Thread: Difficult Math Scheduling Problem

The goal is to make a schedule that will allow 8 teams to play each of 4 games once without playing the same team twice.

For instance,

	Games 1	Game 2	Game 3	Game 4
Week 1	1 vs 8	2 vs 7	3 vs 6	4 vs 5
Week 2
Week 3
Week 4

In week 2, each team must play a different game without ever playing a team that they have previously face.

1-2, 3-4, 5-6, 7-8
1-3, 2-4, 5-7, 6-8
1-4, 2-3, 5-8, 6-7
1-5, 2-6, 3-7, 4-8
Check:
1: 2,3,4,5
2: 1,3,4,6
3: 1,2,4,7
4: 1,2,3,8
5: 1,6,7,8
6: 2,5,7,8
7: 3,5,6,8
8: 4,5,6,7

Originally Posted by Wilmer

1-2, 3-4, 5-6, 7-8
1-3, 2-4, 5-7, 6-8
1-4, 2-3, 5-8, 6-7
1-5, 2-6, 3-7, 4-8
Check:
1: 2,3,4,5
2: 1,3,4,6
3: 1,2,4,7
4: 1,2,3,8
5: 1,6,7,8
6: 2,5,7,8
7: 3,5,6,8
8: 4,5,6,7

I do not understand your answer. Is it in the same format as my table? If so, teams are playing the same game twice

Originally Posted by ben61693

The goal is to make a schedule that will allow 8 teams to play each of 4 games once without playing the same team twice.

Well then, what does this mean: "play each of 4 games once"?

EDIT:
ok ok ! Think I see what you mean:
in your example, team1 cannot play team8 again, PLUS both teams cannot appear under Game1 again; yes?

Tried a bit: can only come close

I'll keep trying...YOU try too

Here you go:

Code:

     G1   G2   G3   G4
W1   12   34   56   78
W2   35   17   28   46
W3   48   26   37   15
W4   67   58   14   23

No charge

Originally Posted by ben61693

The goal is to make a schedule that will allow 8 teams to play each of 4 games once without playing the same team twice.

For instance,

	Games 1	Game 2	Game 3	Game 4
Week 1	1 vs 8	2 vs 7	3 vs 6	4 vs 5
Week 2
Week 3
Week 4

In week 2, each team must play a different game without ever playing a team that they have previously face.

Originally Posted by Wilmer

Here you go:

Code:

     G1   G2   G3   G4
W1   12   34   56   78
W2   35   17   28   46
W3   48   26   37   15
W4   67   58   14   23

No charge

Thank you so much. I kept getting 3vs5 twice for some reason. Just out of curiosity. How did you do it? Pure guessing or some strategy involved?

Wrote short computer program to do about half a case; trial and error for other half.
Here's another solution:

Code:

     G1   G2   G3   G4
W1   17   45   28   36
W2   26   38   15   47
W3   35   27   46   18
W4   48   16   37   25

By the way, your problem really is:
You have 28 2digit numbers:
12,13,14,15,16,17,18,23,24,25,26,27,28,34,35,36,37 ,38,45,46,47,48,56,57,58,67,68,78
Enter 16 of these numbers in a 4 by 4 array such that:
1: the 4 numbers in each row are made up of all digits 1 to 8
2: the 4 numbers in each column are made up of all digits 1 to 8

This makes it relatively easy to write a computer program.