Discussion Forum



1)

216 samm identical cubes are arranged to form a large cube.Now three faces of the largecubes are painted yellow, of which no two faces are opposite each other.Of the remaining faces, two are painted green and the other black.

How many Small cubes have exactly two colors on them?


A) 28

B) 30

C) 37

D) 44

Answer:

Option C

Explanation:

Here , $n^{3}=216 \Rightarrow n=6$

Corners(8)

YYY 1
YYG 2
YYB 1
GGB 2
YGB 2
GGY 1

Edges(12)

YY 3
YG 4
YB 2
BG 2
GG 1

Faces(6)

Y 3
G 2
B 1

 

At corners ,5 caubes have exactly 2 colors.

On the edges(n-2)8 cubes have exactly two colors=32 cubes

$\therefore Total number of cubes=37$