Given a cubic array made up of NxNxN smaller cubes: the cubic array is N cubes wide, N cubes deep and N cubes high.

Question: How many cubes are on the surface of the array.


There are N3 cubes total. If you can calculate how many cubes are hidden you can answer this questions. The number of hidden cubes is simply a number of cubes with sides (N-2)x(N-2)x(N-2). ie. (N-2)3.

Thus, the answer is

N3 - (N-2)3.

Bonus question:

Calculate number of 4D hypercubes on the surface of NxNxNxN hypercubic array

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