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  2. American Mathematics Competitions - Wikipedia

    en.wikipedia.org/wiki/American_Mathematics...

    The AMC 8 is a 25 multiple-choice question, 40-minute competition designed for middle schoolers. [4] No problems require the use of a calculator, and their use has been banned since 2008. Since 2022, the competition has been held in January. The AMC 8 is a standalone competition; students cannot qualify for the AIME via their AMC 8 score alone.

  3. Mathcounts - Wikipedia

    en.wikipedia.org/wiki/Mathcounts

    The Sprint Round consists of 30 problems to be completed within the time limit of 40 minutes. This round is meant to test the accuracy and speed of the competitor. As a result of the difficulty and time constraints, many competitors will not finish all of the problems in the Sprint Round. The Target Round consists of 8 problems.

  4. American Invitational Mathematics Examination - Wikipedia

    en.wikipedia.org/wiki/American_Invitational...

    The American Invitational Mathematics Examination (AIME) is a selective and prestigious 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics examination (formerly known as the AHSME), and starting in 2010, those who rank in the top 2.5% on the AMC 10. Two different versions of the test ...

  5. United States of America Mathematical Olympiad - Wikipedia

    en.wikipedia.org/wiki/United_States_of_America...

    2.Only AMC 12A or AMC 12B takers are eligible for the USAMO (with the slight exception mentioned in item 5 below). 3.Only AMC 10A and AMC 10B takers are eligible for the JMO. (This automatically limits Junior Math Olympiad participation to 10th graders and below.) 4.Approximately the top 260 AMC12 based USAMO indices will be invited to the USAMO.

  6. Cantor's diagonal argument - Wikipedia

    en.wikipedia.org/wiki/Cantor's_diagonal_argument

    In fact, the standard ordering on the reals, extending the ordering of the rational numbers, is not necessarily decidable either. Neither are most properties of interesting classes of functions decidable, by Rice's theorem, i.e. the set of counting numbers for the subcountable sets may not be recursive and can thus fail to be countable. The ...

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  8. Counting problem - Wikipedia

    en.wikipedia.org/wiki/Counting_problem

    Counting problem may refer to: Enumeration; Combinatorial enumeration; Counting problem (complexity) This page was last edited on 21 August 2009, at 19:03 (UTC) ...

  9. Burnside's lemma - Wikipedia

    en.wikipedia.org/wiki/Burnside's_lemma

    Burnside's lemma can compute the number of rotationally distinct colourings of the faces of a cube using three colours.. Let X be the set of 3 6 possible face color combinations that can be applied to a fixed cube, and let the rotation group G of the cube act on X by moving the colored faces: two colorings in X belong to the same orbit precisely when one is a rotation of the other.