# hockey league: how to schedule games between teams

#### jeremyblumes

##### New member
hi everybody,

I run a hockey league that has 8 teams and i'm trying to create a balanced schedule so that each team will play an equal number of games vs one another, i also don't want teams playing back to back games vs. one another, i want them to play the other 7 teams before seeing that same opponent again... i've tried assigning each team a numeral and rotating thru but i'm not sure if what i have is ok, if someone could post the right way to go about it, or the schedule itself that would be greatly appreciated.

day 1
1 vs 2
2 vs 3
4 vs 5
6 vs 7

day 2
1 vs 3
2 vs 4
5 vs 6
7 vs 8

day 3
1 vs 4
3 vs 5
6 vs 8
7 vs 2

day 4
1 vs 5
2 vs 6
3 vs 7
4 vs 8

day 5
1 vs 6
2 vs 5
3 vs 8
7 vs 4

day 6
1 vs 7
2 vs 8
3 vs 4
5 vs 6

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: hockey league

Are there other restrictions?

You have 6 days - each day playing 4 games - total 24 games.

For 8 teams to play each other, at least once, you need

$$\displaystyle \frac{7\cdot 8}{2}\, = \, 28$$

games.

So there will be some teams who have not played each other.

Can you extend the days to 7 (with four games each day)?

#### TchrWill

##### Full Member
Re: hockey league

jeremyblumes said:
hi everybody,

I run a hockey league that has 8 teams and i'm trying to create a balanced schedule so that each team will play an equal number of games vs one another, i also don't want teams playing back to back games vs. one another, i want them to play the other 7 teams before seeing that same opponent again... i've tried assigning each team a numeral and rotating thru but i'm not sure if what i have is ok, if someone could post the right way to go about it, or the schedule itself that would be greatly appreciated.

The total number of pairings for 8 teams is 8C2 = 8!/2!(6!) = 28

The pairings are
AB..BC..CD..DE..EF..FG..GH
AC..BD..CE..DF..EG..FH
AE..BF..CG..DH
AF..BG..CH
AG..BH
AH

Arrange these is 7 days of 4 pairings each day and repeat the result as many times as you want the teams to meet each other.

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: hockey league

If you do set up as 7 days of 4 games each - then remember:

- Every team gets to play 7 games - so - every team must be playing once on each day (otherwise you would end up some teams playing twice a day and not playing at all some day).

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: hockey league

Subhotosh Khan said:
If you do set up as 7 days of 4 games each - then remember:

- Every team gets to play 7 games - so - every team must be playing once on each day (otherwise you would end up some teams playing twice a day and not playing at all some day).

One such sequence could be:

AB....CD....EF....GH

AC....BD....EG....FH

AE....BF....CG....DH

AF....BE....CH....DG

AG....BH....CE....DF

AH....BG....CF....DE

#### PAULK

##### Junior Member
Re: hockey league

jeremyblumes said:
hi everybody,

I run a hockey league that has 8 teams and i'm trying to create a balanced schedule so that each team will play an equal number of games vs one another, i also don't want teams playing back to back games vs. one another, i want them to play the other 7 teams before seeing that same opponent again... i've tried assigning each team a numeral and rotating thru but i'm not sure if what i have is ok, if someone could post the right way to go about it, or the schedule itself that would be greatly appreciated.
Of course, if each team plays each other and plays one game a day, you need 7 days. BUT you want to do stuff like this, I'll give you a number to call: Your local bridge club has all the info you will need for this -- ask the director for his list of HOWELL movements.