Take any number, say 8,675,309. Reverse the digits to get 9,035,768. The difference between the two numbers is 360,459 and this is evenly divisible by 9 since 360,459/9 = 40,051. But there’s even something more interesting. You can re-arrange (or permute) the digits in any random order. Let’s say the new number is 3,580,697. The difference with the original number 8,675,309 is 5,094,612, and that is evenly divisible by 9 since 5,094,612/9 = 566,068.
This will always be true!
“Magic” trick
Number
n
Re-arrange digits/permutation
σ(n)
Always divisible by 9
n – σ(n)
σ(n) – n
But why is this true?
