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What is the minimum number of test-takers necessary to

Suppose a multiple choice test has five questions, each of which has three answer choices

a) If 250 people take the test, prove that at least two people will have the exact same answers.

b) What is the minimum number of test-takers necessary to guarantee that at least four test-takers will have the exact same answers?

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Mathematics: What is the minimum number of test-takers necessary to

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