CS 32 Puzzles, Games & Algorithms Fall 2013
|
|
- Posy Underwood
- 6 years ago
- Views:
Transcription
1 CS 32 Puzzles, Games & Algorithms Fall 2013 Study Guide & Scavenger Hunt #2 November 10, 2014 These problems are chosen to help prepare you for the second midterm exam, scheduled for Friday, November 14, Note: some of these problems are harder than the ones that will appear on the exam. (The problems labeled with a black diamond [ ] are especially challenging.) However, every complete and correct solution that is turned in before you take the midterm will count as one extra credit point added to your midterm exam score, up to a maximum of 15 extra-credit points. You must show all of your work for full credit. And your solutions must be original, that is written using only your own words, with appropriate citations if relevant. EXPLAIN, EXPLAIN, EXPLAIN. GOOD LUCK! 1. A Tower of Hanoi puzzle with 8 disks and three pegs is in the state ( ), i.e., the smallest disk sits on the top of the stack of disks on peg 3, the second smallest disk sit on top of the stack on peg 1,..., the second largest disk sits on the bottom of the stack on peg 3, and the largest disk sits on the bottom of the stack on peg 1. How many moves are required to reach the goal state ( )? Explain On what day of the week will the date 2/22/2222 occur? 3. In a game of bridge 52 cards are dealt to four players: North, South, East, and West. How many different ways can the cards be distributed to each player, so that each hand contains 13 cards? In how many of these deals does North receive all four aces? (Hint: Use the multiplication principle).
2 4. A game of Nim begins in the state ( ). Please list all of the initial moves that would enable the first player to win the game. 5. Nimble is a game that I made up. It is played like Nim, except that the player who plays second has the option of passing on his or her first turn, effectively trading positions with the first player. Consequently, if the game began in the state ( ), and the first player decided to remove say 2 tokens from the last heap, the second player could either remove one or more tokens from any one of the current heaps, or pass forcing the first player to play again. Note that the second player s pass can only be used on his or her first turn. (a) If you were the second player, what would you choose to do in the example provided above, where the current state of the game is ( )? (b) Which player, first, second, or neither, is guaranteed a strategy to win every game of Nimble? Explain.
3 6. One-dimension checkers is played like peg-solitaire in that red tokens can only step or jump to the right, blue tokens to the left, and tokens are only allowed to jump over a token of the opposite color. Moreover, when one player jumps over an opponent s token, that token is captured. Double and multiple jumps are possible, and a player must jump if there is an opportunity to do so. And finally, a player who is not able to move, loses. Rather than develop a strategy for the game, write a function called color-count in racket that returns a list that contains the count of the number of tokens of each color in the given state. Thus (color-count (R E R R E E B B R B)) returns (4 3), indicating 4 red and 3 blue tokens; (color-count (E E E R E E E B B E)) returns (1 2), indicating 1 red and 2 blue tokens.
4 7. Place a unique label at the entrance, goal, and each junction and dead end in the following maze. Then construct an equivalent graph. Make sure that the label of each vertex in your graph matches the label that you assigned to the corresponding feature in the maze. What is the degree of your graph? Is the graph cyclic or acyclic? $
5 8. Apply Trémaux s algorithm for a right bearing mouse in the previous maze: $
6 9. Six coins, labeled 1 through 6, are initially placed in a horizontal grid of seven square cells as shown below Note that the leftmost cell is empty. As in our peg solitaire puzzles, no more than one coin can occupy any given cell. Now, however, each coin can be moved to the right or left, regardless of it shade (or color), either by stepping into the adjacent cell if it is empty, or by jumping over a single coin (of either shade) into the empty cell. Thus, from the initial state only two moves are possible: either the dark coin labeled 1 can be pushed into the empty cell, or the light coin labeled 2 can jump over the 1 into the empty cell. The object of the puzzle is to discover a sequence of legal moves, jumps and steps, that takes the initial state above into the goal state: (a) How many distinct states are reachable from the initial state. (Do not try to realize them: there are too many. Simply try to estimate how many states exist.) (b) Without explicitly solving the puzzle please determine how many total moves (jumps plus steps) are required to reach the goal. (Hint: Although the shades of the tokens have nothing at all to do with the action of the puzzle, the difference between the initial and final shade patterns is an important clue.)
