- #1

SammC

- 17

- 0

**The problem statement**

Suppose you have n beads, each with a different color. You need to string these beads into a necklace. How many distinct necklaces can you make? (A necklace flipped over remains the same and does not count as a distinct necklace.)

**The attempt at a solution**

I decided to figure out the first couple necklaces:

n=3: 3 beads can only be arranged 1 distinct way that can't be duplicated by flipping or rotating.

n=4: 4 beads can be arranged 3 ways.

Browsing the internet, i found some fairly complicated equations that I didn't really understand, but I found one for N beads with K different colors, which simplified down to (n-1)! / 2 for N=K. I tried this out for n=3 and 4, and it worked for both of those, but that's far from proof that it works beyond that.

What i really want to know is if this formula is correct, and if not, a way of thinking about this problem that will lead me down the path to a correct formula.