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Unformatted text preview: Pigeonhole Principle (PhP) [KR, Section 6.2] 10/6/11 Theorem 1. If k is a positive integer and k+1or more objects are to be placed in k boxes, then at least one box contains at least two objects. Problem 3a, Section 6.2 A drawer has a dozen brown socks and a dozen black socks, randomly placed. If you draw socks at random w/o looking at the drawer, how many socks do you need draw to have a pair of socks of the same color? Problem 5 In any group of five integers (not necessarily consecutive), at least two of them have the same remainder when divided by 4. Example 3 The possible scores in a test are 0, 1, ..., 100. What is the minimum number of students that must take the test to guarantee that at least two students have the same score? Problem 3b . How many socks must be taken out to ensure at least two white socks? Worst case scenario: take out all brown socks first before taking out any white sock....
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 Fall '11
 Boppana
 Integers, Natural number, Prime number

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