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After a painted cube is cut into identical small cubes, 96 of them have paint on exactly one face. How many have no paint?

Competition practiceDice & Cubes

A64
B216
C27
D125

Step-by-Step Solution

Each face carries

(n - 2)^{2}

one-face cubes, so

6 (n - 2)^{2} = 96, (n - 2)^{2} = 16, n - 2 = 4

. The unpainted core is

(n - 2)^{3} = 4^{3} = 64

. (216 is the total

6^{3} .

)

Answer: A) 64

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