. Baskerhound had herded Evangeline and her friends into a room containing ve caskets.
Baskerhound stated that sixty minutes after he leaves the room, four of the ve caskets will
disintegrate and release a poisonous gas. The other casket contains the key
MATH 222
Final Exam
Monday, December 16, 2013
Time: 3 hours
Aids:
 one page of notes (standard size front and back)
 a nonprogrammable calculator
Part 1: Fill In the Blanks
 each question is worth 10 marks
 you are not required to show your work
 yo
MATH
Assignment 1

Logic Problems

Coin Weighing Problems

Modular Arithmetic

The Pigeonhole Principle
Group information (you may work by yourself, in a pair, or as a trio)
First Name
Last Name
ID
1
1. Six robots are pointing fingers at one another.
Assignment 1
 Logic Problems
 Coin Weighing Problems
 Modular Arithmetic
 The Pigeonhole Principle
Group information (you may work by yourself, in a pair, or as a trio)
First Name Last Name 1. Six robots are pointing ngers at one another.
C is fau
L
L*
W
L
W
W
L
W
L
W
L
L
W
W
L*
W
L
The first two moves of the winning strategy for the 1st player (player X) are outlined in the
partial state diagram. In each outer losing position (except for the two marked with a *) player
O is forced to block three X
Group information (you may work by yourself, in a pair, or as a trio)
First Name
C‘FFWFU
:22
Assignment 3
 Generalized Caesar’s Code
 Linear Code
 Key Phrase Cipher
 Hill Cipher
 Autokey Cipher
 Vemam Cipher
 The RSA Cryptosystem
— Closed Forms

MATH
Assignment 4

Reccurence Relations

Induction

Strong Induction

Tromino Problems
Group information (you may work by yourself, in a pair, or as a trio)
First Name
Last Name
ID
1. Let be the number of words (strings) of length that can be made usi
MATH
Assignment 4

Reccurence Relations

Induction

Strong Induction

Tromino Problems
Group information (you may work by yourself, in a pair, or as a trio)
First Name
Last Name
ID
J
O
C
A
B
C
C
E
O
1. Let be the number of words (strings) of length th
MATH
Assignment 2

Two Player Games

Nim

Classic Nim

Coding Theory

Campers Problem

Binary numbers

Hamming Code
Group information (you may work by yourself, in a pair, or as a trio)
First Name
Last Name
ID
1
1. The following game is called Tri
MATH
Assignment 2

Two Player Games

Nim

Classic Nim

Coding Theory

Campers Problem

Binary numbers

Hamming Code
Group information (you may work by yourself, in a pair, or as a trio)
First Name
Last Name
ID
1
1. The following game is called Tri
MATH
Assignment 3

Generalized Caesars Code

Linear Code

Key Phrase Cipher

Hill Cipher

Autokey Cipher

Vernam Cipher

The RSA Cryptosystem

Closed Forms

Recurrence Relations
Group information (you may work by yourself, in a pair, or as a trio
1. The following message was encrypted using a linear code. The encoding function used was:
E (x) E 15x 15 (mod 26). Decipher the message.
NYT ENDY
=7 7X=._ Pg) 1
DCN): DQBDZ 7'134lall7t20
DH): DE?)5 762%: 13:tv
DCT) a D67): 767M! 52le
DE> EDCIL) E7 ll1
MATH 222
Final Exam
Tuesday, April 23, 2013
Instructions:
Show all your work and place your answer in the box when provided.
Section:
I: I. E. Leonard
D T. L. Pasanen
Last Name: 5 7L 0 D 6
First Name: K e, X
33
ID: 3 3 mod 223) 1. The following message wa
MATH 222
Final Exam
Tuesday, April 23, 2013
Instructions:
Show all your work and place your answer in the box when provided.
Section:
I. E. Leonard
T. L. Pasanen
Last Name: _
First Name: _
ID: _
1.
The following message was encrypted using a linear code.
MATH 222
Midterm
th
March 7 , 2014
Midterm Aids:

A nonprogrammable calculator
1 page of notes (standard 8.5 x 11 inch front and back)
Part 1: Multiple Choice

each question is worth 2 marks
circle the best answer
Part 2: Long Answer

each question is
MATH 222
Midterm
th
March 8 , 2013
Midterm Aids:

