tag:blogger.com,1999:blog-22031270.post114069719774151406..comments2023-11-03T19:05:08.512+11:00Comments on Harry Clarke: Maths problemsUnknownnoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-22031270.post-1140778309622266432006-02-24T21:51:00.000+11:002006-02-24T21:51:00.000+11:00Proof is by contradiction. Suppose everone shakes ...Proof is by contradiction. Suppose everone shakes hands with a different number of other people. <BR/><BR/>The maximum range of numbers of people one person can shake hands with ranges from 0 to (n-1) assuming no-one shakes hands with anyone else twice. Order them from least to highest numbers of other people they have shaken hands with. <BR/><BR/>One person (#1) shakes hands with nobody else.<BR/>One person (#2) shakes hands with one other person. <BR/>.<BR/>.<BR/>.<BR/><BR/>The nth person (#n) shakes hands with (n-1) other people. <BR/><BR/>But this contradicts the hypothesis that person #1 shook hands with nobody else. <BR/><BR/>Hence it cannot be true that everyone shakes hands with a different number of other people.hchttps://www.blogger.com/profile/13799594181016858701noreply@blogger.com