Problem Solving and Creative Thinking

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Problem Solving and Creative Thinking
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Problem Solving

• What is a Problem?
• A problem arises when a living creature has a
  goal but does not know how this goal is to be
  reached.
• A problem exists whenever one cannot go from
  the given situation to the desired situation
  simply by action. K. Dunker, On Problem Solving,
  (1945) p. 1
• What is Problem Solving?
• Problem Solving is the process of working out or
  discovering how to reach such a goal.

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What is creative thinking?

• Creative thinking is the process of generating
  novel ideas and alternative courses of action, no
  matter how good those ideas and alternatives
  might be.
• Creative thinking should not be seen as an
  alternative to critical thinking
• When you have recognised a problem, then you
  should employ creative thinking to produce some
  options for solving the problem, then you should
  employ critical thinking
• If you havent come up with enough options to
  begin with, then your critical thinking decision
  procedure might produce the wrong result a
  dangerous result!

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Creative Thinking, Critical Thinking, and Problem
Solving

• Creative thinking supports critical thinking
  While critical thinking focuses on step-by-step,
  linear processes aimed at arriving at a correct
  answer, creative thinking begins with
  possibility, multiple ideas, and suspended
  judgement. It might be said that creative
  thinking supports the ideas with which critical
  thinking works. Thus, even though these two
  kinds of thinking work in different ways, they
  actually support one another and aim at the same
  ultimate goal, which is to solve a problem At
  the beginning of the process, creative methods
  are used to examine the problem environment,
  generate ideas, and make associations. Then the
  analysis and judgment faculties are brought into
  play, and the possibilities are analyzed for a
  possible solution. Robert Harris, CB pp. 115-6
  

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Who is this man?
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Archimedes
Great inventor, mathematician etc. The Screw
? The Lever

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Archimedes

Helped protect Syracuse from the Romans in the
siege of 213BC The Mirror The Claw
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Archimedes puzzle

• Did the smithy replace some of the kings gold
  with silver?
• How did Archimedes find out?
• (Not Archimedes style to torture the smithy)

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Solution to Archimedes puzzle.

• The solution, which occurred when he stepped into
  a public bath and caused it to overflow, was to
  put a weight of gold equal to the crown, and
  known to be pure, into a bowl which was filled
  with water to the brim. Then the gold would be
  removed and the kings crown put in, in its
  place. An alloy of lighter silver would increase
  the bulk of the crown and cause the bowl to
  overflow. Vitruvius, De Architectura
• And the wreath was impure!

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Creative thinking!

• It was very useful to Archimedes
• He was well respected and treated in Syracuse
• Marcellus, the Roman general, ordered his life to
  be spared when Syracuse finally fell
• But his obsession with maths was ultimately his
  downfall!
• Can we be like Archimedes?
• Can we learn to be creative thinkers?

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4 Methods for Generating Ideas

• Associative Techniques
• Analytic Techniques
• Brainstorming
• Role Playing

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Associative Techniques

• Compare something familiar to something
  unfamiliar.
• Close analogy e.g. apples and pears
• Remote analogy e.g. Pringles
• Forced analogy

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Forced Analogy 1

• The problem recreating that dazzling 360 degree
  panoramic holiday view
• The forced analogy a wreath
• The answer!

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Forced Analogy 2

• The problem vertigo
• The forced analogy swimming
• The answer!

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Forced Analogy 3

• The problem Carrying lots of shopping when its
  raining
• The forced analogy a tennis player
• The answer!

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Analytic Techniques

• Breaking a problem down into smaller parts
• E.g. How can I make the All Blacks win the Rugby
  World Cup?
• Vital components of the problem
• Henry Just one ensuring the ABs perform to
  their capacity
• Hence the 4 Rs of Henrys regime
• Rest
• Rotation
• Relationships within team are friendly
• Really discreet signaling during matches

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Analytic Techniques

• Unfortunately (as we know), Henry didnt analyse
  the problem thoroughly.
• He missed a vital component of the problem
• The Barnes Factor

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Analytic Techniques

• Good analytic techniques will help to ensure that
  all of the important components of the problem
  are addressed

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Brainstorming

• Deliberately set about coming up with
  alternatives, and write them all down, no matter
  what.
• No idea is a bad idea (at least just yet)
• Edward de Bono 6 hats green hat time
• One company generated 2,200 ideas in one day!

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Roleplaying

• Roleplaying. Attempt to simulate aspects of the
  problem and proposed solutions. Try to imagine
  details of the relevant outcomes after your
  choice has been made, and attempt to put yourself
  in the shoes of other people.
• A good method for gathering information and
  gaining perspective
• E.g. Theoretical vs. practical lecturing
• E.g. Customers-eye-view of displays
• E.g. Hand-out-of-the-car-window aerodynamics

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But Archimedes was not just a creative thinker...

