A problem solver's approach to take you to the goal quickly
Many of us had to face the proverbial needle in the haystack situation sometime or other. A few of the more innovative ones among us might have burned out the haystack and somehow found the needle from the ashes, or a few others might have tried to use a powerful magnet to swiftly get the needle out of its cozy home, but be sure we are not here to suggest you such a sure-shot solution for this problem.
We would first have a look at the real haystack from all angles, ask you some pointed questions regarding the haystack, needle and other things around and then we might suggest you a workable way out. We are definitely cautious in this business of problem solving.
Being realistic, we recognize that in most real life problem situations possible paths to the desired solution may not be too many. In spite of the non-haystack condition, if we approach a problem randomly, either we may not recognize the solution even if we get it or most commonly, we may have to waste inordinate amount of time and effort to reach the solution.
Leaving the usual approach, if we adopt what we call a Problem Solver's Approach, most likely we would reach the solution much quicker and with lots of assurance.
A problem solver's approach is much more than a Problem solving technique in power, scope and use. The one that we are focusing on here is one of the more prominent ones among these special approaches. We call it as End State Analysis Approach and recognize that knowingly or unknowingly, many people have used and would use this approach for their successful real life problem solving.
Genrich Altshuller, father of TRIZ, a powerful and systematic innovation system, introduced perhaps for the first time a similar concept in Initial Final Result or IFR. Later we find, McKinsey, a leading consulting firm, using a similar method for solving complex business problems of their customers. We understand, this approach can be used in any suitable real life problem situation, be it in innovation creation, or in business environment, or in academic area or even in solving personal affective problems.
Journey is more important than the destination
We have encountered this piece of wisdom often, but we really could appreciate its value when we used a systematic problem solving technique or approach for solving a tricky real life problem.
A problem solving approach would devote more attention to the evaluation of alternative paths or methods to reach the solution rather than focus only reaching the solution by any means. This way a problem solving approach is more methodical and tend to select the right path to the solution quicker and with more assurance.
If we select the right path, getting to the solution is automatic and assured.
Problem solving by End State Analysis Approach - a case example
You have to move just two matchsticks and reuse these to transform the figure to four equal squares.
You may spend maximum half an hour’s time to solve the problem. This is a matchstick world and many interesting problem puzzles are available that would challenge your problem solving capability. But we are not here to know the solution, rather our objective is to know how best to reach the solution. Our focus is not on the solution but on the process of arriving at the solution.
Okay, let us take a break here leaving you to solve the problem yourself. Please devote the suggested time to solve the problem. Unless the problem is tried, you won't be able to appreciate the value of the powerful approach we are going to explain. This is not a very hard problem, and you may easily be able to solve the problem. There is no harm in giving it a shot.
Problem Solution with reasoning
Usual approach is random trial and error that takes a lot of time and may not be successful. Moreover, if you get the solution this way, you won’t remember how you reached the solution – in short, you cannot reuse the experience of solving the problem.
Then what is the systematic method to solve the problem?
The approach is to form an idea of the final solution at the initial stage itself and use it intelligently.
To form this Initial Final Solution, we need to analyze the problem first. By initial analysis we conclude:
In the final solution no matchstick can be shared between two squares.
This is the key discovery and binding condition. The reason is - we have exactly 16 matchsticks and four squares can be formed by these 16 matchsticks, but with no single matchstick shared between any two squares. The squares thus cannot have any common side. Each shared side would reduce the number of matchstick required by 1.
We draw such a possible figure shown below right. This is a possible final solution.
At the next step we will examine this possible solution for suitability. How do we do that? Why did we keep the original figure on the left?
The reason why we kept the original configuration of five squares is: we want to compare the new figure with the original one. The new configuration is no doubt a possible final solution, but we need to judge whether it is the final one. To do this, what do we need to know?
We need to know how much similarity or commonality in structure the figures have. If the new figure has a large portion of the structure common to the original one, changes needed to arrive at the new figure from the old will be that much less.
So, by this logic we can conclude that among all the possible final solutions, the ideal final solution will have maximum portion of its structure common to the original configuration. As these figures are pictorial, we can judge commonality by visual inspection only. It should not be a difficult process. The first trial is found to be not a very encouraging one. Let us then see the second possible final configuration.
Still the commonality is not very encouraging. Only two squares are in common position with respect to the problem configuration, and we need to move and reuse many more matchsticks than two required by the problem. Let us try a third possibility.
Well this is an interesting structure. It has four independent squares utilizing all 16 sticks but also has a lot of commonality with the original structure. Let us assume it as the probable final solution and start trying to transform the original.
We see that three squares are exactly same in both the configurations. We then need to destroy two squares in the original and create a new one as the blue dotted square in the new configuration.
Two sides of a square in the new structure already exist. So we just have to move in two more sides and the new square will come to life. Moving two sticks with arrow points will do just that fine. We thus have our final solution.
This method is not only easy and systematic to apply, it can also be used for solving practically all problems involving matchsticks. For totally new matchstick problems, the insight gained from this approach may be used for modifying the method for the new problem.
Matchstick world is an academic artificial world. But in solving real world problems also this powerful problem solving approach is equally effective.
Step by step elaboration of initial final solution based problem solving approach:
Step 1: Analyze the problem and identify the special characteristics of the problem. In our case, this is
In a four square configuration, no two adjacent squares to share a stick, two squares to be destroyed and one new square to be created.
Step 2: With the knowledge gained in the first step, create as many possible final solutions as you can and test each with our problem condition or criteria. In our case the criterion of comparison is:
To identify the possible final solution satisfying the conditions in Step 1 and also having maximum commonality in structure with original configuration.
Identify a target solution. This is your Initial Final solution.
Step 3: Now examine this final solution with respect to your problem criteria and goals, analyze and identify the steps to reach the goal. In our case we identify the three common squares, the two squares that are to be destroyed and the one new square to be created and finally identify the two sticks to be moved and the place where these are to be moved.
Step 4: Implement the solution and check again to see that the solution satisfies all conditions and is indeed your target solution. In our case we actually move the two sticks to reach the final solution.
It is interesting to note that this approach, though sounds simple is powerful enough to be applied in many problem situations. This of course has to be applied with all techniques, tools and larger methodology that are at your disposal and you find suitable for your problem at hand.
In this case we have used the End State Analysis Approach with Initial Final Solution technique and also Pattern identification technique.