Problem of the Month

Two-Colored Necklaces

For this puzzle, I am giving you a large collection of beads; some are yellow, some are blue. Your task is to make necklaces with these beads. Each necklace must contain exactly eight beads.

As an example, here are two of the possible necklaces (keep in mind, the ends of each necklace are joined):

YYBYYYBY
YBBBBBYB

I want no duplicates among the necklaces. Two necklaces are considered the same if you can rotate and/or flip one of them to make it look exactly like the other. For instance, these two necklaces are the same because they are rotations of each other:

YYYYYYBB
YYYBBYYY

And these two necklaces are the same since you can flip one of them over to make it look like the other one:

YYYYBBYB
BYBBYYYY

Under these conditions, how many different necklaces can you make?

Send your answers to this puzzle to me (Joseph DiMuro) at joseph.dimuro@biola.edu by May 31, 2012.