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Math Help - [SOLVED] The Painted Cube

  1. #1
    furyal
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    [SOLVED] The Painted Cube

    A large cube (measuring n x n x n) is made up from smaller cubes (measuring 1 by 1 by 1). The outside of the large cube is to be painted. Investigate how many of the smaller cubes within the larger cube have different numbers of their faces painted. Extend the investigation. HELP!!!
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  2. #2
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    Quote Originally Posted by furyal View Post
    [B]A large cube (measuring n x n x n) is made up from smaller cubes (measuring 1 by 1 by 1). The outside of the large cube is to be painted. Investigate how many of the smaller cubes within the larger cube have different numbers of their faces painted. Extend the investigation. HELP!!!
    Hello, furial,

    a cube has:
    8 vertices
    12 edges
    6 squares

    Therefore you find:
    8 cubes with 3 painted squares
    12*(n-2) cubes with 2 painted squares
    6*(n-2) cubes with 1 painted square

    all other cubes are in the inner space of the cube and have no painted square.

    EB
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