SOLUTION: A wooden cube with edge length n units (where n is an integer) is painted black all over. By slices parallel to its faces, the cube is cut into n3 smaller cubes each of unit length
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Question 841277: A wooden cube with edge length n units (where n is an integer) is painted black all over. By slices parallel to its faces, the cube is cut into n3 smaller cubes each of unit length. Let x0, x1, x2 and x3 be the number of smaller cubes with 0, 1, 2 and 3 faces painted black. If x0 = x1, what is n?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
^3)
(all unpainted faces form a cube of side length n-2)
^2)
(all painted faces that do not share an edge of the large cube).
Since 
we have ^3 = 6(n-2)^2 \Rightarrow (n-2)^3 - 6(n-2)^2 = 0 \Rightarrow (n-2)^2 (n-2 - 6) = 0 \Rightarrow n = 2, n = 8)
.
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