Question 64
Alberto has in front of him 13 boxes arranged one above the other, and he wants to place the numbers from 1 to 10 in them, one per box (three boxes will remain empty). He also wants that, whenever two numbers are written in boxes that touch each other, the upper one is larger. 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) $2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$
(A) $3^{10}$
(B) $2^{11} \cdot 3^{3} \cdot 13$
(C) $2^{16} \cdot 13$
(D) $2^{20}$
(E) $2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$