Answer the following questions based on the information given below-

1. A rectangular wooden block with dimensions length 6 cm, breadth 4 cm and height 1 cm has been taken.

2. The two sides with measurements 4cm × 1cm have been painted Black.

3. The two sides with measurements 6cm × 1cm have been painted Red.

4. The two sides with measurements 6cm × 4cm have been painted Green.

How many cubes are there which have Black, Green and Red colours on, at least, different sides

Sol.

In the figure given above the front and the back surface is painted Red, the left and the right surface is painted Black and the upper (Roof) and the lower (ground) surface is painted Green.

We know that only the corner cube has colours on its three surfaces, but when there is only one layer of cubes, then the corner cube will have four coloured surfaces. Now according to the demand of the question we need a cube/cubes with Black, Red and Green Colours. For this we have to calculate the number of corner cubes and this comes out to be = 4.

Hence option-D is the answer