Programming required to solve a triangle of larger size?

I initially regarded this problem as one that requires "basically" trial and errors. After a few unsuccessful trials (needed 4 dots) by hand, I decided to write a program to do the trial and errors. With that, I got the answer basically same as October12's (i.e., 3rd from the vertex either clockwise or counter clockwise) . Obviously, using computer is kind of cheating. However, after reading all 跟帖, I still think programming is necessary to solve, especially for a triangle of larger size.

不知這想法是否合理?