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  2. Bertrand's ballot theorem - Wikipedia

    en.wikipedia.org/wiki/Bertrand's_ballot_theorem

    The variant problem can be solved by the reflection method in a similar way to the original problem. The number of possible vote sequences is ( p + q q ) {\displaystyle {\tbinom {p+q}{q}}} . Call a sequence "bad" if the second candidate is ever ahead, and if the number of bad sequences can be enumerated then the number of "good" sequences can ...

  3. Monty Hall problem - Wikipedia

    en.wikipedia.org/wiki/Monty_Hall_problem

    Steve Selvin wrote a letter to the American Statistician in 1975, describing a problem based on the game show Let's Make a Deal, [1] dubbing it the "Monty Hall problem" in a subsequent letter. [2] The problem is equivalent mathematically to the Three Prisoners problem described in Martin Gardner's "Mathematical Games" column in Scientific ...

  4. The Hardest Logic Puzzle Ever - Wikipedia

    en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever

    The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. [1][2] Boolos' article includes multiple ways of solving the problem. A translation in Italian was published earlier in the newspaper La Repubblica, under the title L'indovinello ...

  5. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . A continued fraction is a mathematical expression that can be writen as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple ...

  6. Middle-square method - Wikipedia

    en.wikipedia.org/wiki/Middle-square_method

    Directed graph of all 100 2-digit pseudorandom numbers obtained using the middle-square method with n = 2. In mathematics and computer science, the middle-square method is a method of generating pseudorandom numbers. In practice it is a highly flawed method for many practical purposes, since its period is usually very short and it has some ...

  7. Randomized algorithm - Wikipedia

    en.wikipedia.org/wiki/Randomized_algorithm

    A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are ...

  8. Random number generation - Wikipedia

    en.wikipedia.org/wiki/Random_number_generation

    Dice are an example of a mechanical hardware random number generator. When a cubical die is rolled, a random number from 1 to 6 is obtained. Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated.

  9. Chaos game - Wikipedia

    en.wikipedia.org/wiki/Chaos_game

    In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. [1][2] The fractal is created by iteratively creating a sequence of points, starting with the initial random point, in which each point in the sequence is a given fraction of the distance ...

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