the students’ reasoning fails because they assume that their ability to predict the last possible day removes the surprise element, but this ignores the basic definition of a surprise and the inherent uncertainty in the timing of the exam. Thus, the teacher can still surprise them on any day, as the key aspect is their uncertainty about which specific day it will be.
If it were given on. Friday, they’d be surprised their logic failed. Same for the other days.
Faulty definition of surprise