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The Shannon switching game can be seen as a special case of a Maker-Breaker game, in which the winning patterns for the Maker are connecting paths. A weakly-related connection game Hex is played on a grid of hexagons, and has 6-connectivity. Generalized Hex is played on a graph, just like the Shannon game, but instead of coloring the edges, in ...
For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 ≡ 4 (mod 6). Equivalently, n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 1–2–4 loop (the inverse of the 4–2–1 loop of the unaltered function f defined in the Statement of the problem section of ...
The combined LP has both x and y as variables: Maximize 1. subject to Ax ≤ b, A T y ≥ c, c T x ≥ b T y, x ≥ 0, y ≥ 0. If the combined LP has a feasible solution (x,y), then by weak duality, c T x = b T y. So x must be a maximal solution of the primal LP and y must be a minimal solution of the dual LP. If the combined LP has no ...
Planarity is a 2005 puzzle computer game by John Tantalo, based on a concept by Mary Radcliffe at Western Michigan University. [1] The name comes from the concept of planar graphs in graph theory; these are graphs that can be embedded in the Euclidean plane so that no edges intersect.
In November 2023, Desmos gave users the ability to bring sound to their graphs, allowing them to produce tones of a given frequency and gain. [14] Users can create accounts and save the graphs and plots that they have created to them. A permalink can then be generated which allows users to share their graphs and elect to be considered for staff ...
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There are three main types of computer environments for studying school geometry: supposers [vague], dynamic geometry environments (DGEs) and Logo-based programs. [2] Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions.
Puzzles like Hamilton's icosian game, based on finding Hamiltonian cycles in planar graphs, continue to be sold as smartphone apps. [19] Maker-Breaker games based on Hamiltonian cycles were introduced to combinatorial game theory in a 1978 paper by Václav Chvátal and Paul Erdős, [20] [21] and continue to be studied in mathematics. [21]