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The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [8] A puzzle can be expressed as a graph coloring problem. [9] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell.
The word algebra is derived from operations described in the treatise written by the Persian mathematician, Muḥammad ibn Mūsā al-Ḵhwārizmī, titled Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing") on the systematic solution of linear and quadratic equations.
Although this problem seems easier, Valiant and Vazirani have shown [24] that if there is a practical (i.e. randomized polynomial-time) algorithm to solve it, then all problems in NP can be solved just as easily. MAX-SAT, the maximum satisfiability problem, is an FNP generalization of SAT. It asks for the maximum number of clauses which can be ...
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$ 1 million prize for the first correct solution to each problem.
Problem II.8 of the Arithmetica asks how a given square number is split into two other squares; in other words, for a given rational number k, find rational numbers u and v such that k 2 = u 2 + v 2. Diophantus shows how to solve this sum-of-squares problem for k = 4 (the solutions being u = 16/5 and v = 12/5). [29]
General Problem Solver (GPS) is a computer program created in 1957 by Herbert A. Simon, J. C. Shaw, and Allen Newell (RAND Corporation) intended to work as a universal problem solver machine. In contrast to the former Logic Theorist project, the GPS works with means–ends analysis .
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