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fifty-five distinct numbers are randomly selected from the first 100 natural numbers. (a) Prove there must be two which differ by 10, and two which

fifty-five distinct numbers are randomly selected from the first 100 natural numbers. (a) Prove there must be two which differ by 10, and two which differ by 12. (b) Show there doesn't have to be two which differ by 11. (example.)

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