11. Alberto has in front of him 13 boxes stacked one on top of the other, and he wants to insert the numbers from 1 to 10, one per box (three boxes will remain empty). He also wants that if two numbers are written in touching boxes, the one higher up should be greater. In how many ways can he do this?
(A) $3^{10}$
(B) $2^{11} \cdot 3^{3} \cdot 13$
(C) $2^{16} \cdot 13$
(D) $2^{20}$
(E) $2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$
11. The answer is (D). The four blank squares partition the 10 numbers into four subsets (which may be empty). Within each of these subsets, the order of the numbers placed in the squares is determined. Since each of the 10 numbers can end up in any of the four sets, the set of possible arrangements is $4^{10}=2^{20}$.