Applied Mathematics
Computer Science
Mathematics
Mathematics Secondary EducationProblem 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.
“Mathematics has always been something that interested me, but it wasn't until I came to Biola that I really began to develop a passion for the subject.”
-Brittany Lane
Mathematics, 2008
Why Choose Mathematics at Biola?
- Thorough in both educational quality and personal attention to students
- Faculty and students work together to make the study of mathematics a successful and enjoyable learning experience
- Involvement in the Putnam Exam; a nationwide contest for math students
- Experienced faculty who not only teach classes in which they are specialists, but work on research projects with individual students
- Small class sizes
- Readily accessible computing facilities