Binary, Permutation, Communication and Dominance Matrices
|
|
|
- Arnold Hodges
- 6 years ago
- Views:
Transcription
1 Binary, Permutation, ommunication and Dominance Matrices Binary Matrices A binary matrix is a special type of matrix that has only ones and zeros as elements. Some examples of binary matrices; Permutation Matrices A permutation matrix is a square binary matrix where there is only one in each row and column.
2 An identity matrix is a special permutation matrix. Permutation matrices rearrange the elements in another matrix, however an identity matrix keeps the elements in the other matrix the same. Permutation matrices can be pre or post multiplied. Example Define two matrices into your calculator. $ = & = ' ( ) * +, v Multiply &$. Why does the calculator give this answer? v Multiply $&. What do you notice about the elements in $&? v Multiply $ - &. Notice the elements again. What has happened?
3 ommunication Matrices Say we look at the workers in a company. Because of their positions and level of power within the company, not every level of employment communicates with the other. For example; v The EO speaks to the General Manager about financial planning v The Assistant Manager speaks to the General Manager about protocol. v The clerk speaks to the General Manager to ask if he wants coffee. v The General manager on any given workday will talk to the EO, the Assistant Manager and the clerk. We can see that EO does not communicate directly with the Assistant Manager on any given work day, but communicates with the General Manager. This is called a one-step communication link.
4 G A K. = G A K But, the EO can communicate with the Assistant Manager by sending a message via the General Manager, who we can see speaks to both of them. This is called a two-step communication link. While we can use a diagram to work out the one-step and two-step communication links, it is easier to show the two-step links and the total of one-step and two-step links in matrices.. - = G A K 3 G A K
5 So, if we look at the first row, we can see that the EO can talk to Assistant Manager and lerk through the General Manager represented by (). represents a two-step communication link in matrix. represents a two-step communication link in. -. All of the non-zero elements in the leading diagonal (top to bottom; left to right) of a communication matrix, or its powers, represent redundant links in the matrix. It s not very meaningful to see that EO can talk to himself, so it s not providing new information. This is true for all cases. - = G A K 3 G A K
6 (Same as above) But we also know that the EO can talk directly to the General Manager so this matrix isn t showing all the possible outcomes. We can find the total number of one and two-step links in a communication matrix system, T, which is evaluated & = & = = 3 + G A K G A K
7 & = 3 Here there are no elements in the matrix, because all of the people can communicate with each other through the help of others. Like before in matrix. -, the leading diagonal in matrix & is redundant. Dominance In sporting competitions, teams and players are said to be dominant. What does that mean? Dominant means being on top, in control, in power etc. Lets say we choose 5 teams from the AFL. We notice that:
8 v North Melbourne defeated Geelong and Essendon. v Richmond defeated Essendon, North Melbourne and St Kilda. v Essendon defeated Geelong. v Geelong defeated Richmond. v St Kilda defeated North Melbourne, Geelong and Essendon. Which is the dominating team? We could use a network diagram to display this result. Please write down the network diagram for this question, it isn t in the notes J Both Richmond and St Kilda had three wins each so there is a tie. We can find out which is the best team by calculating a dominance score for each team. We do this by constructing a series of dominance matrices. One-step dominances
9 Lets call the teams by corresponding letters. N= North Melbourne, G= Geelong, E= Essendon, R= Richmond, S= St Kilda. v North Melbourne defeated Geelong and Essendon. v Richmond defeated Essendon, North Melbourne and St Kilda. v Essendon defeated Geelong. v Geelong defeated Richmond. v St Kilda defeated North Melbourne, Geelong and Essendon. = N G E R S N=2 G=3 E= R= S=3 So, what I ve done, indicated in the green, is I ve calculated a one-step dominance score for each team by summing the rows of matrix.
10 According to this matrix, Geelong and St Kilda both have the same one-step dominance score of 3. Two-step Dominance This is where we see what team has beaten a team who has beaten another team (make sense?). For example, Geelong has a two-step dominance over Richmond because Geelong defeated Essendon who defeated Richmond. We find two-step dominances the same way we find two-step communications. N G E R S - = N=2 G=6 E= R=3 S=4 Same with communications, with dominance the total score is the one-step matrix plus the two-step matrix.
