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Decision-Making Mathematics : Arranging Combinations of Sport League Fixtures

In addition to each tem playing every other team in the league once at home and once away, the matches should be arranged such that:

(1) each team only has one match per week
(2) for any team no two matches should be successively at home or away
(3) for any team no two successive matches should be against the same opposing team

The question is to make a timetable of matches which fulfilling a best fit to the criteria above for 20 teams.


Solution Preview

To do this, you need to make a single table with the team names across the top and down the left side.

For the middle diagonal (where A plays A, etc.) you should black out the boxes (I put an 'X') to ...

Solution Summary

The method of arranging fixtures so that conditions are met is discussed and shown. The solution is detailed and well presented.