MathDB

In the plane, there is a figure in the form of an

L

-tromino, which is composed of

3

unit squares, which we will denote by

\Phi_0

. On every move, we choose an arbitrary straight line in the plane and using it we construct a new figure. The

\Phi_n

, obtained in the

n

-th move, is obtained as the union of the figure

\Phi_{n-1}

and its axial reflection with respect to the chosen line. Also, for the move to be valid, it is necessary that the surface of the newly obtained piece to be twice as large as the previous one. Is it possible to cover the whole plane in that process?

Problem Statement