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The popular Rubik's Cube puzzle, invented in 1974 by Ernő Rubik, has been used as an illustration of permutation groups.See Rubik's Cube group.. In abstract algebra, group theory studies the algebraic structures known as groups.
A minimal puzzle is a proper puzzle from which no clue can be removed without introducing additional solutions. Solving Sudokus from the viewpoint of a player has been explored in Denis Berthier's book "The Hidden Logic of Sudoku" (2007) [ 7 ] which considers strategies such as "hidden xy-chains".
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Pocket cube with one layer partially turned. The group theory of the 3×3×3 cube can be transferred to the 2×2×2 cube. [3] The elements of the group are typically the moves of that can be executed on the cube (both individual rotations of layers and composite moves from several rotations) and the group operator is a concatenation of the moves.
The manipulations of the Rubik's Cube form the Rubik's Cube group. The Rubik's Cube group (,) represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be ...
Named after the number of tiles in the frame, the 15 puzzle may also be called a "16 puzzle", alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle, which has 8 tiles in a 3×3 frame. The n puzzle is a classical problem for modeling algorithms involving heuristics.
The muddy children puzzle is the most frequently appearing induction puzzle in scientific literature on epistemic logic. [4] [5] [6] Muddy children puzzle is a variant of the well known wise men or cheating wives/husbands puzzles. [7] Hat puzzles are induction puzzle variations that date back to as early as 1961. [8]
In the area of modern algebra known as group theory, the Lyons group Ly or Lyons-Sims group LyS is a sporadic simple group of order 51,765,179,004,000,000 = 2 8 · 3 7 · 5 6 · 7 · 11 · 31 · 37 · 67