Mr. Rand Wise

I just stumbled across a collection of math problems on a blog by a Mr. Rand Wise. As an example, I find this one interesting. It is not too difficult, buy yet requires an inventive and structured approach. And it paves the road to generalizations.

After getting a formula for the general problem  (which I hope is correct), I checked the result with a simple Euler code.

>load perm
  Functions for permutations.
>function pf (x) ...
$  global s;
$  s=s+100*x[1]+10*x[2]+x[3];
$  endfunction
>s=0; forAllChoices("pf",4,3); s,

I removed the answer. I do not want to spoil your efforts.

Update: The answer is now on that page. But without any reasoning or mathematical background, thus worthless.

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