Question 157
There are $n$ empty red boxes numbered $1, 2, \dots, n$ and $n$ empty white boxes numbered $1, 2, \dots, n$ on the table. At each step we choose one red and one white box and put one ball into each chosen box. After finite number of steps it turns out that for any two identically numbered red and white boxes either the red box contains $6$ more balls than the white box or the white box contains $16$ more balls than the red box. Find all possible values of $n$.