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The Buchholz hydra game is a hydra game in mathematical logic, a single player game based on the idea of chopping pieces off a mathematical tree. The hydra game can be used to generate a rapidly growing function B H ( n ) {\displaystyle BH(n)} , which eventually dominates all provably total recursive functions.
A game of sprouts with n initial spots (in blue) that ends in 3n − 1 moves. Each spot starts with three lives and each move reduces the total number of lives in the game by one (two lives are lost at the ends of the line, but the new spot has one life). So at the end of the game there are 3n − m remaining lives.
b 2 is the number of two-dimensional "voids" or "cavities". Thus, for example, a torus has one connected surface component so b 0 = 1, two "circular" holes (one equatorial and one meridional ) so b 1 = 2, and a single cavity enclosed within the surface so b 2 = 1.
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
Cool Math Games (branded as Coolmath Games) [a] is an online web portal that hosts HTML and Flash web browser games targeted at children and young adults. Cool Math Games is operated by Coolmath LLC and first went online in 1997 with the slogan: "Where logic & thinking meets fun & games.".
An impartial game is one in which at any given point in the game, each player is allowed exactly the same set of moves. Normal-play nim is an example of an impartial game. In nim, there are one or more heaps of objects, and two players (we'll call them Alice and Bob), take turns choosing a heap and removing 1 or more objects from it.
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.
A white key peg indicates a code peg that belongs in the solution, but is incorrectly positioned. [10] Screenshot of software implementation (ColorCode) illustrating the example. If there are duplicate colors in the guess, they cannot all be awarded a key peg unless they correspond to the same number of duplicate colors in the hidden code.