11 & = & = + - N G E R S N=4 G=9 E=2 R=4 S=7 Using these total dominance scores we see that Geelong is the clear winner with 9. St Kilda is second with a score of 7 and North Melbourne and Richmond are equal 3 rd with a score of 4. Please do all F Questions from your textbook J
Matrices AT
VCE Further Mathematics Matrices AT 4.1 2016 Part A Outcome 1 Define and explain key concepts and apply related mathematical techniques and models in routine contexts. Outcome 2 Select and apply the mathematical
Probability and Statistics
Probability and Statistics Activity: Do You Know Your s? (Part 1) TEKS: (4.13) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data.
n-person Games in Normal Form
Chapter 5 n-person Games in rmal Form 1 Fundamental Differences with 3 Players: the Spoilers Counterexamples The theorem for games like Chess does not generalize The solution theorem for 0-sum, 2-player
Match Point. 2. Find the probability that Holly wins the game by getting 4 points before Joe does?
Match Point om and olly decide to play 1 game of tennis. he first player who gets to 4 points wins the game. olly has a 60% probability to win any given point against om. Note: he actual rules of a tennis
GAME THEORY Day 5. Section 7.4
GAME THEORY Day 5 Section 7.4 Grab one penny. I will walk around and check your HW. Warm Up A school categorizes its students as distinguished, accomplished, proficient, and developing. Data show that
Dominance Matrices. Text Reference: Section 2.1, p. 114
Dominance Matrices Text Reference: Section 2.1, p. 114 The purpose of this set of exercises is to apply matrices and their powers to questions concerning various forms of competition between individuals
Is muddled about the correspondence between multiplication and division facts, recording, for example: 3 5 = 15, so 5 15 = 3
Is muddled about the correspondence between multiplication and division facts, recording, for example: 3 5 = 15, so 5 15 = 3 Opportunity for: recognising relationships Resources Board with space for four
Game Theory. Problem data representing the situation are constant. They do not vary with respect to time or any other basis.
Game Theory For effective decision making. Decision making is classified into 3 categories: o Deterministic Situation: o o Problem data representing the situation are constant. They do not vary with respect
3. If you can t make the sum with your cards, you must draw one card. 4. Players take turns rolling and discarding cards.
1 to 10 Purpose: The object of the game is to get rid of all your cards. One player gets all the red cards, the other gets all the black cards. Players: 2-4 players Materials: 2 dice, a deck of cards,
Solution Algorithm to the Sam Loyd (n 2 1) Puzzle
Solution Algorithm to the Sam Loyd (n 2 1) Puzzle Kyle A. Bishop Dustin L. Madsen December 15, 2009 Introduction The Sam Loyd puzzle was a 4 4 grid invented in the 1870 s with numbers 0 through 15 on each
Computing optimal strategy for finite two-player games. Simon Taylor
Simon Taylor Bachelor of Science in Computer Science with Honours The University of Bath April 2009 This dissertation may be made available for consultation within the University Library and may be photocopied
Cross Out Singles. 3. Players then find the sums of the rows, columns, and diagonal, and record them in the respective circles.
Materials: Cross Out Singles recording sheet, and 1 die. Cross Out Singles How To Play: 1. The die is rolled. Both players put this number in whichever one of the squares on their Round 1 chart they choose.
Classwork Example 1: Exploring Subtraction with the Integer Game
7.2.5 Lesson Date Understanding Subtraction of Integers Student Objectives I can justify the rule for subtraction: Subtracting a number is the same as adding its opposite. I can relate the rule for subtraction
Chapter 15: Game Theory: The Mathematics of Competition Lesson Plan
Chapter 15: Game Theory: The Mathematics of Competition Lesson Plan For All Practical Purposes Two-Person Total-Conflict Games: Pure Strategies Mathematical Literacy in Today s World, 9th ed. Two-Person
CSE548, AMS542: Analysis of Algorithms, Fall 2016 Date: Sep 25. Homework #1. ( Due: Oct 10 ) Figure 1: The laser game.
