Homework #7: Problem-solving

This assignment challenges you to solve a set of three different kinds of problems, to introspect on your problem-solving strategies, and to make connections with problem-solving research literature. The problems are challenging, so allow yourself plenty of time to do this assignment. The assigned article that accompanies this module is Wiley (1998). For this assignment, you will not write a lab report but rather will focus on the discussion questions at the end of each problem as well as on introspective problem-solving logs.Your grade will not depend upon how well (or correctly) you solve the problems but on how completely you approach them, how clearly you describe the processes and outcomes of your problem-solving attempts, and how completely you address the relevant questions posed after each problem (including citing relevant research where possible). For each problem, keep a written log of your problem-solving approach(es), thoughts, sketches, etc. relevant to solving that problem. Turn in the logs along with the rest of your assignment. In the report portion of the assignment, label and address each problem separately (e.g., Problem #1 or Hobbits-and-Orcs) along with its discussion. For each problem, write the discussion as a coherent narrative, not as a list of answers to the discussion questions.

 

Problem #1: The Hobbits-and-Orcs Problem (Greeno, J. G. (1974). Hobbits and Orcs: Acquisition of a sequential concept. Cognitive Psychology, 6, 270-292.)

Three Hobbits and three Orcs arrive at a river bank, and they all wish to cross onto the other side. Fortunately, there is a boat, but unfortunately, the boat can only hold two creatures at one time. Also, there is another problem. Orcs are vicious creatures, and whenever there are more Orcs than Hobbits on one side of the river, the Orcs will immediately attack the Hobbits and eat them up. Consequently, you should be certain that you never leave more Orcs than Hobbits on any river bank. (Note that the Orcs, though vicious, can be trusted to bring the boat back from across the river!). How should the problem of ferrying everyone across the river be solved?

  1. It might be helpful to approach this problem with a concrete representation (e.g., use coins to represent Orcs and Hobbits). Diagram your various moves in your written log.
  2. This problem makes used of the strategy of difference reduction: choosing moves that reduce the distance (or discrepancy) from the current state to the goal state. Each step further reduces the difference. How does the principle of difference reduction apply to solving this problem?
  3. Puzzles can be created when a problem violates the general rule of thumb of difference reduction. That is, sometimes the only way to solve a problem is to temporarily increase the difference between the current state and the goal state rather than reduce it. The Hobbits-and-Orcs problem is one such puzzle. How does it violate difference reduction (not in all its steps, but in at least one step)? Refer to your problem-solving steps. Did you ever have to go backwards (away from the goal of all on the far side of the river)? Discuss how and why the need to violate the difference reduction principle makes the problem harder and the solution less obvious.

Problem #2: Truthtellers and Liars

You are visiting a strange country in which there are just two kinds of people -- truthtellers and liars. Truthtellers always tell the truth and liars always lie. You become lost on the road, so you hail the first two people you meet and say, "Are you truthtellers or liars?" The first person mumbles something you can't hear. The second person says, "He says he is a truthteller. He is a truthteller and so am I." Can you trust the directions that these two may give you?

  1. Discuss how this problem (including strategies for solving it) is related to hypothesis testing (e.g., in research or in social situations). Be specific.
  2. Some people find that setting up a grid (similar to the one in your textbook on p. 396) helps them keep track of the problem possibilities and outcomes. How might such a grid be helpful in this situation?

Problem #3: The Buddhist Monk Problem (Koestler, A. (1964). The act of creation. London: Hutchinson.)

Exactly at sunrise one morning, a Buddhist monk set out to climb a tall mountain. The narrow path was not more than a foot or two wide, and it wound around the mountain to a beautiful, glittering temple at the mountain peak. The monk climbed the path at varying rates of speed. He stopped many times along the way to rest and to eat the fruit he carried with him. He reached the temple just before sunset. At the temple, he fasted and meditated for several days. Then he began his journey back along the same path, starting at sunrise and walking, as before, at variable speeds with many stops along the way. However, his average speed going down the hill was greater than his average climbing speed. Prove that there must be a spot along the path that the monk will pass on both trips at exactly the same time of day.

  1. For this problem, first identify (describe) in your own words, the goal of the problem (i.e., what are you supposed to do?).
  2. Next, identify (list) all the information in the story that is relevant to solving the problem. Then, list all the information that is irrelevant.
  3. Now, attempt to solve the problem. Keep a record of your approaches, attempts, etc.
  4. This problem is a good example of the importance of correct representation of the initial problem. It also exemplifies how mental set can block problem-solving. Explain how mental set might make a correct representation of this problem difficult for readers (including you).
  5. Discuss some practical implications of the findings of the Wiley (1998) article for solving the monk problem.
  6. Now, go beyond this problem and discuss some specific applications of Wiley's results that are relevant to your own career field. Be creative and flexible here when thinking about examples of the disadvantage of expert knowledge for creative problem-solving.