8 teams, 5 stations, 5 time slots

[Dwayne Williams(Guest)]

Hey,

I am having a Special Science Day at our school.  We have 8 teams playing head to head who need to fit into 5 consecutive time slots.  Each team needs to go to 5 different stations as well.  If they play each other twice, that's fine.

Any suggestions / solutions ?

Thanks.

Friday, November 25 2005, 03:37 pm
Toronto, Ontario

[Ian Wakeling]

Dwayne,

Using a computer search I can find solutions to this problem where only one pair of teams occur twice together.  In the schedule below the repeated pair is (3 8).

   Time   St1    St2    St3    St4    St5
    1    (2 4)  (5 6)  (1 7)  (3 8)   - -
    2    (1 3)  (4 7)  (5 8)   - -   (2 6)
    3    (6 8)  (1 2)   - -   (4 5)  (3 7)
    4    (5 7)   - -   (2 3)  (1 6)  (4 8)
    5     - -   (3 8)  (4 6)  (2 7)  (1 5)

Let me know if this works for you.

If you only had 4 stations and 4 timeslots then this would correspond to half of a round-robin tournament design and solutions would be much easier to find.

Regards,
Ian.

Saturday, November 26 2005, 09:23 am