CSE548, AMS542: Analysis of Algorithms, Fall 2016 Date: Sep 25 Homework #1 ( Due: Oct 10 ) Figure 1: The laser game. Task 1. [ 60 Points ] Laser Game Consider the following game played on an n n board,
Experiments in Probability ----a game of dice ---
Name: Experiments in Probability ----a game of dice --- Part 1 The Duel. A. Friends, Mustangs, Countrymen. Look carefully at your dice and answer the following questions. 1) What color is your dice? 2)
GROUP ROUND INSTRUCTIONS
GROUP ROUND INSTRUCTIONS Your team will have 40 minutes to answer 10 questions. Each team will have the same questions. Each question is worth 6 points. However, some questions are easier than others!
GCSE MATHEMATICS Intermediate Tier, topic sheet. PROBABILITY
GCSE MATHEMATICS Intermediate Tier, topic sheet. PROBABILITY. In a game, a player throws two fair dice, one coloured red the other blue. The score for the throw is the larger of the two numbers showing.
Heights of netballers and footballers
CD40 SS Heights of netballers and footballers Heights of netballers Netball heights gives data showing the heights of all members of the Australian Netball Team, and the eight teams in the Commonwealth
Binary Games. Keep this tetrahedron handy, we will use it when we play the game of Nim.
Binary Games. Binary Guessing Game: a) Build a binary tetrahedron using the net on the next page and look out for patterns: i) on the vertices ii) on each edge iii) on the faces b) For each vertex, we
JINX - 2 Players / 15 Minutes
JINX - 2 Players / 15 Minutes Players are witches who combine secret ingredients to make big and powerful potions. Each witch will contribute one of the ingredients needed to make a potion. If they can
One Zero One. The binary card game. Players: 2 Ages: 8+ Play Time: 10 minutes
One Zero One The binary card game Players: 2 Ages: 8+ Play Time: 10 minutes In the world of computer programming, there can only be one winner - either zeros or ones! One Zero One is a small, tactical
Chapter 2 Integers. Math 20 Activity Packet Page 1
Chapter 2 Integers Contents Chapter 2 Integers... 1 Introduction to Integers... 3 Adding Integers with Context... 5 Adding Integers Practice Game... 7 Subtracting Integers with Context... 9 Mixed Addition
Meaningful Ways to Develop Math Facts
NCTM 206 San Francisco, California Meaningful Ways to Develop Math Facts -5 Sandra Niemiera Elizabeth Cape mathtrailblazer@uic.edu 2 4 5 6 7 Game Analysis Tool of Game Math Involved in the Game This game
JIGSAW ACTIVITY, TASK # Make sure your answer in written in the correct order. Highest powers of x should come first, down to the lowest powers.
JIGSAW ACTIVITY, TASK #1 Your job is to multiply and find all the terms in ( 1) Recall that this means ( + 1)( + 1)( + 1)( + 1) Start by multiplying: ( + 1)( + 1) x x x x. x. + 4 x x. Write your answer
* How many total outcomes are there if you are rolling two dice? (this is assuming that the dice are different, i.e. 1, 6 isn t the same as a 6, 1)
Compound probability and predictions Objective: Student will learn counting techniques * Go over HW -Review counting tree -All possible outcomes is called a sample space Go through Problem on P. 12, #2
CS1800: More Counting. Professor Kevin Gold
CS1800: More Counting Professor Kevin Gold Today Dealing with illegal values Avoiding overcounting Balls-in-bins, or, allocating resources Review problems Dealing with Illegal Values Password systems often
Problem Darts Input File: DartsIn.txt Output File: DartsOut.txt Project File: Darts
Darts Input File: DartsIn.txt Output File: DartsOut.txt Project File: Darts Because of the arguments over the scoring of the dart matches, your dart club has decided to computerize the scoring process.
