A band of thieves comes up with a series of rules for hiding their loot so that they are always able to find it. The rules are as follows: If the house is next to a lake, then the treasure does not go in the kitchen If the tree in the front yard is an elm, then the treasure is in the kitchen The tree in the front yard is an elm or the treasure is buried under the flagpole If the tree in the backyard is an oak then the treasure is in the garage. You observe that the house where the treasure is hidden is next to a lake. Where is the treasure? discrete math

A band of thieves comes up with a series of rules for hiding their loot so that they are always able to find it. The rules are as follows: If the house is next to a lake, then the treasure does not go in the kitchen If the tree in the front yard is an elm, then the treasure is in the kitchen The tree in the front yard is an elm or the treasure is buried under the flagpole If the tree in the backyard is an oak then the treasure is in the garage. You observe that the house where the treasure is hidden is next to a lake. Where is the treasure? discrete math

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section: Chapter Questions

Problem 12RP

See similar textbooks

Similar questions

Write a program using Python to solve the locker riddle which reads as follows: Imagine 100 lockers numbered 1 to 100 with 100 students lined up in front of those 100lockers:The first student opens every locker.The second student closes every 2nd locker.The 3rd student changes every 3rd locker; if it’s closed, she opens it; if it’s open, she closes it.The 4th student changes every fourth locker (e.g., 4th, 8th, etc.).The 5th student changes every 5th locker (e.g., 5th, 10th, etc.).That same pattern continues for all 100 students. Which lockers are left open after all 100 students have walked the rowof lockers?
In Python, Solve the locker riddle which reads as follows:Imagine 100 lockers numbered 1 to 100 with 100 students lined up in front of those 100lockers:The first student opens every locker.The second student closes every 2nd locker.The 3rd student changes every 3rd locker; if it’s closed, she opens it; if it’s open, she closes it.The 4th student changes every fourth locker (e.g., 4th, 8th, etc.).The 5th student changes every 5th locker (e.g., 5th, 10th, etc.).That same pattern continues for all 100 students. Which lockers are left open after all 100 students have walked the rowof lockers?
Suppose you have a knapsack that can carry up to 17 pounds. You can only put certain items, and each item has a weight and a value. You want to put the items that will give you the highest possible value, but you can only carry up to 15 pounds. Here are the items you can put and their weights and values: I Weight value Value/Weight 1 2 10 5 2 4 30 7.5 3 6 50 8.33 4 9 70 7.78 5 10 80 8 Table 1: Caption Your task is to solve the Knapsack Problem using a greedy approach.Hints:- Sort the items by their value-to-weight ratio in descending order. Start with the item with the highest value-to-weight ratio and add it to the knapsack. - Continue adding items to the knapsack in descending order of their value-to-weight ratio until the knapsack is full or there are no more items left. - Your solution should output the total value of the items in the knapsack and the list of items that you have put. -This…
Jack and Jill will play a game called Hotter, Colder. Jill chooses a number from 0 to 100, and Jack makes repeated attempts to guess it. For each guess, Jill will respond with: hotter - if the current guess is closer to her number than the previous guess is colder - if the current guess is farther to her number than the previous guess is same - if the current guess is as far (to her number) as the previous guess is For Jack’s first guess, since there is no previous guess yet, Jill will just answer same. Describe an algorithm or a systematic approach that Jack can follow to win the games faster (fewer guesses). Example: Jill chooses number 40. Note: Jack can guess any number from 0 to 100 at any point of the game. Jack guesses 100. Jill responds same (first guess) Jack guesses 60. Jill responds hotter (60 is closer to 40 than previous guess 100) Jack guesses 80. Jill responds colder (80 is farther from 40 than previous guess 60) Jack guesses…
Java Program Scenario: A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If the locker is open, the student closes it; if it is closed, the student opens it. After all the students have taken their turns, some of the lockers are open and some are closed. Write a program that prompts the user to enter the number of lockers in a school. After the game is over, the program outputs the number of lockers and the…
A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, theprincipal plays the following game: She asks the first student to open all the lockers. She then asks the secondstudent to close all the even-numbered lockers. The third student is asked to check every third locker. If it isopen, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourthlocker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continuethis game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed,the student opens it. After all the students have taken turns, some of the lockers are open and some are closed.The program below, when ran, will prompt the user to enter the number of lockers in the school. After thegame is over, the program will output the number of lockers and the lockers numbers of the lockers…
