If 100 positive integers are randomly selected, at least how many of them are guaranteed to have the same remainder when divided by 7? At least how many positive integers must be selected in order to guarantee (a) At least two of them have the same remainder when divided by 7? (b) At least five of them have the same remainder when divided by 7?

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section11.8: Adding And Subtracting Radicals
Problem 5E
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8. If 100 positive integers are randomly selected, at least how many of them are guaranteed to
have the same remainder when divided by 7?
9. At least how many positive integers must be selected in order to guarantee
(a) At least two of them have the same remainder when divided by 7?
(b) At least five of them have the same remainder when divided by 7?
Transcribed Image Text:8. If 100 positive integers are randomly selected, at least how many of them are guaranteed to have the same remainder when divided by 7? 9. At least how many positive integers must be selected in order to guarantee (a) At least two of them have the same remainder when divided by 7? (b) At least five of them have the same remainder when divided by 7?
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