Jim and Nim. Japheth Wood New York Math Circle. August 6, 2011
Jim and Nim Japheth Wood New York Math Circle August 6, 2011 Outline 1. Games Outline 1. Games 2. Nim Outline 1. Games 2. Nim 3. Strategies Outline 1. Games 2. Nim 3. Strategies 4. Jim Outline 1. Games
Lecture Notes on Game Theory (QTM)
Theory of games: Introduction and basic terminology, pure strategy games (including identification of saddle point and value of the game), Principle of dominance, mixed strategy games (only arithmetic
Fair Game Review. Chapter 2. Name Date. Write the decimal as a fraction Write the fraction as a decimal. 7.
Name Date Chapter Fair Game Review Write the decimal as a fraction.. 0.6. 0.79. 0.7. 0.86 Write the fraction as a decimal.. 8 6. 7. 6 8. 7 0 9. A quarterback completed 0.6 of his passes during a game.
Expansion/Analysis of a Card Trick Comprised of Transformations in 2-Dimensional Matrices Aaron Kazam Sherbany, Clarkstown North High School, NY
Expansion/Analysis of a Card Trick Comprised of Transformations in 2-Dimensional Matrices Aaron Kazam Sherbany, Clarkstown North High School, NY This paper illustrates the properties of a card trick which
Labor s Response to Industrialism
N O T E B O O K G U I D E C H A P T E R Labor s Response to Industrialism 14 Was the rise of industry good for American workers? P R E V I E W In your notebook, describe a time when you were unhappy with
Final Project: Reversi
Final Project: Reversi Reversi is a classic 2-player game played on an 8 by 8 grid of squares. Players take turns placing pieces of their color on the board so that they sandwich and change the color of
Factors and Products. Jamie is 12 years old. Her cousin, 6 Prime Time
Factors and Products Jamie is years old. Her cousin, Emilio, is years old. Her brother, Cam, is. Her neighbor, Esther, is. The following number sentences say that Jamie is times as old as Emilio, times
and Games Developing Numeracy Skills Using Visual Tools A Workshop by Trevor Calkins
Egg Cartons, Brains and Games Developing Numeracy Skills Using Visual Tools A Workshop by Trevor Calkins 809 Kimberley Place, Victoria, B. C. V8X 4R2 Tel: (250) 744-2613 Fax: (250) 744-2673 Cell: (250)
ECO 220 Game Theory. Objectives. Agenda. Simultaneous Move Games. Be able to structure a game in normal form Be able to identify a Nash equilibrium
ECO 220 Game Theory Simultaneous Move Games Objectives Be able to structure a game in normal form Be able to identify a Nash equilibrium Agenda Definitions Equilibrium Concepts Dominance Coordination Games
PLAYERS AGES MINS.
2-4 8+ 20-30 PLAYERS AGES MINS. COMPONENTS: (123 cards in total) 50 Victory Cards--Every combination of 5 colors and 5 shapes, repeated twice (Rainbow Backs) 20 Border Cards (Silver/Grey Backs) 2 48 Hand
Determinants, Part 1
Determinants, Part We shall start with some redundant definitions. Definition. Given a matrix A [ a] we say that determinant of A is det A a. Definition 2. Given a matrix a a a 2 A we say that determinant
A Games-based, Strategy-focused Fluency Plan
A Games-based, Strategy-focused Fluency Plan To have with you for tonight s webinar: ü Deck of Cards ü 2 dice (6-sided or 10-sided) ü Games Recording Sheet ü This powerpoint with Game Boards Jennifer Bay-Williams
LECTURE 8: DETERMINANTS AND PERMUTATIONS
LECTURE 8: DETERMINANTS AND PERMUTATIONS MA1111: LINEAR ALGEBRA I, MICHAELMAS 2016 1 Determinants In the last lecture, we saw some applications of invertible matrices We would now like to describe how
