The correct translation is not reordering digits but removing digits The answer is $987654321$. Proof: See that there can not be two same digits and there can not be a digit $0$, so we bounded the number, we know that it can contain at most 9 digits. The biggest such number is $987654321$ to prove this, with this configuration we have that the digits from right to left are descending,so if we remove a digit then the number still has this configuration. So the sum of digits in odd places - sum of digits in even places is greater than $0$ but less than $9$, so the number does not divide 11 and we are done.