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At a university all students must take a test to see if they understand campus polices....

At a university all students must take a test to see if they understand campus polices. The test has 6 multiple choice questions, each with three possible answers and only one right answer per question. This year every student got at least two questions right. How many possible ways could the students have answered the test questions?

The incoming class this year has 531 students. Prove that at least two students answered the test in the exact same way.

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