cube problem

Replies

• 

  ~on*kiyu

  zero
• 

  Banashree Patra

  ~on*kiyu

  zero

  please explain
• 

  Ramani Aswath

  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
• 

  silverscorpion

  6n[sup]2[/sup] - 12n + 8
  
  I think it can also be expressed as, n[sup]3[/sup] - (n-2)[sup]3[/sup]
• 

  Ramani Aswath

  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.