A Cube's Cubes

Geometry Level 2

Rubik's Cube (3x3 and 2x2) Rubik's Cube (3x3 and 2x2)

A normal 3 3 x 3 3 Rubik's cube has 26 26 cube pieces while a 2 2 x 2 2 has 8 8 pieces. A 4 4 x 4 4 Rubik's cube has 56 56 pieces.

How many cube pieces does a normal 12 12 x 12 12 Rubik's cube have?

Note : The pieces that are referred here are the external cube pieces. Cubes that are hidden or internal (if there are any) are not counted for this problem.


The answer is 728.

Kaizen Cyrus by Kaizen Cyrus , 18, Philippines

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1 solution

The total number of 'external' cubes in an n by n cube is n 3 n^3 - ( n − 2 ) 3 (n-2)^3 . Here n=12. Therefore the answer is 1 2 3 12^3 - 1 0 3 10^3 =728

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