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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A large cube is built using $64$ smaller identical cubes. Three of the faces of the large cube are painted. What is the maximum possible number of small cubes that can have exactly one face painted?

(A) $27$ (B) $28$ (C) $32$ (D) $34$ (E) $40$

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