1. Kimberley Clow kclow2@uwo.ca http://instruct.uwo.ca/psychology/130
Problem Solving
Kimberley Clow

2. Outline Learning vs. Thinking Stages in Creative Thinking
Preparation
Incubation
Illumination
Verification
Hindrances to Problem Solving
Process of Problem Solving
Methods of Problem Solving
The Brain

3. What is Problem Solving?
A situation in which one is trying to reach a goal
Problem Solving
Finding a means for arriving at a goal
Arises when a goal is blocked and the solution is not obvious

4. Learning vs. Thinking
Learning Curve
Puzzle Box

5. First Trial Exploring Sniffing Grooming Tendency to perform Reaching
Scratching
Reaching with paw
Lever-Pressing
Reward

6. Later Trial Lever-pressing Exploring Grooming Tendency to perform
Reaching
Scratching
Reaching with paw
Sniffing

7. Classic Problem Solving
Archimedes
Is the king’s golden crown pure?
Köhler’s Chimps
How do I get at the banana that is outside my cage and beyond my reach?

8. Insight

9. Stages of Creative Thinking
Preparation
Incubation
Illumination
Verification
Formulating problem & making initial attempts to solve it
Leaving the problem while considering other things
Achieving insight to the problem
Testing and/or carrying out the solution

10. Preparation
Different types of problems need different skills and approaches
Problems in Inducing Structure
Analogy Problems
Problems in Transformation
Cheap Necklace
Problems in Arrangement
Anagrams

11. Problems in Inducing Structure
Suppose you are a doctor faced with a patient who has an inoperable stomach tumour. You have at your disposal rays that can destroy human tissue when directed with sufficient intensity.
How can you use these rays to destroy the tumour without destroying the surrounding healthy tissue?

12. Analogy
A general wishes to capture an enemy fortress. Radiating outward from the fortress are many roads, each mined in such a way that the passing of any large force will cause an explosion. This precludes a full-scale direct attack
How can the general attack the fortress?

13. Using Analogies

14. Problems in Transformation
Cheap Necklace Problem
Make a necklace out of 4 chains. It costs 2 cents to open a link and 3 cents to close a link. Make the necklace without spending more than 15 cents.
Given
Goal

15. Evidence for Incubation

16. Problems in Arrangement
Unscramble: xbo
Heuristic
If 2 consonants and a vowel, vowel probably in the middle
Few words start with x, so put b first
box
Algorithm
Generate all possible letter combinations and find which one(s) is(are) real words
xbo
xob
oxb
obx
bxo
box

17. Try Some Set One Set Two Set Three verba luppi bagler thrize prega
rogena
pleap
viole
Set Three
broin
arancy
chifn
relbawr

18. Evidence for Illumination
Draw through all 9 dots with 4 straight lines, without lifting your pencil.

19. Individual Differences
Remote Associations Test (RAT)
What single word is an associate of these three?
 Results
Correlation between RAT performance and the generation of associates
RAT improves following training in the generation of word associations
RAT is a better predictor of implicit learning than IQ
IQ is a better predictor of intentional learning
High and low RAT scorers deploy their attention in different ways

20. Verification
Water Jug Problem

21. Support the candle on the wall so that it doesn’t drip on the table below

22. Hindrances to Problem Solving
Persistence of Set
Old strategies continue to be used -- even if they are less efficient -- if we fail to perceive that the situation has changed
Functional Fixedness
A tendency to use objects in their customary way
Negative Set
A tendency to solve problems in one particular way, even when a different approach might be more productive
Why are these numbers arranged in this order?
8, 5, 4, 9, 1, 7, 6, 3, 2, 0

23. Looking at the Process Sequence of problem solving
Identify the problem
Represent the problem
Plan the solution
Execute the plan
Evaluate the plan
Evaluate the solution
Characteristics of Problem Solving
Goal Directedness
Sequence of Steps
Cognitive Operations
Subgoal Decomposition

24. Definitions Problem Space Operators Goal
Includes the initial, intermediate and goal states of the problem
Also includes the problem solver’s knowledge at each of these steps
Operators
The set of legal moves that can be performed during problem solving
Goal
Ultimate solution to the problem

25. Methods of Problem Solving
Brute Force Search
explore entire problem space
Hill Climbing
always move toward a better state
Work Backward
start with goal and work back to start
Means-Ends Analysis
combination of hill climbing and working backward

26. The Tower of Hanoi

27. The Problem Space

28. Brute Force Search
Go through all possible states until solution is found
Guaranteed to work (eventually)
Impractical with large problem spaces
Example
A 4-letter word meaning “not smart”
456,976 possible states!

29. Hill Climbing

30. Extreme Hill Climbing Dog cannot stop hill climbing toward bone
needs to back up
by going away from the goal for a bit, it will eventually solve the problem
This is a problem for people too…

31. Get the Orcs and Hobbits to the other side of the river BUT
Can’t have more Orcs than Hobbits anywhere
Boat will only take 2 passengers at a time
Someone must steer the boat
Destination
Initial state O O O H H H
Boat

32. Means-End Analysis Five Steps Set up a goal or subgoal
Look at the difference between the current state and the goal/subgoal state
Look for an operator that will reduce or eliminate the difference
Apply the operator
Apply steps 2 to 4 repeatedly until all goals have been achieved

33. Improving Your Problem Solving
Increase Domain Knowledge
Automate Components
Have a systematic Plan
Draw Inferences
Develop Subgoals
Work Backwards
Search for Contradictions and Relations Among Problems
Use Different Problem Representations
Practice!

34. Back to the Brain
Identified brain regions associated with the mapping process in analogical reasoning
Medial Frontal Cortex
Left Prefrontal Cortex
Left Inferior Parietal Cortex
Solving insight problems involves the right hemisphere

35. For the Logic Lover
Three 5-handed monsters were holding three crystal globes.
Because of the quantum-mechanical peculiarities of their neighbourhood, both monsters and globes come in exactly three sizes:
small, medium, and large.
The medium-sized monster was holding the small globe; the small monster was holding the large globe; and the large monster was holding the medium-sized globe.

36. Because this situation offended their keenly developed sense of symmetry, they proceeded to transfer globes from one monster to another so that each monster would have a globe proportionate to his own size.
Monster etiquette complicated the solution of the problem because it requires:
that only one globe may be transferred at a time
that if a monster is holding two globes, only the larger of the two may be transferred
that a globe may not be transferred to a monster who is holding a larger globe.
By what sequence of transfers could the monsters have solved this problem?

37. Symbol Problem Solve the following problem:
Mary is ten years younger than twice Susan’s age.
Five years from now, Mary will be eight years older than Susan’s age at that time.
How old are Mary and Susan?

38. List Person We know that
1. The person with asthma is in Room 101.
2. Ms. Jones has heart disease.
3. Ms Green is in Room 105.
4. Ms. Smith has tuberculosis.
5. The woman with mononucleosis is in Room 104.
6. Ms. Thomas is in Room 101.
7. Ms. Smith is in Room 102.
8. One of the patients, other than Ms. Anderson, has gall bladder disease.
What disease does Ms. Anderson have, and in what room is she?