Problem solver’s approach – use the technique of pattern recognition

Use of Pattern recognition technique for problem solving

Not all things have a purpose

Pattern identification and recognition is one of the most basic capabilities of humans (and also of any living thing). Right from birth, the newborn starts identifying patterns using all its senses including visual and auditory. It learns to speak using language and it learns to identify people and objects attaching complex concepts from their visual patterns. Pattern identification goes on throughout our lives. Our learning ability depends on how strong is our ability of identifying new useful patterns.

When a child goes to school first it learns new behavioral patterns to adapt to. When you take up a new position in your workplace, you have to acquire new patterns necessary for functioning effectively in the new position. Sometimes you change track in your career and go into a totally new but promising area. How can you be effective unless you learn all the required concept patterns in your new work domain?

A new Sudoku player starts playing Sudoku for the first time and gets excited. Such a beautiful game! He starts with two Easy level Sudoku problems and quickly reaches the solutions. Immediately he takes up two medium level problems. He finds them a little harder but solves them. How does he do that? He discovers new patterns that are useful for reaching the solution. He does it continuously. Proceeding this way, within a week he might solve the hardest Sudoku problem in the world if his pattern identification mechanism and a few other abilities are strong.  

We use the Pattern identification technique all the time involuntarily and many times voluntarily or consciously in our daily life. When we navigate the city streets by car, we try to identify whether the streets are in a two axis grid or a star shaped formation. When we are to find a particular house in a street we see whether the numbers on one side of the street are even or odd, increasing or decreasing.

Problem 1: Can you calculate it?

Find the unit’s digit of 8²³.

Before going through the solution, please try to solve the problem for about 5 to 10 minutes.

Solution: At first thought you might want to use your calculator, but on second thoughts and being a problem solver, you will start analyzing the problem systematically instead. A problem solver adopts trial and error method, if at all, only as a last resort.

What actions are available to you? You know from experience that no calculator will take such a large calculation. Can you do anything else? Initially you are stuck and can’t think of anything.

But being a problem solver, you examine the problem more closely and realize that full calculation was not wanted at all, but the single unit’s digit was wanted. Now only you have a clear and precise problem definition. This step is very important.  You are actually adopting a problem solver’s approach. You are not trying to solve the problem in any random way.

Now you are more hopeful and think of any other action than actual calculation of 8¹⁹. You remember that when no course of action seems to be visible you can always resort to Enumeration. So you start seeing how the unit’s digit of powers of 8 is affected by increasing the power systematically starting from 1 to 2 then to 3 and so on. This you can certainly do.

A golden principle: what you can do, just do it.

You do the power of 8 calculations starting with power 1 and find that the unit’s digits of 8¹=8, 8²=64, 8³=512, 8⁴=4096, 8⁵=32768, 8⁶=262144, 8⁷=2097152, and 8⁸=16777216 are 8 4 2 6 8 4 2 6.

Do you see anything peculiar in the unit’s digits of the eight calculations? You are surprised to find every 4^th power the unit’s digit repeats in a cycle of 8, 4, 2, and 6. This is the crucial pattern that you have discovered by the use of Pattern identification and recognition principle and Enumeration technique.

Next you apply the Induction principle. Induction principle is taught at school level and not new to you.

As this pattern holds good every 4^th power, it will continue to hold good for every integer power of 8. The power of 23 falls in the 4x5 + 3, that is, in 3^rd place of the cycle and so we will have unit’s digit as 2.

To summarize:

    First you have analyze and find that calculation is not at all possible-the number would be too large. But you also identify that full calculation is not asked for; only the unit’s digit is wanted. Thus you precisely define the problem.

    You think now what course of action is available to you. At least you can start calculating the powers of 8 starting with power 1 and increasing the power one by one. That is enumeration (or prototyping). When no course of action is available, you do enumeration.

    As you can do this, you just do it. You know this golden principle and immediately set out to apply it.

    After a while, you discover the key pattern of unit’s digit 8, 4, 2 and 6 repeating every 4^th power of 8.

    Now you know you are very near to the solution and use the induction principle: as this pattern has repeated every 4^th power for eight numbers of powers (two cycles), it must repeat for all powers of 8.

    Finally, you arrive at the solution: power 23 being 5 full cycles plus 3^rd step of the sixth cycle, the unit’s digit would be the 3^rd number in the cycle 8, 4, 2 and 6, that is, 2.

Pattern matching and corresponding decision making is at the heart of human decision making. In most situations, this process is involuntary, but in many cases, we may be able to reach a just solution by explicitly searching for a pattern in the given problem world.

Most experts work on pattern identification basis and most emergent decision making are basically pattern based and thus intuitive and instantaneous. By working on your pattern identification abilities it should be possible to improve its power and correspondingly your ability to solve real life problems.
 

