• Banashree Patra

MemberApr 22, 2012

## cube problem

Imagine a cubic array made up of an n*n*n arrangement of unit cubes: the cubic array is n cubes wide, n cubes high and n cubes deep. A special case is a 3*3*3 Rubik’s cube, which you may be familiar with. How many unit cubes are there on the surface of the n * n * n cubic array?
Howdy guest!
Dear guest, you must be logged-in to participate on CrazyEngineers. We would love to have you as a member of our community. Consider creating an account or login.
Replies
• MemberApr 22, 2012

zero
Are you sure? This action cannot be undone.
• MemberApr 23, 2012

~on*kiyu
zero
Are you sure? This action cannot be undone.
• MemberApr 23, 2012

Banashree Patra
Imagine a cubic array made up of an n*n*n arrangement of unit cubes: the cubic array is n cubes wide, n cubes high and n cubes deep. A special case is a 3*3*3 Rubik’s cube, which you may be familiar with. How many unit cubes are there on the surface of the n * n * n cubic array?
6*n^2 - 12*n + 8 for n > 1
Are you sure? This action cannot be undone.
• MemberApr 23, 2012

6n[sup]2[/sup] - 12n + 8

I think it can also be expressed as, n[sup]3[/sup] - (n-2)[sup]3[/sup]
Are you sure? This action cannot be undone.
• MemberApr 23, 2012

silverscorpion
6n[sup]2[/sup] - 12n + 8

I think it can also be expressed as, n[sup]3[/sup] - (n-2)[sup]3[/sup]
The second is more elegant. It represents the actual situation. What we are considering is the outer cube minus the (n-2) cube within it. n^3 is the total number of unit cubes, (n-2)^3 is the number of unit cubes in the contained cube. Aesthetically the second solution is more satisfying.
Are you sure? This action cannot be undone.