Intriguing Little Mathematical Nugget

This will probably seem stupid to some, but it caught my attention...

Any math whizzes reading this, keep your fingers off the keyboard. I'm not talking about "Base 9" or "Base 8" here. I'm talking to Mom and Pop Smith, here, and all they know is "Base 10." I was even reluctant to include this paragraph, here, for fear of generation of confusion.

In any event, Mom and Pop Smith, ordinary numbers -- the numbers that we normal folk use -- are such that,

if a four or five digit number is divisible by 3, then you can rearrange the digits in that number however you like, and it will still be divisible by 3.


When I first heard that, I thought, "Whaaaaaaaat? That's impossible!"

So, let's test it...

17832 is a five digit number divisible by 3.

17832 -:- 3 = 5944.

Okay, let's rearrange the digits in 17832, and divide by 3. I'll put a solidly even number at the end to really try to frustrate the process...

37182 -:- 3 = 12394.

What???!!! It works!!!

Okay, let me really try to frustrate the process. I'll put a three digit odd number at the end of my five digit number which I know in advance isn't divisible by 3, 371, in my five digit number...

82371

...and divide that by 3...

82371 -:- 3 = 27457.

Sheesh! It works!