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The six faces of a cube are painted black.  The cube is then cut into $3^3$ smaller cubes, all the same size.  How many of the smaller cubes have exactly one black face?

 Dec 20, 2023
 #1
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1 has no paint on any face

 

12 have paint on two faces

 

8 have paint on three faces

 

27 - 1 - 8  - 12 =   6 have paint on one face

 

cool cool cool

 Dec 20, 2023

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