7 10. Consider the two-dimensional version of our peg-solitaire puzzle, where the left configuration illustrates the initial state, and the right, the goal state Here the red tokens can only move either to the right or down, stepping one unit into the empty square, or jumping over a single token of either color. Likewise, the blue tokens can only move either to the left or up. Find the minimum sequence of moves that solves the puzzle. You can express your solution by simply listing a sequence of indices that correspond to the squares from which each token is moved. Thus, the sequence 6, 12, 14 indicates that the red token in square 6 steps into square 9; then the blue token in square 12 jumps over the former red token into square 6, and subsequently, the blue token in square 14 jumps over square 13 into square 12.
8 11. Consider a tower of Hanoi puzzle that contains two disks on four pegs, as shown below. Assume the initial peg (1) is on the left, and the goal peg (4) is on the right. (a) How many states (vertices) belong to this puzzle s state transition graph. (b) Construct the puzzle s state transition graph, and label each vertex with an ordered pair of the form (x, y), where x {1, 2, 3, 4} represents the peg on which the small disk is placed, and y represents the same for the large disk. (c) The degree of a vertex is defined to be the number of edges that are incident to it. The degree of a graph is defined to be the maximum degree of all of its vertices. What is the degree of this graph? (d) What is the length of the shortest solution? How many such solutions exist? 12. A tower of Hanoi puzzle is created having eight disks and four pegs. How many states does this puzzle have? What is the degree of its state-transition graph? (Hint: Don t draw the state-transition graph: it is too large. Instead, just imagine a small neighborhood of the graph.) Explain.
9 13. [ ] A kitchen pantry contains two empty bottles, having capacities of 3 and 5 pints, respectively, and a 1 gallon (8 pint) jug that is full of maple syrup (of course it s Vermont Grade A). A pastry chef would like to fill the 5 pint bottle with exactly 4 pints of syrup (which is needed for a certain recipe), leaving exactly 4 pints in the jug. How can this be done using only the three containers? 1 Note that to ensure exactness, each transfer of fluid from one vessel to another must either completely empty one vessel, or completely fill the other, (or on rare occasions, do both). We can analyze this problem by constructing a state-transition graph. Let the list (x, y, z) denote a state in which x pints are contained in the 3 pint bottle, y pints in the 5 pint bottle, and z pints in the gallon jug. Note that 0 x 3, 0 y 5, and 0 z 8, with x + y +z = 8, and x, y, and z assuming integral values. Since z = 8 x y, each state can be represented as a vertex projected onto the two-dimensional x y-coordinate system: 5 y x (a) Using the notation (x, y) for the projection, the initial state would be (0, 0). What coordinate pair corresponds to the goal state? (b) Now we will complete the state-transition graph. There are two initial moves: (i) pour 3 pints of syrup from the jug into the small container, arriving at the state (3,0), or (ii) pour 5 pints of syrup from the jug into the medium container, arriving at state (0, 5). Represent each transition with an edge on the above graph. Are the transitions directed (one-way) or undirected (reversible)? Now continue, and complete the graph. (c) How many states are accessible? What is the degree of the graph? (d) Can you find a sequence of operations that will satisfy the chef? 1 Someone must have run off with all of the measuring cups!
10 14. Consider a Rubik s cube. Let U denote the move that rotates the upper (yellow) face by 90 in the clockwise direction (as shown). Similarly, let F, R, L, B, and D denote 90 rotations in the clockwise direction of the remaining five faces. We use the shorthand R 2 = RR, and R = R 3. Suppose a cube is scrambled according to the following sequence of operations: R 2 BD F 2 U. Construct a sequence of operations that unscrambles the cube. U B L R F D 15. Consider a Rubik s cube. How many different configurations can be reached by a legal sequence of moves? Explain. Don t forget also to review anagrams, Cretan-style labyrinths, the multiplication principle, Tré maux s and Tarry s algorithms, Alcuin s river-crossing problem, the Missionaries and the Cannibals puzzle, the standard Tower of Hanoi puzzle, one and two-dimensional peg solitaire, etc.
