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The unique games conjecture states that for every sufficiently small pair of constants ε, δ > 0, there exists a constant k such that the following promise problem (L yes, L no) is NP-hard: L yes = {G: the value of G is at least 1 − δ} L no = {G: the value of G is at most ε} where G is a unique game whose answers come from a set of size k.
A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. [1] [verification needed] [clarification needed] Often, such games have simple rules and match procedures, such as tic-tac-toe and dots and boxes. Generally, mathematical games need not be conceptually intricate to involve deeper ...
Conway's Soldiers or the checker-jumping problem is a one-person mathematical game or puzzle devised and analyzed by mathematician John Horton Conway in 1961. A variant of peg solitaire, it takes place on an infinite checkerboard. The board is divided by a horizontal line that extends indefinitely.
The Game of Trees is a Mad Math Theory That Is Impossible to Prove The Collatz Conjecture In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific ...
As in the Monty Hall problem, the intuitive answer is 1 / 2 , but the probability is actually 2 / 3 . The Three Prisoners problem, published in Martin Gardner's Mathematical Games column in Scientific American in 1959 [7] [55] is equivalent to the Monty Hall problem. This problem involves three condemned prisoners, a random one of ...
Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of mathematicians.
Determined game (or Strictly determined game) In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. [2] [3] Dictator A player is a strong dictator if he can guarantee any outcome regardless of the other players.
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