# Math Help - Divide a cube

1. ## 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

2. ## 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.