Unique and exclusive combinations

[MartinWoods]

Hi all,

Hope someone can help me, I'm really struggling with a problem that I think should be possible.

I have a sports league of eight teams.

I would like to organise a fixture list so that three teams are at each fixture on a Sunday morning. This would mean that six teams are involved (two exclusive combinations of three teams, each group playing at a different venue) and two teams are resting.

How can I calculate the fixtures so that each team plays each other the same number of times in the season and every team plays each other?

If anyone could give me a steer that would be great - I'm really struggling with it and know there must be a way to do it.... I think...

Martin

 

[shg]

Welcome to the board.

[Table="width:, class:grid"][tr][td="bgcolor:#C0C0C0"][/td][td="bgcolor:#C0C0C0"]

A​

[/td][td="bgcolor:#C0C0C0"]

B​

[/td][td="bgcolor:#C0C0C0"]

C​

[/td][td="bgcolor:#C0C0C0"]

D​

[/td][td="bgcolor:#C0C0C0"]

E​

[/td][td="bgcolor:#C0C0C0"]

F​

[/td][td="bgcolor:#C0C0C0"]

G​

[/td][/tr][tr][td="bgcolor:#C0C0C0"]

3​

[/td][td="bgcolor:#F2F2F2"]

Week​

[/td][td="bgcolor:#F2F2F2"]

Game 1​

[/td][td="bgcolor:#F2F2F2"]

​

[/td][td="bgcolor:#F2F2F2"]

Game 2​

[/td][td="bgcolor:#F2F2F2"]

​

[/td][td="bgcolor:#F2F2F2"]

Game 3​

[/td][td="bgcolor:#F2F2F2"]

​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

4​

[/td][td="bgcolor:#F2F2F2"]

1​

[/td][td="bgcolor:#D9D9D9"]

1​

[/td][td="bgcolor:#D9D9D9"]

8​

[/td][td="bgcolor:#D9D9D9"]

2​

[/td][td="bgcolor:#D9D9D9"]

7​

[/td][td="bgcolor:#D9D9D9"]

3​

[/td][td="bgcolor:#D9D9D9"]

6​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

5​

[/td][td="bgcolor:#F2F2F2"]

2​

[/td][td="bgcolor:#D9D9D9"]

1​

[/td][td="bgcolor:#D9D9D9"]

7​

[/td][td="bgcolor:#D9D9D9"]

8​

[/td][td="bgcolor:#D9D9D9"]

6​

[/td][td="bgcolor:#D9D9D9"]

2​

[/td][td="bgcolor:#D9D9D9"]

5​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

6​

[/td][td="bgcolor:#F2F2F2"]

3​

[/td][td="bgcolor:#D9D9D9"]

1​

[/td][td="bgcolor:#D9D9D9"]

6​

[/td][td="bgcolor:#D9D9D9"]

7​

[/td][td="bgcolor:#D9D9D9"]

5​

[/td][td="bgcolor:#D9D9D9"]

8​

[/td][td="bgcolor:#D9D9D9"]

4​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

7​

[/td][td="bgcolor:#F2F2F2"]

4​

[/td][td="bgcolor:#D9D9D9"]

1​

[/td][td="bgcolor:#D9D9D9"]

5​

[/td][td="bgcolor:#D9D9D9"]

6​

[/td][td="bgcolor:#D9D9D9"]

4​

[/td][td="bgcolor:#D9D9D9"]

7​

[/td][td="bgcolor:#D9D9D9"]

3​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

8​

[/td][td="bgcolor:#F2F2F2"]

5​

[/td][td="bgcolor:#D9D9D9"]

1​

[/td][td="bgcolor:#D9D9D9"]

4​

[/td][td="bgcolor:#D9D9D9"]

5​

[/td][td="bgcolor:#D9D9D9"]

3​

[/td][td="bgcolor:#D9D9D9"]

6​

[/td][td="bgcolor:#D9D9D9"]

2​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

9​

[/td][td="bgcolor:#F2F2F2"]

6​

[/td][td="bgcolor:#D9D9D9"]

1​

[/td][td="bgcolor:#D9D9D9"]

3​

[/td][td="bgcolor:#D9D9D9"]

4​

[/td][td="bgcolor:#D9D9D9"]

2​

[/td][td="bgcolor:#D9D9D9"]

5​

[/td][td="bgcolor:#D9D9D9"]

8​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

10​

[/td][td="bgcolor:#F2F2F2"]

7​

[/td][td="bgcolor:#D9D9D9"]

1​

[/td][td="bgcolor:#D9D9D9"]

2​

[/td][td="bgcolor:#D9D9D9"]

3​

[/td][td="bgcolor:#D9D9D9"]

8​

[/td][td="bgcolor:#D9D9D9"]

4​

[/td][td="bgcolor:#D9D9D9"]

7​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

11​

[/td][td="bgcolor:#F2F2F2"]

8​

[/td][td="bgcolor:#D9D9D9"]

4​

[/td][td="bgcolor:#D9D9D9"]

5​

[/td][td="bgcolor:#D9D9D9"]

3​

[/td][td="bgcolor:#D9D9D9"]

4​

[/td][td="bgcolor:#D9D9D9"]

8​

[/td][td="bgcolor:#D9D9D9"]

2​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

12​

[/td][td="bgcolor:#F2F2F2"]

9​

[/td][td="bgcolor:#D9D9D9"]

2​

[/td][td="bgcolor:#D9D9D9"]

3​

[/td][td="bgcolor:#D9D9D9"]

5​

[/td][td="bgcolor:#D9D9D9"]

6​

[/td][td="bgcolor:#D9D9D9"]

7​

[/td][td="bgcolor:#D9D9D9"]

8​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

13​

[/td][td="bgcolor:#F2F2F2"]

10​

[/td][td="bgcolor:#D9D9D9"]

6​

[/td][td="bgcolor:#D9D9D9"]

7​

[/td][td][/td][td][/td][td][/td][td][/td][/tr]
[/table]

 

[MartinWoods]

Hi shg

Thanks for your quick reply, however it's not quite what I'm looking for.