Games of Skill Lesson 1 of 9, work in pairs
Lesson 1 of 9, work in pairs 21 (basic version) The goal of the game is to get the other player to say the number 21. The person who says 21 loses. The first person starts by saying 1. At each turn, the
More informationMidterm 2 6:00-8:00pm, 16 April
CS70 2 Discrete Mathematics and Probability Theory, Spring 2009 Midterm 2 6:00-8:00pm, 16 April Notes: There are five questions on this midterm. Answer each question part in the space below it, using the
More informationGames of Skill ANSWERS Lesson 1 of 9, work in pairs
Lesson 1 of 9, work in pairs 21 (basic version) The goal of the game is to get the other player to say the number 21. The person who says 21 loses. The first person starts by saying 1. At each turn, the
More informationGrade 7/8 Math Circles. Visual Group Theory
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 25 th /26 th Visual Group Theory Grouping Concepts Together We will start
More informationCheckpoint Questions Due Monday, October 7 at 2:15 PM Remaining Questions Due Friday, October 11 at 2:15 PM
CS13 Handout 8 Fall 13 October 4, 13 Problem Set This second problem set is all about induction and the sheer breadth of applications it entails. By the time you're done with this problem set, you will
More informationSenior Math Circles February 10, 2010 Game Theory II
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Senior Math Circles February 10, 2010 Game Theory II Take-Away Games Last Wednesday, you looked at take-away
More informationGrade 7/8 Math Circles. Visual Group Theory
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 25 th /26 th Visual Group Theory Grouping Concepts Together We will start
More informationNuman Sheikh FC College Lahore
Numan Sheikh FC College Lahore 2 Five men crash-land their airplane on a deserted island in the South Pacific. On their first day they gather as many coconuts as they can find into one big pile. They decide
More informationCS103 Handout 25 Spring 2017 May 5, 2017 Problem Set 5
CS103 Handout 25 Spring 2017 May 5, 2017 Problem Set 5 This problem set the last one purely on discrete mathematics is designed as a cumulative review of the topics we ve covered so far and a proving ground
More informationDirected Towers of Hanoi
Richard Anstee, UBC, Vancouver January 10, 2019 Introduction The original Towers of Hanoi problem considers a problem 3 pegs and with n different sized discs that fit on the pegs. A legal move is to move
More informationFigure 1: The Game of Fifteen
1 FIFTEEN One player has five pennies, the other five dimes. Players alternately cover a number from 1 to 9. You win by covering three numbers somewhere whose sum is 15 (see Figure 1). 1 2 3 4 5 7 8 9
More informationSolving the Rubik s Cube
Solving the Rubik s Cube The Math Behind the Cube: How many different combinations are possible on a 3x3 cube? There are 6 sides each with 9 squares giving 54 squares. Thus there will be 54 53 52 51 50
More informationLecture 19 November 6, 2014
6.890: Algorithmic Lower Bounds: Fun With Hardness Proofs Fall 2014 Prof. Erik Demaine Lecture 19 November 6, 2014 Scribes: Jeffrey Shen, Kevin Wu 1 Overview Today, we ll cover a few more 2 player games
More informationGame, Set, and Match Carl W. Lee September 2016
Game, Set, and Match Carl W. Lee September 2016 Note: Some of the text below comes from Martin Gardner s articles in Scientific American and some from Mathematical Circles by Fomin, Genkin, and Itenberg.
More information1. Compare between monotonic and commutative production system. 2. What is uninformed (or blind) search and how does it differ from informed (or
1. Compare between monotonic and commutative production system. 2. What is uninformed (or blind) search and how does it differ from informed (or heuristic) search? 3. Compare between DFS and BFS. 4. Use
More informationOCTAGON 5 IN 1 GAME SET
OCTAGON 5 IN 1 GAME SET CHESS, CHECKERS, BACKGAMMON, DOMINOES AND POKER DICE Replacement Parts Order direct at or call our Customer Service department at (800) 225-7593 8 am to 4:30 pm Central Standard
More informationarxiv: v1 [cs.cc] 21 Jun 2017
Solving the Rubik s Cube Optimally is NP-complete Erik D. Demaine Sarah Eisenstat Mikhail Rudoy arxiv:1706.06708v1 [cs.cc] 21 Jun 2017 Abstract In this paper, we prove that optimally solving an n n n Rubik
More informationI.M.O. Winter Training Camp 2008: Invariants and Monovariants
I.M.. Winter Training Camp 2008: Invariants and Monovariants n math contests, you will often find yourself trying to analyze a process of some sort. For example, consider the following two problems. Sample
More informationGrade 7/8 Math Circles Game Theory October 27/28, 2015
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Game Theory October 27/28, 2015 Chomp Chomp is a simple 2-player game. There is
