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Thread: Divide a cube

  1. #1
    Feb 2013

    Divide a cube

    Could we divide a cube into 2014 smaller cubes?
    (small cubes not have to be identical...)

    I see this: Cube Dissection -- from Wolfram MathWorld
    And answer is: YES, but how to divide it into 2014 cubes?

    Thank you
    Last edited by feferon11; Feb 4th 2014 at 09:29 PM.
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  2. #2
    MHF Contributor
    Sep 2012

    Re: Divide a cube

    Hey feferon11.

    There are bound to be multiple solutions to your problem. I would suggest that you add a few constraints to your problem.

    I would consider the idea that a cube fits exactly x^x cubes if you are putting cubes of size 1/x relative to the cube. So as an example you have 1,4,27, different cubes for x = 1,2,3.

    If you can solve for the number of cubes to be 2014 then you are done. This means that you are summing each set of cubes in a hierarchical manner. You can look at the problem by solving the equation:

    a*1 + b*2^2 + c*3^3 + d*4^4 + .... + = 2014 where you limit the terms to the appropriate size (i.e. x^x < 2014).

    Hopefully that will get you started.
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