We call a positive integer $n$ "good" if there exists a $n \times n$ matrix such that:
1) Each element is either $0$ or $1$.
2) Sum of elements in each row is distinct.
3) Sum of elements in each column is the same of that in all other columns.
For example 2 is good:
Find the set $\mathbb G$ of good numbers.
I have already tried it on small values of $n$, it seems that such a matrix exists for all $n$ ( that's at least for the values I tried ), is that right? And I'm looking for a concrete proof. Any help would be appreciated. Thanks in advance!