KAPLAN MM250 Unit 4 Midterm Project FALL 2015
For the first four Units of this course, you have learned several topics in discrete mathematics including number representations, logical reasoning, elementary probability, and set theory. You are now being asked to apply this knowledge to real world situations by filling the role of a “subject-matter expert” for an upcoming television show. The working title for this show is “The Patty Madeye Mysteries”. You will be working with the writers and producers for this exciting show. The staff will need your help in interpreting and analyzing evidence for robbery, missing persons, and embezzlement cases, as storylines for the show. The show will be a “cyber-crime” series, including a number of episodes where you will be solving crimes using your mathematics and problem-solving skills. For this Midterm Project, you will help produce the first four episodes. Each episode contains 2-4 scenes with questions to answer. There are 16 total questions.
Episode 1: The Case of the Missing Puppies
Episode 2: The Case of the Noontime Robbery
Episode 3: The Case of the Caribbean Criminals
Episode 4: The Case of the Stolen Chemistry Exam
The star of the show is Patty Madeye, shown to the left. Patty is a crack detective with quite a bit of experience in solving crimes. Based on your knowledge of mathematics, you will be providing research and background information that will make the script more interesting. For example, rather than simply finding a clue with a mailing address on it, Patty will find a portion of an envelope with a Postnet bar-code on it. You will show how that bar-code can be interpreted using a binary numeration system to discover the zip code.
Requirements for completing the Project:
? Your project must be submitted as a Microsoft Word document and uploaded to the Unit 4 Dropbox.
? Please show your work! You are free to use other tools and utilities to prepare your work, but all your answers and the work that supports those answers must be pasted into your Word document. For instance, if you do a calculation in Excel to determine an answer, enter both the calculation formula as well as the answer into your document:
Answer: Using Excel: = (90+5) * 45 results in 4275
? All of the problems require not only the answer, but also an explanation. Unless specifically stated, each explanation should be at minimum 2-3 sentences written in your own words.
TYPE YOUR NAME HERE:
Episode 1: The Case of the Missing Puppies
This first episode of “Patty Madeye Mysteries” is called “The Case of the Missing Puppies”.
shutterstock_12606544
You have been asked to do research for an episode where Patty will be challenged to find a trio of stolen puppies, shown to the right. Their names are Moe, Buttercup, and Fluffy. The owners have been raising the puppies with the hopes of winning big prizes in this spring’s season of dog shows. Patty is asked to help find the puppies.
Episode 1, Scene #1:
This Postnet barcode was found on the floor next to where the puppies were last seen.
Patty knows that Postnet (Postal Numeric Encoding Technique) is a barcoding system used by the United States Postal Service to direct mail. As each piece of mail is processed, a barcode is printed on the envelope indicating the zip code to which the mail is addressed. The barcode is made up of full bars (representing a “1”) and half bars (representing a “0”) in a pattern that encodes the characters of the zip-code using a binary representation.
The barcode starts with a full bar and ends with a half bar & full bar, then each number in the zip code is converted to a four-digit binary representation (e.g. 0010 = “2”), and there is a separator bar between each number in the zip code.
Since you are an expert on binary numbers, you take away all the separators and determine that the zip code is as follows:
1. Can you determine the zip code from this clue?
Be sure to show how you arrived at your answer.
Answer:
Explanation:
Episode 1, Scene #2: In the show, Patty is going to find a ransom note from whomever stole the puppies.
The producers want the ransom note to say:
“If you want to see the puppies ever again, save your money now.”
…. but they want the note to be coded using ASCII hexadecimal representation. The writers want to have the ransom note appear on a computer screen using either spaces or dashes as separators between the characters. For example, “Abc” would be 41 62 63. Remember that lower case and upper case letters have different character codes.
2. Determine what the ransom note should say using ASCII character codes.
Note: Refer to the Unit 1 Course Notes for the ASCII Table.
