MathDB

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?

Problem Statement