A nonprogrammable calculator
1 page of notes (standard 8.5 x 11 inch front and back)
Instructions

each question is worth 4 marks
place your answer in the box provided
you must show your work
Last Name:
MATH 222
Final Exam
Sample
Time: 3 hours
No Calculators
Instructions:
Show all your work and place your answer in the box when provided.
Aids: one page of notes (front and back)
Part 1: Fill In the Blanks
 Each question is worth 10 marks
 The correct an
MATH 222
Final Exam
Wednesday, April 23rd, 2014
Time: 3 hours
Aids:

one page of notes (standard size front and back)
a nonprogrammable calculator
Instructions:

Question 14 are worth 2 points.
Question 58 are worth 3 points.
Place your answer in the
MATH 222
Midterm
nd
March 2 , 2012
Midterm Aids:

A nonprogrammable calculator
1 page of notes (standard 8.5 x 11 inch front and back)
Part 1: Multiple Choice

each question is worth 2 marks
circle the best answer
Part 2: Long Answer

each question is
MATH 222
Final Exam
Monday, December 16, 2013
Time: 3 hours
Aids:

one page of notes (standard size front and back)
a nonprogrammable calculator
Part 1: Fill In the Blanks

each question is worth 10 marks
you are not required to show your work
you may
MATH 222
Midterm
st
July 31 , 2014
Midterm Aids:

A nonprogrammable calculator
1 page of notes (standard 8.5 x 11 inch front and back)
Part 1: Multiple Choice

each question is worth 2 marks
circle the best answer(s)
Part 2: Long Answer

each question
MATH 222
Midterm
th
May 30 , 2014
Midterm Aids:

A nonprogrammable calculator
1 page of notes (standard 8.5 x 11 inch front and back)
Part 1: Multiple Choice

each question is worth 2 marks
circle the best answer
Part 2: Long Answer

each question is
PART 1: Multiple Choice
1) There are 25 coins, all identical except that one is counterfeit and is a different weight
than the others. It is not known whether the counterfeit is heavier or lighter. Dr. Ecco,
using a pan balance, created a scheme that iden
PART 1: Multiple Choice
1) Consider a game of Nim in the following state:
Rowlv: 14 = X+K+z
Row2: 25 =/M+ ,Z/aA/
Row3: 38 = 32+ )(1 z
Row4: 67 s/H 3 t J/
Row5: 88 =M+W1~ g
The player making the next move can follow a winning strategy by taking counters
Lecture 5
Nim
How to play: Place 9 counters as shown. Players take turns removing counters, provided they
are all in the same (horizontal) row. The player that picks up the last counter wins the game.
State the player that can always win.
Represent a stat
Coding Theory and Cryptography
Lecture 6
Warm up problem: Wrong Number. (Similar to page 17 and 5.7 ofEcco)
In a city called Five people are getting very upset. In Five, phone numbers are 5 digits long made
with the numbers 0 to 4, but lately many phone
Lecture 16
The Trominoes
Denition: A (right) tromino is an object made of three unit squares as shown:
a tromino may appear as above, or it may be rotated through some multiple of 90.
Denition: A board is called decient if one unit squares is missing.
Den
Lecture 3
Warm up problem: The Couriers Problem (6.3 Ecco):
Professor Scarlet and Dr. Ecco have been recruited by a general who wants to send a top secret
message to the safe house behind enemy lines. The general has 8 couriers that can be used to
carry t
MATH 222
Final Exam
Monday, December 16, 2013
Time: 3 hours
Aids:
 one page of notes (standard size front and back)
 a nonprogrammable calculator
Part 1: Fill In the Blanks
 each question is worth 10 marks
 you are not required to show your work
 yo
Sign in # C 03'4
MATH 222
Midterm
July 31, 2015
Midterm Aids:
 A nonprogrammable calculator
 1 page of notes (stande 8.5 x 11 inch front and back)
Part 1: Multiple Choice
 each question is worth 2 marks
 circle the best answer
Part 2: Long Answer

MATH 222
Midterm
July 31, 2014
Midterm Aids:
A nonprogrammable calculator
1 page of notes (standard 8.5 x 11 inch front and back)
Part 1: Multiple Choice
each question is worth 2 marks
circle the best answer(s)
Part 2: Long Answer
each question is worth
PART 1: Multiple Choice
1)
Consider the 7bit Hamming Code. Which of the following statements are true?
I.
A maximum of 1 corrupted digit can be corrected in a codeword.
II.
A maximum of 2 corrupted digits can be detected in a codeword.
III.
The code can
Seatrr
MATH 222
Final
August, 2015
Final Aids:
 A nonprogrammable calculator
 1 page of notes (standard 8.5 x 11 inch front and back)
Instructions:
 Questions 1,2,3,5,6 are worth 3 points.
 Question 4 is worth 6 points.
 Place your answer in the box