9 points draw 10 straight lines, requiring at least 3 points per line

Reprinted from: http://blog.csdn.net/wangkechuang/article/details/7618822

The easiest thing to think about is to try to put 9 points into a regular 3 line, as shown in the following figure:

But only 8 lines can be drawn. In fact, each line crosses 3 points, then 10 lines go through 30 points, which requires an average of more than 3 lines across each point. The points in the center and 4 corners of the figure have >=3 lines through, while the other 4 points have only two lines through.   So it is necessary to move these 4 points. Move the point in the middle of the first and third rows to the right, reducing one line (the dashed lines in the graph), but adding two lines (that is, the red line in the graph). This will draw 9 lines, there is a turnaround. The results are shown in the following picture: Again, the graph is symmetrical, but the left and right is not symmetrical. Move the leftmost point of the second line to the right of the symmetrical position, as shown in the following illustration, reduce one line (i.e. dashed lines in the figure), but add two lines (the red line in the picture), just 10 lines, OK. The results are shown in the following diagram: