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The party (Posted on 2002-06-20) Difficulty: 4 of 5
Alice and Bill threw a party and invited four other couples. As each couple arrived there were greetings, including handshakes.

Later in the evening, Bill asked everyone, including Alice how many people they shook hand with. Every answer was different. No one shook hands with his or her own partner.

How many hands did Alice shake?

  Submitted by TomM    
Rating: 3.6923 (13 votes)
Solution: (Hide)
There were ten people at the party. No one shook hands with his or her own partner (and couldn't have shaken with him/herself), so the maximum handshakes a person could have made was 8. The minimum is 0.

There are 9 numbers between 0 and 8, inclusive, and 9 different answers, so each number was used as an answer once.

The person who shook hands eight times shook with everyone but his partner, so none of them can be the person who did not shake at all, so she must be "8's"partner.

After eliminating "0" and "8", the same logic shows that "7" and "1" must be partners, then "6" and "2",followed by "5" and "3". "4's" partner must have also shaken 4 hands. But no two people answered the same. However, Bill did not answer the question, so he is the missing"4" Alice is his partner, so she is the other "4"

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsNo SubjectAssaf2007-02-28 08:13:56
SolutionOh!Adeline Redding2006-10-08 13:04:05
Maybe...Adeline Redding2006-10-08 13:03:18
SolutionDifferent solutionTristan2005-07-02 23:55:05
SolutionFor Alanfriedlinguini2003-05-22 15:53:59
Hints/TipsSolution?BJ2003-01-25 16:40:42
the answer?Kristina2002-08-28 07:36:19
SolutionSolutionJim Lyon2002-06-20 08:35:07
Some ThoughtsI think...Veronica2002-06-20 05:12:29
Some ThoughtsMaybe....Dulanjana2002-06-20 04:52:34
re: Huh? (re: hmm.).Cheradenine2002-06-20 04:39:09
re: Huh? (re: hmm.).Cheradenine2002-06-20 04:38:37
QuestionHuh? (re: hmm.).TomM2002-06-20 03:55:37
hmm..Cheradenine2002-06-20 00:43:37
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