Question

Anwar is stringing wooden beads on a leather thong. He has twelve beads of various sizes and will tie a knot in the thong when he has put them all onto it. How many different necklaces could he make? (Hint: Does the exact opposite order of beads produce a different necklace?)

Answer 1

This type of problem always leads to a lively discussion.
Problem: can the beads be moved past the claps ?
If so, does moving one or more beads from one side to the other without opening the clasp constitute a different necklace?
The general answer to that is no.

(Think of some keys on a keyring.
Flipping the keys around on the ring does not produce a different keyring arrangement, nor does turning the keyring over, only opening the ring itself will produce a new keychain. )

So here is my solution:
Use one of the beads as a "marker", then the others can be arranged in 11! ways.
We then have to divide by 2 to eliminate the opposite order of beads which would not be a new necklace

so I would say: 11!/2

Answer 2

Its 12!/2 man

Answer 3

12!/2