A board is ruled into a 3 by 3 arrangement of nine identical cells. Counting figures of every size, how many rectangles in that drawing are NOT squares?

A rectangle is fixed by choosing 2 of the 4 horizontal lines and 2 of the 4 vertical lines, giving $6\times 6=36$ rectangles in all. The squares among them are 9 of size 1, 4 of size 2 and 1 of size 3, that is 14. So the non-square rectangles number 36 − 14 = 22. The traps: 36 counts every rectangle including the squares, 14 counts the squares themselves, and 27 subtracts only the nine small cells while forgetting the 2 by 2 and 3 by 3 squares.