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I take a box and put $K$ mini boxes inside. Then I chose several of those mini boxes at random and put $K$ micro boxes in each. I continue this procedure indefinitely long. Thereby, at the end each box contains (directly) either K or 0 boxes.
I tell you that there are $M$ boxes, which are not empty. Tell me how many are there empty boxes?

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  • $\begingroup$ The Q is unclear. How does knowing $K$ and $N$ determine a unique solution? And if the process goes on forever, there must be an infinite number of boxes, isn't it? $\endgroup$ Oct 25, 2015 at 16:20
  • $\begingroup$ @ghosts_in_the_code, you mean the answer is unclear?)) You ask about solution, not about question. You can read about this in The Dark Truth's answer. Or I got it wrong? And the process doesn't not go on forever, we just do not know how long it goes on. $\endgroup$
    – klm123
    Oct 25, 2015 at 16:22

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$Empty=1+(M\times K)-M$

In other words:

$1$ (box we start with) $+(M\times K)$ ($K$ boxes we put $M$ times into another box) $-M$ (boxes that are not empty)

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