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Math Help - cube

  1. #1
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    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
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  2. #2
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    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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