Question

Some equal cubes are arranged in the form of a solid block as shown in the adjacent figure. All the visible surfaces of the block (except the bottom) are then painted.

How many cubes have only three faces painted?

• A. $4$
• B. $12$
• C. $6$
• D. $2$

Answer 1

The correct option is C $6$

From the bottom, in first row and second row, we did not have cubes whose three faces painted.
In third row from bottom, number of cubes have only three faces painted $=$ top opened corner cube $=1$
In $4^{th}$ row from bottom, number of cubes have only three faces painted $=0$
In $5^{th}$ row from bottom, number of cubes have only two faces painted $=$ corner cubes $=5$
Then, total cube whose only two faces painted $=1+5=6.$