A 3x3x3 cube is placed on top of a 5x5x5 cube, which is placed on a table. On top of the 3x3x3 cube is placed a unit cube such that the axes of all three cubes coincide. All the visible faces are now painted red. What is the number of unit cubes that have exactly 2 faces painted?

32

Hi Priyankesh,
Could you please explain how you got 32 ?

I suppose number of 2 faces coloured in
Unit cube = 0
3*3*3 = (3-2) * 8 = 8 (Excluding bottom layer as it is on top of another cube)
5*5*5 = (5-2) * 8 = 24 (Excluding bottom layer as it is on table)
Sum = 0+8+24 = 32

I don't know the correct answer. I might have left some.

no of cubes with required criteria from the 5*5*5 cube is (5-1)*8 . ( i did not do (5-2)*8 coz the lowermost cubes touching the table have two painted faces only.) similarly for the 3*3*3 cube : (3-1)*8 . Totally 48.
(if I got it wrong somewhere, please point it out)