3. You are in a small upper-division class with only 10 total students, and you are all quite friendly with each other. The professor tells the class that the upcoming final exam next week will be graded purely on a curve, such that grades will be assigned based on how far above or below the class average each student scores. One of your classmates suggests that you should all agree to spend the weekend relaxing instead of studying. Does this collusion have a good chance of working? How would things change if the class had 50 students instead? What if studying required publicly checking into the library in a way that all your classmates could see?