A cube is painted red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining surfaces. Now the cube is cut into sixty four smaller cubes of equal size. How many smaller cubes have at least one surface painted with green colour?

1. The cube is painted on its:

   • Two adjacent surfaces: Red.
   • Two opposite surfaces (to red): Black.
   • Remaining two surfaces: Green.

2. The cube is divided into $4\times 4\times 4=64$ smaller cubes of equal size.

Step 2: Identify Smaller Cubes with Green Surfaces

Green paint is on two opposite surfaces of the large cube.

1. Green Faces (Outer Layer of Green Surfaces):

   • Each green-painted face is $4\times 4=16$ cubes.
   • Since there are two green-painted faces, the total number of cubes painted with green is:$$16\times 2=32\text{cubes}.$$

2. Overlap of Green Faces:

   • The edges of the green faces overlap with the edges of the red and black faces.
   • To count only those cubes with at least one green face, we consider only the 32 cubes on the green-painted faces.

Step 3: Check Other Possibilities

Smaller cubes with at least one surface painted green are exactly those on the two green-painted outer faces. No additional overlap or adjustments are needed.

Final Answer:

C) 32 smaller cubes have at least one surface painted with green.