37 team knockout fixture

37 teams: 27 byes, 10 teams play Round I, 36 matches over 6 rounds.

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How the 37 team fixture is drawn

Upper half and lower half

37 is odd, so the upper half gets (37 + 1) ÷ 2 = 19 teams (Teams 1–19) and the lower half gets (37 − 1) ÷ 2 = 18 teams (Teams 20–37).

Byes

Byes = next power of 2 − number of teams = 64 − 37 = 27. 27 is odd, so the upper half gets (27 − 1) ÷ 2 = 13 byes and the lower half gets (27 + 1) ÷ 2 = 14 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 37 teams:

  1. Team 37 — last team of the lower half
  2. Team 1 — first team of the upper half
  3. Team 20 — first team of the lower half
  4. Team 19 — last team of the upper half
  5. Team 36 — 2nd-last team of the lower half
  6. Team 2 — 2nd team of the upper half
  7. Team 21 — 2nd team of the lower half
  8. Team 18 — 2nd-last team of the upper half
  9. Team 35 — 3rd-last team of the lower half
  10. Team 3 — 3rd team of the upper half
  11. Team 22 — 3rd team of the lower half
  12. Team 17 — 3rd-last team of the upper half
  13. Team 34 — 4th-last team of the lower half
  14. Team 4 — 4th team of the upper half
  15. Team 23 — 4th team of the lower half
  16. Team 16 — 4th-last team of the upper half
  17. Team 33 — 5th-last team of the lower half
  18. Team 5 — 5th team of the upper half
  19. Team 24 — 5th team of the lower half
  20. Team 15 — 5th-last team of the upper half
  21. Team 32 — 6th-last team of the lower half
  22. Team 6 — 6th team of the upper half
  23. Team 25 — 6th team of the lower half
  24. Team 14 — 6th-last team of the upper half
  25. Team 31 — 7th-last team of the lower half
  26. Team 7 — 7th team of the upper half
  27. Team 26 — 7th 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

37 − 27 = 10 teams play Round I in 5 matches:

  • Match 1: Team 8 vs Team 9
  • Match 2: Team 10 vs Team 11
  • Match 3: Team 12 vs Team 13
  • Match 4: Team 27 vs Team 28
  • Match 5: Team 29 vs Team 30

Total number of matches = number of teams − 1 = 37 − 1 = 36 (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 37 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 37 team knockout fixture?

Byes = next power of 2 − number of teams = 64 − 37 = 27. 27 is odd, so the upper half gets (27 − 1) ÷ 2 = 13 byes and the lower half gets (27 + 1) ÷ 2 = 14 byes. The byes go, in order, to teams 37, 1, 20, 19, 36, 2, 21, 18, 35, 3, 22, 17, 34, 4, 23, 16, 33, 5, 24, 15, 32, 6, 25, 14, 31, 7 and 26. These teams do not play Round I and go straight to Round II.

How many matches and rounds are there for 37 teams?

Total number of matches = number of teams − 1 = 37 − 1 = 36, 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 37 teams divided into the upper and lower half?

37 is odd, so the upper half gets (37 + 1) ÷ 2 = 19 teams (Teams 1–19) and the lower half gets (37 − 1) ÷ 2 = 18 teams (Teams 20–37).

Can I print the 37 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 37 team knockout fixture PDF. The bracket prints on 2 A4 pages (upper half, then lower half) in portrait.