Suppose there are $n$ bins each having $k$ objects. Assume that capacity of each bin is also $k$. Now we want to rearrange the objects such that each bin contains $k$ objects but this time if $x,y$ belong to the same bin, then $x,y$ were in different bins in the original arrangement.
Does there always exist such a rearrangements? why ?
What is the official name of this problem in the literature ?
Any link/hint would be helpful.