Math CentralQuandaries & Queries


Question from Bill, a parent:

I am having trouble with a football schedule that has two divisions of five teams each, 1-5 and 6-10. 1-5 will play against eachother in the first 4 weeks and also the the last 4 weeks with teams 6-10 completing the middle of the schedule. The schedule is 13 weeks. Thank you for your time

We have two responses for you


Can you supply some more information? Does each team play once per week, or is there only one game per week (and eight teams that don't play)?




Because 5 is an odd number, what you want cannot be accomplished.

To get around this problem, you must play one interdivision game each week. That means that the first and last parts of the season last 5 weeks each, and the middle part lasts only 3 weeks. One way to arrange the first and last parts is to use the 6-team tournament we have in our data base:

For the first 5 weeks, assign the labels B through F to each of your 5 teams in each division, with the label A meaning that the team paired with A in one division plays the team in the other division paired with A. You should be able to figure out the rest of the schedule from there; if not, please get back to us.





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