Ethics of take home tests
I don't think that giving a takehome where one asks for no internet is at all unreasonable. At the same time, such an exam should have some precautions against internet use. When I've given takehomes I've generally made sure that the problems didn't turn up with 5-10 minutes of Googling. That said, if this is enough of a problem that students are discussing this, the best thing to do maybe to drop the professor a note and let them know what other students are doig.