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 Unique Necklaces (Posted on 2004-08-18)
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.
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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(3): There is an error is this puzzle | Comment 7 of 15 |
(In reply to re(2): There is an error is this puzzle by Penny)

"white black black white white black
black white white black black white"

Don't forget that if you flip the necklace over, and it's the same as another necklace, then it doesn't count.

If you look at the 4th rotation you made, and then flip the necklace over, it's the same as the one above it.

 Posted by nikki on 2004-08-19 12:58:30

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