1. ## cube

a cube is coloured red on two opposite faces blue on two adjacent faces and yellow on two remaining faces it is then cut into two halves along a plane parallel to red faces One piece is cut into 4 equal cubes and other one into 32 equal cubes how many cubes will not have any face coloured

2. ## Re: cube

Hello, prasum!

Have you ever heard of punctuation?

A cube is coloured red on two opposite faces, blue on two adjacent faces,
and yellow on two remaining faces.
It is then cut into two halves along a plane parallel to red faces.
One piece is cut into 4 equal cubes and other one into 32 equal cubes.
How many cubes will not have any face coloured?

I don't suppose you made a sketch . . .

Consider a 4-inch cube.

Color the top and bottom red.
Color the front and left face blue.
Color the right and back face yellow.

Bisect the cube horizontally.
. . Each half is a $4\!\times\!4\!\times\!2$ block.

The top half is cut into four equal cubes; each is $2\!\times\!2\!\times\!2$
. . All of them will have at least one painted face.

Code:
              * - - - * - - - *
/       /       /|
/   R   /   R   / |
/       /       /  |
* - - - * - - - * Y *
/       /       /|  /
/   R   /   R   / | /
/       /       /  |/
* - - - * - - - * Y *
|       |       |  /
|   B   |   B   | /
|       |       |/
* - - - * - - - *

The bottom half is cut into 32 equal cubes; each is $1\!\times\!1\!\times\!1$
. . The central 4 cubes in the top layer are paintless.

Code:
              * - * - * - * - *
/   /   /   /   /|
* - * - * - * - *Y*
/   / x / x /   /|/|
* - * - * - * - *Y*Y*
/   / x / x /   /|/|/
* - * - * - * - *Y*Y*
/   /   /   /   /|/|/
* - * - * - * - *Y*Y*
| B | B | B | B |/|/
* - * - * - * - *Y*
| B | B | B | B |/
* - * - * - * - *

,

,

### A cube is colored red on two opposite faces blue on two adjacent faces and yellow on the remaining faces . it is then cut into two halves along the plane parallel to the red faces. one piece is then cut into four equal cubes and the other one into thirty

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