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
. 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
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.
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
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

NAME(s): _
ID(s):_
How Many Spiders
What is the largest number of spiders which can amicably share the spider web pictured below?
A spider will tolerate a neighbor only at a distance of 1.1m or more traveling along the web.
This means the spiders do not w
Sign in # _
MATH 222
Midterm
th
March 6 , 2015
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
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 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
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
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#1 Solutions
1. Six robots are pointing fingers at one another.
A:
C is faulty.
B:
Either A is faulty or C is good.
C:
Either D is good or E is faulty.
D:
F is good.
E:
Either C is good or F is faulty.
F:
B is faulty.
A robot which is good
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
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 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
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
Thursday, April 21st, 2016
DO NOT WRITE ON THE BACK OF THE PAGES. This exam will be scanned and
then graded any writing on the back of the pages will be lost and cannot be marked.
You must sit at your assigned seat.
Show all of your wo
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
4
' . 1,. ' B n. The board can be tiled with dominoes if:
. A .4. "J [2 H [a A. SquareslandZare removed
EE L' B. Squaresland3are removed
C. SquaWare removed
D. All ofheeb/E
E. None W If 35
l7.
z. cooEl Suff05 a; e7 c.
Jq PM)!
as UMWWIO
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
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
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
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
1
Cryptography
Definition 1: Cryptography is the practice and study of hiding information. There is a senderreceiver team on one side and a kibitzer on the other side:
Definition 2: Plaintext is the original message from the sender.
Definition 3: The send
1
The Hamming Code
The PuzzleMad Kidnapper (7.1 of Ecco): Baskerhound has kidnapped the son of a wealthy
heiress and has sent her the following message.
I am thinking of a number between 1 and 2000. If you can determine what that number is in 15
or fewer
1
Polyalphabetic Ciphers
Definition 1: A monoalphabetic cipher uses the same substitution across the entire message.
Definition 2: In a polyalphabetic cipher, the substitution may change throughout the message.
Key Phrase Cipher
Also called the Vigenre
1
Graph Theory
Warm up problem: The Odd Doors Problem. (Section 1.3 of Ecco)
Lawrence Terrence III has a problem. His recently departed father has hidden a cache of jewels
in one of two underground labyrinths. Lawrence knows the following facts about the