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  2. Water pouring puzzle - Wikipedia

    en.wikipedia.org/wiki/Water_pouring_puzzle

    Water pouring puzzle. Starting state of the standard puzzle; a jug filled with 8 units of water, and two empty jugs of sizes 5 and 3. The solver must pour the water so that the first and second jugs both contain 4 units, and the third is empty. Water pouring puzzles (also called water jug problems, decanting problems, [1][2] measuring puzzles ...

  3. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins ⁠ 1 1 ⁠, ⁠ 3 2 ⁠, ⁠ 7 5 ⁠, ⁠ 17 12 ⁠, and ⁠ 41 29 ⁠, so the sequence of Pell numbers begins ...

  4. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]

  5. Hilbert's problems - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_problems

    Problems 1, 2, 5, 6, [g] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis), 13 and 16 [h] unresolved, and 4 and 23 as too vague to ever be described as solved. The withdrawn 24 would also be in this class.

  6. Monty Hall problem - Wikipedia

    en.wikipedia.org/wiki/Monty_Hall_problem

    The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975.

  7. Grade (slope) - Wikipedia

    en.wikipedia.org/wiki/Grade_(slope)

    The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt".

  8. Pell's equation - Wikipedia

    en.wikipedia.org/wiki/Pell's_equation

    Pell's equation. Pell's equation for n = 2 and six of its integer solutions. Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form where n is a given positive nonsquare integer, and integer solutions are sought for x and y. In Cartesian coordinates, the equation is represented by a hyperbola; solutions ...

  9. Harmonic progression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Harmonic_progression...

    An excellent example of Harmonic Progression is the Leaning Tower of Lire. In it, uniform blocks are stacked on top of each other to achieve the maximum sideways or lateral distance covered. The blocks are stacked 1/2, 1/4, 1/6, 1/8, 1/10, … distance sideways below the original block.

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