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 Question from Paul, a parent: So I have a question. I noticed you came up with ways to create schedules and we are having a really hard time making our lineup correctly. Basically we have 6 teams that will play over a 12 week period every Monday night. The time slots are 1 hr each playing at 6, 7 and 8. We would like each team to play 3 games at each time slot over the 12 weeks. Is this something that can actually be accomplished? Thanks so much for your help!

Hi Paul,

Here is a schedule.

w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12
t1 6 6 7 7 8 8 6 6 7 7 8 8
t2 7 7 8 8 6 6 6 7 8 6 8 7
t3 8 8 6 6 7 7 8 6 8 7 6 7
t4 6 7 8 6 7 8 7 8 6 6 7 8
t5 7 8 6 7 8 6 7 8 7 8 6 6
t6 8 6 7 8 6 7 8 7 6 8 7 6

Week 1 to week 12 (w1 to w12) by team 1 to team 6 (t1 to t6).

The games are oddly weighted (some teams will play one team 3 times before playing another team once), but the weeks can be permuted.

Scenario:
6 teams
Every Friday for 12 weeks
3 time slots per week (6:00, 7:00, 8:00)

Conditions:
Every team should play 4 times at 6:00, 4 times at 7:00 and 4 times at 8:00
Two teams must play each other no fewer than twice, no more than 3 times.

A loose explanation of my steps:

1) Cut the season in half. I figured if I could do it for the first 6 weeks, then I could do it for 12.

2) Create a 5x5 Latin Square with entries {1,2,3,4,5}
* Entries in Row i - Team i vs. entry (Team plays itself = vs. team 6)
* Entries in column j - Matchups during Week j

3) Copy and paste the 5x5 Latin Square so that it now becomes 5x10, which covers weeks 1-10. Then copy column 1,2 = column 11,12

4) Now that the Matchups are dealt with, the times need to be taken care of:
* 6x12 Matrix with entries {6,7,8} corresponding to times
* Four each of {6,7,8} in every row and Two each of {6,7,8} in every column.
* Lay Matrix over top of Latin Squares created above

5) Result

Eric

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