I need to determine the missing number to fulfill the following reproduction:
$$\pi=\pmatrix{1&2&3&4&5&6&7&8&9\\3&5&9&4&1&2&6&7&8}$$
And here is the representation of $pi$ as the product of transpositions:
$$(1 i) (1 3) (2 5) (9 8) (8 7) (7 6) (3 6) = \pi$$
The result for $i$ must be 2 but I have no clue how to get there. I tried to start at $(3 6)$ and then check on which transposition it gets pictured on but it doesn't seem to work for me. Any ideas on how to generally solve these kind of problems?
-Freddy