More informationSOLITAIRE CLOBBER AS AN OPTIMIZATION PROBLEM ON WORDS
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 (2008), #G04 SOLITAIRE CLOBBER AS AN OPTIMIZATION PROBLEM ON WORDS Vincent D. Blondel Department of Mathematical Engineering, Université catholique
More informationGrade 6 Math Circles Combinatorial Games November 3/4, 2015
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles Combinatorial Games November 3/4, 2015 Chomp Chomp is a simple 2-player game. There
More informationLAMC Junior Circle January 22, Oleg Gleizer. The Hanoi Tower. Part 2
LAMC Junior Circle January 22, 2012 Oleg Gleizer The Hanoi Tower Part 2 Definition 1 An algorithm is a finite set of clear instructions to solve a problem. An algorithm is called optimal, if the solution
More informationGrade 6 Math Circles Combinatorial Games - Solutions November 3/4, 2015
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles Combinatorial Games - Solutions November 3/4, 2015 Chomp Chomp is a simple 2-player
More informationIntroduction to Spring 2009 Artificial Intelligence Final Exam
CS 188 Introduction to Spring 2009 Artificial Intelligence Final Exam INSTRUCTIONS You have 3 hours. The exam is closed book, closed notes except a two-page crib sheet, double-sided. Please use non-programmable
More informationSoutheastern European Regional Programming Contest Bucharest, Romania Vinnytsya, Ukraine October 21, Problem A Concerts
Problem A Concerts File: A.in File: standard output Time Limit: 0.3 seconds (C/C++) Memory Limit: 128 megabytes John enjoys listening to several bands, which we shall denote using A through Z. He wants
More informationPUZZLES ON GRAPHS: THE TOWERS OF HANOI, THE SPIN-OUT PUZZLE, AND THE COMBINATION PUZZLE
PUZZLES ON GRAPHS: THE TOWERS OF HANOI, THE SPIN-OUT PUZZLE, AND THE COMBINATION PUZZLE LINDSAY BAUN AND SONIA CHAUHAN ADVISOR: PAUL CULL OREGON STATE UNIVERSITY ABSTRACT. The Towers of Hanoi is a well
More informationCMPT 310 Assignment 1
CMPT 310 Assignment 1 October 16, 2017 100 points total, worth 10% of the course grade. Turn in on CourSys. Submit a compressed directory (.zip or.tar.gz) with your solutions. Code should be submitted
More informationMidterm Examination. CSCI 561: Artificial Intelligence
Midterm Examination CSCI 561: Artificial Intelligence October 10, 2002 Instructions: 1. Date: 10/10/2002 from 11:00am 12:20 pm 2. Maximum credits/points for this midterm: 100 points (corresponding to 35%
More informationOver ===* Three games of strategy and chance Unique solitaire puzzles. For I to 4 players Ages 12 to adult. PassTM
Over ===* For I to 4 players Ages 12 to adult PassTM Three games of strategy and chance Unique solitaire puzzles A product of Kadon Enterprises, Inc. Over-Pass is a trademark of Arthur Blumberg, used by
More informationWeek 1. 1 What Is Combinatorics?
1 What Is Combinatorics? Week 1 The question that what is combinatorics is similar to the question that what is mathematics. If we say that mathematics is about the study of numbers and figures, then combinatorics
More informationExploring 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
More informationProblem F. Chessboard Coloring
Problem F Chessboard Coloring You have a chessboard with N rows and N columns. You want to color each of the cells with exactly N colors (colors are numbered from 0 to N 1). A coloring is valid if and
More informationAn Intuitive Approach to Groups
Chapter An Intuitive Approach to Groups One of the major topics of this course is groups. The area of mathematics that is concerned with groups is called group theory. Loosely speaking, group theory is
More informationFigure 1: A Checker-Stacks Position
1 1 CHECKER-STACKS This game is played with several stacks of black and red checkers. You can choose any initial configuration you like. See Figure 1 for example (red checkers are drawn as white). Figure
More informationDiscrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand HW 8
CS 70 Discrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand HW 8 1 Sundry Before you start your homewor, write down your team. Who else did you wor with on this homewor? List names and
More informationCrossing Game Strategies
Crossing Game Strategies Chloe Avery, Xiaoyu Qiao, Talon Stark, Jerry Luo March 5, 2015 1 Strategies for Specific Knots The following are a couple of crossing game boards for which we have found which
More information12. 6 jokes are minimal.
Pigeonhole Principle Pigeonhole Principle: When you organize n things into k categories, one of the categories has at least n/k things in it. Proof: If each category had fewer than n/k things in it then
More informationn r for the number. (n r)!r!
Throughout we use both the notations ( ) n r and C n n! r for the number (n r)!r! 1 Ten points are distributed around a circle How many triangles have all three of their vertices in this 10-element set?
