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Hat Exchange (Posted on 2005-02-24) Difficulty: 3 of 5
At a party with N people, each person is identified by a unique number between 1 and N. Each person is also wearing a hat with their number on it. They decide to play a game. Each person passes his or her hat to the person with the next highest number (so person 2 gets hat 1, person 3 gets hat 2, and person 1 gets hat N). The game proceeds from there in rounds; on each round, each person may choose to either keep the hat they currently have, or swap hats with exactly one other person.

What is the minimum number of rounds, as a function of N, that it would take for every person to get their own hat back? Note: each person can see their own hat at any time.

See The Solution Submitted by Avin    
Rating: 3.0000 (5 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Better Solution (spoiler)Hugo2005-02-26 19:12:54
Solutionanswer(in my eyes)chris2005-02-26 06:05:05
SolutionBetter Solution (spoiler)Tristan2005-02-26 03:01:46
re(3): SolutionAvin2005-02-26 02:51:48
re(2): SolutionHugo2005-02-25 16:10:44
re: SolutionAvin2005-02-25 13:15:10
Some ThoughtsMaximumFederico Kereki2005-02-24 15:34:05
SolutionSolutionHugo2005-02-24 15:21:26
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