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A solid cube of each side $8\;cm$, has been painted red, blue and black on pairs of opposite faces. It is then cut into cubical blocks of each side $2\:cm$. How many cubes have no face painted?

1. $0$
2. $4$
3. $8$
4. $12$

OPTION(C)

Total no of blocks = (8/2)×((8/2)×(8/2)= 64

Three coloured blocks = corner blocks = 8

Two coloured blocks (red+blue)= 8

Two coloured blocks (red+black)= 8

Two coloured blocks (blue black) =8

Only red = 8, only black= 8, only blue = 8

No coloured blocks = 8

Total 8+8+8+8+8+8+8+8= 64

we can easily visualize from diagram also :)