how was the problem solved??

I think being able to meet someone who had a different, but meaningful perspective of their son's life was really healing. Also, the way they were able to take care of her and her friend was somehow able to give them a bit of closure. I'm not exactly sure why it worked. I've never been in a situation remotely like this one.
As for the room, each of the character's goes into the room to grieve in his or her own way. They obviously leave his room as it was before he died. It's just a place where they can feel closer to him.

Alexis

"Could you please continue the petty bickering? I find it most intriguing."
-Data

The film only took place in a short period of time. In reality, the grievance of losing a son is a life-long process. The same is true if you any one you love dies. In many points in the film after Andrea dies, there are temporary attempts to settle the grievance. Giovanni did never stop dwelling on the cause of death of his son. This is a subtle establishment in the film.

It seems as if you are a student that has been assigned to analyze this film, judging from your questions.

Why not use your imagination and intelligence to see what possibly Andrea's room symbolized?

I don't think the problem was solved, they just kind of learned to accept what happened. The fact that they find his "ex girlfriend" is important to them. In a way they discover a part of him that they didn't know when he was alive. They take this girl into sympathy, they cling to her a little bit because to them she represents Andrea. They have nothing left of him and they hold on to her as a "connection" to him.

I think realising that Andrea had a whole other aspect that he didn't tell them about made them just a little angry, and that anger helped them with their grief. He was already "pulling away" from them before he died - they
didn't lose an angel or a mirror image of themselves.

To Andrea's parents Arianna represents, like his death, an unknown part of him. Arianna's arrival both brought Andrea back into his parents lives and allowed them a degree of control over this 'unknown'. Being able to deliver Arianna to her destination and say goodbye to her allowed the parents to metaphorically do the same for their son.

I know you are, you said you are, but what am I?

[deleted]

Great movie and great explanation.
I love you guys.

Following Andrea's death, Giovanni experiences an intense period of introspection, and also becomes more observant of the behaviors of his family as well as his patients. He searches for answers while maintaining his methodical ways. He blames himself. It is Paola (his wife) who knows that he is selfish and she sends this message to him. Upon realizing this truth, Giovani drives the two hitchhikers all the way to France as a selfless act. This is how Giovani has changed, by becoming less self-centered. Near the end, when the daughter exclaims that she must return right away for training, Giovani and Paola share an understanding moment, both knowing that their daughter has inherited the same trait of thinking of self first.