1. For which of the following sets does the mean equal the median?
1. For which of the following sets does the mean equal the median? I. {1, 2, 3, 4, 5} II. {3, 9, 6, 15, 12} III. {13, 7, 1, 11, 9, 19} A. I only B. I and II C. I and III D. I, II, and III E. None of the
Lotto! Online Product Guide
BCLC Lotto! Online Product Guide Resource Manual for Lottery Retailers October 18, 2016 The focus of this document is to provide retailers the tools needed in order to feel knowledgeable when selling and
Math 152: Applicable Mathematics and Computing
Math 152: Applicable Mathematics and Computing May 8, 2017 May 8, 2017 1 / 15 Extensive Form: Overview We have been studying the strategic form of a game: we considered only a player s overall strategy,
Partitions and Permutations
Chapter 5 Partitions and Permutations 5.1 Stirling Subset Numbers 5.2 Stirling Cycle Numbers 5.3 Inversions and Ascents 5.4 Derangements 5.5 Exponential Generating Functions 5.6 Posets and Lattices 1 2
Roll for the Tournament -Jousting
Roll for the Tournament -Jousting Roll for the Tournament consists of 3 events: The Joust, Melee with Sword, and Melee on horseback. Roll for the Tournament is a Dice game that uses individual as well
General Principals. Turn Priority - this player may choose which player goes first.
General Principals The player who wins the pre-game roll off may either decide Turn Priority or Deployment Priority. If they choose Turn Priority, then their opponent is granted Deployment Priority. Turn
Chess Handbook: Course One
Chess Handbook: Course One 2012 Vision Academy All Rights Reserved No Reproduction Without Permission WELCOME! Welcome to The Vision Academy! We are pleased to help you learn Chess, one of the world s
Making Middle School Math Come Alive with Games and Activities
Making Middle School Math Come Alive with Games and Activities For more information about the materials you find in this packet, contact: Sharon Rendon (605) 431-0216 sharonrendon@cpm.org 1 2-51. SPECIAL
Milton Public Schools Elementary Summer Math
Milton Public Schools Elementary Summer Math Did you know that the average American child loses between 1 and 3 months of learning in reading and math each summer? You can continue to love and enjoy your
Assignment 6 Play A Game: Minesweeper or Battleship!!! Due: Sunday, December 3rd, :59pm
Assignment 6 Play A Game: Minesweeper or Battleship!!! Due: Sunday, December 3rd, 2017 11:59pm This will be our last assignment in the class, boohoo Grading: For this assignment, you will be graded traditionally,
Number Puzzles & Games LEVEL 4/5. An educational resource that integrates the concepts children need most in their learning of mathematics
IN C L U DES MES 60+GA SMARdT Boar ded! TM clu C D In Number Puzzles & Games LEVEL 4/5 An educational resource that integrates the concepts children need most in their learning of mathematics Celia Baron,
FREE Math & Literacy Centers. Created by: The Curriculum Corner.
FREE Math & Literacy Centers Created by: The Curriculum Corner 1 + 3 9 + 9 4 + 5 6 + 7 2 + 1 3 + 7 8 + 4 5 + 9 4 + 6 8 + 8 7 + 2 9 + 3 1 + 5 4 + 4 8 + 3 4 + 8 8 + 10 5 + 5 1 + 8 4 + 3 6 + 6 8 + 9 7 + 5
Math Circles 9 / 10 Contest Preparation I
Math Circles 9 / 10 Contest Preparation I Centre for Education in Mathematics and Computing CEMC www.cemc.uwaterloo.ca February 4, 2015 Agenda 1 Warm-up Problem 2 Contest Information 3 Contest Format 4
Let's Play Math Games! Activities for Learning, Inc. 2017
Let's Play Math Games! 4 5 6 7 8 9 7 142128354249566370 Games Games Math = Books Reading Games provide instant feedback. Games provide interesting repetition needed for automatic responses in a social
4 by Marilyn Burns. Using games to support extra time. All four games prestudents. Win-Win Math Games. Games can motivate. students, capture their
4 by Marilyn Burns Win-Win Math Games photos: bob adler Games can motivate Using games to support extra time. All four games prestudents math learning sented here are easy to teach and students, capture
Contents Systems of Linear Equations and Determinants
Contents 6. Systems of Linear Equations and Determinants 2 Example 6.9................................. 2 Example 6.10................................ 3 6.5 Determinants................................
