An Investigation Into The Eight Queens Problem Essays - Chess

An Investigation Into The Eight Queens Problem Essays - Chess An Investigation into the Eight Queens Problem Introduction The eight queens problem relies on a very simple chess-based concept. However, no chess knowledge, other than this background, is required. Chess is a game plajghyed on a 8 by 8 grid of 64 squares. The grid is checkered with two colors, usually white and black, the bottom right hand corner being white. The players sit opposite of each other and have sixteen chess pieces that they use to attempt to win the game.1 The objective of the game is to use your sixteen chess pieces to checkmate the king?that is, having the king in a situation where he is unable to move without being in threat of being captured by an opponent?s piece. Each chess piece has certain chess rules which governs the way each chess piece may move. One of the pieces is called the Queen. The Queen is ultimate piece of the chess board being able to move in any direction and for any number of squares.2 How many ways can eight queens be placed on a chess board so that no other queen will attack another?3 A queen can attack any other queen along the eight paths which extend from queen. These paths are vertically, horizontally, and diagonally.4 Development Some observations must be made before attempting to solve this problem. Since there is a 8 by 8 chess board and 8 queens, then there must be a queen on each row. Also, a chess board has four black, and four white squares in each row. That would mean that half of the queens must be placed on black squares and half of the queens must be placed on the white squares.5 Each chess square will be labeled in the method shown in figure 1. Figure 1 Each coordinate on the chess board such as (4,5) or (x,y) will be referred to as being S. Again, a queen can attack anyone diagonally, vertically, or horizontally.6 Mathematically, a queens diagonal dominance can be described by using the coordinates and adding A or B to x and y, and A being a variable in the domain 1-1.7 ( X + A, Y + A ) right diagonal dominance of the queen ( X + B, Y- B) left diagonal dominance ( X, A ) vertical dominance of the queen?s domain ( Y, A ) horizontal dominance of the queen?s domain. The first queen can be placed on the coordinate (1,1). With the above rules, the following is true in Table 1: SA(X+A)(Y+A) (X,A)(A,Y) (1,1)122(1,1)(1,1) 233(1,2)(2,1) 344(1,3)(3,1) 455(1,4)(4,1) 566(1,5)(5,1) 677(1,6)(6,1) 788(1,7)(7,1) 899(1,8)(8,1) Table 1 When any other queens are placed on the chess board, it cannot be placed on any of the coordinates listed in Table 1 because it would fall into this queen?s dominance. This would be true for any other queen that will be placed on the board.8 The second queen will have six squares from which it can be placed since two of them have been dominated by the first queen. The queen will be unable to be placed in the second row in the coordinates (2,2) or (1,2). The second queen is able to be placed on the squares with the coordinates (3,2), (4,2), (5,2), (6,2), (7,2), and (8,2). There are many factors that must be considered before placing the next queen. One goal is to leave as many squares open that do not vertically align with any other squares on any other rows. For example, if a queen is placed on (3,2) then it would leave four squares open on rows 3, 4, 5, 6, and 7. Because there are only 8 squares across a chess board, four being left open in five rows would result in vertically aligned rows.9 (Figure 2) Many of the squares would be eliminated quickly because many are aligned vertically together resulting in less squares made available than 8 because once a queen is placed in any of the remaining "free" squares, then the "free" vertically above and below that queen would be dominated along with the diagonal pathways that the queen would dominate also. Since this is true, then the next queen must

