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September 10th, 2009, 11:44 PM   #1
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the pigeon hole principle

it is known that among any group of three students in a class two of them are friends. the total number of students is 25. prove that there is a student who has at least 12 friends

thnx a gazillion
jc.xd

PS: can you show the entire process thnx
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September 11th, 2009, 12:49 AM   #2
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Re: the pigeon hole principle

Choose 2 people from the group who are not friends, call them A and B. Then there are 23 people left to be chosen. Each person remaining must be friends with either A or B or both. Then:
friends of A + friends of B >= 23. Apply the pigeonhole principle.

(If all people are friends, you have your answer there, of course.)
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