What Norway needs to do to take advantage of the situation is to: 1) Advertise the fact that it is competitive to get into a Norwegian school and subsequently attracts the best students around the world (the best students tend to want to feel special, so they go to schools that have low acceptance rates), 2) That Norwegian schools provide the best possible education available with top notch facilities (for both in-class learning and research), and 3) That Norway believes in providing the best education possible, to the best candidates, for the best price; and no price is better than free.
You REALLY have to drive the fact that the education is top class into the minds of foreigners in. If you really look at it, Harvard does not actually make a lot of money by way of tuition. Their tuition is ridiculously high, but they give out so much financial aid that if your family makes less than 60k a year, you basically pay no tuition. The amount of tuition they actually collect is actually negligible. The tuition is NOT what make top private US schools like Harvard and Yale such great institutions. What make the schools so rich is alumni donations, which allow them to give out a lot of scholarships to top students, who then become wealthy businessmen, who then feel greatful to Harvard for being so kind back in the day, and then they subsequently donate.
Norway doesn't want to charge tuition, so how can they make students feel greatful? First, tell them how much it costs the country of Norway to educate a foreign student. Second, tell them that the moral reason for providing such costly education for free. For example, I'll make up numbers to illustrate my point, "Fact: It costs Norway 40,000 a year to educate 1 foreign student. How much does it cost the student in tuition? Zero. This is because Norway is a country that believes in fostering talent, and we are a country that will provide the best education to the best students for free. This means that it is very competitive. Only 15% of all applicants are accepted." In this way, you let the world know that the education in Norway is of high quality (why else would it cost the country of Norway so much money? $40,000 is no small sum), and there is prestige in going to Norway (only 15% of foreigners get in, that means you feel like an elite). And because the education is free, those who go to Norway will feel greatful to Norway and will donate to Universities in Norway when they become successful.
Essentially, it is my view that schools in Scandanavia fail to advertise how competitive it is to get in, and how much it costs the country to educate the student. People know that there is no tuition, but they don't know exactly what this means. If it only costs Norway 500 dollars to educate a student, then people won't feel as greatful if they know that Norway is shouldering 50,000 dollars.
The tuition itself has very little to do with prestige of a school, a lot of it is how you advertise. Norway has a very good opportunity at the moment to become a very powerful school. You don't have to increase the amount of spots. If there are only 10,000 seats for foreigners, keep it at that amount. Don't accept any more than traditional, but try to increase the amount of applications. So if traditionally only 20,000 apply, and 10,000 get accepted (50% get in), try to increase it it to 100,000 apply but only 10,000 accepted (10% get in). Charge application fee for foreigners to balance out the cost. If you can do this successfully, you will attract the best students possible, and by far will surpass the other Scandanavian countries.
Just my opinion, but i think it is worth a try. How well Norway takes advantage of the situation will depend on how everything is advertised. You can remain tuition free, but give off impression of exclusivity.