2012:04: April Showers Bring May . . . Math Majors!

As the year draws to a close, thxe Math/Stat faculty conducts its annual April ritual: bribing students to become majors.  Throughout the month of April, each professor does a tour of the 100 and 200-level math classes to make his best pitch in hopes of wooing the sophomores before they declare their majors.  There are 14 such Math/Stat classes currently running and 14 faculty here this semester, so they divide the barraging as follows.  List the classes in numerical order: 1.Math 103,  . . . , 14.Stat 201-02 and the faculty in alphabetical order: 1.Adams, . . . , 14.Stoiciu.  On a date of his choosing, a professor begins a circuit, starting with the class that bears the same number as his name.  He visits a class meeting, successfully bribes all of the undeclared students to declare math majors, and then moves on to the next class on the list at the next available class meeting.  But the brilliant plan backfires!  Any time a professor visits a class that has already been bribed, the students (annoyed since they’d already converted) rip up their major declaration forms and tie the professor to his/her office chair—never to escape for additional bribery!  But these same students are now fully capable of being bribed to declare math major again upon the next professor visit, having no chosen major.  If there is never more than one professor visiting a class at a given moment, the question is: how many of the classes remain successfully converted by the May 2 preregistration deadline?