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A painted cube is cut into identical small cubes. The number of small cubes with no paint is exactly equal to the number with paint on exactly one face. How many small cubes are there?

Competition practiceDice & Cubes
  • A216
  • B512
  • C343
  • D729

Step-by-Step Solution

With cubes along an edge, the unpainted core has cubes and the one-face cubes number . Setting them equal: , so and there are small cubes. (216 takes )
Answer: B) 512

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