*Problem #6*

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Recall that in chess, a queen can move an arbitrary number of
(unobstructed) squares in a horizontal, vertical, or diagonal direction.
It is not too difficult to show that for n > 3, the maximum number of
queens which can be placed on an n x n board so that no queen attacks
another is n.

Consider an n x n x n cube. Define a hyperqueen to be a piece which can
move an arbitrary number of (unit) cubes forward or backward, left or
right, up or down, along any of the six diagonal directions parallel to a
face of the cube, or along any of the directions parallel to the four
space diagonals adjoining opposite vertices of the cube.

- What is the maximum number of hyperqueens that can be placed on a 3 x
3 x 3 cube so that no hyperqueen attacks another?
- What about a 4 x 4 x 4 cube?
- An n x n x n cube?