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Gr.12 Data Management

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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 -

    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 -

    Its 12!/2 man

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