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Sarah BennettProfessor WinklerMath 0716 May 2013A Puzzling Piece: Understanding Mechanical Challenges“This skill- the ability to look at a problem and attack it from many different angles- is honed by tackling mechanical puzzles, and is useful in almost every aspect of life, at both work and home”-Will Shortz, Crossword Editor of the New York TimesConventional thinking will not produce anything extraordinary. If every great mind perceived situations in the same way as the average man, then great problems would never have been solved or new challenges ever proposed. This sentiment is clearly illustrated in the world of mechanical puzzles. These entertaining, maddening puzzles challenge traditional thought and force the puzzler to step outside the box in order to create solutions. As asserted by Shortz, creative problem solving is essential in life, both professionally and day-to-day trials. Mechanical puzzles confront the individual with similar challenges, as they require perseverance and innovation. These puzzles have impacted society have been integrated into society since their conception; the wide variety of mechanical puzzles drive creative thinking and continue to intrigue mankind as we explore new realms of thinking and problem solving.My first experience with mechanical puzzles was not a positive one, yet it taught me a lesson that I have carried with me through the rest of my academic career. I was in the second grade when my teacher, Mrs. Higgins, passed around a classic loop and key mechanical puzzle. It was composed of two whole metal pieces, one shaped like a circle and one resembling an old-fashioned key. The object of this puzzle is to separate the two objects. I took the puzzle in my small hands and set to work rotating and sliding the two objects around each other. As my frustrations grew, so did the aggressiveness of my attempts. Yanking on the key and the loop, I tried to utilize my young strength to force the puzzle pieces apart. This method did not work. I passed the puzzle reluctantly and watched curiously as the next student handled the puzzle carefully, not even attempting to untangle the two pieces. He examined the puzzle patiently for nearly ten minutes and then, to my surprise, separated the pieces in three well-planned maneuvers. My failure to solve this mechanical puzzle taught me that brute force is not how one should solve problems; the mind is a valuable tool if one utilizes it correctly. This memory sparked my interest in this category of puzzle as I began to realize how many types of mechanical puzzles have been integrated into popular culture. In the context of this class, there have been numerous examples of mechanical puzzles. They are composed in different ways, even having different objectives. What they all have in common, however, is that they stand apart from the math and logic-based puzzles we tackled during class time; mechanical puzzles were uniquely entertaining and game-like as opposed to the puzzles written on the board. Jim Timmermann of the Los Angeles Times summarized my observations, stating, “mechanical puzzles are distinguished from their crossword, jigsaw and mathematical cousins by the fact that they required active manipulation of a physical object” (Timmermann). Leading puzzle expert and enthusiast Jerry Slocum further generalized what a mechanical puzzle is by asserting that they are simply “hand-held objects that must be manipulated to achieve a specific goal” (Slocum). The definition of what a mechanical puzzle is encompasses an enormous variety of objects. The flexibility in what a mechanical puzzle can be has allowed new shapes and challenges to develop as these puzzles expanded beyond just a mathematical context. They have been incorporated into classrooms to teach important skills, such as geometric thinking. They have also been profoundly successful in educating juvenile criminals (Slocum). My research on this category of puzzle has led me to observe how common these puzzles are in my own life and revealed their interesting history. One can hardly delve into the history of mechanical puzzles without first discussing Jerry Slocum, the leading mechanical puzzle guru of modern times.Slocum has devoted a portion of his mathematical career to puzzles, not only feeding his appetite to solve them, but also informing the world on the role puzzles have played throughout history. His enthusiasm for mechanical puzzles has culminated in a collection with over 8,000 pieces (Timmermann). This collection began in his childhood and, for many years, stayed in his residence. Today, Slocum shares his collection in museums around the world. Slocum did not stop at simply enjoying and collecting puzzles, he is also owns 2,000 volumes devoted to this topic. Slocum’s intense interest, according to Timmermann, makes him a leading expert as this “may also be the world’s largest collection of books about puzzles.” Slocum’s expertise is on both the history and “sociological background” (Timmermann) of mechanical puzzles, meaning that he has researched the interplay between the society, the puzzle, and how each is impacted by the other. Slocum invented the modern classification system of all mechanical puzzles, grouping them not just by their physical characteristics, but also by their interesting histories and origins.Slocum’s extensive study resulted in a much-needed structural system for mechanical puzzles. Finding and learning new mechanical problems was an intimidating, time-consuming process due to the vast number and range of these