Laurie loves multiplying numbers in her head. One day, she decides to multiply two 2-digit numbers $x$ and $y$ such that $x \leq y$ and the two numbers collectively have at least three distinct digits. Unfortunately, she accidentally remembers the digits of each number in the opposite order (for example, instead of remembering $51$ she remembers $15$). Surprisingly, the product of the two numbers after flipping the digits is the same as the product of the two original numbers. How many possible pairs of numbers could Laurie have tried to multiply?

Let's think step by step and output the final answer within \boxed{}.
user