Not only is the number divisible by 3 its divisible by 9!
Say be a number. And let be a permutation of its digits.
Then, and
Thus,
Since .
But,
.
Q.E.D.
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
c0unsel