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It is known that among any three students in a class, two of them are friends. The total number of students is $25$ prove that their is a student with at least $12$ friends.

How do I work this out?

Apurv
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Hunter
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1 Answers1

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Consider the student with the most friends. If he's friend with at least 12 people, your problem is solved. If he is not, there is another student who's not his friend. Let's name those two students A and B. A having strictly less than 12 friends, there is at least 12 people different from B he's not friend with. Any of these people are not friend with A, and A is not a friend of B, hence they are all friends of B. B would then have more friends than A, which is absurd.

GBQT
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