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Math / Discrete Mathematics and Its Applications 7 / Chapter 1.7 / Problem 40E

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

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Use Exercise 39 to show that if the first 10 positive

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QUESTION:

Use Exercise 39 to show that if the first 10 positive integers are placed around a circle, in any order, there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17.EXERCISE 39: Prove that at least one of the real numbers a1, a2…, an is greater than or equal to the average of these numbers. What kind of proof did you use?

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QUESTION:

Use Exercise 39 to show that if the first 10 positive integers are placed around a circle, in any order, there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17.EXERCISE 39: Prove that at least one of the real numbers a1, a2…, an is greater than or equal to the average of these numbers. What kind of proof did you use?

ANSWER:

SOLUTIONStep 1Let be the first 10 positive integers placed around a circle in some order.

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