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

Hayden used small cubes of side 1 to build a large cube with side 4. Then he painted three of the faces of his large cube red and the other three faces blue. When he finished, there was no small cube that had three faces painted red. How many small cubes had both red and blue faces?

(A) $18$ (B) $20$ (C) $22$ (D) $24$ (E) $26$

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