Problem

Source:

Tags: MATHCOUNTS, rotation



A series of figures is shown in the picture below, each one of them created by following a secret rule. If the leftmost figure is considered the first figure, how many squares will the 21st figure have? Note: only the little squares are to be counted (i.e., the $2 \times 2$ squares, $3 \times 3$ squares, $\dots$ should not be counted) Extra (not part of the original problem): How many squares will the 21st figure have, if we consider all $1 \times 1$ squares, all $2 \times 2$ squares, all $3 \times 3$ squares, and so on?.