if you studied that hard, you should know all the answers. Again, study them (as if you have another exam). Go to the Prof, tell him to ask you any question and recite it verbally in-front of him.
If this is your final exam with that prof, after he has cleared you and given you the score (and grade for the exam), express your dissatisfaction to him and to the department. Dont do this before you know your score/grade though.
Good Luck.
I had a similar issue with one of our final exams. Exam was open book open notes. We went to the prof website for previous quarter (took some guess work). Prof had a sample final exam with solutions on the previous quarters site. Since it was open book/open notes exam, we (me and our friends) printed out the solutions, just in case.
On the final exam, there were about 2 (very hard) questions that were exactly the same as from that previous quarters sample exam. Since we had the solutions, we just copied it down. He reported us to the SJA for cheating...we just showed the solutions to SJA the prof website for previous quarter and SJA let us go. We argued that if the prof was so concerned about this, he should have removed his website for the previous quarter. (and this was for a CS class...not like the prof didnt know about computers)
The crappiest part was that professor left the classroom in mid-exam and there was no one in the room while the class was taking the exam. The entire class was cheating on the exam with each other (it was a very hard final exam as compared to his mid-term exam)
Some Profs are just like that....they will think that students cannot solve a question that they put, and when couple of students solve those questions, they will think that the students cheated.