Problem 3. Suppose that there is a group of n people, where n 2 2. Prove that there are at least two people in the group with the same number of friends. Some notes: every two people are either friends or are not, if a is a friend of b then b is a friend of a, and no person is their own friend - in other words, friendship is a symmetric, irreflexive relation on this set of n peo- ple. (Hints: use the pigeonhole principle, start by explaining why it's not possible for one per- son to have 0 friends and another person to have n-1 friends.)

Problem 3. Suppose that there is a group of n people, where n 2 2. Prove that there are at least two people in the group with the same number of friends. Some notes: every two people are either friends or are not, if a is a friend of b then b is a friend of a, and no person is their own friend - in other words, friendship is a symmetric, irreflexive relation on this set of n peo- ple. (Hints: use the pigeonhole principle, start by explaining why it's not possible for one per- son to have 0 friends and another person to have n-1 friends.)

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Description: Problem 3. Suppose that there is a group of n people, where n 2 2. Prove that there are atleast two people in the group with the same number of friends. Some notes: every two peopleare either friends or are not, if a is a friend of b then b is a fri

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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