Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Statements and Logic
Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.
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### Question 4 How many people must be selected to guarantee that at least 4 have a birthday in the same month? [Text Box for Input] --- The question is asking for the minimum number of people that need to be chosen to ensure that at least four of them share a birthday month. This type of problem is usually solved using the Pigeonhole Principle. The principle states that if *n* items are put into *m* containers, with *n > m*, then at least one container must contain more than one item. In this scenario, the containers are the months of the year (12 in total), and we want at least one month to contain at least 4 birthdays. To solve: 1. Realize that each of the 12 months can have up to 3 people without having 4 in any month. 2. Therefore, if each month has 3 people, we have 3 * 12 = 36 people. 3. Adding one more person (37th person) will guarantee that at least one month will have 4 people, because there are no more months left to distribute any new person without repeating. Thus, the answer is 37.
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Transcribed Image Text:### Question 4 How many people must be selected to guarantee that at least 4 have a birthday in the same month? [Text Box for Input] --- The question is asking for the minimum number of people that need to be chosen to ensure that at least four of them share a birthday month. This type of problem is usually solved using the Pigeonhole Principle. The principle states that if *n* items are put into *m* containers, with *n > m*, then at least one container must contain more than one item. In this scenario, the containers are the months of the year (12 in total), and we want at least one month to contain at least 4 birthdays. To solve: 1. Realize that each of the 12 months can have up to 3 people without having 4 in any month. 2. Therefore, if each month has 3 people, we have 3 * 12 = 36 people. 3. Adding one more person (37th person) will guarantee that at least one month will have 4 people, because there are no more months left to distribute any new person without repeating. Thus, the answer is 37.
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