More information1 Introduction. 2 An Easy Start. KenKen. Charlotte Teachers Institute, 2015
1 Introduction R is a puzzle whose solution requires a combination of logic and simple arithmetic and combinatorial skills 1 The puzzles range in difficulty from very simple to incredibly difficult Students
More informationFinal Exam, Math 6105
Final Exam, Math 6105 SWIM, June 29, 2006 Your name Throughout this test you must show your work. 1. Base 5 arithmetic (a) Construct the addition and multiplication table for the base five digits. (b)
More informationa b c d e f g h 1 a b c d e f g h C A B B A C C X X C C X X C C A B B A C Diagram 1-2 Square names
Chapter Rules and notation Diagram - shows the standard notation for Othello. The columns are labeled a through h from left to right, and the rows are labeled through from top to bottom. In this book,
More informationWHAT IS THIS GAME ABOUT?
A development game for 1-5 players aged 12 and up Playing time: 20 minutes per player WHAT IS THIS GAME ABOUT? As the owner of a major fishing company in Nusfjord on the Lofoten archipelago, your goal
More informationCMPT 310 Assignment 1
CMPT 310 Assignment 1 October 4, 2017 100 points total, worth 10% of the course grade. Turn in on CourSys. Submit a compressed directory (.zip or.tar.gz) with your solutions. Code should be submitted as
More informationNANYANG TECHNOLOGICAL UNIVERSITY SEMESTER II EXAMINATION MH1301 DISCRETE MATHEMATICS. Time Allowed: 2 hours
NANYANG TECHNOLOGICAL UNIVERSITY SEMESTER II EXAMINATION 206-207 DISCRETE MATHEMATICS May 207 Time Allowed: 2 hours INSTRUCTIONS TO CANDIDATES. This examination paper contains FOUR (4) questions and comprises
More informationTechniques for Generating Sudoku Instances
Chapter Techniques for Generating Sudoku Instances Overview Sudoku puzzles become worldwide popular among many players in different intellectual levels. In this chapter, we are going to discuss different
More informationTutorial 1. (ii) There are finite many possible positions. (iii) The players take turns to make moves.
1 Tutorial 1 1. Combinatorial games. Recall that a game is called a combinatorial game if it satisfies the following axioms. (i) There are 2 players. (ii) There are finite many possible positions. (iii)
More informationBillions of Combinations, One Solution Meet Your Cube Twisting Hints RUBIK S Cube Sequences RUBIK S Cube Games...
SOLUTION BOOKLET Billions of Combinations, One Solution...... 2 Meet Your Cube.................... 3 Twisting Hints..................... 6 RUBIK S Cube Sequences............... 9 RUBIK S Cube Games.................
More informationGame Theory and Algorithms Lecture 19: Nim & Impartial Combinatorial Games
Game Theory and Algorithms Lecture 19: Nim & Impartial Combinatorial Games May 17, 2011 Summary: We give a winning strategy for the counter-taking game called Nim; surprisingly, it involves computations
More informationEpisode 3 16 th 19 th March Made In India and Regions by Prasanna Seshadri
and Episode 3 16 th 19 th March 2018 by Prasanna Seshadri Puzzle Ramayan rounds will also serve as qualifiers for Indian Puzzle Championship for year 2018. Please check http://logicmastersindia.com/pr/2018pr.asp
More informationDELUXE 3 IN 1 GAME SET
Chess, Checkers and Backgammon August 2012 UPC Code 7-19265-51276-9 HOW TO PLAY CHESS Chess Includes: 16 Dark Chess Pieces 16 Light Chess Pieces Board Start Up Chess is a game played by two players. One
More informationCPSC 217 Assignment 3
CPSC 217 Assignment 3 Due: Friday November 24, 2017 at 11:55pm Weight: 7% Sample Solution Length: Less than 100 lines, including blank lines and some comments (not including the provided code) Individual
More informationSurreal Numbers and Games. February 2010
Surreal Numbers and Games February 2010 1 Last week we began looking at doing arithmetic with impartial games using their Sprague-Grundy values. Today we ll look at an alternative way to represent games
More informationHomework Assignment #1
CS 540-2: Introduction to Artificial Intelligence Homework Assignment #1 Assigned: Thursday, February 1, 2018 Due: Sunday, February 11, 2018 Hand-in Instructions: This homework assignment includes two
More informationCODINCA. Print & Play. Contained in this document are the files needed to print out and make the following game components:
CODINCA Print & Play Contained in this document are the files needed to print out and make the following game components: 1 Playing Board 16 Playing Tiles 24 Key Discs 24 Trap Cards 4 Luck Action Cards
More informationSolving the 4 x 4 Cube
Solving the 4 x 4 Cube How to Reference and Talk About the Cube: Like the 3 x 3 cube, we will refer to three main types of pieces centers (4 per side), edges (2 per edge) and corners. The main approach
More information4. The terms of a sequence of positive integers satisfy an+3 = an+2(an+1 + an), for n = 1, 2, 3,... If a6 = 8820, what is a7?
