Question 107
Some objects are in each of four rooms. Let $n \ge 2$ be an integer. We move one $n$-th of objects from the first room to the second one. Then we move one $n$-th of (the new number of) objects from the second room to the third one. Then we move similarly objects from the third room to the fourth one and from the fourth room to the first one. (We move the whole units of objects only.) Finally the same number of the objects is in every room. Find the minimum possible number of the objects in the second room. For which $n$ does the minimum come?