BOOM! subtract 15. add 3. multiply by 10% round to. nearest integer. START: multiply by 2. multiply by 4. subtract 35. divide by 2
GAME 3: Math skills, speed and luck come together in a fun way with Boom! Students roll a die to find out their starting number and then progress along a mathematical path where they ll practice their
You ve seen them played in coffee shops, on planes, and
Every Sudoku variation you can think of comes with its own set of interesting open questions There is math to be had here. So get working! Taking Sudoku Seriously Laura Taalman James Madison University
Stat 155: solutions to midterm exam
Stat 155: solutions to midterm exam Michael Lugo October 21, 2010 1. We have a board consisting of infinitely many squares labeled 0, 1, 2, 3,... from left to right. Finitely many counters are placed on
An Adaptive-Learning Analysis of the Dice Game Hog Rounds
An Adaptive-Learning Analysis of the Dice Game Hog Rounds Lucy Longo August 11, 2011 Lucy Longo (UCI) Hog Rounds August 11, 2011 1 / 16 Introduction Overview The rules of Hog Rounds Adaptive-learning Modeling
37 Game Theory. Bebe b1 b2 b3. a Abe a a A Two-Person Zero-Sum Game
37 Game Theory Game theory is one of the most interesting topics of discrete mathematics. The principal theorem of game theory is sublime and wonderful. We will merely assume this theorem and use it to
Lesson 3: Multiplying Matrices. You can only multiply two matrices if
Lesson 3: Multiplying Why Do We Multiply? When the Baltimore Ravens won the Super Bowl in 2013, Dan knew that his NFL Sports attire business would go crazy! He started to produce hats, shirts, sweatshirts,
The game of Reversi was invented around 1880 by two. Englishmen, Lewis Waterman and John W. Mollett. It later became
Reversi Meng Tran tranm@seas.upenn.edu Faculty Advisor: Dr. Barry Silverman Abstract: The game of Reversi was invented around 1880 by two Englishmen, Lewis Waterman and John W. Mollett. It later became
Junior Circle Meeting 5 Probability. May 2, ii. In an actual experiment, can one get a different number of heads when flipping a coin 100 times?
Junior Circle Meeting 5 Probability May 2, 2010 1. We have a standard coin with one side that we call heads (H) and one side that we call tails (T). a. Let s say that we flip this coin 100 times. i. How
Making Middle School Math Come Alive with Games and Activities
Making Middle School Math Come Alive with Games and Activities For more information about the materials you find in this packet, contact: Chris Mikles 916-719-3077 chrismikles@cpm.org 1 2 2-51. SPECIAL
Instruction Cards Sample
Instruction Cards Sample mheducation.com/prek-12 Instruction Cards Table of Contents Level A: Tunnel to 100... 1 Level B: Race to the Rescue...15 Level C: Fruit Collector...35 Level D: Riddles in the Labyrinth...41
1 HB By Representatives Boothe, Clouse, Rowe and Martin. 4 RFD: State Government. 5 First Read: 02-MAR-17. Page 0
1 HB354 2 183292-1 3 By Representatives Boothe, Clouse, Rowe and Martin 4 RFD: State Government 5 First Read: 02-MAR-17 Page 0 1 183292-1:n:03/01/2017:MA/mfc LRS2017-868 2 3 4 5 6 7 8 SYNOPSIS: Under existing
Skateboard Bingo (cont.)
Skateboard Bingo (cont.) Length of Play: 10-15 min. Group Size: Small Group (2-4 players) Learning Goals This activity is designed to help children strengthen their subitizing skills as they: Recognize
Game Theory. Chapter 2 Solution Methods for Matrix Games. Instructor: Chih-Wen Chang. Chih-Wen NCKU. Game Theory, Ch2 1
Game Theory Chapter 2 Solution Methods for Matrix Games Instructor: Chih-Wen Chang Chih-Wen Chang @ NCKU Game Theory, Ch2 1 Contents 2.1 Solution of some special games 2.2 Invertible matrix games 2.3 Symmetric
Another Form of Matrix Nim
Another Form of Matrix Nim Thomas S. Ferguson Mathematics Department UCLA, Los Angeles CA 90095, USA tom@math.ucla.edu Submitted: February 28, 2000; Accepted: February 6, 2001. MR Subject Classifications:
Materials: Game board, dice (preferable one 10 sided die), 2 sets of colored game board markers.
