mathschallenge.net

Problem

By joining dots together, how many squares can you draw on a grid measuring 4 dots by 4 dots?

Solution

Consider the following diagrams.

So there would be 1 + 4 + 9 + 4 + 2 = 20 squares that can be drawn on a 4 4 grid.

What about 5 5 grids?

Can you generalise for any size grid?