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 |/
* - * - * - * - *

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a cube is painted red on two opposite faces,blue on two adjacent faces and yellow on two remaining faces.it is then cut into two halves along the plane parallel to the red faces .one piece is then cut into 4 equal cubes and the other one into 32 equal cub

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