Difference between revisions of "Complementary counting"

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'''Complementary counting''' is [[counting]] the [[complement]] of the [[set]] we want to count, and subtracting that from the total number of possibilities, or the universal set for that particular problem. A big hint that complementary counting may lead to a quick solution is the phrase "at least".
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'''Complementary counting''' is [[counting]] the [[complement]] of the [[set]] we want to count, and subtracting that from the total number of possibilities, or the universal set for that particular problem. In problems that involve complex or overly complicated and tedious [[casework]], complementary counting is often a far easier and more efficient approach. Within a problem statement, a large hint that complementary counting may lead to a quick solution is the phrase "at least".
  
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==Video==
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This is a video explaining the basics of casework, complementary counting, and overcounting (PIE):
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https://youtu.be/Zhsb5lv6jCI
  
 
== Examples ==
 
== Examples ==
 
=== Introductory ===
 
=== Introductory ===
 
* [[2006_AMC_10A_Problems/Problem_21 | 2006 AMC 10A Problem 21]]
 
* [[2006_AMC_10A_Problems/Problem_21 | 2006 AMC 10A Problem 21]]
* [[2002 AIME I Problems/Problem 1| 2002 AIME I Problem 1]]
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* [[2002 AIME I Problems/Problem 1 | 2002 AIME I Problem 1]]
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* [[2008 AMC 12B Problems/Problem 22 | 2008 AMC 12B Problem 22]]
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=== Somewhat Harder ===
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* [[2004 AIME I Problems/Problem 15]]
  
 
=== See also ===
 
=== See also ===

Revision as of 04:40, 19 September 2020

Complementary counting is counting the complement of the set we want to count, and subtracting that from the total number of possibilities, or the universal set for that particular problem. In problems that involve complex or overly complicated and tedious casework, complementary counting is often a far easier and more efficient approach. Within a problem statement, a large hint that complementary counting may lead to a quick solution is the phrase "at least".


Video

This is a video explaining the basics of casework, complementary counting, and overcounting (PIE): https://youtu.be/Zhsb5lv6jCI

Examples

Introductory

Somewhat Harder

See also