Paint It And Disassemble It
The above is a wooden cube block of size , whose outer faces are painted in blue.
Now, the whole block is cut into smaller cubes .
How many cubes have precisely 1 of its faces painted blue?
The answer is 150.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
It is easy to see, that exactly those unit cubes will have exactly one blue face, which are in the middle (that is, none of their sides form a part of an edge of the original 7 × 7 × 7 cube).
Each face of our original cube is cut into 7 × 7 = 49 unit cubes. Out of these, 5 × 5 = 25 cubes are in the middle (and these are distinct from the middle cubes forming the other faces of the original cube).
As the cube has 6 faces, our answer should be:
6 × 5 × 5 = 1 5 0