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Posted by Tournament
on 6/8/2009, 5:18 pm
OK, so this puzzle is for a real life application. I am scheduling a tournament of fourteen (14) teams where each team gets four (4) games. Every team makes the playoffs, and there are going to be a lot of teams with identical records. We need a fair method for tie-breakers and obviously they can't all play each other. Our answer is "common opponents." What we want is for every team to have either played, or share a common opponent with, every other team.
For my own attempts, I made an Excel grid and table to help me keep track of who played whom, and who has common opponents with whom. It is a very helpful tool. Email me if you would like to see it. It would be nice if your answer was in the form of a table where the vertical axis is Teams 1-14 and the horizontal is simply Games 1, 2, 3, 4. The blank cells will be their opponents.
I have come very close to solving this puzzle, but haven't gotten it perfect. I am by no means a top puzzler so I know someone out there must be witty enough to conquer it. If you nail it, you can go on to 15, 16, and 17. We already have all solutions up to 13. An 18 team tournament is mathematically impossible for reasons you can probably figure out.
Good luck.
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