Question 21
Initially there is a positive integer $N$ written on the blackboard. The following operations are allowed:
* Replace the number by a positive multiple of itself.
* Replace the number by another which has the same digits in a different order (it is allowed for the new number to begin with 0). For example, if $2022$ is written on the blackboard, with this operation one can write any of the numbers $222$, $2202$ or $2220$.
Find all values of $N$ such that it is possible to obtain $1$ after a sequence of operations.
* Replace the number by a positive multiple of itself.
* Replace the number by another which has the same digits in a different order (it is allowed for the new number to begin with 0). For example, if $2022$ is written on the blackboard, with this operation one can write any of the numbers $222$, $2202$ or $2220$.
Find all values of $N$ such that it is possible to obtain $1$ after a sequence of operations.