Chapter 2
Problem Solving
Chapter 2: Problem Solving
1
Problem Solving
How To Solve It
A great discovery solves a great problem but there is a grain of
discovery in the solution of any problem. Your problem may be
modest; but if it challenges your curiosity and brings into play
your inventive faculties, and if you solve it by your own means,
you may experience the tension and enjoy the triumph of
discovery. Such experiences at a susceptible age may create a
taste for mental work and leave their imprint on mind and
character for a lifetime.
– George Pólya
Chapter 2
Problem Solving
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Problem Solving Process
Phase 1: Understanding the problem
Phase 2: Devising a plan
Phase 3: Carrying out the plan
Phase 4: Looking back
Chapter 2
Problem Solving Process
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1: Understanding the problem
What is the unknown? What are the data?
What is the condition? Is it possible to satisfy
the condition? Is the condition sufficient to
determine the unknown?
Draw a figure. Introduce suitable notation.
Chapter 2
Phase 1: Understanding the
problem
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2: Devising a plan
How you seen the problem before? Do you
know a related problem?
Look at the unknown. Think of a problem
having the same or similar unknown.
Split the problem into smaller sub-problems.
If you can’t solve it, solve a more general
version, or a special case, or part of it.
Chapter 2
Phase 2: Devising a plan
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3: Carrying out the plan
Carry out your plan of the solution. Check
each step.
Can you see clearly that the step is correct?
Can you prove that it is correct?
Chapter 2
Phase 3: Carrying out the plan
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4: Looking back
Can you check the result?
Can you derive the result differently?
Can you use the result, or the method, for
some other problem?
Chapter 2
Phase 4: Looking back
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Area of circle
What is the data? Side of
square = 2a
What is the unknown? Area
of circle, C.
2a
What is the condition? If
radius r is known, C can be
calculated.
How to obtain r?
Chapter 2
Area of circle
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Area of circle
Pythagoras’ theorem
a
r
r2 = 2 * a2
a
Area of circle
C =  * r2 =  * 2 * a2
Chapter 2
Area of circle
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Pascal’s triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Chapter 2
nC
k
Pascal's triangle
= n! / (k! * (n-k)!)
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NE-paths
To find number of NE-paths between any
two points.
C
A
Chapter 2
NE-paths
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Creative thinking
Most new discoveries are suddenly-seen
things that were always there. A new
idea is a light that illuminates presences
while simply had no form for us before
the light fell on them.
Susan Langer
Chapter 2
Creative thinking
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Creative thinking
Myths
Creativity requires genius
You have to be odd
Creative thinking isn’t rigorous, but uses
simple processes
Chapter 2
Creative thinking
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Homework
Try exercises behind chapter 2.
Chapter 2
Homework
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