3.3. We will call a figure the union of unit squares that do not share sides, and the vertices of the figure - the vertices of these squares. $F(M)$ is the union of the images of the figure $M$ under central symmetries relative to all vertices of the figure $M$. Find the area of the figure $F(F(\ldots F(M) \ldots))$ ( $F$ is repeated 2010 times), where $M$ is a unit square.

## Fourth Round
3.3. Answer: $\left(3^{2010}+1\right) / 2$.

It is easy to see that on the $k$-th step, the figure represents a set of black cells of a $3^{k} \times 3^{k}$ square, painted in a checkerboard pattern (the central cell is black). Their number is $\left(3^{k}+1\right) / 2$.

## Fourth Round