What if you took the paper and folded a piece onto its self? Is this allowed in the rules? The solution is trivial by folding it. Basically when you unfold the paper it looks like you lifted your pen off the paper but you never actually do. (I don't have anyway to scan in my hand drawing here.) Once its folded you are still drawing in 2-dimensions though and you pen never leaves the surface of the paper.
Working in the third dimension by folding gives you an extra degree of freedom (similiar to the guy poking a hole in the paper).
Its also similail to how a 'worm hole' in outer space would work. Instead with a worm hole 3-d space is folded onto its self instead of 2-D space being folded onto itsself.