The trick is that "being surprised", or more accurately "not knowing on which day the exam will take place", is changing over time. "D" being the day at which

The trick is that "being surprised", or more accurately "not knowing on which day the exam will take place", is changing over time. "D" being the day at which the exam takes place, "not knowing D on Monday" is not the same proposition as "not knowing D on Thursday". If you change the proposition tested at each inductive step, your induction is invalid.