IMO Shortlist 1988 problem 14
Dodao/la:
arhiva2. travnja 2012. For what values of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
does there exist an
![n \times n](/media/m/9/d/8/9d8eac5b3234425afb9f970edbfe93ef.png)
array of entries -1, 0 or 1 such that the
![2 \cdot n](/media/m/8/d/8/8d8ddbc3ab45a1531e504d0f224b473f.png)
sums obtained by summing the elements of the rows and the columns are all different?
%V0
For what values of $n$ does there exist an $n \times n$ array of entries -1, 0 or 1 such that the $2 \cdot n$ sums obtained by summing the elements of the rows and the columns are all different?
Izvor: Međunarodna matematička olimpijada, shortlist 1988