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jeremyblumes
05-10-2008, 09:46 AM
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
05-10-2008, 11:31 AM
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

\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)?

Loren
05-10-2008, 12:35 PM

TchrWill
05-10-2008, 02:44 PM
[quote="jeremyblumes"]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
05-11-2008, 10:04 AM
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
05-11-2008, 10:18 AM
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
05-11-2008, 10:32 AM
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.