puzzles. The first attempt to organize mechanical puzzles was by Professor Angelo Louis Hoffman in his book, Puzzles Old and New, published in 1893 (Slocum). Hoffman’s text included 400 examples, but as time continued on, his classification became obsolete. Slocum devised a system with 10 categories broad enough to encompass the entire spectrum of mechanical puzzles.The first category is titled “put together” puzzles, which have been present since the early history of man and continue to be popular today (Slocum). This category includes any puzzles whose objective is to “assemble or fit pieces together” (Slocum). These puzzles have been around since the third century BC when Archimedes invented “The Stomachion.” Archimedes’ challenging puzzle consists of a square cut into fourteen pieces that needs to be reassembled to form the original figure (Slocum). This category of puzzle also caused the “first puzzle craze in Europe and America,” brought on by the Tangram (Slocum). Tangrams were first popular in China at the beginning of the 19th century and continue to be purchased today (Slocum). Personally, I have experienced this category of mechanical puzzle numerous times, in the form of the common jigsaw puzzle. I have fond memories of solving 1,500 piece jigsaw puzzles with my mother. The pieces came together to form a beautiful, intricate image, and I still remember the satisfaction of placing the final piece. Solving these puzzles is not just about figuring out a problem, it also creates a new object in the process.The second classification is titled “take apart puzzles,” and they are the exact opposite of the first category. While my experience with this type of puzzles is limited, I was fascinated by the origins of these mechanical puzzles. Rather than arising out of intellectual curiosity, these take-apart puzzles have roots in practical purposes. Take-apart puzzles may have been first used in the seventeenth century in order to increase security. Trick locks were invented so that the common thief could not penetrate the lock using explosives, but instead had to disconnect the many interconnected pieces (Slocum). The idea of taking apart complex pieces was then applied to other common items, such as matchboxes and pocket knives. The manufacturers of these products began to incorporate take-apart mechanisms so that the owner could prevent the matches from sparking in their pants pocket or the blade from opening unintentionally (Slocum). The Potawatomi tribe utilized take-apart puzzles in another intriguing way. Now referred to as “the American Indian Puzzle Purse,” the Potawatomi women used this puzzle bag to gamble while the men danced. The purse was sewn on both sides and was threaded to the woman’s belt by strips of deerskin. To open the purse, one had to pull the deerskin strips in specific way through the stitching on the side of the bag. This puzzle not only held gambling winnings securely, but also hid the sum from the men in the tribe (Slocum). This classification of puzzle seems to have touched history throughout the ages.The next two categories defined by Slocum are “interlocking” and “disentanglement” puzzles. Although they are separate entities, there are many similarities between these two groups. Interlocking puzzles have the objective of “taking them apart and then putting them back together” (Slocum). If one embarks to solve this type of problem, one has to understand the nature of the mechanical puzzle. The structure must be studied in order to gain insight into its overall design in order to destroy and successfully recreate the figure. Disentanglement puzzles, on the other hand, are primarily focused on “freeing and attaching a part of a puzzle” (Slocum). The entire structure, then, does not have to be understood in the same way, simply how that part relates to the whole puzzle. One historical example of disentanglement puzzles is the “horse hobble puzzle” utilized by cowboys in the seventeenth century. This devise is comprised of two loops that encompass the legs of the horse, and a complex system of rope in between. This mechanism made it possible for horses to graze without running away or being stolen by Indians (Slocum). Arguably the most famous examples of mechanical puzzles in popular culture fall under the next classification. This type of puzzle is referred to as “sequential-movement puzzles,” and requires “moving parts of a puzzle to a given goal following the rules” (Slocum). Two of history’s most well-known puzzles both fall under this category. The classic “15” puzzle was invented in 1880 by Noyes Chapman, the New York postmaster (Kelly). This game consists of a 4x4 grid with tiles numbered 1 to15, and one square unoccupied. This puzzle swept the nation as the craze to solve “15” culminated in prizes of up to $1,000 to solve the puzzle at certain starting arrangements. Through modern analysis, it has been proven that only about half of all possible starting arrangements can be solved (Kelly). This game was further developed in the 1990’s to make the game Rush Hour (Kelly). This game uses the concept of “15,” except, rather than arranging a sequence of numbers, the objective of this board game is to free a small red car from a grid packed with other vehicles. The only way to maneuver around the board is by sliding the vehicles into open spaces on the grid. This board game may be entertaining, but it can pose intense mental challenges. As stated by John Kelly from How Things Work, “It might look like child’s play to solve the puzzle…yet the solution can be so complex that it seems impossible.” The