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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: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolution using Polya's theoryTristan2004-09-30 18:44:14
QuestionHey SilverKnightBob Marsh2004-08-24 04:46:09
FormulaCandy2004-08-22 09:01:50
re(7): There is an error is this puzzleRichard2004-08-21 13:16:55
re(7): There is an error is this puzzlePenny2004-08-21 07:24:02
re(6): There is an error is this puzzleThalamus2004-08-20 08:10:10
re(5): There is an error is this puzzleRichard2004-08-19 21:00:57
re(4): There is an error is this puzzlePenny2004-08-19 13:17:37
re(3): There is an error is this puzzlenikki2004-08-19 12:58:30
re(2): There is an error is this puzzlePenny2004-08-19 12:14:56
re: There is an error is this puzzleSilverKnight2004-08-19 12:03:29
There is an error is this puzzlePenny2004-08-19 10:07:43
QUOTING "SLOANE'S ENCYCLOPEDIA"Ady TZIDON2004-08-19 03:27:45
SolutionBeyond me, but... (spoiler)Charlie2004-08-18 15:04:00
Some Thoughtshalf a solutionDanny2004-08-18 13:50:58
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