document.write( "Question 1143356: A school has 731 students. Prove that there must be at least three students that have the same birthday assuming that no one has a birthday on Feb 29.
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Algebra.Com's Answer #764147 by greenestamps(13200) $\"\"$ $\"About$

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Look at the question this way: you are trying to find as many people as you can without any three of them having the same birthday.

\n" ); document.write( "Assuming nobody has a birthday on February 29, you have 365 days in the year that can be a person's birthday.

\n" ); document.write( "The worst case scenario is that you find exactly 2 people who have birthdays on each of the 365 days of the year. You still have no 3 people with the same birthday; and the number of people you have will be 2*365 = 730.

\n" ); document.write( "But then the 731st person has to have a birthday on one of those 365 days; that means you will have three people with the same birthday.

\n" ); document.write( "And of course it is unlikely that you will easily find 730 people without having 3 of them with the same birthday; that means with 731 people you would almost certainly have more than one date that is a birthday for 3 people; and you could easily have one birthday that is shared by MORE THAN 3 of the people. \n" ); document.write( "

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