So I had this thought experiment.
I take an arbitrary n digit number, and the only condition is that all of the digits cannot have the same value, like the numbers 33, 333 and so on. However, I can assume there can be at most n-1 digits that are the same, such as 1112, 229 and so on. What I noticed is that regardless of any two permutations of the n digit number that I take, the difference between them is always an integer multiple of 9.
For example, I choose the number 229. The possible arrangements I can get are 229, 292 and 922. I pick any two of these numbers at random, the difference is always an integer multiple of 9.
292-229=63, an integer multiple of 9.
922-292=630, again an integer multiple of 9.
922-229=693, yet again an integer multiple of 9.
I do not have much knowledge on number theory and stuff, so it would be much appreciated if someone could explain what is going on.