In cryptography, a Caesar cipher is a very simple encryption techniques in which each letter in the plain text is replaced by a letter some fixed number of positions down the alphabet. For example, with a shift of 3, A would be replaced by D, B would become E, and so on. The method is named after Julius Caesar, who used it to communicate with his generals. ROT-13 (“rotate by 13 places”) is a widely used example of a Caesar cipher where the shift is 13. In Python, the key for ROT-13 may be represented by means of the following dictionary: key = {‘a’:’n’, ‘b’:’o’, ‘c’:’p’, ‘d’:’q’, ‘e’:’r’, ‘f’:’s’, ‘g’:’t’, ‘h’:’u’,‘i’:’v’, ‘j’:’w’, ‘k’:’x’, ‘l’:’y’, ‘m’:’z’, ‘n’:’a’, ‘o’:’b’, ‘p’:’c’,‘q’:’d’, ‘r’:’e’, ‘s’:’f’, ‘t’:’g’, ‘u’:’h’, ‘v’:’i’, ‘w’:’j’, ‘x’:’k’,‘y’:’l’, ‘z’:’m’, ‘A’:’N’, ‘B’:’O’, ‘C’:’P’, ‘D’:’Q’, ‘E’:’R’, ‘F’:’S’,‘G’:’T’, ‘H’:’U’, ‘I’:’V’, ‘J’:’W’, ‘K’:’X’, ‘L’:’Y’, ‘M’:’Z’, ‘N’:’A’,‘O’:’B’, ‘P’:’C’, ‘Q’:’D’, ‘R’:’E’, ‘S’:’F’, ‘T’:’G’, ‘U’:’H’, ‘V’:’I’,‘W’:’J’, ‘X’:’K’,…
In cryptography, a Caesar cipher is a very simple encryption techniques in which each letter in the plain text is replaced by a letter some fixed number of positions down the alphabet. For example, with a shift of 3, A would be replaced by D, B would become E, and so on. The method is named after Julius Caesar, who used it to communicate with his generals. ROT-13 (“rotate by 13 places”) is a widely used example of a Caesar cipher where the shift is 13. In Python, the key for ROT-13 may be represented by means of the following dictionary: key = {‘a’:’n’, ‘b’:’o’, ‘c’:’p’, ‘d’:’q’, ‘e’:’r’, ‘f’:’s’, ‘g’:’t’, ‘h’:’u’,‘i’:’v’, ‘j’:’w’, ‘k’:’x’, ‘l’:’y’, ‘m’:’z’, ‘n’:’a’, ‘o’:’b’, ‘p’:’c’,‘q’:’d’, ‘r’:’e’, ‘s’:’f’, ‘t’:’g’, ‘u’:’h’, ‘v’:’i’, ‘w’:’j’, ‘x’:’k’,‘y’:’l’, ‘z’:’m’, ‘A’:’N’, ‘B’:’O’, ‘C’:’P’, ‘D’:’Q’, ‘E’:’R’, ‘F’:’S’,‘G’:’T’, ‘H’:’U’, ‘I’:’V’, ‘J’:’W’, ‘K’:’X’, ‘L’:’Y’, ‘M’:’Z’, ‘N’:’A’,‘O’:’B’, ‘P’:’C’, ‘Q’:’D’, ‘R’:’E’, ‘S’:’F’, ‘T’:’G’, ‘U’:’H’, ‘V’:’I’,‘W’:’J’, ‘X’:’K’,…
In programming, we use the mask concept to indicate information that can be shown to the user and information that must be “masked”, that is, hidden. In an implementation of a hangman game, we use a mask to indicate which secret word positions the player has already guessed right (whose the contents must therefore be shown to the player), and which positions must remain hidden. Each time that the player hits a letter of the hidden word, the mask is updated so that it has little dashes in the places of letters that the player has not hit yet and show it, in their proper place, the letters that he already hit it. For example, if the word is "cards", the current mask is: - a - - s and the player guesses the letter "d", the mask should be updated to: - a - ds.Write a function called update_mask that takes as input a string containing the word secret (in the example above, this word would be “cards”), a list whose elements are the characters of the current mask (in the example above…
Write a program that calculates (using a Monte Carlo simulation) what the probability is that two bishops, randomly placed on an 8 by 8 chessboard, are in an attacking position? On a chessboard, bishops can move in a diagonal line. So two bishops are in attacking position if they both sit on the same diagonal line. On the 8x8 chessboard below, B1 and B2 are in attacking position. B3 is NOT in attacking position of either B1 or B2. B4 and B1 are also in attacking position to each other. But B4 is not in attacking position to B2, or B3.
A safe is locked by a combination of of four binary digits (that is, 0 or 1), but theowner has forgotten the combination. The safe is designed in such a way that nomatter how many digits have been pressed, if the correct combination of three digitsis pressed at any point, then the safe automatically opens (there is no ”enter” key).Our goal is to find the minimum number of digits that one needs to key in in order toguarantee that the safe opens. In other words, we wish to find the smallest possiblelength of a binary sequence containing every four-digit sequence in it.(a) Create a digraph whose vertex set consists of three-digit binary sequences. Fromeach vertex labelled xyz, there is one outgoing edge (labelled 0) leading to vertexyz0, and another outgoing edge (labelled 1) leading to vertex yz1.(b) Explain why every edge represents a four digit sequence and why an Euleriantour of this graph represents the desired sequence of keystrokes.(c) Find the minimum number of digits that one…
Bob and Alice want to send each other secret messages that no one else will have access to. They have decided that they will use a locked box to hold the secret messages, and they will drop the box off in each other’s mailboxes. The problem is that if they use a combination lock, they will have to send the combination to the box and someone might intercept it. Here are the materials they have access to: A box that can be locked with a combination lock Two combination locks (the kinds that click shut that you might use on a school locker) Paper Pencil Describe a protocol Bob and Alice can set up to deliver these messages securely.