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Checkers is a two-player game with the most common variant played on an 8×8 checkerboard with each player starts with twelve pieces of a fixed color on opposite sites of the ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the ...

Find the m×n array of single digits which contains the maximum possible number of primes, where allowable primes may lie along any horizontal, vertical, or diagonal line. For ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

Sudoku (literally, "single number"), sometimes also is a pencil-and-paper logic puzzle whose goal is to complete a grid satisfying various constraints. In the "classic" ...

Szemerédi's theorem states that every sequence of integers that has positive upper Banach density contains arbitrarily long arithmetic progressions. A corollary states that, ...

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...