Oplossing week 49 A tacit assumption in the formulation of the problem is that the relationship of friendship is symmetric: two people are friends iff each is a friend of the other. However, friendship is not reflexive: no one is his own friend.
Reference R. Solution 1 A person at the party can have 0 up to N-1 friends at the party.
tarbiyatulqulub.com/gyk-real-mobile-tracking.php However, if someone has 0 friends at the party, then no one at the party has N-1 friends at the party, and if someone has N-1 friends at the party, then no one has 0 friends at the party. Hence the number of possibilities for the number of friends the N people at the party have must be less than N.
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Hence two people at the party have the same number of friends at the party. Solution 2 Note, as in the first solution, that in general, in a group of N people, a fellow may have 0, 1, 2, Assume to the contrary that all N people have different number of friends.
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