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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]
Petersen's theorem can also be applied to show that every maximal planar graph can be decomposed into a set of edge-disjoint paths of length three. In this case, the dual graph is cubic and bridgeless, so by Petersen's theorem it has a matching, which corresponds in the original graph to a pairing of adjacent triangle faces. Each pair of ...
Mathematically, edge-matching puzzles are two-dimensional. A 3D edge-matching puzzle is such a puzzle that is not flat in Euclidean space, so involves tiling a three-dimensional area such as the surface of a regular polyhedron. As before, polygonal pieces have distinguished edges to require that the edges of adjacent pieces match.
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. [1] In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a matching in a bipartite graph can be treated as a network flow problem.
To show this, we give a coloring of K 5 with red and blue that does not contain a triangle with all edges the same color. We draw K 5 as a pentagon surrounding a star (a pentagram). We color the edges of the pentagon red and the edges of the star blue. Thus, 6 is the smallest number for which we can claim the conclusion of the theorem.
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
These templates shows a chess diagram, a graphic representation of a position in a chess game, using standardised symbols resembling the pieces of the standard Staunton chess set.
A symmetric layout of Charlieplexed LEDs. On left, 3 pins drive 6 LEDs arranged in a triangle. On right, 4 pins drive 12 LEDs arranged in a tetrahedron.. The Charlieplexing configuration may be viewed as a directed graph, where the drive pins are vertices and the LEDs are directed edges; there is an outward-pointing edge connected from each vertex to each other vertex, hence with n drive pins ...