I'm not sure exactly how to visualize this riddle. Can someone help me?. It goes as this:
Mike has many identical cubes whose faces are white. He decides to take one of those cubes and places it inside of an empty box. After doing this, he begans to take one cube at a time and paints some of its faces and places in the box. However he keeps doing this only if the cube is different from the cube which was already in the box. Find the maximum number of cubes which can be in the box.
What I've attempted to so was using this logic:
What I'm assuming is that the maximum will be perhaps $7$?. As each block will have its color "to remain white" as it is slowly being filled with green color. There's a maximum of $6$ faces in a cube. So adding this to the existing white block inside the box, it would be $7$. Am I right with this conclusion?. If possible can someone add some drawing to justify this?.
The part where it makes me feel not very convinces is that I'm assuming that he paints the faces contiguously to each other. But what if he skips one face, how can I account for it?. Or it wouldn't matter?. Can someone help me here?.
The original source of this riddle comes from a book titled Hability and Logic and dates from an unknown publisher going back 2019. I don't know if this is critical in the solution but looks required for reference.