Puzzles - Correlation to Problem

¶ … Puzzles - correlation to problem context

Problems contexts as social constructs

Problem analysis deems a software application to be a sort of software machine. A software development plan tries to change the problem context by producing a software machine and making it an addition to the problem context, where it will result in specific desired effects.

The specific portion of the problem context that is of attention in correlation with a particular problem -- the particular segment of the problem context that shapes the circumstance of the problem -- is named the application domain. Subsequent to the software development project has been completed, and the software machine has been placed in into the problem context, the problem context will include both the application domain and the machine (Jackson, 2005).

The problem context includes the machine and the application domain. The machine interface is where the Machine and the application domain convene and interrelate. The starting point will be to explore, in a little detail, what might be meant by the idea of a problem, especially as this is used in Systems Analysis. This discussion is based on the views of Dardenne, et al. (2004) who distinguishes clearly between problems and messes. This idea can be extended to three points on a spectrum: puzzles, problems and messes, each being intended to depict a different way in which people use the word "problem." These, however, are not the only ways - they serve as archetypes on the spectrum of possible uses.

Puzzles

In these terms, a "puzzle" is a set of circumstances in which there is no ambiguity whatsoever once some thought has been given to what is happening or needs to be done. The issues that need to be faced are entirely clear, the range of options is completely known and there exists a single correct solution to the puzzle. Thus, in the terms to be used later, the puzzle is fully structured, and it is possible to be sure that a solution to the puzzle is correct once it has been found (Galliers, 2010). The term "puzzle" is used here because common parlance refers to crossword puzzles and jigsaw puzzles.

These are exercises with well- understood structures and, usually, a single correct solution. This contrasts with open-ended tasks in which many different approaches are possible. There may be various ways to attack a crossword puzzle, but the definition of the puzzle is complete and there should only be a single correct solution. The same is true of a jigsaw puzzle; some people start with the edges, some start in the centre and others start with the corners - but there is only a single correct solution (Chan, et al. 2006). With this in mind, people who have studied mathematics will recognize that when they were told to ?complete all the problems on page 42? Or to ?have a go at this problem sheet?, they were being asked to engage in a puzzle-solving activity.

The idea is to give practice in the use of particular methods and to help students to generalize their use. If their maths is less than perfect, such students may find themselves turning to the back pages of the textbook in the hope of finding the answers. They are likely to be upset (and confused!) if those model solutions turn out to be wrong, as sometimes they do. Why should they be upset? There seem to be two reasons for this.

The first is due to their inevitable disappointment after putting in a lot of hard work. The second is that we expect puzzles to have a single correct solution and if the 'solution' offered turns out to be wrong, then this can cause great frustration. Most of us can often learn quite a lot by trying to work back from the given answer, if it is correct, to the question. Indeed, this is one of the strategies suggested by Walsham, (2005) in his book on problem-solving in mathematics and also by Bleistein, et al. (2004). Although the nature of puzzles is simple, they are not always simple to solve. Sometimes they are, but setters of exam papers are quick to learn how to devise puzzles that will stretch their students, whether these are first-graders or postgraduates.

So puzzles are not necessarily easy, but they are solvable and the correctness of the solution can be demonstrated (Chan, et al. 2006). There may even be several different ways to get from the puzzle as presented to the correct solution. I well recall, at the age of 12, taking a geometry exam in school and being faced with the need to prove a small theorem and being totally unable to recall how to do it. In a panic I invoked a theorem that I could prove, and tried (unsuccessfully) to get to the result that I needed. Needless to say, my exam performance that day was not good. However, the maths teacher took me on one side and asked how I'd thought of tackling the puzzle the way that I had. At the age of 12 all I could do was blush, mumble and apologize.

(Galliers, 2010).

Problems

A problem is more complicated than a puzzle, but less complicated than a mess. This complication stems from the fact that a problem has no single answer that is definitely known to be correct. At the heart of a problem is an issue that must be tackled. As they arise in real-world Management Science, an analyst is more likely to face a problem than a puzzle. An example might be, ?How many depots do we need in order to provide daily replenishment of stocks at all our supermarkets?

As a question, this seems straightforward enough and is relatively unambiguous; however, this is just the tip of the iceberg. Such a question, based on an important issue, rarely has a single correct solution, for problems, in the way that the term is used here, there may be agreement about the core issue to be tackled but there might turn out to be several, equally valid, solutions. Consider again the issue of the number of depots needed to service a set of supermarkets. One way of construing this issue might be to reformulate it as something like the following: assuming that the depots stay at their current size and the supermarkets do the same, how many depots would we need to meet current demand and to guarantee delivery to each of the stores within an agreed 30-minute time window each day?

Once formulated in this, much tighter, way there may indeed be only a single correct solution (Chan, et al. 2006).

But to achieve this, a problem, with its core issue, has been transformed (some would say reduced) to the form of a puzzle. To illustrate this point yet further, an alternative formulation of the problem might be something like: Assuming that the supermarkets and depots stay at their current sizes and are grouped into regions as now, how many depots would be needed to meet current demand in each region and to guarantee delivery to each of the stores within an agreed 30-minute time window?

Needless to say, the second formulation may produce a solution different from the first one (Dardenne. et al. 2004). There is a further reason why problems, as defined here, may lead to a range of solutions that are all acceptable, and this is to do with the approaches taken in working toward a solution. As an example, consider the type of case exercises, often known as Harvard-type cases, with which most business administration students are familiar. When used for teaching, the normal mode of use is to distribute copies of a case to the class in advance of a discussion session.

The case papers, which may be 20 or more pages long, give background on a company or market, provide extensive data and pose some issues. Later, possibly the following day, the class will assemble and, under the guidance of an instructor, students will propose approaches and solutions (Galliers, 2010). Clearly, given a range of suggested approaches, some of them will be wrong, but more than one may be plausible. There are likely to be several possible approaches, each of which may be used in sensible attempts to tackle the core issues of the case. Even when people are agreed about how to construe the basic issues, they may employ different approaches in an attempt to solve the problem. This may be due to their backgrounds, to their expertise or whatever. But there may be no real way of declaring one solution to be superior to all others, even after the removal of those that are obviously wrong (Chan, et al. 2006). This is why the case method is a good way of encouraging discussion in a class of bright students. It is also the reason why the case method of teaching business administration is preferred by some teachers who do not regard management as a generalizable science (Jackson, 2005).