Thread: 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

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 block.

The top half is cut into four equal cubes; each is
. . 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
. . 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 |/
      * - * - * - * - *