Flaws or Incoherence of the Surprise Test Paradox

INDIVIDUAL ESSAY: Answer section 1 (200 words) and section 2 (100 words)
ESSAY SECTIONS
1) Your first goal is to do your best to resolve the surprise test paradox, as it is formulated above. Doing this will involve doing one of the following:
a) Show why Prof wins! Clearly explain the flaw in the Student’s Argument given below and how this flaw accounts for the fact that it is possible for Prof to create a strategy that guarantees that Stu is surprised. What would Prof’s strategy be?
b) Show why Stu wins! Clearly explain how it is possible that (even if there were a hundred boxes, or a million boxes) there are no boxes that Prof could hide the test in that would guarantee that Stu would be surprised. In other words, how can Stu (who is fully rational) have sufficient evidence to justify believing that the test will be on every upcoming day in an arbitrarily long series of days.
c) Show that the formulation of the Surprise Test Paradox is fundamentally flawed! Clearly explain what specific problem exists in the statement of the paradox that tricks us into thinking that there is a paradox here, where none actually exists. In other words, why is the statement of the problem itself logically incoherent? Explaining this error would also need to explain what goes wrong in the Student’s Argument.
2) Your second goal is to demonstrate that you understand the shortcomings (i.e., problems or deficiencies) in the resolution that you have just offered.
3) Your third goal is to offer any further interesting critical insights into this paradox, similar to what was done in the other paradox resolutions.*
* In thinking about #3 above, here are some of the things you could discuss:
• Other possible resolutions, and objections to these.
• Other objections to your resolution, and responses to these.
• Ways to strengthen the paradox to make it harder to resolve or more relevant.
• Valuable lessons that can be learned from the paradox or your method of resolving it, such as how it can be applied to how people live their lives.
• Discussion of potential reasons to think that the paradox is incoherent or based on some flawed presupposition.