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

Home > General
Unique Necklaces (Posted on 2004-08-18) Difficulty: 5 of 5
A circular necklace contains n beads. Each bead is black or white. How many different necklaces can be made with n beads?

There is no clasp to identify a specific point on the chain, and a flipped over necklace is still the same necklace.
_____________________________

To get you started:

With 1 bead, the necklace can be either 1 black or 1 white bead.

With 2 beads, the necklace can be either 2 black, 2 white, or 1 black-1 white

With 3 beads, the necklace can be either 3 black, 3 white, 2 black-1 white, 2 white-1 black, etc...

# Beads  Number of Necklaces
   1          2
   2          3
   3          4
   4          6
   5          8
   6         13

No Solution Yet Submitted by SilverKnight    
Rating: 4.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): There is an error is this puzzle | Comment 6 of 15 |
(In reply to re: There is an error is this puzzle by SilverKnight)

Unless I'm missing something (wouldn't be the first time), I don't see how those two are equivalent:

white black black white white black
white black black white black white

If you begin to rotate the second one, one bead at a time, you get:

white black black white white black
black black white black white white

white black black white white black
black white black white white black

white black black white white black
white black white white black black

white black black white white black
black white white black black white

white black black white white black
white white black black white black

white black black white white black
white black black white black white

And we're back to the beginning. 

 

 


  Posted by Penny on 2004-08-19 12:14:56
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information