Question 32
A square with side length $3$ is partitioned into a $3 \times 3$ grid with $9$ unit squares. In each of the $9$ unit squares a distinct positive integer greater than or equal to $1$ and less than or equal to $9$ is inserted. For each of the $3$ columns the second largest of the $3$ numbers appearing on that column is marked. How many possible arrangements of the $9$ integers are there if the second largest of the $3$ marked numbers is $5$?