[MUSIC] So now that we have a general definition of what a problem is let's look at the different categories of problems. In general according to Robertson, there are seven broad categories that problems can fit into. They are knowledge lean problems, knowledge-rich problems, well-defined problems, ill-defined problems, semantically lean problems, semantically rich problems and insight problems. In this lesson we'll look at the first four kinds of problems. And in the next lesson we'll look at the last three kinds of problems. Knowledge-Lean Problems are problems where little prior knowledge is needed to solve them. Examples include thought problems, puzzles, and brain teasers. Prior knowledge can help with these, especially when it comes to developing models or using heuristics, which are general strategies for problem solving. But overall, they do not necessarily require any additional resources. An example of a knowledge-lean problem is the small town haircuts problem based on William Briggs. Jane is travelling around outback Australia and needs a haircut. She arrives at a small town in Queensland and finds only two hair dressers. Everyone in the town gets their hair cut at one or the other. One of the hair dressers has a gorgeous hair cut. The other hair dresser has an ugly hair cut. Neither of the hair dressers cut their own hair. Which hairdresser should Jane go to? The answer to this thought problem is relatively easy. Jane should choose the second hairdresser, the one with the ugly haircut. Why? Because she gets her hair cut by the first hairdresser, who obviously does a bad job. The first hair dresser, who has a gorgeous haircut, must his haircut by the second hair dresser. All of the information needed to answer this problem is given to you in the problem. And this is characteristic of a knowledge name problem. Now we'll look at knowledge-rich problems. These are problems where lots of prior knowledge is usually required. Tasks can be in the form of complex mathematical problems, analytical essay questions, or new scientific hypotheses. These kinds of problems are frequent in academic study and are often used to give students the chance to demonstrate their knowledge of a particular subject area. Because of this, they require you to have specific knowledge in your field. This can be knowing specific vocabulary or formulas or understanding theories and concepts that were taught. Let's have a look at the following example. Discuss the process of becoming an expert in light of Merleau Ponty's theory of phenomenology. As you can see, in this question, if you don't know what Merleau Ponty's theory of phenomenology is or what the process of becoming an expert is, you will be unable to answer the question, regardless of how intelligent you are. Thus, for knowledge rich problems, unless you have specific knowledge in the field or are willing to go off and research for a while, you will not be able to answer them. The third category of problems is well-defined problems. A well defined problem is a problem that does not require analysis or evaluation. All of the information is either explicitly given or can be inferred, they have clear solution paths and goals, and often use basic concepts and formulas. Solving basic math equations, such as the one from our last lesson, find the hypotenuse of a right angle triangle when one side is 10 centimeters and the other side is 8 centimeters is an example. The initial state is clear. Here is a formula that can be applied and the goal is stated explicitly. Furthermore, when it comes to well-defined problems, it is clear when the solution has been found. Another example of a well-defined problem is the Nine-Dot Problem. The Nine-Dot Problem is a great example of how even well-defined problems can be very difficult. In one study, after being given a clue, only 20% of subjects were able to complete it successfully. Grab a piece of paper and see if you can do it. All you need to do is draw nine dots in a three by three grid pattern, like so. And then link all of the nine dots using at most four straight lines without lifting the pen from the paper or retracing any line. Did anyone manage to do it? In Lesson 4.2 we'll have a look at some strategies that might tell us how to solve this problem. But don't skip ahead. Next, we have Ill-Defined Problems. An ill-defined problem cannot be solved using a basic formula or concept. Either the solution path or the goal is undefined or uncertain and needs to be investigated. The solution, when found, may not be obvious and may need to be justified. Ill-defined problems are common throughout life. From a simple problem like fix my computer to something more academic, such as explain how you would advise a local government in an Australian city to address the problem of obesity within their community. In the next lesson, we will look at semantically rich problems, lean problems, and inside problems. [MUSIC]
