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Friends and Parties

  • Show that at a party of \(n\) people, there are two people who have the same number of friends in the party. Assume that friendship is symmetric.

  • There are \(2n\) people at a party. Each person has an even number of friends at the party. Prove that there are two people who have an even number of common friends at the party. Assume that friendship is symmetric.

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