Gr.12 Data Management
posted by avm on .
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?)

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 
Its 12!/2 man