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## Interview Question

Interview Santa Ana, CA

# Given a cube made of NxN sub cubes, find the number of

cubes that are no exposed to the outside.

0

6N**2 - 12N + 4

Interview Candidate on Nov 8, 2010
2

Let N^2 = n^3 Hence total number of sub-cubes : n^3 Number of cubes on one face : n^2 Total # of cubes/face = 6n^2 - Common cubes Common cubes = common on the edge + common on the corner Common on the edge = (n-2) * Number of edges (=12) = 12n - 24 Common on the corner = counted 3 times for neighboring faces. Will need to take into account the 2 extra = 2*number of corners = 2*8 Hence the total number of visible cubes = 6n^2 - 12n + 8 Total number of not visible cubes = n^3 - (visible cubes) replacing n by N Soln: N^2 - 6N^(4/3) + 12N^(2/3) - 8

sum1 on Jan 9, 2011
0

Its simply : No. of small cubes in Outer Cube - No. of small cubes in inner cube n^3 - (n-2)^3 = 6n^2 - 12n + 8 for n &gt;=2

Gaurav on Jun 16, 2011
2

The question is for cubes "no exposed to the outside". So the answer is just the count of inner cubes which is (n-2)^3 for n&gt;=2 But more precisely the question should be "Given a cube made of N^3 sub cubes".

Simon on Oct 12, 2011
0

n^3 -(6 n^2 ) + (12n) - 8

Shoaib on Apr 21, 2015