Problem solving and creative thinking are related processes. Creative thinking involves generating novel ideas and alternatives, while critical thinking analyzes and evaluates those ideas. To solve problems creatively: 1) Ensure the problem is represented fully and accurately without assumptions; 2) Look for structural similarities to other problems; 3) Use techniques like association, analysis, brainstorming and roleplaying to generate many ideas for solving the problem. Representing the problem correctly is key to finding fruitful solutions.

1. Problem Solving and Creative
Thinking

2. 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.

3. 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 haven’t come up with enough options to begin with, then
your critical thinking decision procedure might produce the
wrong result… a dangerous result!

4. 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]

5. Who is this man?

6. Archimedes
Great inventor, mathematician etc.
The Screw 
The Lever

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

8. 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)

9. 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 king’s
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!

10. 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?

11. 4 Methods for Generating Ideas
1. Associative Techniques
2. Analytic Techniques
3. Brainstorming
4. Role Playing

12. Associative Techniques
1. Compare something familiar to something
unfamiliar.
a) Close analogy e.g. apples and pears
b) Remote analogy e.g. Pringles
c) Forced analogy…

13. Forced Analogy 1
• The problem: recreating that dazzling 360
degree panoramic holiday view
• The forced analogy: a wreath
• The answer!

15. Forced Analogy 2
• The problem: vertigo
• The forced analogy: swimming
• The answer!

17. Forced Analogy 3
• The problem: Carrying lots of shopping
when its raining
• The forced analogy: a tennis player
• The answer!

19. Analytic Techniques
2. 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 Henry’s regime
– Rest
– Rotation
– Relationships within team are friendly
– Really discreet signaling during matches

20. Analytic Techniques
• Unfortunately (as we know), Henry didn’t
analyse the problem thoroughly.
• He missed a vital component of the
problem:
• The Barnes Factor

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

22. Brainstorming
3. 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!

23. Roleplaying
4. 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

24. 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

25. Solving real problems is a two step process:
Problem Model Solution
The Main Message
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.

26. C
B
A
•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
The Lights Example

27. 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
The Lights Example

28. Solving real problems is a two step process:
Problem Model Solution
The Main Message
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.

29. 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?

30. The Bird-Train Problem (Posner, 1973)

31. Solving real problems is a two step process:
Problem Model Solution
The Main Message
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.

32. The Drop Block Problem
What will happen to the block of
wood when the person lets go of it?

33. The Drop Block Problem
The block will drop down as it is drawn to earth by gravity

34. The Drop Block Problem
… so long as the person is on earth.

35. The Drop Block Problem
It will float up if the person is under water.

36. The Drop Block Problem
And it will go nowhere (or a little bit sideways?!) if the
person is in space.

37. Solving real problems is a two step process:
Problem Model Solution
The Main Message
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.

38. So, how can I best represent a problem?
Suggestion 1: Drop presuppositions that aren’t explicit
in the original statement of the problem

39. 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 can’t 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…

40. Solution to The Nine Dot Problem (Maier, 1931)

41. How can I best represent a problem?
Suggestion 1: Drop presuppositions that aren’t explicit
in the original statement of the problem.

42. 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
can’t operate, that’s 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

43. How can I best represent a problem?
Suggestion 1: Drop presuppositions that aren’t explicit
in the original statement of the problem.

44. How can I best represent a problem?
Suggestion 1: Drop presuppositions that aren’t explicit
in the original statement of the problem.
Suggestion 2: Make sure you represent everything
explicit in the original statement of the problem.

45. 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 Ted’s sons are? How?
2 old high school math club pals meet up after
many years

46. 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

47. 36 1 1
18 2 1
12 3 1
9 4 1
9 2 2
6 6 1
6 3 2
4 3 3
“The product of their ages is 36”:
x y z
2 old high school math club pals meet up after
many years

48. 36 + 1 + 1 = 38
18 + 2 + 1 = 21
12 + 3 + 1 = 16
9 + 4 + 1 = 14
9 + 2 + 2 = 13
6 + 6 + 1 = 13
6 + 3 + 2 = 11
4 + 3 + 3 = 10
“The sum of their ages is equal to the number of
windows in the building next to us…”
x y z
2 old high school math club pals meet up after
many years

49. How can I best represent a problem?
Suggestion 2: Make sure you represent everything
explicit in the original statement of the problem.

50. 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?

51. House 1 2 3 4 5
Color
Drink
Country
Car
Pet

52. House 1 2 3 4 5
Color blue
Drink milk
Country Norwegian
Car
Pet

53. 7 6 2 4 5
5 8 2
6 9 3 8
8 9 5
1 2 6 3
3 1 9
9 3 6 4
5 9 8
4 2 9 6 7

54. 7 6 2 4 5
5 8 2
6 9 3 8
8 9 5
1 2 6 3
3 1 9
9 3 6 4
5 9 8 4
4 2 9 6 7

55. How can I best represent a problem?
Suggestion 2: Make sure you represent everything
explicit in the original statement of the problem.

56. How can I best represent a problem?
Suggestion 1: Drop presuppositions that aren’t 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..

57. 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%

58. 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.

59. ACTUAL MICROSOFT INTERVIEW QUESTIONS
Interview Questions with a Determinate Answer
1. 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?
2. 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.
3. 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?

60. ACTUAL MICROSOFT INTERVIEW QUESTIONS
Impossible Interview Questions
An Impossible Interview Question is one that has no single
acceptable answer.
1. How many piano tuners are there in the world?
2. How long would it take to move Mount Fuji?
• Strategy:
– Don’t freak out!
– Don’t give a joke answer (e.g. depends if we get Chuck Norris to help)
– Suggest a potential approach
– Ask them questions

61. How to solve problems creatively:
• Make sure you represent the problem in the right way!
i. Don’t assume restrictions that aren’t stipulated
ii. Do represent everything explicit in the question
iii. Do compare the structure of the problem with similar
ones
• Then generate lots of creative ideas with:
i. Associative techniques
ii. Analytic techniques
iii. Brainstorming
iv. Roleplaying
Summary