Entry

Problem solving: Method: Working backwards: What is the 'working backward from solution' method?

May 2nd, 2008 07:36
Knud van Eeden, Sakir Ali,

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--- Knud van Eeden --- 12 October 2020 - 07:08 am --------------------
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Problem solving: Method: Working backwards: What is the 'working 
backward from solution' method?
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Start from the goal, and work backwards to the given.
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Or as a special case, work backwards from the answer.
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For example, ask yourself 'What do I need to know in order to get the
solution of the goal?',
in other words which information do you minimally need to know or
fullfil to be able to solve the problem.
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For example:
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1. First ask yourself 'What is my goal?'
  I want to climb that mountain. So that is your goal.
2. Then you ask yourself 'What are the means to achieve this goal?'
 1. Create a list of the necessary means to achieve the goal
  So you ask yourself: 'What do I need to to be able to climb that
  mountain'? Answers are for example: a good physical condition, money,
  time, training, ... After that you try to solve this subproblems. How
  to get this money? How to get this time (e.g. vacation), ... So you
  work backwards from the goal towards the means or input, in order to
  solve the problem.
3. Then solve or find as much means necessary to solve your goal
 First start to train, save money, organize the trip, ...
 Finally start climbing, and possibly reach your goal.
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Beginning at the end. When a particular solution state is clearly
defined, a problem can often be more easily solved by starting with the
solution and working backwards toward the problem, filling in the
necessary steps along the way.
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The classic example is the problem: Divide a triangle into three parts
so that the parts can be put together to form a square.
That is very hard.
But if you start from the solution end, with a square, it is easy to
divide it into three parts all of which form a triangle.
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[Internet: source: http://www.google.com search for 'working forward 
problem solving': http://www.virtualsalt.com/crebook4.htm]
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Use this backwards working method e.g. when the goal state is clear but
the present state is ambiguous.
e.g.
President Kennedy stated that he wanted an American spacecraft to go as
first to the moon.
Here the goal is clear: 'go to the moon'.
The means to achieve this goal where less clear:
So ask yourself 'how would it be possible to reach the moon?'
So possibly generate some mental visual chain of the path from the moon
back to the earth.
Identify the parts of this chain and work backwards to the beginning.
e.g.
How would I get land it on the moon.
How would I approach it to the moon.
How would I fly it to the moon.
How would I start it from the earth.
How would I get money for it.
and so on.
After you have solved all that, then you put the pieces together again,
such that you possibly reach your goal.
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So use this backwards solution method e.g. for:
1. Working backwards to find facts that support hypothesis
2. Use it for diagnosis (medical e.g. MYCIN or general)
3. Use it for extrapolating from the present to the past
4. Use it to follow the path from consequent to antecedent
5. Use it when goal-driven top-down reasoning is necessary
6. As search method, the depth-first search is most easily facilitated
   here
7. The consequents determine the search
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Internet: see also:
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Problem Solving Methods
http://www.it.bton.ac.uk/staff/rng/teaching/notes/ProbSolvMethods.html
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Problem solving: Introduction to Computing for Engineers
http://www.cc.gatech.edu/classes/AY2004/cs1371_fall/lectures/CS1371_09_
Problem_Solving.ppt
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Problem solving:
http://www.computing.surrey.ac.uk/courses/csm10/7_problem_solving.pdf
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