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 black1 white
With 3 beads, the necklace can be either 3 black, 3 white, 2 black1 white, 2 white1 black, etc...
# Beads Number of Necklaces
1 2
2 3
3 4
4 6
5 8
6 13
(In reply to
re(5): There is an error is this puzzle by Richard)
Richard,
If you read that page carefully, I think you will find that the number
14 is not, in fact, correct. It would be correct, if we don't
respect flipping the necklace over, but the problem clearly states that
you should.
The page refers to two similar, but different scenarios, as "fixed" and
"free" necklacesthe latter able to be pulled out of the plane and
"flipped over". It is this latter scenario that corresponds to
this problem.

Posted by Thalamus
on 20040820 08:10:10 