Combinatorics · Counting · Tree structures · Invariants
Into a box, \(k\) smaller boxes are placed. Then \(k\) still smaller boxes are placed into some of the smaller boxes, each, and this procedure is repeated several times. If, at the end, \(m\) of all these boxes are filled, how many of them are empty? (A box is called filled if some smaller box lies in it.)
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Serbian Municipal Competition 1999, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source