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Question: a let n be a natural number and let a1...

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a) Let n be a natural number and let a1, a2, . . . , an be a set of n real numbers. Prove that at least one of these numbers is less than, or equal to the average of these numbers. What kind of proof did you use?

b) Use part a) to show that if the first 12 strictly positive integers are placed around a circle, in any order, then there exist three integers in consecutive locations around the circle that have a sum smaller than or equal to 19.

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