Even and Odd Lines is a great way to reinforce the concept of even and odd numbers in a fun and engaging way for students of all ages. Each turn is comprised of multiple steps that are simple yet allow
Exploring Concepts with Cubes. A resource book
Exploring Concepts with Cubes A resource book ACTIVITY 1 Gauss s method Gauss s method is a fast and efficient way of determining the sum of an arithmetic series. Let s illustrate the method using the
Let s Play Math Games!
Let s Play Math Games! July, at : pm Arizona Families for Home Education Conference presented by Kathleen Cotter Lawler based on the work of Dr. Joan A. Cotter // Games Math Games Games provide instant
LEARN HOW TO PLAY MINI-BRIDGE
MINI BRIDGE - WINTER 2016 - WEEK 1 LAST REVISED ON JANUARY 29, 2016 COPYRIGHT 2016 BY DAVID L. MARCH INTRODUCTION THE PLAYERS MiniBridge is a game for four players divided into two partnerships. The partners
Attention! Choking hazard! Small pieces, not for children under three years old. Figure 01 - Set Up for Kick Off. corner arc. corner square.
Figure 01 - Set Up for Kick Off A B C D E F G H 1 corner square goal area corner arc 1 2 3 4 5 6 7 penalty area 2 3 4 5 6 7 8 center spin circle 8 rows 8 8 7 7 6 6 5 4 3 2 1 penalty arc penalty spot goal
Overview. Equipment. Setup. A Single Turn. Drawing a Domino
Overview Euronimoes is a Euro-style game of dominoes for 2-4 players. Players attempt to play their dominoes in their own personal area in such a way as to minimize their point count at the end of the
Easy Games and Hard Games
Easy Games and Hard Games Igor Minevich April 30, 2014 Outline 1 Lights Out Puzzle 2 NP Completeness 3 Sokoban 4 Timeline 5 Mancala Original Lights Out Puzzle There is an m n grid of lamps that can be
BMT 2018 Combinatorics Test Solutions March 18, 2018
. Bob has 3 different fountain pens and different ink colors. How many ways can he fill his fountain pens with ink if he can only put one ink in each pen? Answer: 0 Solution: He has options to fill his
Print and Play Instructions: 1. Print Swamped Print and Play.pdf on 6 pages front and back. Cut all odd-numbered pages.
SWAMPED Print and Play Rules Game Design by Ben Gerber Development by Bellwether Games LLC & Lumné You ve only just met your team a motley assemblage of characters from different parts of the world. Each
1111: Linear Algebra I
1111: Linear Algebra I Dr. Vladimir Dotsenko (Vlad) Lecture 7 Dr. Vladimir Dotsenko (Vlad) 1111: Linear Algebra I Lecture 7 1 / 8 Invertible matrices Theorem. 1. An elementary matrix is invertible. 2.
The first player, Fred, turns on the calculator, presses a digit key and then presses the
1. The number pad of your calculator or your cellphone can be used to play a game between two players. Number pads for telephones are usually opposite way up from those of calculators, but that does not
######################################################################
Write a MATLAB program which asks the user to enter three numbers. - The program should figure out the median value and the average value and print these out. Do not use the predefined MATLAB functions
Table of Contents. Table of Contents 1
Table of Contents 1) The Factor Game a) Investigation b) Rules c) Game Boards d) Game Table- Possible First Moves 2) Toying with Tiles a) Introduction b) Tiles 1-10 c) Tiles 11-16 d) Tiles 17-20 e) Tiles
Section 1.6 The Factor Game
Section 1.6 The Factor Game Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Play the Factor Game. Factor pairs (1.1) Adding integers (1.3)
UNITED KINGDOM MATHEMATICS TRUST GROUP ROUND. There are 15 questions to try to answer in the time allowed.
