Difference between revisions of "Complementary counting"
Expilncalc (talk | contribs) (Added another problem which contains this technique) |
|||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | '''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. | + | '''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 == | == Examples == | ||
| Line 9: | Line 14: | ||
=== Somewhat Harder === | === Somewhat Harder === | ||
| − | * [[ | + | * [[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