Research of an Innovative Hardware Object Essays

Research of an Innovative Hardware Object Essays Research of an Innovative Hardware Object Essay Research of an Innovative Hardware Object Essay After you create your object using your computer assisted software or CAD, he digital AD model is saved as a SST file and sent to the printer. Before you start printing anything you have to add a select amount of the material that you have decided to use (plaster, ballistic, polyurethane, polyester, epoxy, metal etc. ). Then the printer prints out your object on a bed and youre finished. There is another method that you can use to AD print your desired object, this method is called fused deposition modeling or FED. In this method molten polymer is sprayed onto a support layer and the object is built layer by layer until complete. What companies manufacture AD printers? The market for AD printers Is beginning to grow. There are many companies that specialize In producing and selling AD printers but for this assignment Im going to focus on the following. Some of the companies that manufacture industrial AD printers are; Object Geometries founded in 1998, Z Corporation founded in 1994, Strategy founded in 1988, disesteems founded in 1986. Some of the companies that manufacture AD printers for home use are; Makeover Industries founded in 2009, Ultimate founded in 2011, and Potboil founded by disesteems. What are the models that are made by various companies? Models made by: Z Corporation: The Project 3510 SD produces high quality parts perfect for engineering and mechanical design applications. Strategy: The Forts mace system builds durable and accurate parts as large as 914 x 610 x mm. It also has 11 different material options suitable for anything from bulging fixtures and factory tooling to end-use parts and even functional prototypes. disesteems: The Cube X Duo is one of the best and most popular desktop/personal ad printers with the ability to print and object as big as a basketball! Makeover: The Makeover Replicated ZOO is so advanced that you can create and print two objects at the same time. App and cloud enabled so you can connect with wife and USB with no problems at all. Ultimate: The ultimate 2 has the industry leading print to size ratio. It has the smallest footprint and highest build volume among all desktop AD printers. Also, it is an open filament system meaning that the cost of material is very low compared to other ad printers because you can use any filament you choose. Potboil: The Cube X has an advanced settings option that allows you to specialized and personalized the way you print In 8 different colors! Also, It Includes Its own printing sof tware. Strengths of this component Include: Cheap Manufacturing: AD printing is increasingly being used by large companies sun as converse or Ales to replace some AT tenet normal maturating meet This is achieved through lower shipping and packaging costs from overseas parts suppliers, less human work and cheaper and reliable materials. Quicker Production: The speed of AD printing compared to ordering parts from different suppliers all over the world is like comparing the speed of a turtle and the speed of a race car. Why old you want to wait weeks or maybe months for parts to arrive when you could have the entire object built right in front of you in a couple of hours. Also if you dont like the design you have created, you can Just start from scratch or mould your design into something different using the computer program used to print. New Shapes and Structures: Regular manufacturing methods rely on moulds and cutting technologies to make a limited number of shapes but AD printing changes this altogether. The AD printers spray tool can build an infinite number of complex figures limited only by human imagination. Combinations of New Materials: Before AD printing, mixing different raw materials wasnt possible due to their physical and chemical properties but people believe that ad printings potential has not been reached yet so many companies now offer tens of different materials with different finishes giving the look and feel of metal, ceramic or glass with different strengths and melting temperatures. Weaknesses of this component: AD printers use up a large amount of energy even when printing something the size of a necklace. When melting plastic and other materials with heat or lasers, AD printers use up to 50-100 times more electrical energy that injection molding to make n item of the same weight and size meaning that when it comes to industrial AD printing, the time you save might not be worth the money your spending on electric or production fees. One of the materials mostly used in AD printing is plastic. Possibly the biggest environmental movements in recent history has been to reduce the use of plastics, the most popular and cheapest AD printers use plastic filament and wires to print objects. If AD printing starts to become more industrialized then excess plastic from either print beds or scraped projects that werent used needs to e recyclable or biodegradable but until then, AD printing will become a wasteful way of creating parts or any objects. There are many things you can print with a AD printer for example; a toy for small children or a wheel for a bus or bicycle, the problem is you could also print out a gun or weapon of some sort and that could be illegal in the country that you created it. The printer itself is not going to not allow you to print out a weapon because it doesnt know the difference. There is also going to be an issue with printing out counterfeit products. To print an object, all you need s the software the model was created on and the actual file itself. You can also print out credit cards and I. Dos as well as copies of other private belongings. How much does a AD printer cost? There are 3 main types of AD printers, these types include; personal, professional and industrial. Personal AD printers are plainly and simply used for small projects that you can create such as, toys, miniature structures and tools. Professional AD printers are uses In large commercial Dulling Ana companies; teen use ten printers for parts that need to be made with specific detail because shipping from other entries around the world is too expensive. Industrial AD printers are used for creating objects and parts to be sold and manufactured to other large companies, usually for more value.