I'm looking for the teams to be grouped in two groups of three (where they would all play against each other), instead of three groups of two.

The fixture table would look a bit like this:

[TABLE="width: 432"]
<tbody>[TR]
[TD][/TD]
[TD="colspan: 3"]Group 1[/TD]
[TD][/TD]
[TD="colspan: 3"]Group 2[/TD]
[TD][/TD]
[TD="colspan: 2"]Not playing[/TD]
[/TR]
[TR]
[TD]Week 1[/TD]
[TD]1[/TD]
[TD]3[/TD]
[TD]5[/TD]
[TD][/TD]
[TD]7[/TD]
[TD]2[/TD]
[TD]4[/TD]
[TD][/TD]
[TD]6[/TD]
[TD]8[/TD]
[/TR]
[TR]
[TD]Week 2[/TD]
[TD]2[/TD]
[TD]4[/TD]
[TD]6[/TD]
[TD][/TD]
[TD]8[/TD]
[TD]3[/TD]
[TD]5[/TD]
[TD][/TD]
[TD]7[/TD]
[TD]1[/TD]
[/TR]
[TR]
[TD]Week 3[/TD]
[TD]3[/TD]
[TD]5[/TD]
[TD]7[/TD]
[TD][/TD]
[TD]1[/TD]
[TD]4[/TD]
[TD]6[/TD]
[TD][/TD]
[TD]8[/TD]
[TD]2[/TD]
[/TR]
[TR]
[TD]Week 4[/TD]
[TD]4[/TD]
[TD]6[/TD]
[TD]8[/TD]
[TD][/TD]
[TD]2[/TD]
[TD]5[/TD]
[TD]7[/TD]
[TD][/TD]
[TD]1[/TD]
[TD]3[/TD]
[/TR]
[TR]
[TD]Week 5[/TD]
[TD]5[/TD]
[TD]7[/TD]
[TD]1[/TD]
[TD][/TD]
[TD]3[/TD]
[TD]6[/TD]
[TD]8[/TD]
[TD][/TD]
[TD]2[/TD]
[TD]4[/TD]
[/TR]
[TR]
[TD]Week 6[/TD]
[TD]6[/TD]
[TD]8[/TD]
[TD]2[/TD]
[TD][/TD]
[TD]4[/TD]
[TD]7[/TD]
[TD]1[/TD]
[TD][/TD]
[TD]3[/TD]
[TD]5[/TD]
[/TR]
[TR]
[TD]Week 7[/TD]
[TD]7[/TD]
[TD]1[/TD]
[TD]3[/TD]
[TD][/TD]
[TD]5[/TD]
[TD]8[/TD]
[TD]2[/TD]
[TD][/TD]
[TD]4[/TD]
[TD]6[/TD]
[/TR]
[TR]
[TD]Week 8[/TD]
[TD]8[/TD]
[TD]2[/TD]
[TD]4[/TD]
[TD][/TD]
[TD]6[/TD]
[TD]1[/TD]
[TD]3[/TD]
[TD][/TD]
[TD]5[/TD]
[TD]7[/TD]
[/TR]
</tbody>[/TABLE]

However one of the flaws in the above table is that Team 8 is in a group of three with teams 6 and 2 three times in the season, but not be in a group with teams 1 or 7 at all.

I'm sorry to impose on you guys and really appreciate any time you can put into helping me solve this problem.

Many thanks and kind regads

Martin

 

[shg]

Hi, Martin,

Complements of a nice person at golfsoftware.com,

[Table="width:, class:grid"][tr][td="bgcolor:#C0C0C0"][/td][td="bgcolor:#C0C0C0"]

A​

[/td][td="bgcolor:#C0C0C0"]

B​

[/td][td="bgcolor:#C0C0C0"]

C​

[/td][td="bgcolor:#C0C0C0"]

D​

[/td][/tr][tr][td="bgcolor:#C0C0C0"]

1​

[/td][td="bgcolor:#F3F3F3"]

Week​

[/td][td="bgcolor:#F3F3F3"]

Group1​

[/td][td="bgcolor:#F3F3F3"]

Group2​

[/td][td="bgcolor:#F3F3F3"]

Group3​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

2​

[/td][td]

1​

[/td][td]

123​

[/td][td]

456​

[/td][td="bgcolor:#FFFF00"]

789​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

3​

[/td][td]

2​

[/td][td]

752​

[/td][td="bgcolor:#FFFF00"]

439​

[/td][td]

186​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

4​

[/td][td]

3​

[/td][td]

583​

[/td][td="bgcolor:#FFFF00"]

269​

[/td][td]

471​

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

5​

[/td][td]

4​

[/td][td="bgcolor:#FFFF00"]

519​

[/td][td]

763​

[/td][td]

482​

[/td][/tr]
[/table]

That consumes all 36 pairings (9 choose 2). You only have 8 players, so 9 is a bye.

Repeat for the second four weeks.

 

[shg]

This may be easier to grok:

1​	123​	456​	78​
2​	257​	168​	34​
3​	358​	147​	26​
4​	367​	248​	15​

[td="bgcolor:#F3F3F3"]

Week​

[/td][td="bgcolor:#F3F3F3"]

Group1​

[/td][td="bgcolor:#F3F3F3"]

Group2​

[/td][td="bgcolor:#F3F3F3"]

Bye​

[/td]