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Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves , algebraic surfaces , or, more generally, algebraic sets , their study is a part of algebraic geometry that is called Diophantine geometry .
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
Word ladder (also known as Doublets, [1] word-links, change-the-word puzzles, paragrams, laddergrams, [2] or word golf) is a word game invented by Lewis Carroll. A word ladder puzzle begins with two words, and to solve the puzzle one must find a chain of other words to link the two, in which two adjacent words (that is, words in successive ...
A system for solving the Missionaries and Cannibals problem whereby the current state is represented by a simple vector m, c, b . The vector's elements represent the number of missionaries, cannibals, and whether the boat is on the wrong side, respectively.
One strategy for solving this version of the hat problem employs Hamming codes, which are commonly used to detect and correct errors in data transmission. The probability for winning will be much higher than 50%, depending on the number of players in the puzzle configuration: for example, a winning probability of 87.5% for 7 players.
These embeddings solve versions of the puzzle in which the houses and companies are drawn on a coffee mug or other such surface instead of a flat plane. [20] There is even enough additional freedom on the torus to solve a version of the puzzle with four houses and four utilities.
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