Below are two all-play-all round robin schedules for 10 teams. Note that they have the
court balance property where teams occur at least once and at most twice in each column. Furthermore, note that rounds 1 to 5 in any single column contain all 10 teams exactly once. The same is true for rounds 5 to 9.
Round
1 (C F) (H A) (J B) (D I) (E G)
2 (D E) (G B) (I A) (C J) (H F)
3 (J H) (I F) (G D) (E B) (C A)
4 (I G) (J E) (H C) (F A) (B D)
5 (A B) (C D) (E F) (G H) (I J)
6 (G J) (E H) (C I) (A D) (F B)
7 (H I) (F G) (D J) (B C) (A E)
8 (E C) (B I) (A G) (J F) (D H)
9 (F D) (A J) (B H) (I E) (G C)
Round
1 (A I) (B G) (J C) (H F) (D E)
2 (B J) (A H) (I D) (E G) (C F)
3 (F G) (D J) (A E) (C B) (H I)
4 (E H) (C I) (B F) (A D) (G J)
5 (C D) (E F) (G H) (I J) (A B)
6 (H B) (J A) (E I) (G C) (F D)
7 (I F) (G D) (C A) (B E) (J H)
8 (G A) (I B) (F J) (D H) (E C)
9 (J E) (H C) (D B) (F A) (I G)
Rearrange the first schedule above to obtain weeks 1-12 below and the second second to obtain weeks 13-24.
Week Game1 Game2 Game3 Game4 Byes
1 (A B)
2 (C F) (D E) (J H) (I G) [AB]
3 (H A) (G B) (I F) (J E) [CD]
4 (J B) (I A) (G D) (H C) [EF]
5 (D I) (C J) (E B) (F A) [GH]
6 (E G) (H F) (C A) (B D) [IJ]
7 (G J) (H I) (E C) (F D) [AB]
8 (E H) (F G) (B I) (A J) [CD]
9 (C I) (D J) (A G) (B H) [EF]
10 (A D) (B C) (J F) (I E) [GH]
11 (F B) (A E) (D H) (G C) [IJ]
12 (C D) (E F) (G H) (I J) [AB]
13 (A I) (B J) (F G) (E H) [CD]
14 (B G) (A H) (D J) (C I) [EF]
15 (J C) (I D) (A E) (B F) [GH]
16 (H F) (E G) (C B) (A D) [IJ]
17 (D E) (C F) (H I) (G J) [AB]
18 (H B) (I F) (G A) (J E) [CD]
19 (J A) (G D) (I B) (H C) [EF]
20 (E I) (C A) (F J) (D B) [GH]
21 (G C) (B E) (D H) (F A) [IJ]
22 (F D) (J H) (E C) (I G) [AB]
23 (E F) (G H) (I J) (A B) [CD]
24 (C D)
This should give you the byes as regularly spaced as possible. Ignoring the start and end of the season all teams have the same pattern of 4 weeks on, followed by one week off.
Ian.
