27 Cubes, 3 Colors

Discrete Mathematics Level pending

You have 27 cubes of the following colors:

  • 9 orange
  • 9 green
  • 9 blue

How many ways can you put them together to forma a 3x3x3 cube so that no row in any of the three Cartesian directions (\(x,y\), and \(z\)) contains the same color?

Assume that all the cubes of one color are indistinguishable, so if you swap two it counts as the same arrangement.

Also, assume that the edges of the 3x3x3 cube are aligned with the x, y and z axes.

Image credit: http://www.paintingandvino.com/


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