An aged King, after losing his only son in battle, determines to divide his kingdom amongst his wisest advisors.
He presents two solid cubes, one made of gold, the other made of silver, and a wooden box into which can fit either of the cubes perfectly.
He explains that he will divide his kingdom among those who are able to find all the ways to fill the box with pieces cut from the gold and silver cubes.
The rules are as follows:
The pieces may not be curved. They must be formed by planes.
The corners of each piece must meet one of the corners of the box.
Also, the same exact configuration of gold and silver pieces, rotated differently, will count as a unique way to fill the box if that rotation/configuration is not identical to one you previously counted.
The king does not know the answer, but is looking for those who can solve the riddle and prove it correct, in a way he can understand.
What answer would you give him?
I've researched this for quite some time but have been unable to come up with a solution. Any ideas are welcome!
This image is an example of a cube being divided in different legal ways: