Question 163
The integers from $1$ to $9$ are placed in the cells of a $3 \times 3$ grid. For $i=1$, $2$ and $3$, let $\ell_{i}$ denote the largest integer in the $i^{\text{th}}$ row and $c_{i}$ the smallest integer in the $i^{\text{th}}$ column.
How many grids are there such that $\min \left\{\ell_{1}, \ell_{2}, \ell_{3}\right\}=\max \left\{c_{1}, c_{2}, c_{3}\right\}=4$?
How many grids are there such that $\min \left\{\ell_{1}, \ell_{2}, \ell_{3}\right\}=\max \left\{c_{1}, c_{2}, c_{3}\right\}=4$?