The product of the digits of a two-digit number is 18. When 27 is subtracted from the number, its digits get interchanged. What is the number?

Explanation

1. 01

   Let the number be $10a + b$ with $ab = 18$.

2. 02

   Subtracting 27 reverses it: $9(a - b) = 27$, so $a - b = 3$.

3. 03

   Digit pairs with product 18: (2, 9), (3, 6), (6, 3), (9, 2). Only 6 and 3 differ by 3 with $a > b$.

4. 04

   The number is 63 (check: $63 - 27 = 36$).