complexity of such puzzles is more objectively evaluated by a computer program called “PSPACE-complete” (Kelly). This program evaluates the challenge of a mechanical puzzle by considering the possible combinations of moves, the length of the sequence of the solution, and other such factors.It would be unjust to discuss sequential-movement puzzles without devoting time to the most famous example, the Rubik’s Cube. Having sold over 1 million copies, this mechanical puzzle sparked the “biggest puzzle craze so far” in history (Slocum). This famous cube was invented by Erno Rubik in the 1970’s (Fisher). He is a Hungarian professor who had created this object to help instruct his students on how to think about spatial relationships (Timmermann). A Rubik’s cube can be thought of as a “3-D variation on a sliding puzzle,” like Rush Hour or “15” (Kelly). The cube is composed of 26 exposed “subcubes,” each containing one of six possible colored stickers on the exposed faces. Over 43 quintillion combinations are possible on this cube, which makes solving the puzzle extremely difficult (Fisher). A puzzler seeks to align all like-colored stickers on the same face of the cube, a considerable challenge given all the possible combinations. When the game was first sold, people across the globe devoted time and energy to solving their Rubik’s cubes. This puzzle sparked more than a fun game; it has given rise to brilliant mathematical formulas and algorithms in an attempt to explain the solutions of the cube. Past theories took around 50 moves to solve any starting position on the cube. That is why a recent discovery by a professor of UCLA has created a lot of interest. Richard Korf asserts that his program on the Sun workstation computer can solve any Rubik’s cube configuration in a maximum of 18 moves (Fisher). The program requires anywhere from “several hours to several weeks,” but was able to produce solutions to ten proposed configurations (Fisher). The sequential-movement category of mechanical puzzles has been repeatedly integrated into pop culture. This category poses intense challenges and captivates the puzzler as the solution appears to be only a single flip, slide, or rotation away.Continuing through Slocum’s list of mechanical puzzles, we next explore the puzzles classified as “dexterity puzzles.” These are any puzzle that requires focus and coordination, challenging both the mind and motor skills of those attempting to find the solution. Slocum notes that the frustration from these puzzles often arises from the lack of attention to the challenge at hand. One attempting these puzzles usually delves immediately into the motor aspect of dexterity puzzles without pausing to realize that “logic is often the key to the solution” (Slocum). Elements that can be overlooked may actually solve the puzzle. For example, some puzzles pose intense motor challenges, but can be solved with centrifugal force if one simply spins the object (Slocum). Dexterity puzzles seem to have their origins in the necessity of teaching finely tuned motor skills to children. Hand-eye coordination is essential to hunting and other survival skills. Therefore, it is logical that many of the earliest dexterity puzzles helped hone coordination and teach persistence and focus (Slocum). A more modern use for this type of puzzle came about during the First World War. The R. Journet and Company of London manufactured maze puzzles where one had to maneuver a ball through the maze by tilting the board in various directions. The movements had to be controlled and smooth, as the surfaced of the board was filled with holes that the ball could fall through. The company sent these puzzles to British prisoners of war being held in Germany. The trick was that when one solved this special maze, the puzzle opened to reveal a “hacksaw blade, a compass and a map to help the British prisoners escape and return to allied-controlled territory” (Slocum). Here, through careful study and determination, British soldiers found that solving a puzzle also meant salvation from their detainment.The next category of puzzle may not have been the first invented, however the originals are some of the “oldest surviving mechanical puzzles” (Slocum). These puzzles are classified as “puzzle vessels” and have the capacity to contain liquids. Their trick is to extract the liquid in a non-traditional way. This is because a series of holes near the top of the vessel prevent pouring the liquid out of the top, as the contents would instead flow out the sides from the holes. Many of these puzzles rely on a secret hole that must be covered by the fingers in order to create a vacuum when a different hole is covered by the mouth and used like a straw. Examples of such crafty puzzles exist in the form of century-old pottery (Slocum).The next two classifications of mechanical puzzles are somewhat similar, though the mechanism used to reach the objective is different for each. The first is titled “vanish puzzles” and the next is called “folding puzzles.” Vanish puzzles have a complete image when the pieces are in their original configuration, but, when rearranged into new configurations, part of the image disappears. The folding puzzles have a similar idea, that by folding the puzzle in various ways, the images in the puzzle can be combined to form something new or conceal part of the original image. One famous example was a folding puzzle piece of propaganda used during World War II. The original image had four pigs, but, once folded properly, a fifth pig was revealed and had the face of Adolf Hitler (Slocum). These puzzles