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Painted Cube Exam favourite

Count painted faces with 8, 12(n−2), 6(n−2)², (n−2)³

The Rule

  1. 1A painted n×n×n cube is cut into n³ small cubes.
  2. 23 faces painted: 8 (the corners). 2 faces: 12(n − 2) (along the edges).
  3. 31 face: 6(n − 2)² (face centres). None: (n − 2)³ (the hidden core).