In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=". The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any equality is an equation.
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general n queens problem of placing n non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers n with the exception of n = 2 and n = 3.
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles.
A logic puzzle is a puzzle deriving from the mathematical field of deduction.
Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle.
Verbal arithmetic, also known as alphametics, cryptarithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters of the alphabet. The goal is to identify the value of each letter. The name can be extended to puzzles that use non-alphabetic symbols instead of letters.
Kakuro or Kakkuro or Kakoro is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword. Kakuro puzzles are regular features in many math-and-logic puzzle publications across the world. In 1966, Canadian Jacob E. Funk, an employee of Dell Magazines, came up with the original English name Cross Sums and other names such as Cross Addition have also been used, but the Japanese name Kakuro, abbreviation of Japanese kasan kurosu, seems to have gained general acceptance and the puzzles appear to be titled this way now in most publications. The popularity of Kakuro in Japan is immense, second only to Sudoku among Nikoli's famed logic-puzzle offerings.
Sudoku is a logic-based, combinatorial number-placement puzzle. In classic sudoku, the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids that compose the grid contain all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
Sudoku puzzles can be studied mathematically to answer questions such as "How many filled Sudoku grids are there?", "What is the minimal number of clues in a valid puzzle?" and "In what ways can Sudoku grids be symmetric?" through the use of combinatorics and group theory.
Killer sudoku is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic; the hardest ones, however, can take hours to crack.
This is a glossary of Sudoku terms and jargon. It is organized thematically, with links to references and example usage provided as ([1]). Sudoku with a 9×9 grid is assumed, unless otherwise noted.
Ariadne's thread, named for the legend of Ariadne, is solving a problem by multiple means—such as a physical maze, a logic puzzle, or an ethical dilemma—through an exhaustive application of logic to all available routes. It is the particular method used that is able to follow completely through to trace steps or take point by point a series of found truths in a contingent, ordered search that reaches an end position. This process can take the form of a mental record, a physical marking, or even a philosophical debate; it is the process itself that assumes the name.
In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion is sometimes used to justify the intractability of certain problems. Examples of such problems include certain mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function.
A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box. A Sudoku starts with some cells containing numbers (clues), and the goal is to solve the remaining cells. Proper Sudokus have one solution. Players and investigators use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties.
A Survo puzzle is a kind of logic puzzle presented and studied by Seppo Mustonen. The name of the puzzle is associated with Mustonen's Survo system, which is a general environment for statistical computing and related areas.
A software calculator is a calculator that has been implemented as a computer program, rather than as a physical hardware device.
The World Sudoku Championship (WSC) is an annual international puzzle competition organised by a member of the World Puzzle Federation. The first event was held in Lucca in 2006. National teams are determined by local affiliates of the World Puzzle Federation. The competition typically consists of 100 or more puzzles solved by all competitors over multiple timed rounds, including classic sudoku, variations and other puzzle types, normally followed by a playoff for the top qualifiers to determine a champion. Examples of rounds include the Relay round, where an answer from one puzzle contributes digits to the start of the next sudoku, and the "World Record" round, in which solvers competed to set a Guinness World Record for fastest sudoku solution.
Str8ts is a logic-based number-placement puzzle, invented by Jeff Widderich in 2008. It is distinct from, but shares some properties and rules with Sudoku. The name is derived from the poker straight. The puzzle is published in a number of newspapers internationally, in two book collections, and in downloadable apps. It was featured on the Canadian television show Dragons' Den on November 24, 2010.
Sudoku codes are non-linear forward error correcting codes following rules of sudoku puzzles designed for an erasure channel. Based on this model, the transmitter sends a sequence of all symbols of a solved sudoku. The receiver either receives a symbol correctly or an erasure symbol to indicate that the symbol was not received. The decoder gets a matrix with missing entries and uses the constraints of sudoku puzzles to reconstruct a limited amount of erased symbols.
Taking Sudoku Seriously: The math behind the world's most popular pencil puzzle is a book on the mathematics of Sudoku. It was written by Jason Rosenhouse and Laura Taalman, and published in 2011 by the Oxford University Press. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. It was the 2012 winner of the PROSE Awards in the popular science and popular mathematics category.
