In a class of three students, the teacher says an astrochemechanicalculus exam will be given next week. He warns that after the tests are graded, he will swap the highest and lowest scores. For example, a set of 0, 50, & 100 will result in the perfect scorer receiving a zero while the bum gets a 100.
Each student has a job that pays $1 per hour (they work at underground child labour sweatshops). Meanwhile, their parents will give them $1 for every point they score on the test.
Every hour the student studies, they would earn 1 point on the test. If the money is the goal, what is the optimum strategy on how long one student should study?
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