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Problem Solving and Creative Thinking

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.

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!

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

Who is this man?

Archimedes

Great inventor, mathematician etc. The Screw

? The Lever

Archimedes

Helped protect Syracuse from the Romans in the

siege of 213BC The Mirror The Claw

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)

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!

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?

4 Methods for Generating Ideas

- Associative Techniques
- Analytic Techniques
- Brainstorming
- Role Playing

Associative Techniques

- Compare something familiar to something

unfamiliar. - Close analogy e.g. apples and pears
- Remote analogy e.g. Pringles
- Forced analogy

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

Analytic Techniques

- Unfortunately (as we know), Henry didnt analyse

the problem thoroughly. - He missed a vital component of the problem
- The Barnes Factor

Analytic Techniques

- Good analytic techniques will help to ensure that

all of the important components of the problem

are addressed

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!

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

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

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.

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

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

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.

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?

The Bird-Train Problem (Posner, 1973)

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.

The Drop Block Problem

- What will happen to the block of wood when the

person lets go of it?

The Drop Block Problem

- The block will drop down as it is drawn to earth

by gravity

The Drop Block Problem

- so long as the person is on earth.

The Drop Block Problem

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

The Drop Block Problem

- And it will go nowhere (or a little bit

sideways?!) if the person is in space.

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.

So, how can I best represent a problem?

- Suggestion 1 Drop presuppositions that arent

explicit in the original statement of the problem

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

Solution to The Nine Dot Problem (Maier, 1931)

How can I best represent a problem?

- Suggestion 1 Drop presuppositions that arent

explicit in the original statement of the problem.

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

How can I best represent a problem?

- Suggestion 1 Drop presuppositions that arent

explicit in the original statement of the problem.

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.

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?

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

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

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

How can I best represent a problem?

- Suggestion 2 Make sure you represent everything

explicit in the original statement of the

problem.

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.

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..

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

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.

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?

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

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

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