Posted by **avm** on Wednesday, September 23, 2009 at 9:21pm.

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?)

- Gr.12 Data Management -
**Reiny**, Wednesday, September 23, 2009 at 9:48pm
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

- Gr.12 Data Management -
**Logan**, Monday, October 1, 2012 at 7:59pm
Its 12!/2 man

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