{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

exam-2-091112 - MATH 681 Exam#2 Answer exactly four of the...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 681 Exam #2 Answer exactly four of the following six questions. Indicate which four you would like graded! Binomial coefficients, Stirling numbers, and arithmetic expressions need not be simplified in your answers. 1. (10 points) A necklace consists of 6 gems; the gems can be garnets, tourmaline, or zircons. Two necklaces are considered to be identical if one can be obtained by rotating or flipping the other. (a) (5 points) Find a pattern inventory for all such necklaces. You need not alge- braically expand the pattern inventory. (b) (5 points) Either using your pattern inventory or by other means, determine the number of necklaces which use two of each gemstone. 2. (10 points) A 1 × n checkerboard is to be covered with dominoes (which cover two squares) and checkers (which cover one each). We have dominoes in four colors: green, yellow, purple, and octarine, and checkers in four other colors: black, white, cyan, and red. A checkerboard-covering is called magical if it contains exactly one octarine domino, and to the right of the octarine domino uses only checkers.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern