Appendix: Methods to Solving Problems
Methods for solving problems have been studied in many different fields. Here is an extensive list, but it is not comprehensive. It draws from a variety of fields and disciplines and is meant to serve as inspiration for further study of problem solving as a discipline as well as to suggest specific approaches to solving the problems of an in-progress game design.
Also keep in mind that many of these approaches are best used when combined or iteratively. For instance, once a problem space has been defined, sometimes it becomes clear that the next step is to find an expert who can help. Or, if following the money turns up nothing but dead ends, perhaps try this method again, but this time, follow the thread of who is exerting power to get the answer.
Make a list.
A common way of tackling a large project or problem is to break it down into sections or steps, list these steps in order, then simply start crossing things off the list as they are accomplished or solved.
Find a pattern.
Many problems include hidden patterns within their structure or echo patterns found elsewhere. If these patterns are identified, they can often be analyzed and managed, mitigating, if not solving, the problem.
Work backward.
Without a clear vision of the destination, it is extremely difficult to reach it. So sometimes the best problem-solving approach is to clearly define what an ideal “solved state” looks like; then deconstruct and reverse engineer it, connecting it back to the original “problem state.” This way a roadmap to success has been clearly laid out, and no one has to cast around blindly from the middle of the problem.
Make a table.
If a problem or the data involved in it can be rephrased or reorganized into a table, often solutions become clearer. Tables force elements to be classified as they are grouped together into rows or columns, and relationships between elements can become clear as they are juxtaposed or juggled. This can take a simple form, as in speeding up a too-slow shopping trip by grouping items together that are likely to be found in the same aisle, or it can be as complicated as deductive logic puzzles. These puzzles use specific types of tables to identify missing information, as in truth tables and solution matrices where relationships become clear as roles are matched to individuals. Think of those word problems where someone’s child’s brother is John Doe’s uncle, and your job is to figure out who owns the parrot based on how John is related to Eli, who sold the parrot to his niece.
Draw a picture.
Looking at a problem in a new way can often bring solutions to light. Sometimes making the problem into a concrete thing, using images, is all it takes to identify a solution. Other times, detailed schematics can help create efficient plans, as in technical blueprints for a new building, which can solve the problem of how much brick to purchase. Either way, the act of translating a problem into a new system of thought or a new way of communicating about it can be a powerful problem-solving approach.
Guess and check, aka the scientific method.
The heart of the scientific method is the same as a more casually named problem-solving approach known as guess and check. That is, make an educated guess about what the solution to the problem will look like, then run experiments to find out if the guess is close to correct or invalid.It’s important to note that this method is iterative. Almost no guess (or hypothesis) is absolutely correct. Usually when it is measured something is missing or confusing, and the process can be used again to make a new guess, which can once again be checked for accuracy.
Follow the money.
When faced with a mystery or confusing event in the real world, the problem-solving approach used by detectives and journalists is often some variation on “follow the money.” That is, carefully analyzing who benefits from the problematic situation as it stands often sheds light on any mystery and suggests ways to root it out. Money and motive don’t always have to be the thread, though. Often the act of focusing on one element and clearly defining that element’s position throughout the problem space can help untangle otherwise jumbled disasters.
Make a flowchart.
Most useful when trying to solve a dynamic problem or to hit a moving target, flowcharts help clarify and visualize process and causality. No game design document is complete without at least one flowchart.
Reword the problem.
Sometimes cognitive biases can lock us in to one way of viewing a problem, thereby obfuscating the solution. Simply finding new words to describe the problem can be enough. This is essentially the definition of a riddle—a simple statement reworded into something obscure and surprising. And in this case, if it works one way, it often works the other. Things that look obscure and surprising can sometimes become mundane and eminently solvable when put into simpler or clearer words.
Define the problem space.
Going off on tangents and ending up in dead ends can seriously delay or impede problem solving in general. After they clearly define what exactly the problem is, and what it is not, those working on the problem can focus their efforts in useful directions rather than wandering off down unrelated though interesting paths.
Solve a similar problem first.
Sometimes there can seem like no way to solve a problem, but if the team tackles a related problem instead, an approach for the insolvable problem will present itself. For instance, balancing a national budget can seem like an impossible task, but balancing a household budget with fewer zeros appended to the end of the numbers is easier to grasp. Balancing the household budget uses similar principles on a smaller scale and can suggest methods for tackling the larger problem.
Brainstorm.
This classic problem-solving technique involves coming up with as many solutions as possible, whether they are viable, likely, or even especially relevant. The act of random creativity can generate surprisingly useful results (see Brainstorming Methods).
Come at it sideways.
Humans instinctively approach things from the ends: They look at the beginning of creation or the last sputtering moment. Especially when problem solving, it is easy to get hyperfocused on the point of the spear or the most exciting or inflammatory part of the problem. Yet, if an attack is made on the middle of the problem, sometimes the whole thing crumbles. Similarly, a stealth approach is sometimes better than tackling something head-on. Try getting to know more about the problem, and even try looking at it as if it is not a problem, to at least begin to see how it functions. Remember the adage “Keep your friends close and your enemies closer.”
Create something a little closer to solved, then repeat.
This approach is at the heart of the Agile Development methodology. If a perfect solution cannot be created overnight (or at all), sometimes the best approach is to make something that is a “close” solution, without being a complete solution. This method works especially well iteratively, as in Agile sprints, where each burst of effort improves and refines the existing solution, bringing it asymptotically closer to perfect.
Try combining two unexpected elements.
