MEMO 2015 ekipno problem 4
Dodao/la:
arhiva28. kolovoza 2018. Let
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
be a positive integer. In each of the
![N^2](/media/m/2/4/f/24f6e579b6a8f8a794957e33cdb55565.png)
unit squares of an
![N \times N](/media/m/5/a/1/5a1dcced39ff6f1ff58e60b80b2b1ec9.png)
board, one of the two diagonals is drawn. The drawn diagonals divide the
![N \times N](/media/m/5/a/1/5a1dcced39ff6f1ff58e60b80b2b1ec9.png)
board into
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
regions. For each
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
, determine the smallest and the largest possible values of
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
.
{{ Greška pri preuzimanju img datoteke. (Nevaljan broj?) }}
%V0 Let $N$ be a positive integer. In each of the $N^2$ unit squares of an $N \times N$ board, one of the two diagonals is drawn. The drawn diagonals divide the $N \times N$ board into $K$ regions. For each $N$, determine the smallest and the largest possible values of $K$.
[img attachment=1 width=300px height=300px]
Izvor: Srednjoeuropska matematička olimpijada 2015, ekipno natjecanje, problem 4