Finally, here is the solution to this enigma... I hope you enjoyed it, and that you'll enjoy the one of this week...
If we consider that in the ENSEEIHT we have n students. Let's evaluate if it's possible that no one has the same number of friends. Then, one student must have 0 friends, an other one must have only one friend, an other one only two friends... and so on until the last student who will have (n-1) friends. But this means that he is friend with everybody else. And that's impossible since the first student has no friends. That shows that it is impossible for every student to have a different number of friends, so there must be at least two students with the same number of friends.
Congratulations to Florian, and Irene who managed to find this answer.
