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A hundred identical cubic boxes are currently arranged in fo

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by BTGmoderatorDC » Fri Aug 24, 2018 1:01 pm

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A hundred identical cubic boxes are currently arranged in four cubes: a single cubic box, a 2 x 2 x 2 cube, a 3 x 3 x 3 cube, and a 4 x 4 x 4 cube. These four are not touching each other. All outward faces are painted and all inward faces are not painted. These four cubes are going to be dismantled and reassembled as a flat 10 x 10 square. The top and all the edges of this 10 x 10 square must be painted, but there is no requirement for paint on the bottom. How many individual faces will have to be painted to accommodate the requirements of this new design?

(A) 0
(B) 5
(C) 9
(D) 16
(E) 27

OA C

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by deloitte247 » Sat Sep 08, 2018 11:06 am
The number of individual faces to be painted can be obtained by simply counting the number of small cubes that are not painted outward.
In the single cubic box (1 * 1 * 1 box) = There is no such cubes.
In the 2 * 2 * 2 box = There is no such cubes
In the 3 * 3 * 3 * 3 box = 1 such cube is located at the center of the cubic box.
In 4 * 4 * 4 box = 8 such cubes that are located in the center of the cubic box.
As we have to use all 100 small cubes to make 10 * 10 square,
Thus 8 + 1 = 9 individual faces to be painted.
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