Difference between revisions of "Constructive counting"

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'''Constructive counting''' is counting the number of integers, lists, etc., that satisfy a certain property by "constructing" them. This is easier explained through examples.
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'''Constructive counting''' is counting the number of integers, lists, etc., that satisfy a certain property by "constructing" it. This strategy is useful for complicated counting or combinatorics questions, as the problem can be broken down into cases, the number of possibilities in each case can be computed, and those numbers can be summed to find the final answer.  
  
 
== Examples ==
 
== Examples ==
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* [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45&year=2004&p=377954 AIME 2004I/6]
 
* [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45&year=2004&p=377954 AIME 2004I/6]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=509050#p509050 AIME 2003I/9]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=509050#p509050 AIME 2003I/9]
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This video is a great introduction to permutations, combinations, and constructive counting:
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https://www.youtube.com/watch?v=t6a4uHEwQnM&t=1868s
  
 
===See also===
 
===See also===
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[[Category:Combinatorics]]
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[[Category:Definition]]

Latest revision as of 20:27, 21 June 2020

Constructive counting is counting the number of integers, lists, etc., that satisfy a certain property by "constructing" it. This strategy is useful for complicated counting or combinatorics questions, as the problem can be broken down into cases, the number of possibilities in each case can be computed, and those numbers can be summed to find the final answer.

Examples


This video is a great introduction to permutations, combinations, and constructive counting: https://www.youtube.com/watch?v=t6a4uHEwQnM&t=1868s

See also

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