Count the total number of 3×2 rectangles in the 5×5 grid above.
Observation: The grid in the top left corner of a rectangle of given length and width, defines the rectangle.
(Alternatively, this means that given the size of the rectangle, and given the top left grid, you can only specify one rectangle. None of the other possible rectangles have the same size, or have the same top left grid.)
Because of this observation, if we change the top left corner of the 3×2 rectangle, we immediately know that it is different from the previous rectangle.
But 2×3 rectangles should also count. So we have to consider them too.
For 3×2 and 2×3 rectangles, each of the types have 12 possible top left corners. Can you count them?
Answer = 12 + 12 = 24