Question 14
A magic number is a positive integer with distinct digits such that the difference between the number obtained by writing its digits in descending order and the number obtained by writing its digits in ascending order is equal to the positive integer itself. For example, 495 is a magic number since 954-459=495, and 6174 is another magic number since 7641-1467=6174. Are there five-digit magic numbers? If so, find an example. If not, give an explanation.