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  2. Four fours - Wikipedia

    en.wikipedia.org/wiki/Four_fours

    For example, when d=4, the hash table for two occurrences of d would contain the key-value pair 8 and 4+4, and the one for three occurrences, the key-value pair 2 and (4+4)/4 (strings shown in bold). The task is then reduced to recursively computing these hash tables for increasing n , starting from n=1 and continuing up to e.g. n=4.

  3. Optimal solutions for the Rubik's Cube - Wikipedia

    en.wikipedia.org/wiki/Optimal_solutions_for_the...

    A randomly scrambled Rubik's Cube will most likely be optimally solvable in 18 moves (~ 67.0%), 17 moves (~ 26.7%), 19 moves (~ 3.4%) or 16 moves (~ 2.6%) in HTM. [4] By the same token, it is estimated that there is only 1 configuration which needs 20 moves to be solved optimally in almost 90×10 9, or 90 billion, random scrambles. The exact ...

  4. Rubik's Revenge - Wikipedia

    en.wikipedia.org/wiki/Rubik's_Revenge

    A solved Rubik's Revenge cube. The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube.It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. [1]

  5. Speedcubing - Wikipedia

    en.wikipedia.org/wiki/Speedcubing

    Additionally, specialized formats such as 3×3, 4×4, and 5×5 blindfolded, 3×3 one-handed (OH), 3×3 Fewest Moves, and 3×3 multi-blind are also regulated and hosted in competitions. [1] As of February 2025, the world record for the fastest single solve of a Rubik's cube in a competitive setting stands at 3.08 seconds.

  6. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.

  7. Quartic function - Wikipedia

    en.wikipedia.org/wiki/Quartic_function

    be the general quartic equation we want to solve. Dividing by a 4, provides the equivalent equation x 4 + bx 3 + cx 2 + dx + e = 0, with b = ⁠ a 3 / a 4 ⁠, c = ⁠ a 2 / a 4 ⁠, d = ⁠ a 1 / a 4 ⁠, and e = ⁠ a 0 / a 4 ⁠. Substituting y − ⁠ b / 4 ⁠ for x gives, after regrouping the terms, the equation y 4 + py 2 + qy + r = 0, where

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    mail.aol.com

    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    In contrast, the graph of the function f(x) + k = x 2 + k is a parabola shifted upward by k whose vertex is at (0, k), as shown in the center figure. Combining both horizontal and vertical shifts yields f(x − h) + k = (x − h) 2 + k is a parabola shifted to the right by h and upward by k whose vertex is at (h, k), as shown in the bottom figure.