# Difficult Math Scheduling Problem

• May 9th 2012, 08:07 PM
ben61693
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.
• May 10th 2012, 07:42 PM
Wilmer
Re: Difficult Math Scheduling Problem
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
• May 10th 2012, 07:46 PM
ben61693
Re: Difficult Math Scheduling Problem
Quote:

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
• May 10th 2012, 09:24 PM
Wilmer
Re: Difficult Math Scheduling Problem
Quote:

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 (Crying)

I'll keep trying...YOU try too (Wink)
• May 11th 2012, 08:55 AM
Wilmer
Re: Difficult Math Scheduling Problem
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 (Wink)
• May 11th 2012, 05:06 PM
ben61693
Re: Difficult Math Scheduling Problem
Quote:

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.

Quote:

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 (Wink)

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?
• May 11th 2012, 05:21 PM
Wilmer
Re: Difficult Math Scheduling Problem
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```
• May 12th 2012, 11:49 AM
Wilmer
Re: Difficult Math Scheduling Problem
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.