MEMO 2010 ekipno problem 4
Kvaliteta:
Avg: 0,0Težina:
Avg: 0,0 Let
be a positive integer. A square
is partitioned into
unit squares. Each of them is divided into two triangles by the diagonal parallel to
. Some of the vertices of the unit squares are colored red in such a way that each of these
triangles contains at least one red vertex. Find the least number of red vertices.
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
![n^2](/media/m/3/6/a/36a0dd5a7e7ff0e6bbc714e33ddb1d63.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![2n^2](/media/m/b/d/b/bdba3c0944d0ab1031d8b1c04a24b53b.png)
Izvor: Srednjoeuropska matematička olimpijada 2010, ekipno natjecanje, problem 4