Lecture 19: Problem Solving

Question 1

Mental Operators

Answer 1

Applied to the initial state, get to a new state, apply more operators, and so on searching for the goal state

Question 2

Well structured

Answer 2

stages are well defined (math)
○ You know what the initial state, goal state, and mental operators are

Question 3

Ill Structured

Answer 3

stages are not clear (choosing a career)

Question 4

Stages in Problems, Solving

Answer 4

○ Representing the problem
§ Very important, using graphs may make a problem easier or harder
○ Planning the problem
○ Executing the plan
○ Checking if it work
○ Retrying if needed

Question 5

Buddhist Monk Example

Answer 5

• Monk travels up a mountain, a few days later travels back down, is there a spot on the mountain the monk will be at on the same spot as another monk at the same time?
  ○ Easier to solve with a visual representation; of course the monks will cross paths
  
  • Useful to retrieve a similar representation of the problem you are solving

Question 6

Ray Problem

Answer 6

Figure out how to apply radiation to a tumor; the solution is to shoot weak waves in many directions that all converge
* Same thing works in a military problem, but it is hard to find the analogy between the two and solve one problem after the other
* It helps to give a hint to connect the problem; people can use relevant analogies but often fail to notice them

Question 7

Top-Down Preconceptions

Answer 7

What you already know can sometimes hinder problem solving

Question 8

Functional Fixedness

Answer 8

People assume the function of some object is fixed

* In the candle problem you have a tack, candle, and tack box, and most people don’t consider using the tack box because it is a box not a support
* Same thing in the two-rope problem, people do not think about tying the pair of pliers to one of the ropes

Question 9

Trains meeting problem

Answer 9

This bird flies back and forth between two trains driving towards each other. People well versed in calculus tried to solve using that but there is a much easier way to solve it

Question 10

Luchin’s Water Jar Problem

Answer 10

People solve a task where you have to fill up bottles of water and get a specific quantity by filling it up and pouring out etc. and if you solve 5 or 6 problems in a row using the same sequence then people will stick with that strategy when it no longer applies, this is them being stuck in a mental set

Question 11

Algorithms

Answer 11

The way you might program a computer; a sequence of steps that is guaranteed to produce a correct answer but requires a lot of way
* Unscrambling a word, guessing a password

Question 12

Heuristics

Answer 12

Shortcuts that are not guaranteed but are fast and easy

Question 13

Difference Reduction Heuristic

Answer 13

The idea of choosing the mental operator; if you have a lot you choose the one that reduces the difference the most between the goal and initial state
* Does not always work; sometimes we have to take a step back

Question 14

Chess study

Answer 14

Expertise is pretty domain specific; being good at chess does not mean they are smart
* Experts are better at remembering chess boards that make sense, where novices are better at the opposite

Question 14

Means-End Analysis Heuristic

Answer 14

Analyze the end and see what means may allow you to achieve that end
- Identify biggest difference between initial and goal state
- Do operator subgoaling; find the operator that will reduce the difference and satisfy the preconditions
- Flight, plan, airport, money, ticket, etc.

Question 15

Hobbits and Orcs

Answer 15

3 hobbits and 3 orcs on one side of a river and one boat; get them to the other side but the orcs cant outnumber the hobits, What is the correct sequence of getting everyone across the river
* The solution looks like an early state, and many people give up at that point thinking they are not making progress when they in fact are.

Question 16

Power Law

Answer 16

You improve very rapidly initially, then it slows down

Question 16

Experts vs. Novices

Answer 16

• Experts tend to have rich, organized schemas and use very specific representations, novices don’t
• Experts use less heuristics
  Experts rely a lot of long-term memory and novices rely on working memory