MA 1115 Quiz 23 Worksheet
Monday, April 2, 2012
1.
What is the mathematical notation for ve factorial ?
2.
What number is ve factorial equal to? (Actually multiply it out, and give the resulting number.)
3.
A circuit is a path that starts and ends at the
MA 1115 Quiz 11 Worksheet
Wednesday, September 28, 2011.
1.
In a game of Divider-Chooser, if the Divider divides the cake into two pieces of equal size (two 180
slices), is this necessarily a correct cut?
2.
In a game of Divider-Chooser using a cake worth
MA 1115 Quiz 12 Worksheet
Friday, February 24, 2012.
For Problems 1-7, Alice, Bob, and Carol are going to play Lone Divider with a $12 cake. Alice is the Divider,
and cuts the cake correctly.
1.
How many slices are there?
2.
What is the value of Slice 1 t
MA 1115 Quiz 10 Worksheet
Monday, September 26, 2011.
Were looking at a $12 cake that is half strawberry and half chocolate. Our three players are Alice, Bob, and
Carol. Alice likes strawberry twice as much as chocolate. Bob likes chocolate twice as much
MA 1115 Quiz 09 Worksheet
Friday, February 17, 2012
Notes on Formatting Answers
You should correctly round your values to the nearest cent. For example, if you get $5.3333333333 from your
calculator, you should enter $5.33. If you get, $2.666666666, you s
MA 1115 Quiz 08 Worksheet
Wednesday, February 8, 2012.
For Problems 1-5, use [6: 5, 4,1].
1.
How many sequential coalitions are there?
2.
In the sequential coalition P3 , P2, P1 , who is the pivotal player? Enter Player 1, Player 2, or
Player 3.
3.
What i
MA 1115 Quiz 07 Worksheet
Monday, February 6, 2012.
For Problems 1-5, nd the Banzhaf Power Indices for each of the players using [4: 3,2,1].
1.
How many winning coalitions are there? Just enter the number.
2.
How many instances of a player being critical
MA 1115 Quiz 06 Worksheet
Friday, February 3, 2012.
For Problems 1-6, use the weighted voting system [100 : 101, 99, 1].
1.
How many winning coalitions are there? Just enter the number.
2.
Is P1 , P3 a winning coalition? Enter Yes or No.
3.
If so, is P1 c
MA 1115 Quiz 05 Worksheet
Wednesday, February 1, 2012.
Consider the following preference schedule.
1st choice
2nd choice
3rd choice
4th choice
20
A
B
C
D
10
B
C
D
A
15
C
B
D
A
1.
Rank the candidates using the Plurality Method. Enter your answer in order f
MA 1115 Quiz 13 Worksheet
Monday, February 27, 2012
Alice, Bob, and Carol are going to play Lone Chooser with a $12 cake. Alice is Divider I, and Bob is Divider
II. Alice makes her initial cut correctly.
1.
At this point, how many pieces are there?
2.
Wha
MA 1115 Quiz 15 Worksheet
Friday, March 2, 2012
We have four players splitting a car collection with ve cars, an old Ford, a old Chevy convertible, an MG,
a Jaguar, and a classic Mustang. Here are the bids:
Player
Player
Player
Player
1
2
3
4
Ford Chevy
$
MA 1115 Quiz 14 Worksheet
Wednesday, February 29, 2012.
Suppose we have ve players, Alice, Bob, Carol, Dave, and Elaine, who are going to play Last Diminisher
in the order listed (i.e., Alice is Player 1, Bob is Player 2, etc.). We have a cake worth $30.
MA 1115 Quiz 22 Worksheet
Friday, March 30, 2012.
1.
Suppose you have a graph with 12 odd vertices, and you need to Eulerize it. What is the smallest
possible number of extra edges needed?
2.
Are there graphs with 12 odd vertices that need more extra edge
MA 1115 Quiz 21 Worksheet
Wednesday, March 28, 2012.
For Problems 1-10, use this graph.
1.
How many vertices are there in this graph?
2.
How many edges are there?
3.
What is the degree of the vertex in the upper-left corner?
4.
Is that vertex odd or even?
MA 1115 Quiz 24 Worksheet
Wednesday, April 4, 2012.
For Problems 1-3, refer to this graph.
1.
Does this graph have any circuits?
