2. A man must ferry a goat, a wolf, and a head of cabbage across a river. The available boat, however, can carry only the man and one other thing. The goat cannot be left with the cabbage, nor can the wolf be left with the goat. How should the man ferry the three items across the river?

2. A man must ferry a goat, a wolf, and a head of cabbage across a river. The available boat, however, can carry only the man and one other thing. The goat cannot be left with the cabbage, nor can the wolf be left with the goat. How should the man ferry the three items across the river?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter23: Simulation With The Excel Add-in @risk

Section: Chapter Questions

Problem 8RP

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2. In Africa there is a very special species of bee. Every year, the female bees of such species give birth to one male bee, while the male bees give birth to one male bee and one female bee, and then they die! Now scientists have accidentally found one “magical female bee” of such special species to the effect that she is immortal, but still able to give birth once a year as all the other female bees. The scientists would like to know how many bees there will be after N years. Please write a program that helps them find the number of male bees and the total number of all bees after N years. Input Each line of input contains an integer N (≥ 0). Input ends with a case where N = −1. (This case should NOT be processed.) Output Each line of output should have two numbers, the first one being the number of male bees after N years, and the second one being the total number of bees after N years. (The two numbers will not exceed 232.) Sample Input 1 3 -1 Sample Output 1 2 4 7
With this exercise, we shall develop a solution to the following riddle. Two adults, their three children, and their dog are on a walk when they come upon a river. They have a boat, but it can only hold a maximum of one adult with either one child or the dog; or three chidren; or two children and the dog. Anyone (other than the dog) can row the boat; but it would be too much work for one child to row across by themself. How can they all get across the river? You are required to solve this riddle by modelling it using a labelled transition system (LTS). 1. What are the states of your LTS consist of? Make sure you consider all the aspects of the riddle. Justify your notion of state. 2. What are the actions of your LTS? List all the actions. Justify your choice of actions. 3. Drawing out the entire LTS may be a time consuming task as there could be very many states and transitions. However, drawing out only part of the LTS is doable. Draw part of the LTS, anywhere between 7 and 12…
Four individuals wish to traverse an unstable bridge; they all start on the same side. You have 17 minutes to get everyone to the opposite side. Night has fallen, and they have only one torch. Two individuals may cross the bridge at once at most. Any crossing party, whether one or two individuals, must carry a torch. The torch must be carried back and forth; it cannot, for instance, be hurled. Person 1 crosses the bridge in one minute, person 2 in two minutes, person 3 in five minutes, and person 4 in ten minutes. A dyad must trek together at the slower individual's cadence. Create the algorithm specification that solves the problem.
1) Long before H. G. Wells wrote The Invisible Man, Plato (428– 348 BC), in The Republic, described a shepherd named Gyges who, according to a Greek legend, discovers a ring that enables him to become invisible when he turns its bezel. Gyges uses his magical powers to seduce the queen, kill the king, and take over an empire. If we have similar powers, why should we feel bound by moral constraints? In particular, if professionals are sufficiently powerful to pursue their desires without being caught for malfeasance, why should they care about the good of the wider public?
5. What if my movie marathon consists of exactly five distinct movies: two movies from one of the trilogies, 2 movies from a 2nd trilogy, and 1 movie from a 3rd. The movies can be watched in whatever order I choose and the same five movies watched in a different order constitute a different marathon. Now how many movie marathons are possible?
Algorithm
John is training for a marathon and he can easily alternate between running a mile and walking a mile. If he runs for 2 miles in a row, he becomes fatigued, and must then walk for 2 miles in a row in order to no longer be fatigued. When he is fatigued, he can still alternate between running a mile and walking a mile, but if he runs 2 miles in a row while already fatigued, he will collapse on the side of the road. If he runs 3 miles in a row at any point, he will also collapse. Let the letter 'a' stand for John running 1 mile, and the letter 'b' stand for John walking 1 mile. Draw a DFA which accepts all possible runs in which John does not collapse on the side of the road.
A detachment of n soldiers must cross a wide and deep river with no bridge in sight. They notice two 12-year-old boys playing in a rowboat by the shore. The boat is so tiny, however, that it can only hold two boys or one soldier. How can the soldiers get across the river and leave the boys in joint possession of the boat? How many times need the boat pass from shore to shore?
A farmer has goat , a wolf & a cabbage on the west side of a river. He wants to get all of his animals & his cabbage across the river onto the east side. The farmer has row boat but he only has enough room for himself & one other thing . The wolf will eat the goat if they are left together alone. The goat will eat the cabbage if they are left together alone. How can the farmer get everything on the east side? i. Formulate this puzzle as search. ii.Find solution for this problem.
A club has eight members. Three are to be chosen to go as a group to a nationalmeeting.(a) How many distinct groups of three can be chosen?(b) If the club contains four men and four women, how many distinct groups of four containtwo men and one woman?
We have a club consisting of 6 distinct men and 5 distinct women: a. In how many ways can we select a committee of 5 persons? b. In how many ways can we select a committee of five persons consisting of three men and two women? c. In how many ways can we select a committee of five persons that has at most one man? d. In how many ways can we select a committee of five persons that has at least two women? e. Club members Jana and Ben are in a relationship. In how many ways can we select a committee of five persons so that Jana and Ben serve together? f. Jana and Ben have had a fight and do not want to serve on the committee together, so in how many ways can we select a committee of five that do not contain BOTH Jana and. Ben?
To reduce traffic congestion in downtown Winburg, Indiana, the mayor convinces the city toset up a public transportation system. Bus-only lanes are to be established, and commuterswill be encouraged to “park and ride”; that is, to park their cars in suburban parking lots andthen take buses from there to work and back at cost of one dollar per ride. Each bus is tohave a fare machine that accepts only one dollar bills. Passengers insert a bill into the slotsas they enter the bus. Sensors inside the fare machine scan the bill, and the software in themachine uses an image recognition algorithm to decide whether the passenger has indeedinserted a valid dollar bill into the slot. It is important that the fare machine be accuratebecause, once the news gets out that any piece of paper will do the trick, fare income willplummet to effectively zero. Conversely, if the machine regularly rejects valid dollar bills,passengers will be reluctant to use the buses. In addition, the fare machine must be…