I have observed that if one takes a whole number, between 10 and 9999, then re-arranges the digits in any way. Then, one subtracts the lesser number from the greater, the answer is always divisible by three. Eg let 5124 be original number. Re-arranged to be 4512. 5124 - 4512 = 612, which is divisible by three.
Is there a proof as to why this is so?
Many thanks if anyone can help