Ten digit numbers divisible by 3. I came across an interesting property of 10-digit numbers that are constructed using each digit only once: e.g. $9867534210$ or $352147890$. These numbers are exactly divisible by $3$. Each and every of the $10!$ combinations are also divisible by $3$.
But why is this property emerging, i have no idea. Can somebody explain this to me why this happens??

You have $10$ digits $[0,1,2,3,4,5,6,7,8,9]$ and if you construct any possible number by taking each digits once,you'll get $10!$ numbers.

A number is divided by $3$,if sum of the digits of the number is divided by $3$

For all these numbers (Sum of digits)=$(0+1++2+3+4+5+6+7+8+9)=45$ is divided by $3$.
So,all these number are divisible by $3$.
