Сolor the cubes

Versão para impressão

Task number 1 (Algebra):

We assume that all the colored cubes is a shell cube-4. Inside, the cube-4 is a cube-2, which consists of 8 small cubes. Because no matter what shell, these 8 cubes should be completely white.
Cube-4 consists of six points with four blocks. These cubes can be painted on one side. Hence, the number of blocks must be equal to 24. The edges of the cube-4 consisted of four blocks (two corners and two Central). 2 central should be painted on two faces. Their number is 24. A corner cube 8.

For cube 4- 64 small cubes. 8 of them must be painted in red on the three adjacent faces of the 24 painted in red on two adjacent faces, 24 painted in red on one face only, 8 painted entirely in white.

Task number 2:

Solution to the task number 2 follows from the task number 1.
The number of cubes in a cube-N is equal to N³. The number of dice equal to the shell (N-2) ³, as the edge of the cube shell is less than 2 cubic edges of the cube. This is the number of white cubes.
The number of blocks that have only one face painted as well (N-2) ² * 6 as the cube consists of 6 points.
The number of angular blocks, which are painted three adjacent faces, remains unchanged for each cube and equal to 8.
The number of cubes, which are painted two adjacent sides is equal to (N-2) * 12.