Problem Solving And Solutions

Written By: Vasanthan Senguttuvan

1. Problem

A problem is directly related to the actor who finds the obstacles to reach the goals. Those obstacles are called problem(s). To reach the goal it should be finite. Based on the perspective of the actor a problem can be broken into subproblems. Note the word 'broken'. Just like materials some could be joined and some cannot. i.e, some problems when broken can never be joined as exactly as it is but few can be joined to produce the exact result. The problem or the obstacles are based on the perspective of the actor only.

To simplify the understanding a problem has a source or the current state and a destination or the end state. The solutions move the actor from the source state to the destination state. The destination is generally called as the goal.

1.1 Well-defined Problems

A well-defined problem will have a single point source and single point destination. In other words the route to the problem is a straight line. Irrespective of the path the goal never changes. e.g. Traveling to a new place from home. Its a problem of finding the path to the new place from home. This is a well defined problem because the solution should make the actor to be in the destination when completed.

1.2 Blurred Problems

A blurred problem will have a single point source and the path that extents towards the destination, but the destination is not known. i.e., most often the point where the actor exhausts will be considered as the destination. Simply speaking the destination is considered to be place other than source. e.g. A man's wish to eat tasty food. Its a blurred problem, because there is no destination, but only the direction is known. In this example the actor could decide that if the food is tasty then the solution is in forward direction, if not its in the reverse direction. Once the man is finds something that is tastiest then the man finalize it as the destination which is not know at the initial stage.

1.3 Adaptive Problems

An adaptive problem has single point of source and multiple destinations. Each destination put forth a new destination, without going back to the source. These kinds of problems are derivative of well-defined problem and blurred problems. e.g. A famous story will explain this type of problem¹. Once a swami² came to a village in order to teach morals to the people. He usually take pity on humans and animals (a well-defined problem). Since the people of the village wanted to help the swami, they gifted him a cow (a blurred problem, they wanted to help but don't know how). Since the swami could not take care of the cow properly (because of well-defined problem+blurred problem) he requested the villagers a housemaid. Because of the problems from the society over the housemaid, swami married the girl and the story goes on. Since swami is married he was no longer respected by people. Here swami faced the problem of loosing his status which came by adaptive nature. i.e., the well-defined problem directed the blurred-problem to give an adaptive problem.

2. Non Problems

A goal less operations are not called as problems or either solutions. Since this can happen only by the actor, they cannot be reproduced by another actor. Two problems that can be solved need not to have a single solution when the two problems are combined. Since the solution for a problem is considered to be a straight line. If the problems are in orthogonal in nature the two straight lines (solutions) may not be in the same plane. Explaining this would take long time, unless the following sections are not read.

3. Problem of Problems

This document focus on how to solve a problem. For clarification this section will take only the well-defined problem for the reference.

Consider an actor who can do addition and subtraction. Now the actor was given with numbers 2 and 3 and is requested to give 5 as the output. The solution is addition of 2 and 3 gives the result 5. No matter what the actor can do, the solution is: addition of 2 and 3. In simple terms the solution has the finite and minimal set of actions performed by the actor in order to achieve the goal. With respect to actor if the actor cannot produce the output by the lack of operations then the problem is not solvable by the actor.

If the actor can achieve the goals in 'n' ways, the solution is the smallest subset compared to other ways. Now the problem has to be broken into subproblems. Each subproblems are then broken until the actors capability is reached. The actual problem of problem comes the actor can perform an action in large number of ways(ex. typical microprocessor). Since out of large number of possible action finding the smallest subset of actions that solve the problem is difficult. If the actions are grouped, then the possibility of assembling the solutions are less, which is easier for humans to handle with.

4. Solutions and problems

A solution forms a (solvable)problem. A solution represents the set of actions performed by the actor to achieve the goal.

To start with all the problems can be viewed as a definite problems. The actor can visualize two points, one which represents the source point of the problem and another point which represent the destination. Once the straight line path is set the action has to be filled up in this straight line. For that there can be any number of ways.

a. from the source the actor's actions can be arranged

b. from the destination the actor's actions can be guessed back

c. from some middle point the actions can be guessed back and forth

d. start with few set of middle points and try to join them with other middle points or the endpoints

Grouping actions

In a solution there may be repeated action from the actor. These contiguous actions that are repeated can be grouped together, in order to optimize the solution. The grouping will not directly affect the solution but the actor.

To be continued...

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