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The first subproblem should be easier to solve in comparison with the second.
let's take a 4 digit number.
Recall that the decimal expansion of any number greater than 10 is of the form ...1000a_{4} + 100a_{3} + 10a_{2} + a_{1}, where all a_{i} are positive integers Rearranging the digits of the number will also lead to a similar expansion, say 1000a_{3} + 100a_{4} + 10a_{1} + a_{2}
Subtraction of the second from the first, or vice versa, will lead to a difference which will be like
900 a_{4} + (-900) a_{3} + 9a_{2} - 9a_{1}.
It isn't a big surprise that the difference is a multiple of 9.