Cut The Blue Cube Puzzle : Solution

What is the puzzle?

Apart from the 8 cubes at the center all 4 x 4 x 4 - 8 = 56 will have some paint on ones side at least. See below the 1/4 th cube is taken out.

The cubes at the 8 corners will have blue paint on three sides.

The cubes between corner cubes along 12 edges of big cube will have 2 sides painted. That is 12 x 2 = 24 cubes will painted with blue on 2 sides.

And 4 center cubes on each of 6 faces (left, right, top, bottom, front, back) will have only 1 side painted with blue. That is , there are 6 x 4 = 24 cubes having paint on one side only.

To conclude, out of 56 painted cubes,

24 cubes have paint on 1 side,

24 cubes painted with 2 sides,

8 are painted with three sides.