The painted cube
The question
A big cube of sugar, 4 small cubes wide each way, is dipped so every outer face is coated, then broken into 4 × 4 × 4 small cubes.
How many of the small cubes have paint on exactly one face?
Where a cube sits decides how many faces are painted
block size:4
2×2=4
6×4=24
- A cube 4 little cubes on each side is painted all over and cut apart. We want the ones with paint on exactly one face.
- One painted face means a cube in the middle of a face, off every edge. That middle is 2 × 2 = 4 on each face.
- A cube has 6 faces, so 6 × 4 = 24 little cubes have one painted face.
How it works.
- 01
A cube 4 little cubes on each side is painted all over and cut apart. We want the ones with paint on exactly one face.
- 02
One painted face means a cube in the middle of a face, off every edge. That middle is 2 × 2 = 4 on each face.
- 03
A cube has 6 faces, so 6 × 4 = 24 little cubes have one painted face.