All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Hat Exchange (Posted on 2005-02-24)
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: ( Back to comment list | You must be logged in to post comments.)
 Maximum | Comment 2 of 8 |
As in each round, by doing swaps, half the "wrong-hat" people can manage to get their hats back, a maximum is the base 2 logarithm of N, rounded up.
 Posted by Federico Kereki on 2005-02-24 15:34:05

 Search: Search body:
Forums (0)
Random Problem
Site Statistics
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox: