BG-MO 1992 Problem 6

There are given one black box and $n$ white boxes ( $n$ is a random natural number). White boxes are numbered with the numbers $1,2,\ldots,n$ . In them are put $n$ balls. It is allowed the following rearrangement of the balls: if in the box with number $k$ there are exactly $k$ balls, that box is made empty - one of the balls is put in the black box and the other $k-1$ balls are put in the boxes with numbers: $1,2,\ldots,k-1$ . (Ivan Tonov)