Answer:
Explanation:
Episode 1, Scene #3: Patty Madeye (the heroine of the show) is pretty handy with Internet sniffers, and in the show, she will be able to discover the IP address of the source of the e-mail containing the ransom note:
19.99.108.24 (in decimal)
The writers want to show off Patty’s technical expertise, so they are going to include a scene where Patty converts the IP address from four 8-digit binary numbers
(e.g. 11111111.00000000.11111111.00000000) into the above number. Note that each segment of the IP address MUST be padded out to 8-digits.
3. You need to determine what the 4 binary numbers that Patty should use to represent the four numbers in the IP address above.
Answer:
Explanation:
Episode 2: The Case of the Noontime Robbery
This week Patty Madeye will be investigating a bank robbery. The Main Street bank was robbed at exactly noon on Tuesday by either 3 or 4 men. The group escaped in a getaway car, which has not been recovered.
From the police investigators here’s what we will have learned about the case:
- All the robbers appeared to be men, although they may have been attempting to disguise their appearances.
- There were either 3 or 4 robbers - we’re not sure due to conflicting eyewitness accounts.
- The getaway car was a late-model 4-door sedan that was a dark color (i.e. blue, black or dark green).
Episode 2, Scene #1: In the first scene of Episode 2, Patty will be told all the known information by the police investigators who responded to the emergency call at 12:05pm on Tuesday. This will consist of the separate eyewitness accounts the police investigators collected as well as police conjectures.
She likes to record her notes using simple logic statements. Use the following 4 statements to express the given compound statement given by each eye-witness and the police investigators:
p: There were 4 bank robbers
q: All the bank robbers were men
r: One robber had a ponytail
s: The getaway car was blue
You may use AND, OR, NOT, XOR, and ARROW instead of the logic symbols used in the notes, but be sure to use parentheses as needed to represent precedence. For example, p AND q ARROW r is not the same thing as p AND (q ARROW r).
4. One robber had a ponytail or all the bank robbers were men, but there were 4 bank robbers.
5. There were 4 bank robbers, but the getaway car was blue and all the bank robbers were men.
6. If there were 4 bank robbers and none of the robbers had a ponytail, then all the bank robbers were men.
Answer:
Evaluation:
7. If the getaway car was red then none of the robbers had a ponytail and there were not 4 bank robbers.
Answer:
Explanation:
8. Either the getaway car was black or none of the robbers had a ponytail (but not both), and all the bank robbers were men.
Answer:
Explanation:
Episode 2, Scene #2:
9. The writers can’t decide who the leader of the bank robbers should be. They think that the leader should either be a female (disguised as a man) or someone with black hair (but not both), and the leader should also be tall (over 5’ 10”).
Since you have studied logic, the writers ask you to compose a truth table to figure out all the combinations of these three characteristics (gender, hair color, and short/tall). Given these 3 simple statements, determine the correct compound statement for the condition stated above, and then determine a truth table for that statement.
p: The leader is a female
q: The leader has black hair
r: The leader is tall (over 5’ 10”)
Complete the table:
p
q
r
T
T
T
T
T
F
T
F
T
T
F
F
F
T
T
F
T
F
F
F
T
F
F
F
Episode 3: The Case of the Caribbean Criminals
This next episode Patty Madeye is helping the script-writers on a case of embezzlement at a local law practice, Dewey, Cheatem, and Howe. [Get it?]
The characters of the “Patty Madeye Mysteries” will be investigating a case of embezzlement planned and executed by a team of 2 people who work at the law firm. The story goes that the male/female pair of criminals is both married (to other people) but is involved in a love affair with each other. They have stolen over $2 million in funds from company accounts and have disappeared to somewhere in the Caribbean. shutterstock_12763516
Your job will be to use your knowledge of probability and counting methods to help the writers identify possible candidates to be written into the script.
