Cut Cube Puzzle - Solution

The Puzzle:

Cut Cube
A solid, four-inch cube of wood is coated with blue paint on all six sides.

Then the cube is cut into smaller one-inch cubes.

These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides. How many of each will there be?

Our Solution:

There are 8 with three sides colored, 24 with two sides colored, 24 with one side colored, and 8 with no sides colored.

Here I have done one face, and also shown you that "inside" there are 8 with no paint at all:

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