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?
closed as off-topic by Deusovi♦, AJL, Ric, xnor, ghosts_in_the_code Oct 26 '15 at 5:00
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Deusovi, AJL, Ric, xnor, ghosts_in_the_code
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)