• He was also a prolific problem solver
• So, how can we harness these 4 idea creation
  techniques to help us solve problems?
• Ideas should be generated after the problem has
  been properly understood and represented

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The Main Message
Solving real problems is a two step process
Model
Solution
Problem
In order to generate potentially fruitful ideas,
and thereby make it more likely that you solve
your problem, make sure you represent the problem
in the right way.
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The Lights Example

• One and only one of the switches (A, B C) on
  the outside of the room turns on all of the
  lights (x, y z) in the room
• From outside, you cannot see into the room
• The wiring is hidden from view
• You are not allowed to damage any of the property
• Is there a way of knowing for sure which switch
  turns the lights on?
• Once you enter the room, you cannot leave again
  to rearrange the switches

x y z
C B A
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The Lights Example
Switches Possible arrangements
A 1 1 1 1 0 0 0 0 B 1 1 0 0 1 1 0 0
C 1 0 1 0 1 0 1 0 1 on, 0 off
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The Main Message
Solving real problems is a two step process
Model
Solution
Problem
In order to generate potentially fruitful ideas,
and thereby make it more likely that you solve
your problem, make sure you represent the problem
in the right way.
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The Bird-Train Problem (Posner, 1973)

• Station 1 and Station 2 are 50 miles apart on a
  straight train track
• Train 1 leaves Station 1 at the same time that
  Train 2 leaves Station 2
• Both trains travel at 25 miles per hour toward
  the other station
• The bird starts directly above Train 1 and flies
  above the track until it reaches Train 2. Then it
  flies back to Train 1 etc.
• The bird flies at 230 miles per hour
• How far has the bird flown by the time the trains
  meet?

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The Bird-Train Problem (Posner, 1973)
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The Main Message
Solving real problems is a two step process
Model
Solution
Problem
In order to generate potentially fruitful ideas,
and thereby make it more likely that you solve
your problem, make sure you represent the problem
in the right way.
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The Drop Block Problem

• What will happen to the block of wood when the
  person lets go of it?

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The Drop Block Problem

• The block will drop down as it is drawn to earth
  by gravity

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The Drop Block Problem

• so long as the person is on earth.

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The Drop Block Problem

• It will float up if the person is under water.

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The Drop Block Problem

• And it will go nowhere (or a little bit
  sideways?!) if the person is in space.

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The Main Message
Solving real problems is a two step process
Model
Solution
Problem
In order to generate potentially fruitful ideas,
and thereby make it more likely that you solve
your problem, make sure you represent the problem
in the right way.
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So, how can I best represent a problem?

• Suggestion 1 Drop presuppositions that arent
  explicit in the original statement of the problem

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The Nine Dot Problem (Maier, 1931)

• Can you connect all of the dots with just 4
  straight lines?
• You cannot take your pen off the paper
• You cant use a ridiculously big pen
• The second line must start where the first line
  finished. The third line must start where the
  second line finished etc.
• Imagine the dots are drawn on a flat an immovable
  surface
• The solution

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Solution to The Nine Dot Problem (Maier, 1931)
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How can I best represent a problem?

• Suggestion 1 Drop presuppositions that arent
  explicit in the original statement of the problem.

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A Terrible Accident

• There was a terrible accident on the motorway
  coming into Wellington
• A man was killed on impact and his son was rushed
  to hospital with life-threatening injuries
• At the hospital, the surgeon saw the boy and
  said I cant operate, thats my son
• What is going on here?
• Many of us assume that surgeons have to be male,
  making us come up with crazy answers for a simple
  question

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How can I best represent a problem?

• Suggestion 1 Drop presuppositions that arent
  explicit in the original statement of the problem.

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How can I best represent a problem?

• Suggestion 1 Drop presuppositions that arent
  explicit in the original statement of the
  problem.
• Suggestion 2 Make sure you represent everything
  explicit in the original statement of the
  problem.

