For those acquainted with Permutations and Combinations,
. . but unfamiliar with the "Circular Table Problem",
. . this is a classic "trick question."
There are six people to be seated in six chairs set around a circular table.
In how many ways can they be seated?
We must understand that a rotation of an arrangement is not a different arrangement.
. . These two seating are considered equivalent. Code:
A B F A
* - - * * - - *
/ \ / \
F* *C E* *B
\ / \ /
* - - * * - - *
E D D C
The reasoning is like this . . .
The first person can sit anywhere . . . it doesn't matter.
. . Then the other five can be seated in ways.
With a bracelet, an additional "trick" is involved.
Once again, rotations are not counted.
In addition, reflections are also not counted.
. . These two bracelets are considered equivalent. Code:
A B B A
* - - * * - - *
/ \ / \
F* *C C * *F
\ / \ /
* - - * * - - *
E D D E
With twelve (distinguishable) beads on a bracelet,
. . there are: . circular arrangements.
And we must eliminate reflections.
. . There are: . possible bracelets.