UNITED KINGDOM MATHEMATICS TRUST GROUP ROUND Time allowed: 45 minutes. There are 15 questions to try to answer in the time allowed. Each question is worth four marks. A question is marked either correct
Whole Numbers. Predecessor and successor Given any natural number, you can add 1 to that number and get the next number i.e. you
Whole Numbers Chapter.1 Introduction As we know, we use 1,, 3, 4,... when we begin to count. They come naturally when we start counting. Hence, mathematicians call the counting numbers as Natural numbers.
Digital Photographs and Matrices
Digital Photographs and Matrices Digital Photographs Color Model for 24-bit Visualization of Matrix Addition Visualization of Matrix Scalar Multiplication Color Separation Illustration Decoding with a
ECE 5325/6325: Wireless Communication Systems Lecture Notes, Spring 2013
ECE 5325/6325: Wireless Communication Systems Lecture Notes, Spring 2013 Lecture 18 Today: (1) da Silva Discussion, (2) Error Correction Coding, (3) Error Detection (CRC) HW 8 due Tue. HW 9 (on Lectures
The Expected Number Of Dice Rolls To Get YAHTZEE
POTW #- YAHTZEE The Expected Number Of Dice Rolls To Get YAHTZEE John Snyder, FSA January, 0 :0 EST Problem For those not familiar, YAHTZEE is a game played with five standard dice where each player completes
Chained Permutations. Dylan Heuer. North Dakota State University. July 26, 2018
Chained Permutations Dylan Heuer North Dakota State University July 26, 2018 Three person chessboard Three person chessboard Three person chessboard Three person chessboard - Rearranged Two new families
Volume 12 Sept Oct 2011
L e t s M a k e M a t h Fu n Volume 12 Sept Oct 2011 10 Ways to Get Kids to Love Math Fun Fruit Board Games Have We Found the 15 Greatest Board Let sgames Make Mathin Funthe World? www.makingmathmorefun.com
ECON 2100 Principles of Microeconomics (Summer 2016) Game Theory and Oligopoly
ECON 2100 Principles of Microeconomics (Summer 2016) Game Theory and Oligopoly Relevant readings from the textbook: Mankiw, Ch. 17 Oligopoly Suggested problems from the textbook: Chapter 17 Questions for
Chapter 4: Patterns and Relationships
Chapter : Patterns and Relationships Getting Started, p. 13 1. a) The factors of 1 are 1,, 3,, 6, and 1. The factors of are 1,,, 7, 1, and. The greatest common factor is. b) The factors of 16 are 1,,,,
Sudoku Touch. 1-4 players, adult recommended. Sudoku Touch by. Bring your family back together!
Sudoku Touch Sudoku Touch by Bring your family back together! 1-4 players, adult recommended Sudoku Touch is a logic game, allowing up to 4 users to play at once. The game can be played with individual
NORMAL FORM (SIMULTANEOUS MOVE) GAMES
NORMAL FORM (SIMULTANEOUS MOVE) GAMES 1 For These Games Choices are simultaneous made independently and without observing the other players actions Players have complete information, which means they know
Introduction to Game Theory a Discovery Approach. Jennifer Firkins Nordstrom
Introduction to Game Theory a Discovery Approach Jennifer Firkins Nordstrom Contents 1. Preface iv Chapter 1. Introduction to Game Theory 1 1. The Assumptions 1 2. Game Matrices and Payoff Vectors 4 Chapter
Activity 1: Play comparison games involving fractions, decimals and/or integers.
Students will be able to: Lesson Fractions, Decimals, Percents and Integers. Play comparison games involving fractions, decimals and/or integers,. Complete percent increase and decrease problems, and.
BALTIMORE COUNTY PUBLIC SCHOOLS. Rock n Roll
Number cube labeled 1-6 (A template to make a cube is at the back of this packet.)36 counters Rock n Roll Paper Pencil None The first player rolls the number cube to find out how many groups of counters
The Product Game: Playing the Product Game
The Product Game: Playing the Product Game Students learn how to play the Product Game. As they play the game, students develop understanding of factors, multiples, and the relationships between them.