Skin allergy Research Paper Example | Topics and Well Written Essays - 750 words

Skin allergy - Research Paper Example Urticaria or hives is an itchy rash, due to hypersensitive reaction by the skin (Linscott, Emedicine). The condition may be acute or chronic and there are several variants to this condition. Itching can occur without any rash and may be due to some disease related to that part of the skin. Even some medications can cause itching. As far as atopic dermatitis is concerned, the cause is actually unknown. However, several researchers have attributed genetic and environmental mechanisms to the development of atopic dermatitis. Factors which contribute to the development of atopic dermatitis are infection, poor hygiene, extremes of climate, food antigens and aeroallergens (Kraffchik, Emedicine). Several chemicals sensitize the skin and cause allergic contact dermatitis. Some of the important chemicals are poison ivy, Nickel, rubber gloves, p-phenylenediamine, dyes, formaldehyde, wash and wear chemicals and preservatives (Hogan, Emedicine). In urticaria, the cause is unknown most of the times. However, ingections, foods, stress, drugs, exposure to certain temperatures and climates and exposure to latex can trigger the development of the condition (Linscott Emedicine). In atopic dermatitis, the pathophysiology is poorly understood. However, it has been thought that sensitization of IgE and epithelial barrier disturbance secondary to some kind of immune dysfunction is the cause for the allergic rashes. Another important defect attributed to this condition is defective epithelial cells contributing to defective barrier mechanism (Kraffchik, Emedicine). The main immune disturbance is imbalance in the T-lymphocytes with TH2 cells dominating the system and causing release of cytokines like granulocyte macrophage stimulating factor and interleukins 4,5, 12 and 13. All these amount to an increase in IgE levels and fall in interferon gamma levels. In those with chronic

Wal-Mart Essay Example | Topics and Well Written Essays - 1750 words

Wal-Mart - Essay Example This requires a benefit and wage package that accounts for the basic expenses and area-specific cost of living involved in supporting a family comfortably. By definition of their regions specific living wage standards are known to vary as compared to minimum wages offered by the federals. This is because the minimum wages do not begin to meet the family or the working people needs anywhere in the country; and on the contrary, it puts a child and parent below the poverty federal lines. This issue can effectively be addressed by the implementation of a more reasonable minimum and living wage at a local level that will not affect the family’s way of life. Our living wage standard like in many other municipal standards across the country combines some benefits with the wage standard to cater for employees and families that need it the most. The City of Washington, D.C government recently wanted to introduce a legislation that would ensure that large corporations running business i n the city would pay a "living wage" of $12.50 per hour to all employees hired in the city. Wal-Mart, one of the largest business corporations in the whole world responded by threatening to close stores in the city, and not to open planned stores because of the legislation. Such policies are meant to protect the public from exploitation by business companies and to ensure that employees are well remunerated. Is the living wage policy good? The question whether the policy is a good one can be argued from both ways, but on this paper, the argument will lean more on the positive aspects of the policy. This policy is good and its implementation would be beneficial for the employees, future employees, the families of the employees and ultimately the city of Washington, D.C. One advantage that can be achieved through its implementation is that the minimum income of the citizens would rise considerably. This will help in improving the lives of the employees and enable them meet their basic and secondary needs. In addition, it is also beneficial to women because over time they have been earning lower wages than the men have. The wage policy will ensure than women and men earn similar salaries that are based on their skills and work rather than gender. In this aspect, the policy would benefit most families of the employees. Through this, it can be regarded as an added benefit to the recovery of the economy as a whole from the family level. Others still view its implementation as an indirect form of justice for those affected by the economy crisis since within its implementation, there are dockets that would allow for effective compensations and responsibility mainly by the employers and managements and this would in effect protect the workers from any form of abuse. The policy is also beneficial to companies such as Wal-Mart because an increased wage will ensure that the employees are motivated to perform highly and yield more and high quality productivity. Due to thes e facts, it is clear that the policy is a good one. The people who support the implementation of the living wage policy state that all individuals should be provided with direct means of affording living costs in-terms of shelter, food, transport and usual basic needs, fiscal conservatives. On the other hand, those who do not support it refuse to uphold the idea of a minimum wage since according to them it makes it hard to determine the regional scale cost of labor appropriately. They adequately argue that the minimum wage increases the services and goods prices while also affecting disproportionally the minorities. Even with this argument and counter argument, it is still unfortunate that a major aspect is still not answered by this debate