Read my other blogs on Innovative idea generation and its basic principles and Get smart, get innovative usingTRIZ

Learn problem solving by actually solving a problem

To know how to solve problems, you need to actually solve problems

Learning basics

Just as you can’t learn swimming by reading about swimming, you can’t become a problem solver just by reading books or attending lectures on problem solving. You have to actually solve problems and analyze the problem solving experience for learning to solve further.

It might be that you intend to learn real life problem solving but can’t think of any significant real life problem that you may solve. Learning mathematics or any other subject is much easier! Isn’t it? There are too many problem exercises available in the books for you to solve in a lifetime.

One way to get around this problem is to solve artificial problems that are carefully designed for exercising your general problem solving abilities such as deductive reasoning, problem breakdown, analysis, evaluation criteria formulation, pattern identification and recognition, abstraction, innovation and so on. Once you solve such a problem and analyze the process of your problem solving, you are on the path of assimilating the principles, concepts, techniques and approaches of real life problem solving. This enables you to test your skills as a real life problem solver when you confront such a problem as a DA or a problem owner. This practice is to be continuous as will be your growth in abilities. In a short span of time it is possible for you to be able to confront a problem not in a random manner but with confidence being equipped with new resources for systematically tackling any kind of problem that may come.

It doesn’t mean you will become an expert problem solver in no time, it only means your approach towards problem solving will change from random or heuristic to systematic and analytical which will further result in improved quality of the solutions you will reach.

To be able to acquire problem solver’s abilities you have to solve specially designed problems (and real life problems if you get them) and through the process of solving the problems will acquire what I call the Problem Solving Armory (PSA) resources.

Problem Solving Armory resources

Our Mental Problem Solving Framework (or MPSF) uses a suitable set of Problem Solving Armory (or PSA) resources to solve a particular problem that we face at any point of time. The PSA resources may consist of collections of:

·         Basic problem solving principles: these are abstract principles effective in many problem solving situations. You have been exposed to a few. List of such principles is open-ended and personal. You can form your own set of basic principles that you found effective in solving your problems.

·         TRIZ 40 principles: this is a set of 40 inventive principles primarily meant to be used for generating innovative solutions systematically. These are part of TRIZ, a large system for systematic innovation.

·         Problem Solving Techniques: these are different from principles, as each of these techniques gives you a mechanism for dealing with a particular type of problem situation. A technique is not a principle and consists of steps and processes. Examples are: deductive reasoning, problem breakdown, key information discovery, find the troubleshooter, find the champion, find the expert, pattern identification, enumeration, prototyping and so on. There are many and these are not difficult to understand. Knowing a set of these powerful techniques will automatically increase your problem solving ability.

·         Problem solving tools: these are not the same as techniques. For example, computer spreadsheet software is a powerful tool for making the life of a problem solver more comfortable. Further examples are: Venn diagram, Set theory, Sudoku, Alert mechanisms, Graph theory and so on. Working knowledge of such tools automatically increases problem solving ability.

·         Problem solving methodologies: over time many approaches or systems have been created for problem solving by groups of people working in different domains. All are valuable, generally without conflict with each other and practiced by specific groups of practitioners. When we can learn good things from every domain, why should we limit our learning in only one domain? Methodologies are generally large and complex to understand and apply. Examples are: TRIZ, AHP, lateral thinking, brain storming, Synectics and so on.

·         Problem solver’s skills: if we can identify the required skills, we may improve a set of such more important skill of problem solving through prescribed or our own methods. Some of the skills are: Definition, Prioritization, Abstraction, Analysis, Reasoning, Information discovery, Pattern identification, Innovation and so on.

·         Problem solving approaches: these are the most important components of the all-important PSA. By analyzing the problem at hand, MPSF selects a suitable approach and only then proceeds to go further. Approaches are most important.

If you thought or if I had told you that overnight you may become a problem solver, you thought wrong. It takes a lifetime to become a problem solver. On the other hand it is also possible to start walking the path of a problem solver anytime. More than an innovator, you need to become a self-aware problem solver. 

If you solve well-designed artificial problems, analyzing the process, principles, techniques, methods and approaches used in solving the problems you gradually incorporate these in your mental problem solving framework (or MPSF). This in turn will enable you to apply these when you face a real life problem. Unless you had learned the special approaches and techniques that you have used effectively in solving the academic but well-designed problems, you may still have approached a real life problem solving in a random manner, without any finesse.

These specially designed problems are formulated specifically to bring out one or more than one technique or principle valuable for solving real life problems also.

As a first step we will solve one such problem and analyze our learning.

Four square problem

 

Now you have to answer 4 questions about this square. You will have to be ready and think quickly. Okay?

Question 1: Divide the light grey unshaded area of square A into two equal pieces.

Take a pause and think.

Got the answer? Fine. It’s easy, isn’t it?

Just draw a diagonal line from top right corner of the inner shaded square to the upper right corner of the enveloping square.

Get ready for the second question.

Question 2: Divide the light grey unshaded area of square B into three equal pieces.

Still easier? Should be.