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.

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

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

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)

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)

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?

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

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.