# cube

• Aug 8th 2011, 04:42 PM
prasum
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
• Aug 10th 2011, 09:00 PM
Soroban
Re: cube
Hello, prasum!

Have you ever heard of punctuation?

Quote:

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 $\displaystyle 4\!\times\!4\!\times\!2$ block.

The top half is cut into four equal cubes; each is $\displaystyle 2\!\times\!2\!\times\!2$
. . 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 $\displaystyle 1\!\times\!1\!\times\!1$
. . 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 |/       * - * - * - * - *