40 team knockout fixture

40 teams: 24 byes, 16 teams play Round I, 39 matches over 6 rounds.

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How the 40 team fixture is drawn

Upper half and lower half

40 is even, so each half gets 40 ÷ 2 = 20 teams: Teams 1–20 in the upper half and Teams 21–40 in the lower half.

Byes

Byes = next power of 2 − number of teams = 64 − 40 = 24. 24 is even, so each half gets 24 ÷ 2 = 12 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 40 teams:

  1. Team 40 — last team of the lower half
  2. Team 1 — first team of the upper half
  3. Team 21 — first team of the lower half
  4. Team 20 — last team of the upper half
  5. Team 39 — 2nd-last team of the lower half
  6. Team 2 — 2nd team of the upper half
  7. Team 22 — 2nd team of the lower half
  8. Team 19 — 2nd-last team of the upper half
  9. Team 38 — 3rd-last team of the lower half
  10. Team 3 — 3rd team of the upper half
  11. Team 23 — 3rd team of the lower half
  12. Team 18 — 3rd-last team of the upper half
  13. Team 37 — 4th-last team of the lower half
  14. Team 4 — 4th team of the upper half
  15. Team 24 — 4th team of the lower half
  16. Team 17 — 4th-last team of the upper half
  17. Team 36 — 5th-last team of the lower half
  18. Team 5 — 5th team of the upper half
  19. Team 25 — 5th team of the lower half
  20. Team 16 — 5th-last team of the upper half
  21. Team 35 — 6th-last team of the lower half
  22. Team 6 — 6th team of the upper half
  23. Team 26 — 6th team of the lower half
  24. Team 15 — 6th-last team of the upper half

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

Round I and total matches

40 − 24 = 16 teams play Round I in 8 matches:

  • Match 1: Team 7 vs Team 8
  • Match 2: Team 9 vs Team 10
  • Match 3: Team 11 vs Team 12
  • Match 4: Team 13 vs Team 14
  • Match 5: Team 27 vs Team 28
  • Match 6: Team 29 vs Team 30
  • Match 7: Team 31 vs Team 32
  • Match 8: Team 33 vs Team 34

Total number of matches = number of teams − 1 = 40 − 1 = 39 (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 40 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 40 team knockout fixture?

Byes = next power of 2 − number of teams = 64 − 40 = 24. 24 is even, so each half gets 24 ÷ 2 = 12 byes. The byes go, in order, to teams 40, 1, 21, 20, 39, 2, 22, 19, 38, 3, 23, 18, 37, 4, 24, 17, 36, 5, 25, 16, 35, 6, 26 and 15. These teams do not play Round I and go straight to Round II.

How many matches and rounds are there for 40 teams?

Total number of matches = number of teams − 1 = 40 − 1 = 39, 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 40 teams divided into the upper and lower half?

40 is even, so each half gets 40 ÷ 2 = 20 teams: Teams 1–20 in the upper half and Teams 21–40 in the lower half.

Can I print the 40 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 40 team knockout fixture PDF. The bracket prints on 2 A4 pages (upper half, then lower half) in portrait.