Problem Solving
A.P. Psychology - Chapter 8
• Can you solve the following problems:
• In the Thompson family there are five brothers, and each
brother has one sister. If you count Mrs. Thompson, how
many females are in the Thompson family.
• Fifteen percent of the people in Topeka have unlisted
telephone numbers. You select 200 names at random from
the Topeka phone book. How many of these can you
expect to have unlisted phone numbers?
Answers to the Questions
• #1  There are 2 females ~ Mrs.
Thompson & her one daughter, who is the
sister to each of her brothers.
• #2  None ~ you won’t find any unlisted
phone numbers in the phone book.
Types of Problems
• Problems of Inducing Structure
• Require people to discover the relations between
numbers, words, symbols or ideas
» Analogy problems
» Series completion problems
• Problems of Arrangement
• Require people to arrange the parts of a problem in a way that
satisfies some criterion – usually there are many ways, but only
a few form a solution
• Problems of Transformation
• Require people to carry out a sequence of transformations in
order to reach a specific goal
Problems of Inducing Structure
• What word completes
the analogy?
– Merchant: Sell ::
Customer : ________
– Lawyer : Client ::
Doctor : __________
• What number or letter
completes each
series?
– 1 2 8 3 4 6 5 6 __
– A B M C D M __
Problems of Arrangement
• The String Problem
• Two strings have from the ceiling but are too far apart to allow a
person to hold one and walk to the other. On the table are a book of
matches, a screwdriver, a few pieces of cotton. How could the
strings be tied together?
• Insight
• Sudden discovery of the correct solution following incorrect attempts
based primarily on trial & error
• Often helps to solve Arrangement Problems
Problems of Transformation
Barriers to Effective Problem Solving
• Irrelevant Information
– Many problems include
information that is irrelevant to
solving the problem
– Leads people astray
• Functional Fixedness
– The tendency to perceive an
item only in terms of its most
common use
• Ex. In the string problem,
people see a screwdriver in
terms of its most common use,
not as a possible weight.
• Mental Set
– Exists when people persist
in using problem-solving
strategies that have worked
in the past
• Unnecessary Constraints
Approaches to Problem Solving
• Working Backward
• Search for Analogies
• Forming Sub-goals
– Use intermediate steps
• Change Representation of the Problem
– Change how you see the problem
• Algorithms
– Methodical, step-by-step procedure for trying all possible
alternatives in searching for a solution
– Ex. Anagram IHCRA – you would list out all the possible arrangements of
the letters
• Heuristics
– A guiding principle or “rule of thumb” used in solving problems or
making decisions
Try some more problems
The Tower of Hanoi – move rings from peg A to peg C. You can only move the top ring
on a peg and you can’t place a larger ring above a smaller one
Try some more problems
• The water lilies on the surface of a small pond
double in area every 24 hours. From the time
the first water lily appears until the pond is
completely covered takes 60 days. On what day
is half of the pond covered with lilies?
• A teacher had 23 pupils in his class. All but 7
went on a museum trip and thus were away for
the day. How many students remained in class
that day?
Decision Making
• Evaluating alternatives & making choices
among those alternatives
• Herbert Simon
– Theory of Bounded Rationality
• People tend to use simple strategies & focus only
on a few facets of available options resulting in
“irrational” decisions
Selecting an Alternative
• Additive Strategy
• List personally
important attributes
then rate choices based
on each
• Elimination by Aspects
• Gradually eliminate less
attractive alternatives
• When any alternative
fails to satisfy criterion, it
is eliminated
Which Strategy Do We Use?
• John Payne (1976)
• When there are few options with few attributes to
evaluate by  additive strategies
• More options & more factors  elimination by aspects
• We adapt out approach to the demands of the task
• Tversky & Shafir (1992)
• We delay our decisions when alternatives are not
dramatically different
• We struggle with conflict & so seek out additional info
Risky Decision Making
• Making choices under conditions of uncertainty
• Strategies
– Expected value – extrinsic reward
– Subjective utility- intrinsic worth
– Subjective probability – personal estimates of worth
Heuristics in Judgements of Probability
• Amos Tversky & Daniel Kahneman
– Availability Heuristic
• Estimated probability based on the ease with which
relevant instances come to mind
– EX. Divorce Rate based off of how many of your friends are
divorced
– Representativeness Heuristic
• Estimated probability based on how similar the event is
to the typical prototype of that event
– EX. Flipping a coin 6 times
» 1. T T T T T T
» 2. H T T H T H
Pitfalls in Reasoning about Decisions
• Law of Small Numbers
• Gamblers Fallacy
• Odds of a chance event
increase if an event has
not happened recently
• Misleading results tend to
happen in smaller samples –
small samples lead to flukes
• Misplaced faith in small
numbers explains why people
are often willing to draw
general conclusions based on
a few individual cases
» Chance of getting all
“heads” flipping a coin 5
times is much better than
100 times
Pitfalls in Reasoning about Decisions
• Overestimating the
Improbable
• Overestimation of the
dramatic, vivid – but
infrequent events
• Confirmation Bias
• Seeking info that supports
your decisions while
ignoring disconfirming info
• Belief Perseverance
Actual Mortality Rates for
Causes of Death
Asthma
2,000
Accidental Falls
6,021
Tuberculosis
400
Suicide
11,300
Tornados
25
• Hanging onto beliefs in the
face of contradictory
evidence