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Eighteen small cubes are glued into this block, 3 by 3 and two layers high. The whole outside, including the base, is painted and the cubes are pulled apart. How many cubes have exactly two painted faces?

Competition practiceDice & Cubes
  • A4
  • B8
  • C12
  • D2

Step-by-Step Solution

Every cube is in the top or bottom layer, so each has that face painted. A cube in the middle of a side edge of a layer has one more side painted: 4 per layer, 8 in all. Corner cubes have three painted faces and the two centre cubes only one.
Answer: B) 8

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