A sheet of graph paper is ruled into 3 rows and 4 columns, giving 12 identical small squares. Counting squares of every size that can be traced along the ruled lines, how many squares does the figure hold?

Count size by size. Squares one cell wide: $3\times 4=12$. Squares two cells wide need 2 rows and 2 columns of room, so $2\times 3=6$ fit. Squares three cells wide need 3 rows and 3 columns, so $1\times 2=2$ fit. Nothing bigger fits, because the figure is only 3 rows deep. The total is 12 + 6 + 2 = 20. The traps: 12 counts only the smallest cells; 14 counts the smallest ones and the two largest ones while skipping the whole middle family; 18 forgets that a three-cell square can be placed at all in a figure only three rows deep.