Name
Gender
Position
Status
Kelly
Female
Specialist
Married
Andrea
Female
Attorney
Single
Ashley
Female
Associate
Single
Bruce
Male
Attorney-Partner
Married
Serge
Male
Specialist
Married
Karen
Female
Paralegal
Single
Amy
Female
Specialist
Married
Marion
Female
Attorney
Single
James
Male
Attorney-Partner
Married
Janice
Female
Specialist
Married
Lori
Female
Associate
Single
Timothy
Male
Associate
Married
Robert
Male
Attorney-Partner
Single
Marvin
Male
Paralegal
Married
Eric
Male
Attorney-Partner
Single
Stephen
Male
Attorney-Partner
Single
Dana
Female
Associate
Married
Joseph
Male
Associate
Married
Kathleen
Female
Attorney
Single
Carissa
Female
Associate
Single
Don
Male
Specialist
Married
Michael
Male
Attorney-Partner
Married
Anne
Female
Specialist
Single
Scott
Male
Attorney-Partner
Single
William
Male
Associate
Married
John
Male
Attorney
Married
Penny
Female
Associate
Single
Elaine
Female
Specialist
Single
Daniel
Male
Associate
Married
Justin
Male
Attorney
Married
Episode 3, Scene #1: In your first meeting with the writers, they show you the list of the character sketches for the employees that work at the law practice.
The writers think that the male embezzler should be one of the partners of the law firm, indicated in this list by “Attorney-Partner”. For the female embezzler, they have chosen someone who is listed as a “Specialist”. Specialists are employees of the firm who offer subject-matter expertise in specific areas such as real estate or accounting.
10. How many different choices do we have for the male/female team of embezzlers?
[Remember: both members of the team are married.]
Answer:
Explanation:
11. How would this answer be different if the 2 members of the male/female team don’t have to be married? In other words, they could be either single or married.
Answer:
Explanation:
Episode 3, Scene #2: The writers want to include an accomplice in the story – that would be someone else in the firm who knew that the pair was stealing from the company.
12. If the accomplice is selected at random from the remaining employees, what is the probability that the accomplice is male?
Answer:
Explanation:
Episode 4: The Case of the Stolen Chemistry Exam
This episode Patty Madeye is going to be investigating the theft of a final exam for Chemistry 101 at a local university. At this university, some students are considered resident students (meaning that they live on campus) and some are considered commuter students (they live elsewhere).
Patty learns that there are 150 students taking Chemistry 101 this semester. She considers every one of them a suspect in the theft of the exam, since they could benefit from seeing the exam. Since Patty has taken Discrete Mathematics, she uses P to represent the set of suspects.
P = {Set of all students taking Chemistry 101}
Episode 4, Scene #1:
In the first scene of the episode, Patty will find the envelope in which the exams had been placed. The discarded envelope is in the garbage can near the student lounge frequented by commuter students, which seems to indicate that whoever took the exam is a commuter student.
13. Using the forms of set notation that you learned about in this unit your first task is to express this set of suspect students, which we will call C. Be sure to specify both the set-builder notation and the descriptive notation.
Answer:
Explanation:
Episode 4, Scene #2:
14. Patty learns that there are 300 students are commuter students, 10 of which are taking Chemistry 101. She needs some help representing these 10 students using the sets from above.
How would you represent the set containing all commuter students who are taking Chemistry 101 using a set operation on C and P?
Answer:
Explanation:
Episode 4, Scene #3:
15. Further research from the security video tapes for the building where the exams were stolen indicates that there were 86 people who entered the building around the time of the theft. Of these 86 people (which we will identify as set V), 16 visited the commuter student lounge and 20 of them were identified by the professor as being in the Chemistry 101 class. 51 of the visitors are neither commuters nor students in the Chemistry class. Patty needs you to summarize all these clues, as follows:
Complete this column with your answer
Explain your answer in this column
n(C) =
n(P) =
n(V) =
n(C ? P) =
n(C ? V) =
n(V ? P) =
n(C U P) =
n((C U P)’ U V) =
Episode 4, Scene #4:
16. Patty looks at all these clues and does some quick figuring and says “I’ve got it! I know who stole the exams!” She asks you to draw a Venn Diagram, then write an explanation of how you arrived at the numbers in the diagram. How does Patty know who stole the exams?