Question 50
Initially, a positive integer $N$ is written on the blackboard. We repeatedly replace the number according to the following rules:
- replace the number on the board by a positive multiple of itself,
- replace the number by a number with the same digits in a different order. (The new number is allowed to start with one or more zeros, which are then omitted.)
Determine for which values of $N$ it is possible to obtain 1 after a series of moves.
An example of valid moves is $5 \rightarrow 20 \rightarrow 140 \rightarrow 041=41$.
- replace the number on the board by a positive multiple of itself,
- replace the number by a number with the same digits in a different order. (The new number is allowed to start with one or more zeros, which are then omitted.)
Determine for which values of $N$ it is possible to obtain 1 after a series of moves.
An example of valid moves is $5 \rightarrow 20 \rightarrow 140 \rightarrow 041=41$.