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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.)
Question Hey SilverKnight | Comment 14 of 15 |
Since there is no clasp, are rotations also considered the same necklace?  i.e. is sliding beads around without changing the order still the same?
  Posted by Bob Marsh on 2004-08-24 04:46:09
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