Question 69
In a one man game there are $n$ boxes numbered $1, 2, 3, \dots, n$. In the beginning there are $21k$ balls in box $k$, $k = 1, 2, 3, \dots, n$. In each turn you take two balls from box $k$, put one of the balls in box $k-1$, and throw the last ball away, $1 \lt k \le n$. For which $n$ is it possible to get an equal number of balls in each box after a finite number of turns?