Cubes with one painted face — Aptitude Question
Cubes with one painted face: A painted cube is cut into 64 equal smaller cubes. How many have exactly one face… Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 105 seconds
Question
A painted cube is cut into 64 equal smaller cubes. How many have exactly one face painted?
Options
- 8
- 16
- 24
- 36
Show the answer and the worked solution
Correct answer: C. 24
Worked solution
- 64 cubes form a 4 × 4 × 4 block, so n = 4.
- Cubes with one painted face = 6(n − 2)² = 6 × 4 = 24.
Answer: 24.
The idea
Apply the standard formulas rather than counting. For n = 4: 8 corners, 24 edges, 24 faces and 8 hidden cubes, totalling 64. ✓
Shortcut. Each face is a 4 × 4 grid whose inner 2 × 2 block of 4 cubes has one painted face; six faces × 4 = 24.
Common trap. "8" — giving the hidden 2 × 2 × 2 core (no face painted) or the 8 corners instead of the cubes in the middle of each face.