Sixty-four identical cubes are stacked in a $4 \times 4 \times 4$ arrangement and then some of the cubes are removed from the front as shown. No cube hidden from sight has been removed. How many cubes remain in the arrangement?
(A) 46
(B) 40
(C) 52
(D) 55
(E) 49

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-086.jpg?height=398&width=407&top_left_y=1465&top_left_x=1290)
There are 64 cubes to start.

If we look at the bottom layer of cubes, we see that there are 6 uncovered cubes, each of which is missing 3 cubes above it. These are the only cubes that are missing.

Thus, there are $6(3)=18$ missing cubes, so there are $64-18=46$ cubes remaining.

ANSWER: (A)