Question 60
Let $X$ be the set of natural numbers that cannot be written in base ten with a single digit repeated several times. For each $n \in X$ we define $A_{n}$ as the set of numbers obtained by permuting the digits of $n$ in all possible ways and let $d_{n}$ be the greatest common divisor of all the numbers of $A_{n}$. For example, if $n=1120$,
$$
A_{1120}=\{112,121,211,1012,1021,1102,1120,1201,1210,2011,2101,2110\}
$$
and $d_{1120}=1$ (112 and 121 are first among them). Determine the maximum possible value of $d_{n}$.
$$
A_{1120}=\{112,121,211,1012,1021,1102,1120,1201,1210,2011,2101,2110\}
$$
and $d_{1120}=1$ (112 and 121 are first among them). Determine the maximum possible value of $d_{n}$.