In the diagram, there are 26 levels, labelled $A, B, C, \ldots, Z$. There is one dot on level $A$. Each of levels $B, D, F, H, J, \ldots$, and $Z$ contains twice as many dots as the level immediately above. Each of levels $C, E, G, I, K, \ldots$, and $Y$ contains the same number of dots as the level immediately above. How many dots does level $Z$ contain?
(A) 1024
(B) 2048
(C) 4096
(D) 8192
(E) 16384

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-076.jpg?height=331&width=266&top_left_y=2095&top_left_x=1298)

$\vdots$
Since level C contains the same number of dots as level B and level D contains twice as many dots as level C, then level D contains twice as many dots as level B.

Similarly, level F contains twice as many dots as level D, level $\mathrm{H}$ contains twice as many dots as level $\mathrm{F}$, and so on.

Put another way, the number of dots doubles from level B to level D, from level D to level F, from level $\mathrm{F}$ to level $\mathrm{H}$, and so on.

Since there are 26 levels, then there are 24 levels after level B.

Thus, the number of dots doubles $24 \div 2=12$ times from level $\mathrm{B}$ to level $\mathrm{Z}$.

Therefore, the number of dots on level Z is $2 \times 2^{12}=2^{13}=8192$.

ANSWER: (D)