If $p$ and $q$ are positive integers, $\max (p, q)$ is the maximum of $p$ and $q$ and $\min (p, q)$ is the minimum of $p$ and $q$. For example, $\max (30,40)=40$ and $\min (30,40)=30$. Also, $\max (30,30)=30$ and $\min (30,30)=30$.

Determine the number of ordered pairs $(x, y)$ that satisfy the equation

$$
\max (60, \min (x, y))=\min (\max (60, x), y)
$$

where $x$ and $y$ are positive integers with $x \leq 100$ and $y \leq 100$.

## PART B

For each question in Part B, your solution must be well organized and contain words of explanation or justification when appropriate. Marks are awarded for completeness, clarity, and style of presentation. A correct solution, poorly presented, will not earn full marks.