Finding a Number from a Digit-Pair Condition
Number Theory · Math Count PH 2025
Given a three-digit positive integer $ x $, let $ f(x) $ be the largest two-digit positive integer that can be formed using any two of its digits. For example, $ f(198) = 98 $, $ f(628) = 86 $, and $ f(332) = 33 $. What is the value of the three-digit positive integer $ P $ such that $ f(P) - f(P + 1) = 8 $?