Human Rights and English law (LLB), Discuss why it is that freedom of Essay

Human Rights and English law (LLB), Discuss why it is that freedom of expression is widely considered to be a fundamental human right, and the extent, if any, t - Essay Example ring protection is not questioned, the degree of immunity accorded to it is a frequently debated issue insofar as restrictions regarding its protection are concerned, challenging its character as a fundamental right. Given the issues surrounding the freedom of expression, this essay will therefore argue that the freedom of expression is a fundamental human right, whose protection, although guaranteed, is not absolute such that restrictions must be placed to ensure that its exercise is in accordance with the laws of the land and the responsibilities required of citizens. The freedom of expression is recognised as among the â€Å"human rights and fundamental freedoms [that are] the birthright of all human beings† (cited in Smith, 2004, p. 1). Its fundamental character lies in its significance as a pillar of democratic society, and as a human right intimately connected with the exercise of individual life and liberty. As illustrated in Handyside v. United Kingdom1, the â€Å"[f]reedom of expression constitutes one of the essential foundations of [a democratic] society, one of the basic conditions for its progress and for the development of every man†, such that its protection is extended â€Å"not only to ‘information’ or ‘ideas’ that are favourably received or regarded as inoffensive or as a matter of indifference, but also to those that offend, shock or disturb the State or any sector of the population.† Hence, freedom of expression is a fundamental right, whose exercise is necessary for citizens to par ticipate in the democratic process and the functioning of society (Stone, 2004, p.1). On the other hand, the freedom of expression is also a human right whose exercise directly affects other fundamental human rights as recognised by the ECHR. Whereas Article 9 of the ECHR recognises the freedom of religion, the exercise of such freedom is incomplete if individuals are restricted in their expression of religious beliefs. Freedom of expression is therefore

Magic Realism in One Hundred Years of Solitude

Magic Realism in One Hundred Years of Solitude Magic Realism is a term found by art historian Franz Roh in 1925, to describe a visual arts movement emerging throughout Europe. It is known that a large number of critical terms in literature are borrowed from painting. Magic Realism is one of those terms. The usage of that technique leads the author make the themes and subjects are more imaginary, outlandish and with a fantastic dream like quality. Gabriel Garcia Marquez, who is the author of One Hundred Years of Solitude, does not like to be considered a writer of Magic Realism, even it is clear to see Magic Realism technique in his novel, he claims only to be realist without much exaggeration in his work. He states, As the final judgment runs, the source of all creation is reality. In One Hundred Years of Solitude for example, the banana company treats its workers so badly that they all go on strike. They gathered in the main square of the town, where the government has them surrounded by soldiers armed with machine guns. When the crowed refuses to disperse, the order is given to open fire, and three thousand people are killed. Their corpses are, then, put into the trains and sent off to the sea, and the whole incident is officially denied to the point that Jose Arcadio Segundo finds it impossible to persuade anyone that it has taken place. For a European observer, the ability of a government to hide such incidents is indeed unbelievable. However, in Latin America, as well in the most of the third world countries, the situation is still worse than can be imagined. To the eye of European and North American common sense, the career of the Central character in One Hundred Years of Solitude Colonel Aureliano clearly belongs to the realm of magic and fantasy and not of reality. For, in the course of his career he, Organized thirty two armed uprisings and he lost them all, he had seventeen male children by seventeen different women and they were exterminated one after the other in a single night he survived fourteen attempts on his life, seventy three ambushes and a firing squad. He lived through a doze of strychnine in his coffee that was enough to kill a horse. He refused the Order of Merit He rose to be the commander in chief of the revolutionary forces with jurisdiction and command from one border to the other and the man most feared by the government Although he always fought at the head of his men, the only wound that he received was the one he gave himself. He shot himself in the chest with a pistol and the bullet came out through his back wi th out damaging any vital organ. (MÃ ¡rquez, 2003) Early in the novel, a mysterious girls arrives who either cannot or will not speak and whom they call Rebecca. She brings with her the sickness of insomnia of which the most fearsome part, as an Indian woman explains, was not the impossibility of sleeping, for the body did not feel any fatigue at all, but its inexorable evolution towards a more critical manifestation; a loss of memory. Melquiades, a man of letters discovered its remedy but before him, Jose Arcadia has already invented a memory machine in which he has recorded almost fourteen thousand entries. World, in this way, becomes a slave of dictionary as it refuses all possibility of change by overcoming the loss of memory. It is not difficult to count a number of reasons for these apparently incredible details, which Gabriel Garcia Marquez provides in his work, but the most convincing one is, perhaps the obvious mundane purpose of enabling him to avoid censorship. Marquez technique has also been described as a kind of narrative hyperbole which seeks to expand the sensibility with which we perceive the world we live in. In One Hundred Years of Solitude, Marquezs characters are often endowed with a kind of supernatural power. Aureliano can see the future. Remedios The Beauty is taken up into the clouds as a divine being. Melquiades survives death, and stays on earth as a ghost. Ursula chooses not to die and lives for over a hundred years. In One Hundred Years ofnSolitude, if the resolution is strong enough, nothing can overpower it. It is perfectly possible for people to have power over even death. The characters struggle to create and define their own worlds, their fight is against time, history and fate. It could be said that Marquez endowment of his characters with special power is an illustration of our powerlessness against forces which remain outside our control. By crossing the border of normal possibility, Marquez reminds us of the limit ations of our own real lives, but also of the possibility of viewing the world in an entirely different way. Marquezs characters struggle to control, and to create their own world. It is through this act of creation that we can truly escape the forces in life over which we have no control. Marquez suggests that literature is the means by which we can gain understanding of a world-view different from our own, and therefore an understanding of our common humanity. While politics and ideology have the power to de-humanise, literature has the power to remind us of our humanity. Through imagination, and art, we can be elevated from the restrictions we face in day to day life, and we can also be enlightened as to the true potential of our lives, and our own individual power to create and shape our own destinies. Bibliography MÃ ¡rquez, G. G. (2003). PURPLE PATCH: Liberal Paradise . Retrieved from Daily Times: http://www.dailytimes.com.pk/default.asp?page=story_3-12-2003_pg3_7

