Question 1200033
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The large cube consists of   6 x 6 x 6 = 216   small cubes,  in total.



The painted on exactly one surface are those and only those small cubes,

that are at the surface and not contacting with the edges.


The number of such cubes is &nbsp;&nbsp;6*(4*4) = 6*16 = 96.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>


The factor/(multiplier) &nbsp;6 &nbsp;does represent &nbsp;6 &nbsp;faces of the large cube.


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Solved.