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Football Inequality

If you consider the statement Team A defeats Team B to mean something like Team A is better than Team B, then there are some interesting consequences of the first two weeks of the NFL season.  The Jets, Patriots, Bengals, and Ravens have all played two games, each against other teams in that group of four.  The results can be organized like this:

For example, the Bengals lost to the Patriots but beat the Ravens.  Notice, by transitivity, the Jets are therefore better than every one of the those teams, including themselves!

Obviously, there are some flawed assumptions here (such as?), but there are some interesting general questions regarding the transitivity of relationships.

One particularly cool way to explore some counter-intuitive results of this nature  is through non-transitive dice.

Click here to see more in Challenge.


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