Question

all the opposite faces of a big cube are colored with yellow blue and orange colors. after that the cube is cut into 64 small equal cubes.22 how many small cubes have atleast two faces coloured?

Answer 1

Hi friend!

64 is a cube number, 4 is its cube root. So in each dimension, there would be 4 small cubes.

Let's visualise the cube.

"Hmm... This seems like a 4x4 Rubik's Cube. Let's solve it!
...
...
Hmm... It seems like only the edge and corner pieces are coloured on at least 2 sides. Let's count them!

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...
13, oops! Already counted that one.
Ya, 13, 14, 15, 16, 17, 18, 19, 20...
(Next face) Oho, again 8 remaining to count this face. So we reached 28.
The fourth face... 29, 30, 31 & 32.

Now for the top and bottom faces. (Turns the cube)
33, 34; wait a minute!
It seems like we have already counted these when we were counting the edges of the four sides. But how?...

Oh ya! We did this when we were counting the edge pieces on the top and bottom of the face. So we have only 32 of the 64 cubes, which are coloured on at least 2 sides. That seems like a lot!"

So, we've got our answer! There are 32 small cubes which are coloured on at least 2 sides.

Hope you found my answer interesting and useful. Keep Smiling!