1. If the numbers 2 n and 5 n (where n is a positive integer) start with the same digit, what is this digit? The numbers are written in decimal notation, with no leading zeroes. 2. At a movie theater,
More informationOrganization Team Team ID# If each of the congruent figures has area 1, what is the area of the square?
1. [4] A square can be divided into four congruent figures as shown: If each of the congruent figures has area 1, what is the area of the square? 2. [4] John has a 1 liter bottle of pure orange juice.
More informationA GRAPH THEORETICAL APPROACH TO SOLVING SCRAMBLE SQUARES PUZZLES. 1. Introduction
GRPH THEORETICL PPROCH TO SOLVING SCRMLE SQURES PUZZLES SRH MSON ND MLI ZHNG bstract. Scramble Squares puzzle is made up of nine square pieces such that each edge of each piece contains half of an image.
More informationCoin Cappers. Tic Tac Toe
Coin Cappers Tic Tac Toe Two students are playing tic tac toe with nickels and dimes. The player with the nickels has just moved. Itʼs now your turn. The challenge is to place your dime in the only square
More informationWordy Problems for MathyTeachers
December 2012 Wordy Problems for MathyTeachers 1st Issue Buffalo State College 1 Preface When looking over articles that were submitted to our journal we had one thing in mind: How can you implement this
More informationAn Exploration of the Minimum Clue Sudoku Problem
Sacred Heart University DigitalCommons@SHU Academic Festival Apr 21st, 12:30 PM - 1:45 PM An Exploration of the Minimum Clue Sudoku Problem Lauren Puskar Follow this and additional works at: http://digitalcommons.sacredheart.edu/acadfest
More informationThe 2013 British Informatics Olympiad
Sponsored by Time allowed: 3 hours The 2013 British Informatics Olympiad Instructions You should write a program for part (a) of each question, and produce written answers to the remaining parts. Programs
More informationSMT 2014 Advanced Topics Test Solutions February 15, 2014
1. David flips a fair coin five times. Compute the probability that the fourth coin flip is the first coin flip that lands heads. 1 Answer: 16 ( ) 1 4 Solution: David must flip three tails, then heads.
More information6.042/18.062J Mathematics for Computer Science December 17, 2008 Tom Leighton and Marten van Dijk. Final Exam
6.042/18.062J Mathematics for Computer Science December 17, 2008 Tom Leighton and Marten van Dijk Final Exam Problem 1. [25 points] The Final Breakdown Suppose the 6.042 final consists of: 36 true/false
More informationTic-Tac-Toe on graphs
AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 72(1) (2018), Pages 106 112 Tic-Tac-Toe on graphs Robert A. Beeler Department of Mathematics and Statistics East Tennessee State University Johnson City, TN
More informationJUST THE MATHS UNIT NUMBER PROBABILITY 2 (Permutations and combinations) A.J.Hobson
JUST THE MATHS UNIT NUMBER 19.2 PROBABILITY 2 (Permutations and combinations) by A.J.Hobson 19.2.1 Introduction 19.2.2 Rules of permutations and combinations 19.2.3 Permutations of sets with some objects
More informationSolutions of problems for grade R5
International Mathematical Olympiad Formula of Unity / The Third Millennium Year 016/017. Round Solutions of problems for grade R5 1. Paul is drawing points on a sheet of squared paper, at intersections
More informationGraph Nim. PURE Insights. Breeann Flesch Western Oregon University,
PURE Insights Volume rticle 0 Graph Nim reeann Flesch Western Oregon University, fleschb@mail.wou.edu kaanchya Pradhan Western Oregon University, apradhan0@mail.wou.edu Follow this and additional works
More informationFor 1 to 4 players Ages 12 to adult. Ternion Factor TM. Three games of strategy Solitaire puzzles. A product of Kadon Enterprises, Inc.
For 1 to 4 players Ages 12 to adult Ternion Factor TM Three games of strategy Solitaire puzzles A product of Kadon Enterprises, Inc. The Ternion Factor, Ternion Spaces, and Escape! are trademarks of Arthur
More informationThe Sorcerer s Chamber
The Sorcerer s Chamber by Tim Schutz Rev. 2.0 2-4 players 60 minutes Game requires: One complete piecepack and One piecepack pyramid set Story Welcome to the Sorcerer s Chamber. No this is not some cozy
More informationUMBC 671 Midterm Exam 19 October 2009
Name: 0 1 2 3 4 5 6 total 0 20 25 30 30 25 20 150 UMBC 671 Midterm Exam 19 October 2009 Write all of your answers on this exam, which is closed book and consists of six problems, summing to 160 points.