Violence in the Media Essay -- Papers

Violence in the Media America has become the most violent nation in the industrialized world. The many violent images seen in movies and on television on a daily basis, though not the only cause, are a strong contributing factor. There are those that feel the point-of-view from which the audience views the violence varies directly with the way the scene affects them. A film's perspective determines the audience's reaction. In "slasher" films, for example, the point of view shifts between the attacker and the victim. So the audience feels the terror of the victim and the lust of the victimizer. If the viewer shares the experience with the victim they feel helplessness, fear, and also the rage that comes with being attacked. However, when the viewer is allowed to share the experience of the attacker the perspective is different, they get the sense of power and being in control. In many sexual assault scenes the camera focuses on the victim's face, which puts the viewer in the position of the rapist. What is of concern is that many Americans want to identify with the powerful attacker. It can be argued whether or not this is a direct cause of imitative violence but it, with out a doubt, offers viewers the vicarious experience of violence related to sex. (Censorship, 1985) Television does not make people commit crimes, but it provides the ideas, social sanction, and often the instruction that encourages anti-social behavior according to Madeline Levine, psychologist. (Viewing Violence, 1996) Dr. Jib Fowles, a researcher from the University of Houston would disagree. He testified to the U.S. Congress that TV violence was a good way to relieve tension. Dr. Radecki strongly disagreed saying that "Fowles has never done a si... ...itable role models for them. Bibliography: Croteau, David and William Hoynes. 1997. Media/Society: Industries, . Images, and Audiences. London: Pine Forge Press. Dudley, William,ed. 1999. Media Violence: Opposing Viewpoints. San . Diego: Greenhaven Press, Inc. Fiske, John. 1989. Understanding Popular Culture. New York: Routledge. Holland, Keating. 1999. "Violence in the Media Should be Regulated." . CNN Poll. http://www.ultranet.com/crowleyn/ccnnpoll.html Levine, Madeline. 1996. Viewing Violence. New York: Double Day. O'Neill, Terry. 1985. Censorship: Opposing Viewpoints. St. Paul, MO: Green Haven Press, Inc. University of California at Los Angeles. Television Monitoring Report. . http://www.cep.org/tvviolence.html