MathDB

Initially, a positive integer

N

is written on a blackboard. We repeatedly replace the number according to the following rules: 1) replace the number by a positive multiple of itself 2) replace the number by a number with the same digits in a different order. (The new number is allowed to have leading digits, which are then deleted.) A possible sequence of moves is given by

5 \to 20 \to 140 \to 041=41

. Determine for which values of

N

it is possible to obtain

1

after a finite number of such moves.

Problem Statement