = 2 × 2 × 2 × 2 × 2 × 2 (worked out from the textbook illustrations, not a textbook formula).

How are 35 teams divided into the upper and lower half?

35 is odd, so the upper half gets (35 + 1) ÷ 2 = 18 teams (Teams 1–18) and the lower half gets (35 − 1) ÷ 2 = 17 teams (Teams 19–35).

Can I print the 35 team knockout fixture or save it as a PDF?

Yes. Tap “Print fixture (A4)” and choose “Save as PDF” as the printer to get a 35 team knockout fixture PDF. The bracket prints on 2 A4 pages (upper half, then lower half) in portrait.