seem intriguing because they defy the psychological principle of object permanence. It is intuitive to think that an object, once known to exist, will continue to exist. However, both these puzzles challenge the individual to create a new image out of nothing or make something cease to exist in the same form. This grabs the attention as one grapples with the concept of creating something entirely new when, at first, it does not seem possible.The final possible type of mechanical puzzle has the most intriguing title. Referred to as “impossible puzzles,” these are simply the mechanical puzzles that “seem to defy Newton’s Laws of Physics” (Slocum). The most famous of this category is the “Arrow through the Coke Bottle” puzzle. This interesting object is composed of a whole glass piece and a whole wooden arrow, however, the object is arranged such that the arrow pierces through the bottle. The allure of this puzzle is that it is one of the “only puzzles where the solution is a closely held secret” (Slocum). The solution was once printed by Albert Hopkin in his 1897 novel, Magic, but the average modern man is still oblivious to this solution (Slocum). These impossible puzzles are almost too strange to truly believe, their mystery and apparent impossibility capture the attention of puzzle enthusiasts around the world.The world of mechanical puzzles is vast, and society has been impacted by these puzzles since their respective inventions. These puzzles attract so much attention because, as I first asserted, they relate to the problems one faces in everyday life. Mechanical puzzles can take infinitely different forms and have no universal algorithm capable of solving them all. After a struggle with difficult problem in life, it is common to appreciate the lessons learned during the trial. In the same way, there is a satisfying rush to finding the solution to a mechanical puzzle. Fortunately, however, my research led me to find some methods for solving mechanical puzzles. These methods cannot guarantee success; they are simply solid pieces of advice when approaching complex puzzles, or even difficult life problems. Martin Gardner coined the term of finding the “aha of puzzling solving,” and the following advice will hopefully help lead to this euphoric moment (Gallant). John Kelly asserts that one must first “study the design carefully before it’s scrambled. It’s harder to solve if you’re not clear about the final outcome” (Kelly). It is important to take that problem at hand and understand it fully. Once you understand where the problem begins, it is then necessary to define the objective and proceed logically in order to attain that end goal. Whether it is a puzzle or a problem at work or home, understanding the underlying issue makes it possible to later solve that problem.The most profound advice for mechanical puzzles resonates with anyone who has faced a seemingly impossible task. One must simply “keep trying” (Gallant). Persistence and follow-through will eventually guide you to a solution. When efforts seems futile, it is interesting to hear that the largest trick held by puzzle enthusiasts is not advanced mathematics or higher-level intuition. Instead, “the real secret that applies to solving every sliding puzzle ever invented can be summed up in one word: patience” (Kelly). Committing to the task that lies ahead means acknowledging that the solution will take work. In fact, no great puzzle has an obvious solution. The journey to solve the puzzle is a large part of what makes the destination, the solution, so sweet.Mechanical puzzles instill these important life lessons, but ultimately they have captured the public’s attention because of their incredible power to break down preconceived notions and force the puzzler to see the situation in a new light. Jim Timmermann describes change in perspective saying, “like art, most challenging puzzles also forces the player to view the world from a different perspective” (Timmermann). Unique puzzles makes people pause and think for a minute. We must work to break through conventional thinking in order to see a creative solution. Mechanical puzzles help “develop an intuition” (Kelly) for how to solve unique situations and appreciate the beauty of a challenge.Jerry Slocum eloquently summarizes the beauty of puzzles in the following statement: “Puzzles are designed primarily for entertainment, that’s why we do them. But it’s nice to know that we’re becoming smarter and better human beings in the process.” These puzzles are a creative outlet for those locked in the box of conventional thought; they teach lessons on determination and patience, and have a riveting history. Mechanical puzzles are more than mere games; these twisting, rotating, interlocking objects have captivated mankind’s imagination and challenged human logic since the beginning of history. All signs seem to indicate that they will continue to do so for future generations as well. Works CitedFisher, Arthur. “Rubik’s Reduced.” Times Mirror Magazine 251.4 (Oct 1997): 58. ProQuest. Web. 9 May 2013.Gallant, Andrew and Janet Gallant. “Perplexing Puzzles: Getting to the ‘Aha!’.” The Washington Post 1 Dec 1988. ProQuest. Web. 9 May 2013.Kelly, John. How Sliding Puzzles Work. Discovery Channel, n.d. Web. 9 May 2013.Slocum, Jerry. Mechanical Puzzles: Their History and Their Challenge. Katonah Museum of Art, n.d. Web. 9 May 2013.Timmermann, Jim. “A Mechanical Collection: Beverly Hills Puzzle Expert Finds Answers.” Los Angeles Times 23 May 1984. ProQuest. Web. 9 May 2013. ................
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