45 team knockout fixture

45 teams: 19 byes, 26 teams play Round I, 44 matches over 6 rounds.

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How the 45 team fixture is drawn

Upper half and lower half

45 is odd, so the upper half gets (45 + 1) ÷ 2 = 23 teams (Teams 1–23) and the lower half gets (45 − 1) ÷ 2 = 22 teams (Teams 24–45).

Byes

Byes = next power of 2 − number of teams = 64 − 45 = 19. 19 is odd, so the upper half gets (19 − 1) ÷ 2 = 9 byes and the lower half gets (19 + 1) ÷ 2 = 10 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 45 teams:

  1. Team 45 — last team of the lower half
  2. Team 1 — first team of the upper half
  3. Team 24 — first team of the lower half
  4. Team 23 — last team of the upper half
  5. Team 44 — 2nd-last team of the lower half
  6. Team 2 — 2nd team of the upper half
  7. Team 25 — 2nd team of the lower half
  8. Team 22 — 2nd-last team of the upper half
  9. Team 43 — 3rd-last team of the lower half
  10. Team 3 — 3rd team of the upper half
  11. Team 26 — 3rd team of the lower half
  12. Team 21 — 3rd-last team of the upper half
  13. Team 42 — 4th-last team of the lower half
  14. Team 4 — 4th team of the upper half
  15. Team 27 — 4th team of the lower half
  16. Team 20 — 4th-last team of the upper half
  17. Team 41 — 5th-last team of the lower half
  18. Team 5 — 5th team of the upper half
  19. Team 28 — 5th 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

45 − 19 = 26 teams play Round I in 13 matches:

  • Match 1: Team 6 vs Team 7
  • Match 2: Team 8 vs Team 9
  • Match 3: Team 10 vs Team 11
  • Match 4: Team 12 vs Team 13
  • Match 5: Team 14 vs Team 15
  • Match 6: Team 16 vs Team 17
  • Match 7: Team 18 vs Team 19
  • Match 8: Team 29 vs Team 30
  • Match 9: Team 31 vs Team 32
  • Match 10: Team 33 vs Team 34
  • Match 11: Team 35 vs Team 36
  • Match 12: Team 37 vs Team 38
  • Match 13: Team 39 vs Team 40

Total number of matches = number of teams − 1 = 45 − 1 = 44 (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 45 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 45 team knockout fixture?

Byes = next power of 2 − number of teams = 64 − 45 = 19. 19 is odd, so the upper half gets (19 − 1) ÷ 2 = 9 byes and the lower half gets (19 + 1) ÷ 2 = 10 byes. The byes go, in order, to teams 45, 1, 24, 23, 44, 2, 25, 22, 43, 3, 26, 21, 42, 4, 27, 20, 41, 5 and 28. These teams do not play Round I and go straight to Round II.

How many matches and rounds are there for 45 teams?

Total number of matches = number of teams − 1 = 45 − 1 = 44, 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 45 teams divided into the upper and lower half?

45 is odd, so the upper half gets (45 + 1) ÷ 2 = 23 teams (Teams 1–23) and the lower half gets (45 − 1) ÷ 2 = 22 teams (Teams 24–45).

Can I print the 45 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 45 team knockout fixture PDF. The bracket prints on 2 A4 pages (upper half, then lower half) in portrait.