More information(b) In the position given in the figure below, find a winning move, if any. (b) In the position given in Figure 4.2, find a winning move, if any.
Math 5750-1: Game Theory Midterm Exam Mar. 6, 2015 You have a choice of any four of the five problems. (If you do all 5, each will count 1/5, meaning there is no advantage.) This is a closed-book exam,
More informationCaltech Harvey Mudd Mathematics Competition February 20, 2010
Mixer Round Solutions Caltech Harvey Mudd Mathematics Competition February 0, 00. (Ying-Ying Tran) Compute x such that 009 00 x (mod 0) and 0 x < 0. Solution: We can chec that 0 is prime. By Fermat s Little
More informationWPF PUZZLE GP 2016 ROUND 8 INSTRUCTION BOOKLET. Host Country: Russia. Andrey Bogdanov. Special Notes: No special notes for this round.
WPF PUZZLE GP 01 INSTRUTION OOKLET Host ountry: Russia ndrey ogdanov Special Notes: No special notes for this round. Points, asual Section: Points, ompetitive Section: 1. Not Like the Others 1. Not Like
More informationSelected Game Examples
Games in the Classroom ~Examples~ Genevieve Orr Willamette University Salem, Oregon gorr@willamette.edu Sciences in Colleges Northwestern Region Selected Game Examples Craps - dice War - cards Mancala
More informationFind the items on your list...but first find your list! Overview: Definitions: Setup:
Scavenger Hunt II A game for the piecepack by Brad Lackey. Version 1.1, 29 August 2006. Copyright (c) 2005, Brad Lackey. 4 Players, 60-80 Minutes. Equipment: eight distinct piecepack suits. Find the items
More informationSTUDENT S BOOKLET. Geometry 2. Contents. Meeting 7 Student s Booklet. May 24 UCI. 1 Circular Mountains 2 Rotations
Meeting 7 Student s Booklet Geometry 2 Contents May 24 2017 @ UCI 1 Circular Mountains 2 Rotations STUDENT S BOOKLET UC IRVINE MATH CEO http://www.math.uci.edu/mathceo/ 1 CIRCULAR MOUNTAINS 2 1 CIRCULAR
More informationJob Cards and Other Activities. Write a Story for...
Job Cards and Other Activities Introduction. This Appendix gives some examples of the types of Job Cards and games that we used at the Saturday Clubs. We usually set out one type of card per table, along
More informationUNIVERSITY of PENNSYLVANIA CIS 391/521: Fundamentals of AI Midterm 1, Spring 2010
UNIVERSITY of PENNSYLVANIA CIS 391/521: Fundamentals of AI Midterm 1, Spring 2010 Question Points 1 Environments /2 2 Python /18 3 Local and Heuristic Search /35 4 Adversarial Search /20 5 Constraint Satisfaction
More informationModeling a Rubik s Cube in 3D
Modeling a Rubik s Cube in 3D Robert Kaucic Math 198, Fall 2015 1 Abstract Rubik s Cubes are a classic example of a three dimensional puzzle thoroughly based in mathematics. In the trigonometry and geometry
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053 Optimization Methods in Management Science (Spring 2007) Problem Set 7 Due April 12 th, 2007 at :30 pm. You will need 157 points out of 185 to receive a grade
More informationConversion Masters in IT (MIT) AI as Representation and Search. (Representation and Search Strategies) Lecture 002. Sandro Spina
Conversion Masters in IT (MIT) AI as Representation and Search (Representation and Search Strategies) Lecture 002 Sandro Spina Physical Symbol System Hypothesis Intelligent Activity is achieved through
More informationYear 6 SATS revision cards
The numbers in this sequence increase by 75 each time. Write the two missing numbers. A square always has four sides. Grange School collects money for three charities. This pictogram shows how much they
More informationThe 2016 ACM-ICPC Asia China-Final Contest Problems
Problems Problem A. Number Theory Problem.... 1 Problem B. Hemi Palindrome........ 2 Problem C. Mr. Panda and Strips...... Problem D. Ice Cream Tower........ 5 Problem E. Bet............... 6 Problem F.
