Calculate the number 823

The night before one exam, two students tied one on, (well, actually, tied two on, one each), and managed to sleep through the final. They realized they were in serious trouble, so they agreed to tell the professor that they had a flat tire on the way to the exam.
``No problem." said the Professor, ``Come by my office at 5 P.M. and I'll give you the exam then."
Feeling pretty clever, the students spent the intervening time getting information on the exam from students who had already taken it, and making sure they knew how to do the problems. Coming to the professor's office that evening, they were told, ``Leave your books in my office, and I'll put you in two separate rooms for the exam." They were both ecstatic to see that the Professor had given them the exact same exam taken by the class that morning. However, there was an additional page tacked on the end, upon which was written, "For 50% of the grade, which tire was flat?"