Of course I offered those tests without any ambition to accurately represent the kind of questions my young colleagues will really have to face, and with a big disclaimer. I feel that in these dark ages it is best if I repeat the disclaimer also in this post, so here goes:
I am not part of the INFN selection committee. I have no connection to the selection committee, nor any insider information on how the exam will be structured. All I know about it is what is contained in the official call, available to everybody. I do have some previous experience with INFN selections of researchers, but this needs not be relevant for this year's selection.
That said, I think I can offer some more bits of wisdom in this post. The reason for doing this is that I am rooting for my readers! Of the 700 candidates to the positions, I figure some 10 to 20% are probably readers of this blog - erratic or steady as they may be. So maybe I can try to help them further, by offering common-sense advice on how to face such an important moment of their professional career. Really, I do not pretend my short list to be very helpful; but I have observed that even intelligent people must sometimes be reminded of obvious things they could otherwise overlook.
1 - Arrive in Rome the day before, eat lightly, go to bed early.
As silly as this advice sounds, it is very important. I am sure not everybody has considered it necessary to add one day to the trip to Rome. Most of the candidates are certainly well-trained frequent travelers, and they may consider it quite acceptable to take an early train to Rome on Monday morning. However that is a big mistake. Our brain works less well if we are tired, if we have slept less, or if we have sustained some stress (such as the one of being on a tight schedule). And these kind of exams can really strain you, so you need all your wits around you.
2 - Concentration, concentration.
Let all that concerns you be physics problem-solving for one day. Don't engage in email exchanges about other work tasks. I'd even say, don't read your email before the exam (but I'd be the first one to disattend such an advice...)
3 - Sit far from anybody you know
As bad as this sounds, you are on your own during such a written test. Don't expect any help from colleagues, and do not grant any. You are competing against everybody else, so you do not want anybody to bother you during the precious minutes you are given to answer your questions or write your composition.
4 - Don't get stuck
If the exam consists in a set of questions, you will be tempted to spend some time reading everything in detail once you are given the printout. As you proceed reading the questions you might feel panic set in: you don't know the answer to some of those questions! This is to be avoided. Remember: nobody will answer perfectly a well-tuned set of questions, as the exam must allow for the competitive grading of 700 people! You will probably be given much less time than it would take a very good physicist to answer them exhaustively. Hence, you better not get stuck. Time is precious. The most effective way to face such a challenge is to start with the questions that are the least challenging to you, and progressively work your way to the hardest ones. Don't get stuck! If you find yourself thinking for too long on a question, just skip it. Move to another one: you can get back to it when you are done with all the others, if you still have time. Beware, this is very important. I was in a similar exam in 2005 and I know colleagues who did not pass it because they had this habit of knocking their heads on a hard problem until they could solve it. Not a good thing to do here.
5 - Don't be accurate
If the questions ask for an open answer (i.e., if they are not of the "multiple choice" kind) you want to provide a sound answer to each, but you do not want to spend too much time on them. Here is a common instance of "the better is the enemy of the good". Remember that the examiners will have even less time to judge your answers than you had to fill them in: so to them, a good answer will be good, and a better one will probably still be good - I doubt they will be able of micromanaging the task of rating 700 tests! (However, see again my disclaimer at the top of the post).
What is left is to wish you all the best of luck - I would love it if INFN could hire you all (well, ok, let's say 50% of you), but unfortunately the budget of basic research in Italy is what it is. So you start with 8% odds (58/720 to be precise), but if you follow my advices above I am sure you are already above 10% ;-)