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CORE11-114 Knowledge Society

CORE11-114 Knowledge Society. Week 12 Lecture. Problem Solving. Overview. Education is not just about learning lots of different material and content, passing exams and assignments A problem is a question that cannot be answered immediately

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CORE11-114 Knowledge Society

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  1. CORE11-114 Knowledge Society Week 12 Lecture

  2. Problem Solving

  3. Overview • Education is not just about learning lots of different material and content, passing exams and assignments • A problem is a question that cannot be answered immediately • Problems are often open-ended, paradoxical, and sometimes unsolvable, and often require investigation • An exercise, however, tests a student's mastery of a narrowly focussed technique, that has usually been covered in the subject content

  4. Problem Solving • The art and science of problem solving is often considered the most complex of all intellectual activities • Problem solving occurs when an agent (a human being or artificial intelligence) moves from a given state (the problem description) to a desired goal state (i.e., a solution or set of solutions) • Problem solving requires the use of inferencing techniques

  5. Problem Solving • Consider:

  6. Problem 1 (cont) • An ancient puzzle • The objective of the puzzle is to move the entire stack to another rod • The rules of the game are: 1. One disk may be moved at a time 2. Each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod 3. No disk may be placed on top of a smaller disk • Try it for yourself!

  7. Problem 1 (cont) • Known as the “Towers of Hanoi” • A problem rather than an exercise • Not immediately obvious how to move from the problem state to the goal state • The important part of problem solving is coming across the solution technique

  8. How did you solve it? • Problem solving processes differ across knowledge domains and across levels of expertise • Many equally valid ways of deriving a solution to a particular problem • As many solutions techniques exist as there are problems!

  9. How did you solve it? (cont) • Divide and Conquer • Break down a large complex problem into smaller problems • As the sub problems are small, they should be easier to solve • Often practised in science • Trial and error • A common, naïve strategy • Alternative solutions are progressively trialled until a successful one is found

  10. How did you solve it? (cont) • Brainstorming • Talking over the problem with friends and colleagues until a mutually acceptable solution is reached • Research • Study what others have done • Maybe this problem has been solved before? • “Don't re-invent the wheel” • Analogy • Asks the question, has this problem been solved before, maybe in a different field?

  11. How did you solve it? (cont) • Reduction • Changing the problem into another problem that has already been solved • Incubation • Relying on the sub-conscience to solve the problem • Looking at the problem initially and understanding its scope … • … then stop focussing on it and think about something else • The solution, or strategy, will hopefully “pop” into your head • More common and more successful than you may think

  12. How did you solve it? (cont) • Outside help • Ask friends or online communities to help you solve the problem • Delegation • Get somebody to solve the problem for you • Very common approach, particularly in hierarchically oriented organisations • The WWXXD Method • Short for “What would XX Do?” • Think about the problem in the way another person would approach it • E.g., WWCND (“What would Chuck Norris Do?”) requires thinking like Chuck Norris • Couple of major drawbacks: • how can you really know how somebody else thinks • who would you choose?

  13. How did you solve it? (cont) • Edward de Bono's “Six Thinking Hats” • Instead of trying to think along many directions simultaneously, a thinker should think of one thing at a time • One of the problems in problem solving (according to de Bono) is that we try to do too much at once • Emotions, information, logic, hope and creativity all crowd the thinker's thoughts • Like trying to juggle with too many balls …

  14. How did you solve it? (cont) • Algorithmic approach • An algorithm (or procedure) is simply a set of steps that are performed in sequence that will solve a problem • Like a recipe • The algorithmist can take a problem and “slice” it in to a number of small, precisely defined, steps • As the steps are precisely defined, they can be automated (i.e., performed on a computer) • Thus, algorithms are pre-cursors to programs • Graphical Approach • Draw the problem! • The mind seems to work much better with pictures than it does words and numbers • Helps you to understand the problem, and thus will help to come up with the strategy • Did you use this for the Towers of Hanoi?

  15. How did you solve it? (cont) • There are many approaches that you can try • These will vary according to the nature of the problem and what one is comfortable in doing • Often hybrid approaches (combining two or more techniques) are also possible

  16. Problem 2 “A man has to take a wolf, a goat and a cabbage across a river. His rowboat has enough room for the man plus the wolf or the goat or the cabbage. If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the man is present are the goat and the cabbage safe from their enemies. How should the man carry the wolf, goat and cabbage across the river?” This is a problem from AD 732, and is still being used today! Solve it!

  17. Information? When a young man paid the cashier for his breakfast, she noticed that he had drawn a triangle on the back of the receipt. Underneath the triangle he had written 13 × 2 = 26. The cashier smiled. “I see you are a sailor” she said. How did the cashier know that he was a sailor?

  18. Problem Solving Guidelines • There are no “instant” recipes to be able to solve new and novel problem • Guideline 1: • Always keep in mind “Occam’s Razor”: • “when you have two competing theories that make exactly the same predictions, the simpler one is the better.” • The simplest solution is nearly always the best. • The solution must still account for all the aspects of the problem

  19. Problem Solving Guidelines (cont) • Guideline 2: • The following rules are from “Puzzle-based learning: Introduction to critical thinking, mathematics, and problem solving” by ZbigniewMichalewicz and Matthew Michalewicz: • Rule 1: Be sure you understand the problem, and all the basic terms and expressions used to define it • Rule 2: Do not rely on your intuition too much; solid calculations are far more reliable • Rule 3: Solid calculations and reasoning are more meaningful when you build a model of the problem by defining its variables, constraints, and objectives

  20. Problem Solving Guidelines (cont) • Guideline 1: (cont) • A couple of refinements on Occam’s Razor are: • “Simplicity is the ultimate sophistication.” Leonardo da Vinci • “Make everything as simple as possible, but not simpler.” Albert Einstein

  21. A Model ... • A model is a representation of the problem, not the problem itself • Models, necessarily leave things out of the problem, otherwise the problem itself maybe too complex and unwieldy • A framework by which we can solve the problem, proceeding thus: Problem Model Solution

  22. Problem 4 (From Zbigniew and Zbigniew) There are three cards in a bag. The first card has the symbol X written on both sides, the second has the symbol O written on both sides, and the third card has an X on one side and an O on the other. You draw out one card at random and examine one side of this card. You see an X. What is the probability that there is also an X on the other side?

  23. Decision Making and Problem Solving in Organisations • Individuals, groups and organisations can make decisions from based on information • Five stages can be used: • Intelligence gathering stage • Identify potential problems and opportunities • Define the cause and the scope of the problem • Decision stage • Design alternative solutions to the problem • How feasible is each of these? • Choice stage • Take one of the alternatives

  24. Decision Making and Problem Solving in Organisations • Five stages can be used: (cont) • Implementation stage • Put the action into effect • May or may not involve a computerised solution • Monitoring stage • Is the solution effective? • What are the quantitative and qualitative indicators and the results obtained by them? • Should the course of action be altered or even completely changed?

  25. Real World Problem Environments • Are often dynamic, as characteristics and parameters of the problem change while they are being solved • Many conflicting objectives arise, e.g., profitability versus timeliness versus resource utilisation • Problems and projects solved in multi-disciplinary teams, sometimes spanning the globe …

  26. Problem Puzzles • Sudoku • Castle Mouse • General problems and puzzles

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