16. An array of 25 equally spaced dots is drawn in a square grid as shown. Point $O$ is in the bottom left corner. Linda wants to draw a straight line through the diagram which passes through $O$ and exactly one other point.
How many such lines can Linda draw?
A 4
B 6
C 8
D 12
E 24
Solution
C

In the diagram on the right the solid lines go through $O$ and exactly one other point, and the dotted lines go through $O$ and at least two other points.

There is a line through every point so all possible lines have been considered.

The solid lines are the lines that Linda can draw. We therefore see that the number of lines that Linda can draw is 8 .