Question

Imagine that we paint a 4x4x4 cube blue on every side. (or you can dip the 4x4x4 cube in blue paint)
How many of the small cubes have 3 blue faces?
How many have 2 blue faces?
How many have 1 blue face?
How many have not been painted at all?
Think visually!

Answer 1

Only the corner cubes have 3 faces, and a cube has 8 corners. So there are 8 cubes that have 3 blue faces.

16 cubes have 2 blue faces. These cubes are the ones in between the corners of a side.

The 4 center cubes have only one side painted. Since there are 6 sides, and each side has 4 center cubes, 6 x 4 = 24. So there are 24 cubes with 1 blue face.

There are exactly 8 cubes on the inside of the larger cube. So, 8 cubes have not been painted at all.

I hope this helps!