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  2. Monty Hall problem - Wikipedia

    en.wikipedia.org/wiki/Monty_Hall_problem

    The answer to the first question is ⁠ 2 / 3 ⁠, as is shown correctly by the "simple" solutions. But the answer to the second question is now different: the conditional probability the car is behind door 1 or door 2 given the host has opened door 3 (the door on the right) is ⁠ 1 / 2 ⁠.

  3. The monkey and the coconuts - Wikipedia

    en.wikipedia.org/wiki/The_monkey_and_the_coconuts

    This Diophantine equation has a solution which follows directly from the Euclidean algorithm; in fact, it has infinitely many periodic solutions positive and negative. If (x 0, y 0) is a solution of 1024x–15625y=1, then N 0 =x 0 · 8404, F 0 =y 0 · 8404 is a solution of (2), which means any solution must have the form

  4. 100 prisoners problem - Wikipedia

    en.wikipedia.org/wiki/100_prisoners_problem

    Each prisoner has to find their own number in one of 100 drawers, but may open only 50 of the drawers. The 100 prisoners problem is a mathematical problem in probability theory and combinatorics.

  5. Arithmetic topology - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_topology

    A number field corresponds to a closed, orientable 3-manifold; Ideals in the ring of integers correspond to links, and prime ideals correspond to knots. The field Q of rational numbers corresponds to the 3-sphere. Expanding on the last two examples, there is an analogy between knots and prime numbers in which

  6. Miller Analogies Test - Wikipedia

    en.wikipedia.org/wiki/Miller_Analogies_Test

    The Miller Analogies Test (MAT) was a standardized test used both for graduate school admissions in the United States and entrance to high I.Q. societies. Created and published by Harcourt Assessment (now a division of Pearson Education ), the MAT consisted of 120 questions in 60 minutes (an earlier iteration was 100 questions in 50 minutes).

  7. Analogy - Wikipedia

    en.wikipedia.org/wiki/Analogy

    Analogy is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share. [1]In logic, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction.

  8. Hilbert's paradox of the Grand Hotel - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_paradox_of_the...

    One solution is to convert each arrival's address into a binary number in which ones are used as separators at the start of each layer, while a number within a given layer (such as a guest's coach number) is represented with that many zeroes. Thus, a guest with the prior address 2-5-1-3-1 (five infinite layers) would go to room ...

  9. Interesting number paradox - Wikipedia

    en.wikipedia.org/wiki/Interesting_number_paradox

    The number fitting this definition later became 12407 from November 2009 until at least November 2011, then 13794 as of April 2012, until it appeared in sequence OEIS: A218631 as of 3 November 2012. Since November 2013, that number was 14228, at least until 14 April 2014. [5] In May 2021, the number was 20067.