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Suppose I have 9 integers such that

$i_1>i_2>i_3$

$i_4>i_5>i_6$

$i_7>i_1$

$i_2>i_4>i_8$

and $i_9>i_3>i_5$.

From this we then know that as $i_3>i_5$ and $i_4>i_5$ then $i_7>i_1>i_2>i_5$, and we can make similar deductions.

Given this information how many possible rankings of largest to smallest are there for $i_1$ through $i_9$?

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