cube problem

Banashree Patra

Banashree Patra

@banashree-patra-m0OJwR • Oct 25, 2024
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?
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  • ~on*kiyu

    ~on*kiyu

    @onkiyu-I1FNB7 • Apr 22, 2012

    zero
    0
  • Banashree Patra

    Banashree Patra

    @banashree-patra-m0OJwR • Apr 23, 2012

    ~on*kiyu
    zero
    please explain
    0
  • Ramani Aswath

    Ramani Aswath

    @ramani-VR4O43 • Apr 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
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  • silverscorpion

    silverscorpion

    @silverscorpion-iJKtdQ • Apr 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]
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  • Ramani Aswath

    Ramani Aswath

    @ramani-VR4O43 • Apr 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.
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