This is the “salted caramel” solution. These two culinary ingredients don’t sound appealing as a combination. They are an unexpected pairing that solves the problem of how to make caramel taste even better than usual. Unexpected combinations are not always successful (chocolate and bacon is unreliable as a taste sensation), but when a problem seems insoluble, this approach can yield good results—or at least suggestions for new avenues of discovery.
Add an unexpected element.
This is a trick used by authors who are facing writer’s block. They solve this debilitating problem by adding some unexpected element—a cat, for instance. If writing on a novel or nonfiction project ever stalls, a writer might get herself going again by throwing in something silly, random, or at least unexpected. They may go back and delete that section later, but the creative juices get flowing again simply because the problem has been shaken up and they can take a fresh look at it.
Take a step back.
Many problems are solved in the subconscious before that solution ever bubbles up to conscious awareness. Sometimes that intuitive leap is blocked when too much time is spent consciously focused on the problem. Taking a break or stepping away from the problem often lets a person relax enough to hear what their subconscious is trying to say. This is what happens when a solution “just comes to mind out of the blue” while someone is standing in the shower or looking at a sunset. These moments of inspiration can never strike if breaks are never taken.
Solve in parts and combine.
Sometimes the principle of synergy is detrimental, as a combination of factors can result in a problem that is larger than the sum of its parts. This can result in what seems like an insolvable problem. Yet, if the parts are addressed individually, they will stop working together and the huge problem will evaporate.
Try to prove it can’t be solved.
This approach is often used in the field of mathematics, but it applies to any problem. If it can be definitively proved that a problem can never be solved . . . well, it usually can’t, but along the way to finding out why it can’t be solved, several options for potential solutions will usually be uncovered.
Simplify elements until the problem resembles a previously solved problem.
The problem of landing a person on the moon may seem overwhelmingly complex, but it is essentially the same thing as shooting a bullet and hitting a target. Although this is a great oversimplification, the bulls-eye on a gun range is a solved problem. The math, methods, and materials all exist. Looked at in this light, the problem of a moon landing becomes much more manageable, as existing tools can be used, at least to get the solution process started.
Solve the opposite problem.
The problem of cooling a house can seem insurmountable, but the problem of heating a house, while technically the direct opposite problem, can result in clear solutions for cooling. For instance, insulation is key in both cases, as is air flow. Both solutions rely on most of the same principles, and the solution for one type of problem often suggests the solution for its opposite.
Has anybody else solved a similar problem?
This approach relates to the idea of “don’t reinvent the wheel.” Sometimes a solution that seems impossible has already been solved by someone else, and proper research will uncover it.
Prototype.
See Prototyping and Paper Prototyping.
Think out loud.
Often the act of putting thoughts into words, rambling and strange as they may be, will help organize them in ways that suggest solutions.
Get help.
This one is simple. In many situations, an expert can be brought in to provide guidance or an outright solution. For instance, health problems are often best solved by doctors rather than the patient who has the problem. Similarly, cooperation among peers can result in quick solutions.
Act it out.
Actively roleplaying or paper prototyping can bring to light solutions that are not obvious when the pieces are not in motion.
Explain it to your grandfather.
Similar to thinking out loud, this approach doesn’t actually require a relative. It’s the act of explaining the problem to someone who is not an expert that sometimes illuminates solutions. Whether the listener has suggestions or questions or no input at all, explaining things in their simplest forms can help clarify the problem.
Look at it from the other side.
Turn the puzzle upside down. Look behind the curtain. Try to look at the villain as a hero instead. A fresh perspective often reveals approaches for solutions.
Measure and write it in numbers.
Sometimes a lack of clarity and definition can result in a moving target that is always out of reach. It’s hard to know when something is “better,” but it is easy to know when it has improved by two percentage points.
Turn numbers into words.
The inverse of writing a problem in numbers is to translate the numbers in a problem into words. For instance, math equations or flowcharts can seem hopelessly confusing, but if spoken or changed into a relatable situation like taking apples off a table, the answer can be more obvious.
Try on a solution for size.
When facing big decisions in life, like which college to attend or which job to take, psychiatry suggests “trying on” a solution—that is, pretending that one or the other decision is the one and behaving as if this were the true plan for a while. Often, this approach reveals problems with the temporary solution (Oh, our budget doesn’t fit that pay cut.) that were not obvious before, or it confirms that this is the correct solution.
Watch out for ultimatums/dichotomies/negatives.
This is another problem-solving approach from the soft sciences; examine the problem statement for ultimatums (always, never), dichotomies (black or white), and assumed negatives (Are you sure there really is no budget for this bug fix?). The real world is usually full of shades of grey, exceptions to the rules, and incorrect assumptions; yet, if the problem statement is built on these unreal expectations, potential solutions may be ignored.
Check for neutrality.
Is a solution being ignored because of personal bias somewhere? No one is perfect.
Use Judo.
The essence of Judo is to use the opponent’s strengths against him, and conversely, to find ways to make weakness into a strength. Sometimes the best solution to a problem is to retreat and simply not solve it, and sometimes the problem can be reframed into an asset. Sometimes its big, overwhelming nature can be used as a distraction while the core of the problem is eaten away bit by bit.
Find the weakest link.
Analyze the relative strengths and weaknesses of each part of the problem; then focus attention on the weakest point. Often, breaking this one element can cause the whole problem to collapse, but if it doesn’t, this is another case where iteration works. When the weakest/easiest part of the problem is solved, move on to the next easiest/weakest, and so on until all parts are solved. Often the mental practice and incremental development of tools at each step of the process means that the solvers are better equipped to tackle the next section as it comes along.