|Main index||Individual-pairs explanation||About author|
Julian D. A. Wiseman, June 2003
This 16-player individual-pairs tournament design, last updated in June 2003, is based on an original by Matt Fayers of The Department of Mathematics at Queen Mary, University of London (formerly of The Department of Pure Mathematics and Mathematical Statistics at The University of Cambridge).
|PDF (A4)||Schedule, in score-sheet, with running totals; Schedule by player; Blank score sheet, with running totals|
|PDF (A3)||Schedule, in score-sheet, with running totals; Schedule by player; Blank score sheet, with running totals|
|PDF (USL)||Schedule, in score-sheet, with running totals; Schedule by player; Blank score sheet, with running totals|
|Text||Human-readable schedule, machine-readable schedule|
|Also see the individual-pairs explanation and the links to designs for other numbers of players.|
There is another design of a 16-player individual pairs tournament, in which no set of three players meet together more than once. In contrast, this design, in which groups of four players play a mini-tournament amongst themselves, before changing venues and groups after three games, is quicker but less sociable.
Properties of this tournament design:
i ii iii iv 1 D+E:N+K G+I:B+P H+O:A+J F+M:C+L 2 E+N:K+D I+B:P+G J+H:O+A M+C:L+F 3 N+D:E+K B+G:I+P H+A:J+O C+F:M+L 4 P+E:J+C B+M:K+H L+A:G+N F+I:D+O 5 E+J:C+P H+B:M+K A+G:N+L I+D:O+F 6 J+P:E+C B+K:H+M G+L:A+N D+F:I+O 7 C+N:H+I K+P:A+F O+L:E+B J+M:G+D 8 I+C:N+H P+A:F+K L+E:B+O M+G:D+J 9 C+H:I+N A+K:P+F E+O:L+B G+J:M+D 10 I+M:E+A D+P:H+L F+N:B+J K+O:C+G 11 M+E:A+I L+D:P+H N+B:J+F O+C:G+K 12 E+I:M+A D+H:L+P B+F:N+J C+K:O+G 13 A+D:B+C G+H:F+E K+L:J+I O+P:N+M 14 C+A:D+B H+F:E+G L+J:I+K P+N:M+O 15 A+B:C+D F+G:H+E J+K:L+I N+O:P+M
This is an individual pairs for 16 players.
Each player partners each of the others exactly once.
Each player opposes each of the others exactly twice.
Each group of four players that meet do so for three consecutive games at same venue, playing a mini-tournament amongst themselves.
Between such three-game mini-tournaments one player must remain at each venue. Only players A and B do this twice.
In each mini-tournament one player must stay at the same side of the venue. Players A to D do this twice, once on each side; players E to P only once.
Players A to H play 8 games on the left and 7 on the right.
Players I to P play 7 games on the left and 8 on the right.
Players play on the venues with distributions as follows: 6 players 6:6:3:0; 6 players 9:3:3:0; 2 players 9:6:0:0; 2 players 6:3:3:3.
This design is based on the unique affine plane of order 4. Such a tournament is possible for 4n players if and only if a resolvable (4n,4,1)-design exists; this trivially requires n congruent to 1 mod 3, so a number of players congruent to 4 mod 12. As far as we can tell, it remains unknown whether such designs exist for n>7.
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