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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. There are 92 solutions. The problem was first posed in the mid-19th century.
Backtracking is an important tool for solving constraint satisfaction problems, [2] such as crosswords, verbal arithmetic, Sudoku, and many other puzzles. It is often the most convenient technique for parsing , [ 3 ] for the knapsack problem and other combinatorial optimization problems.
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables , which is solved by constraint satisfaction methods.
Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm. Constraint satisfaction as a general problem originated in the field of artificial intelligence in the 1970s (see for example (Laurière 1978)).
Named after the number of tiles in the frame, the 15 puzzle may also be called a "16 puzzle", alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle, which has 8 tiles in a 3×3 frame. The n puzzle is a classical problem for modeling algorithms involving heuristics.
Some of the puzzles are well known classics, some are variations of known puzzles making them more algorithmic, and some are new. [4] They include: Puzzles involving chessboards, including the eight queens puzzle, knight's tours, and the mutilated chessboard problem [1] [3] [4] Balance puzzles [3] River crossing puzzles [3] [4] The Tower of ...
The missionaries and cannibals problem, and the closely related jealous husbands problem, are classic river-crossing logic puzzles. [1] The missionaries and cannibals problem is a well-known toy problem in artificial intelligence , where it was used by Saul Amarel as an example of problem representation.
Parsons' programming puzzles became known as Parsons puzzles [2] and then Parsons problems. [3] Parsons problems have become popular as they are easier to grade than written code while capturing the students problem solving ability shown in a code creation process.