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