The Mathematics Problem of the Week is intended to give students an opportunity to use the knowledge they gain from their classes to solve interesting mathematical problems from various areas of mathematics. Submissions are scored, and the student with the highest cumulative score each semester will be award a $100 gift certificate to the Spirit Shoppe!
Rules:
- Every Lindenwood student is eligible to participate and can join the contest at any time.
- To join the contest, turn in your solution with your full name, e-mail address, and code name to Dr. Wintz in Young 314B. The code name will be used for posting results.
- Each problem is worth 10 points.
- The deadline for each week's problem is the following Monday at noon.
- Solutions will be checked for correctness and assigned a score. The student(s) with the highest cumulative score at the end of the semester will be declared the winner(s), and will be awarded a $100 gift certificate to the Spirit Shoppe!
The problems for the Fall 2014 semester are posted below.
Formore information about the Problem on the Week, please contact Dr. Nick Wintz.
FALL 2014
Problem 1: Abby is twice as old as Bart. Four years ago, Bart was twice as old as Caitlin. David is five years older than Bart. In 10 years, Abby will be twice as old as Caitlin. How old are Abby, Bart, Caitlin and David now?
Problem 2: Decipher the following message from a famous mathematician. Provide the algorithm used to decipher the message. Hint: C equals A.
HXO CBH SR LSAPU MCHXOMCHAIE ISPEAEHE AP RAPLAPU HXCH EVOIACJ ICEO QXAIX ISPHCAPE CJJ HXO UOBME SR UOPOBCJAHW. - LCNAL XAJFOBH
Problem 3: Answer the following:
- Determine how many distinct paths exist starting at Node a, ending at Node z, and following the arrows toward the right.
- What percentage of the paths pass through Node n?
Problem 4: The triangular numbers T_{n} = 1, 3, 6, 10, ... are defined by: T_{n}+1 = T_{n} + (n + 1), T_{1} = 1.
The square numbers S_{n} = 1, 4, 9, 16, ... are d fined by: S_{n}+1 = T_{n}+1 + T_{n}, S_{1}= 1.
The pentagonal numbers P_{n} = 1, 5, 12, 22, ... are def ned by: P_{n}+1 = S_{n}+1 + T_{n}, P_{1} = 1.
What is the 15th pentagonal number, P_{15}?
Problem 5: Differentiate and simplify: