the painted cube ? ? ? ? ? ?

Question

the outside surfaces of a cube are painted blue. the cube is then cut up into 27 small cubes(3x3x3). how many of the small cubes have no blue faces? 1 blue face? 2 blue faces? 3 blue faces? 4 blue faces? 5 blue faces? 6 blue faces?

Answer 1

0 faces = 1 (center one)
1 face = 6 (center of each side)
2 faces = 12 (center of each edge)
3 faces = 8 (corners)
4 - 6 faces = none

Total of 27 cubes

If you were to look at the cube as 3 layers of 9 cubes, you could represent it as follows:

Top layer:
3 2 3
2 1 2
3 2 3

Middle layer
2 1 2
1 0 1
2 1 2

Bottom layer:
3 2 3
2 1 2
3 2 3

As you can see:
1 cube has 0 faces
6 cubes have 1 face
12 cubes have 2 faces
8 cubes have 3 faces

1 + 6 + 12 + 8 = 27

This is from my intimate knowledge of the Rubik's cube. :)

Answer 2

Try to visualize the 27 cubes. Only one, the very centre, touches no outside face and so isn't painted. So one cube has 0 blue faces.

The corners of the cube will have 3 blue faces, so that's eight smaller cubes.

The non-corner edges of the cube will have 2 blue faces, so that's 12. (This is the trickiest to imagine...try drawing the sliced cube to picture which ones I'm talking about.)

The centre of each face of the cube will have one blue side, so that's 6.

1 + 8 + 12 + 6 = 27. That's all the small cubes. As you visualize it, you'll realize that no small cube can have more than 3 blue sides.

Answer 3

No blue face - 1
1 blue face - 6
2 blue faces - 12
3 blue faces - 8
4 blue faces - 0
5 blue faces - 0
6 blue faces - 0

Answer 4

human beings here don't have ESP. they at the instant are not going to be waiting to wager the content fabric of a lesson from its call to any extent further than you ought to tell me the whole first financial disaster of a e book purely understanding its call.

Answer 5

only 1 infact ..the one at the centre

Answer 6

um figure it out yourself!!!!!!!!!!