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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.
The V-Cube 7 is a combination puzzle in the form of a 7×7×7 cube. The first mass-produced 7×7×7 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a number of Chinese companies, [ 1 ] some of which have mechanisms which improve on the original.
The 6×6×6 and 7×7×7 events are ranked by a straight mean of three—only three solves, none of which are disregarded. In 3×3×3 blindfolded and 3×3×3 fewest moves challenges, either a straight mean of 3 or the best of 3 is used, while 4×4×4 blindfolded, 5×5×5 blindfolded, and multiple blindfolded challenges are ranked using the best ...
7x7 may refer to: Boeing 7x7 series, Boeing's "7-Series" of airliners; Boeing 767, wide-body aircraft codenamed "7X7" during development; 7x7, a San Francisco-focused fashion, food, and entertainment magazine; 7x7 (website), a Russian website; V-Cube 7, the 7×7×7 version of Rubik's Cube
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A wider family are the uniform 7-polytopes, constructed from fundamental symmetry domains of reflection, each domain defined by a Coxeter group. Each uniform polytope is defined by a ringed Coxeter-Dynkin diagram. The 7-demicube is a unique polytope from the D 7 family, and 3 21, 2 31, and 1 32 polytopes from the E 7 family.
Other, usually more recently available, hardware forms of the cube come in size 2 (Pocket Cube), size 5 (Professor's Cube), size 6 (V-Cube 6), and size 7 (V-Cube 7). Lesser known hardware cubes of larger sizes have also been produced. Currently, the largest hardware cube made is size 49, and the largest mass-produced is size 21. [1]
It turns out that, if one allows the prisoners to hear the colors called out by the other prisoners, it is possible to guarantee the life of every prisoner except the first, who dies with a 50% probability. To do this, we define the same equivalence relation as above and again select a representative sequence from each equivalence class.