Switching the order of the digits
Source: Rioplatense L-3 2022 #6
December 13, 2022
combinatoricsnumber theory
Problem Statement
In a board, the positive integer is written. In each round, Olive can realize any one of the following operations:
I - Switch the current number by a positive multiple of the current number.
II - Switch the current number by a number with the same digits of the current number, but the digits are written in another order(leading zeros are allowed). For instance, if the current number is , Olive can write any of the following numbers .
Determine all the positive integers , such that, Olive can write the number after a finite quantity of rounds.