More informationSolitaire Games. MATH 171 Freshman Seminar for Mathematics Majors. J. Robert Buchanan. Department of Mathematics. Fall 2010
Solitaire Games MATH 171 Freshman Seminar for Mathematics Majors J. Robert Buchanan Department of Mathematics Fall 2010 Standard Checkerboard Challenge 1 Suppose two diagonally opposite corners of the
More informationExcellence In MathematicS Seventh Grade Test Seventeenth Annual Mathematics Contest January 28 th, 2017
The 17 th ontest handler-gilbert ommunity ollege presents Excellence In MathematicS Seventh Grade Test Seventeenth nnual Mathematics ontest January 28 th, 2017 I. Do not open the test booklet or begin
More informationContest 1. October 20, 2009
Contest 1 October 20, 2009 Problem 1 What value of x satisfies x(x-2009) = x(x+2009)? Problem 1 What value of x satisfies x(x-2009) = x(x+2009)? By inspection, x = 0 satisfies the equation. Problem 1 What
More informationAdventures with Rubik s UFO. Bill Higgins Wittenberg University
Adventures with Rubik s UFO Bill Higgins Wittenberg University Introduction Enro Rubik invented the puzzle which is now known as Rubik s Cube in the 1970's. More than 100 million cubes have been sold worldwide.
More informationLet start by revisiting the standard (recursive) version of the Hanoi towers problem. Figure 1: Initial position of the Hanoi towers.
Coding Denis TRYSTRAM Lecture notes Maths for Computer Science MOSIG 1 2017 1 Summary/Objective Coding the instances of a problem is a tricky question that has a big influence on the way to obtain the
More informationMath Kangaroo Practice
Math Kangaroo Practice March 9, 2014 1. In how many ways can 5 people be arranged to sit at 5 desks (so that only one person sits at a desk)? 2. A large cube with side length 4 cm is made with small cubes
More informationCard Racer. By Brad Bachelor and Mike Nicholson
2-4 Players 30-50 Minutes Ages 10+ Card Racer By Brad Bachelor and Mike Nicholson It s 2066, and you race the barren desert of Indianapolis. The crowd s attention span isn t what it used to be, however.
More informationCSE 312 Midterm Exam May 7, 2014
Name: CSE 312 Midterm Exam May 7, 2014 Instructions: You have 50 minutes to complete the exam. Feel free to ask for clarification if something is unclear. Please do not turn the page until you are instructed
More informationGEOGRAPHY PLAYED ON AN N-CYCLE TIMES A 4-CYCLE
GEOGRAPHY PLAYED ON AN N-CYCLE TIMES A 4-CYCLE M. S. Hogan 1 Department of Mathematics and Computer Science, University of Prince Edward Island, Charlottetown, PE C1A 4P3, Canada D. G. Horrocks 2 Department
More informationThe patterns considered here are black and white and represented by a rectangular grid of cells. Here is a typical pattern: [Redundant]
Pattern Tours The patterns considered here are black and white and represented by a rectangular grid of cells. Here is a typical pattern: [Redundant] A sequence of cell locations is called a path. A path
More informationThese Are a Few of My Favorite Things
Lesson.1 Assignment Name Date These Are a Few of My Favorite Things Modeling Probability 1. A board game includes the spinner shown in the figure that players must use to advance a game piece around the
More informationCoin-Moving Puzzles. arxiv:cs/ v1 [cs.dm] 31 Mar Introduction. Erik D. Demaine Martin L. Demaine Helena A. Verrill
Coin-Moving Puzzles Erik D. Demaine Martin L. Demaine Helena A. Verrill arxiv:cs/0000v [cs.dm] Mar 00 Abstract We introduce a new family of one-player games, involving the movement of coins from one configuration
More informationa. Find the solution (x,y) that satisfies both of the following equations: Equation 1: 2x + 3y = 13 Equation 2: 3x - 2y = 0
Economics 102 Fall 2015 Answers to Homework #1 Due Monday, September 21, 2015 Directions: The homework will be collected in a box before the large lecture. Please place your name, TA name and section number
More informationPRIMES STEP Plays Games
PRIMES STEP Plays Games arxiv:1707.07201v1 [math.co] 22 Jul 2017 Pratik Alladi Neel Bhalla Tanya Khovanova Nathan Sheffield Eddie Song William Sun Andrew The Alan Wang Naor Wiesel Kevin Zhang Kevin Zhao
More informationA game by Marcel Süßelbeck and Marco Ruskowski for 2 4 players Parfum transports players to the wonderful world of fragrances, which dates.
A game by Marcel Süßelbeck and Marco Ruskowski for 2 4 players Parfum transports players to the wonderful world of fragrances, which dates back hundreds of years to when aromatic scents were first used
More informationMaking 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
More information