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. 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

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