57 team knockout fixture

57 teams: 7 byes, 50 teams play Round I, 56 matches over 6 rounds.

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How the 57 team fixture is drawn

Upper half and lower half

57 is odd, so the upper half gets (57 + 1) ÷ 2 = 29 teams (Teams 1–29) and the lower half gets (57 − 1) ÷ 2 = 28 teams (Teams 30–57).

Byes

Byes = next power of 2 − number of teams = 64 − 57 = 7. 7 is odd, so the upper half gets (7 − 1) ÷ 2 = 3 byes and the lower half gets (7 + 1) ÷ 2 = 4 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 57 teams:

  1. Team 57 — last team of the lower half
  2. Team 1 — first team of the upper half
  3. Team 30 — first team of the lower half
  4. Team 29 — last team of the upper half
  5. Team 56 — 2nd-last team of the lower half
  6. Team 2 — 2nd team of the upper half
  7. Team 31 — 2nd 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

57 − 7 = 50 teams play Round I in 25 matches:

  • Match 1: Team 3 vs Team 4
  • Match 2: Team 5 vs Team 6
  • Match 3: Team 7 vs Team 8
  • Match 4: Team 9 vs Team 10
  • Match 5: Team 11 vs Team 12
  • Match 6: Team 13 vs Team 14
  • Match 7: Team 15 vs Team 16
  • Match 8: Team 17 vs Team 18
  • Match 9: Team 19 vs Team 20
  • Match 10: Team 21 vs Team 22
  • Match 11: Team 23 vs Team 24
  • Match 12: Team 25 vs Team 26
  • Match 13: Team 27 vs Team 28
  • Match 14: Team 32 vs Team 33
  • Match 15: Team 34 vs Team 35
  • Match 16: Team 36 vs Team 37
  • Match 17: Team 38 vs Team 39
  • Match 18: Team 40 vs Team 41
  • Match 19: Team 42 vs Team 43
  • Match 20: Team 44 vs Team 45
  • Match 21: Team 46 vs Team 47
  • Match 22: Team 48 vs Team 49
  • Match 23: Team 50 vs Team 51
  • Match 24: Team 52 vs Team 53
  • Match 25: Team 54 vs Team 55

Total number of matches = number of teams − 1 = 57 − 1 = 56 (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 57 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 57 team knockout fixture?

Byes = next power of 2 − number of teams = 64 − 57 = 7. 7 is odd, so the upper half gets (7 − 1) ÷ 2 = 3 byes and the lower half gets (7 + 1) ÷ 2 = 4 byes. The byes go, in order, to teams 57, 1, 30, 29, 56, 2 and 31. These teams do not play Round I and go straight to Round II.

How many matches and rounds are there for 57 teams?

Total number of matches = number of teams − 1 = 57 − 1 = 56, 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 57 teams divided into the upper and lower half?

57 is odd, so the upper half gets (57 + 1) ÷ 2 = 29 teams (Teams 1–29) and the lower half gets (57 − 1) ÷ 2 = 28 teams (Teams 30–57).

Can I print the 57 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 57 team knockout fixture PDF. The bracket prints on 2 A4 pages (upper half, then lower half) in portrait.