13) A grasshopper moves by making jumps of exactly $10 \mathrm{~cm}$. Its motion follows this pattern: it makes a certain number of jumps in a given direction, then turns $120^{\circ}$ to its left and makes, in the new direction, twice the number of jumps it had made in the previous direction. At this point, it turns again by $120^{\circ}$ to the left and doubles the number of jumps once more. Knowing that it starts by making a single jump in a given direction, how far from the starting point will it be after 17 jumps?
(A) $20 \mathrm{~cm}$
(B) $20 \sqrt{3} \mathrm{~cm}$
(C) $40 \mathrm{~cm}$
(D) $40 \sqrt{3} \mathrm{~cm}$
(E) $50 \mathrm{~cm}$
13. The answer is $(\mathbf{E})$.

The grasshopper travels along the broken line highlighted in the figure, constructed on the sides of adjacent equilateral triangles, where the points represent the position at the start and after each jump. It follows that after 17 jumps, the grasshopper is precisely at $5 \cdot 10 \mathrm{~cm}$ distance from the starting point.

[Problem proposed by S. Monica.]