2.
Is it connected?
3.
Is it a tree?
For Problems 4-6, refer to this graph.
4.
Does this graph have any circuits?
5.
Is it con
MA 1115 Quiz 25 Worksheet
Friday, April 6, 2012.
Note: It seems that D2L sometimes scrambles the order of the answers for multiple choice questions, so be
careful. They might be in the same order as theyre listed here, but maybe not.
1.
Given a graph, the
MA 1115 Quiz 19 Worksheet
Friday, March 23, 2012.
1.
In D2L, youre going to see our ve apportionment methods and ve descriptions, and youll be asked to
match them up. D2Ls format for matching is not what I would like, but well deal with it (well, you will
MA 1115 Quiz 18 Worksheet
Wednesday, March 21, 2012.
For Problems 1-8, youre going to use Jeersons Method to apportion the legislature of a country with
1,400,000 people, 40 seats, and four states. Just to make things interesting, use a rst guess of M = 3
MA 1115 Quiz 17 Worksheet
Monday, March 19, 2012.
Note: Do your computations keeping all of your digits, and in the end round your answers to two decimal
places, like 56.47, unless the answer is a whole number, then either 12 or 12.00 would be ne.
We have
MA 1115 Quiz 16 Worksheet
Friday, March 16, 2012.
Note: Do your computations keeping all of your digits, and in the end round your answers to two decimal
places, like 56.47
We have a country with 200,000 people, and its legislature has 400 seats. There ar
MA 1115 Quiz 02 Worksheet
Wednesday, January 25, 2012.
For all of these problems, use the following preference schedule.
1st choice
2nd choice
3rd choice
3
A
B
C
2
B
A
C
10
C
A
B
8
B
A
C
15
C
A
B
For problems 1-6, use the Plurality Method to rank the cand
MA 1115 Quiz 03 Worksheet
Friday, January 27, 2012.
For Problems 1 through 5, use this preference schedule.
1st choice
2nd choice
3rd choice
3
A
B
C
4
B
A
C
10
C
A
B
20
B
A
C
15
C
A
B
For Problems 1-11, use the Plurality Method to rank the candidates.
1.
MA 1115 Lecture 21 - Graphs and Euler Circuits
Wednesday, March 28, 2012.
Objectives: Discuss Knigsberg Bridge Problem, and dene graphs, and Euler circuits/paths.
o
The Konigsberg Bridge Problem
We started talking last time about this problem, and it went
MA 1115 Lecture 22 - Eulerizations
Friday, March 30, 2012.
Objectives: Most ecient circuits that use every edge at least once.
Heres the graph for the Knigsberg Bridge Problem. It has four odd vertices, so we know that there is no
o
Euler circuit.
Heres a
MA 1115 Lecture 25 - Steiner Trees
Friday, April 6, 2012.
Objectives: Introduction to Steiner Trees.
When nding a minimal spanning tree, we choose edges with minimum weight that already exist in a graph.
Well be doing something similar here, but extending
MA 1115 Lecture 23 - Traveling Salesman Problem
Monday, April 2, 2012.
Objectives: Introduction to the Traveling Salesman Problem.
Heres another kind of graph theory problem. The following is an example of a traveling salesman problem
(nowadays, it may be
MA 1115 Lecture 20 - Graphs and Euler Circuits
Monday, March 26, 2012.
Objectives: Discuss Knigsberg Bridge Problem and graphs.
o
The Konigsberg Bridge Problem
One of our more famous mathematicians is a guy named Leonhard Euler (generally pronounced like
MA 1115 Lecture 19 - Other Apportionment Methods
Friday, March 23, 2012.
Objectives: Overview of Apportionment methods.
Overview of Apportionment Methods
All of our apportionment methods start o the same way. We compute the standard divisor
total populati
MA 1115 Lecture 16 - Apportionment
Friday, March 9, 2012.
Objectives: Introduce Apportionment
Were going to start looking at a dierent sort of sharing, called apportionment.
Apportionment applies mostly to situations arising in representative government.
MA 1115 Lecture 18 - Jeersons Method
Wednesday, March 21, 2012.
Objectives: Jeersons Method
Jeffersons Method
One of the problems with Hamiltons Method is that we only look at the fractional part when we give
back the extra seats. The main problem with th