This question is based on this great puzzle: Puzzle about 6 infinite cylinders in space
What is the most number of identical cubes that can be placed, such that every cube touches all the other cubes at some location? Cubes cannot overlap.
I propose two versions of this puzzle, thanks to @JaapScherphuis:
- Two cubes are considered touching if they touch anywhere, including at a corner, edge or face.
- Two cubes are considered touching if they touch at a face.