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2 old high school math club pals meet up after
many years
On a street somewhere Ted All three of my sons
celebrate their birthday today. Can you tell me
how old each one is? (Ted is a bit weird) Fred
Yes, but you have to tell me something about
them Ted The product of their ages is 36. Fred
I need more info Ted The sum of their ages is
equal to the number of windows in the building
next to us Fred I need more info Ted My
oldest son has blue eyes. Fred That is
sufficient! ? Can Fred really know how old Teds
sons are? How?
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2 old high school math club pals meet up after
many years

• Age of the first son x
• Age of the second son y
• Age of the third son z
• Safe assumption x y z

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2 old high school math club pals meet up after
many years
The product of their ages is 36
x y z

• 1 1
• 2 1
• 3 1
• 9 4 1
• 9 2 2
• 6 6 1
• 6 3 2
• 4 3 3

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2 old high school math club pals meet up after
many years
The sum of their ages is equal to the number of
windows in the building next to us
x y z

• 1 1 38
• 2 1 21
• 3 1 16
• 9 4 1 14
• 9 2 2 13
• 6 6 1 13
• 6 3 2 11
• 4 3 3 10

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How can I best represent a problem?

• Suggestion 2 Make sure you represent everything
  explicit in the original statement of the
  problem.

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There are five houses, each of a different color
and inhabited by men of different nationalities,
with one unique pet, drink, and car. Some facts
are given 1. The Englishman lives in the red
house. 2. The Spaniard owns the dog. 3. The man
in the green house drinks cocoa. 4. The Ukrainian
drinks eggnog. 5. The green house is immediately
to the right (your right) of the ivory house. 6.
The owner of the Oldsmobile also owns snails. 7.
The owner of the Ford lives in the yellow
house. 8. The man in the middle house drinks
milk. 9. The Norwegian lives in the first house
on the left. 10. The man who owns the Chevrolet
lives in the house next to the house where the
man owns a fox. 11. The Ford
owner's house is next to the house where the
horse is kept. 12. The Mercedes-Benz owner drinks
orange juice. 13. The Japanese drives a
Volkswagen. 14. The Norwegian lives next to the
blue house. Who owns the Zebra?
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How can I best represent a problem?

• Suggestion 2 Make sure you represent everything
  explicit in the original statement of the
  problem.

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How can I best represent a problem?

• Suggestion 1 Drop presuppositions that arent
  explicit in the original statement of the
  problem.
• Suggestion 2 Make sure you represent everything
  explicit in the original statement of the
  problem.
• Suggestion 3 When thinking about how you could
  represent a problem, look for structural
  similarities between this problem and one you
  know the answer to..

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Structural Similarities

• Suggestion 3 When thinking about how you could
  represent a problem, look for structural
  similarities between this problem and one you
  know the answer to.
• This certainly works with IQ tests and
  brainteasers
• But also with (real life!) problem solving in
  general
• Radiotherapy treatment for stomach cancer
• - A structurally similar dictator analogy helped
  1 20
• - The analogy with an answer helped 1 75

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Why should solving logic puzzles be relevant or
important to me?

• An ability to solve logic puzzles is thought to
  be positively correlated with an ability to think
  creatively and solve problems of any kind.
• Whether or not such a correlation really exist,
  it is commonly believed to exist.
• Employers care more about creative thinking and
  problem solving abilities in the workforce more
  than any other general skill..
• Creative thinking and problem solving abilities
  are among the most important skills sought after
  by universities..
• Hence, universities and employers will screen
  candidates on the basis of their ability to solve
  logic puzzles.

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ACTUAL MICROSOFT INTERVIEW QUESTIONSInterview
Questions with a Determinate Answer

• You have twenty blue socks, twenty brown socks,
  and two black sock in a drawer in your room. If
  it is night time, and the room is completely
  dark, how many would you have to take out to be
  sure you have 2 of the same colour?
• A mother sent her child to the lake and told him
  to bring back exactly 7 litres of water. She
  gave him a 5 litre bucket and a 3 litre bucket.
  How can the child measure out exactly 7 litres of
  water using nothing but the two buckets.
• You've got someone working for you for seven days
  and a gold bar to pay them. The gold bar is
  segmented into seven connected pieces. You must
  give them a piece of gold at the end of every
  day. If you are only allowed to make two breaks
  in the gold bar, how do you pay your worker?

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ACTUAL MICROSOFT INTERVIEW QUESTIONSImpossible
Interview Questions

• An Impossible Interview Question is one that has
  no single acceptable answer.
• How many piano tuners are there in the world?
• How long would it take to move Mount Fuji?
• Strategy
• Dont freak out!
• Dont give a joke answer (e.g. depends if we get
  Chuck Norris to help)
• Suggest a potential approach
• Ask them questions

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Summary

• How to solve problems creatively
• Make sure you represent the problem in the right
  way!
• Dont assume restrictions that arent stipulated
• Do represent everything explicit in the question
• Do compare the structure of the problem with
  similar ones
• Then generate lots of creative ideas with
• Associative techniques
• Analytic techniques
• Brainstorming
• Roleplaying