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06 Dec 2017, 22:57
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B
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Difficulty:
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Question Stats:
81% (01:31) correct
19%
(01:36)
wrong
based on 53
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The large solid wooden cube above is composed of 8 smaller cubes of equal size, and the total surface of the large cube is painted purple. If each of the smaller cubes is then cut into 8 cubes of equal size, how many of the smallest cubes will have exactly 3 purple faces?
(A) 4
(B) 8
(C) 16
(D) 24
(E) 32
Attachment:
2017-12-07_0955.png [ 3.72 KiB | Viewed 2928 times ]
07 Dec 2017, 12:36
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When we cut the large solid wooden cube into 8 smaller cubes of equal size,
all the eight cubes will have 3 of the 6 faces which are painted purple.
Hence, the total number of cubes with 3 purple faces will be 8(Option B)
07 Dec 2017, 15:51
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Bunuel
This problem initially made me imagine a parade of horribles. Then I noticed: all 8 cubes now are corners.
Their being corners allows their three purple faces to show (such that the whole surface of the big figure is painted).
All cuboids have 8 corners, whether the cuboid is divided into 8 cubes or 64 cubes. Cut up 8 cubes that are also corners -- and you still have 8 corners. But you have preserved only one tiny cube per division that, because it is cut off the corner, is itself a corner just like the original.
That is, when each cube here is divided, only one tiny cube will be a corresponding corner, like the original, with three painted faces.
Example: The upper left front cube now, when divided by 8, will yield only one corner exactly like itself: the upper left front cube of ITS eight divided cubes.
The other bigger cubes will follow suit.
So the 8 larger cubes, when divided, end up having only one tiny cube -- a corresponding corner -- with exactly 3 purple faces.
(8 * 1) = 8
Answer B
