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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Solution to puzzle with 3 L and 5 L jugs, a tap and a drain Two solutions on a Cartesian grid, the upper one equivalent to the diagram on the left. The rules are sometimes formulated by adding a tap (a source "jug" with infinite water) and a sink (a drain "jug" that accepts any amount of water without limit).
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
Welcome to Math Class: A Collection of Marilyn's Favorite Lessons, Grades K-6. Houghton Mifflin Harcourt. ISBN 978-1935099529. Burns, Marilyn (25 March 2015). About Teaching Mathematics: A K-4 Resource (4th ed.). Houghton Mifflin Harcourt. ISBN 978-1935099321. [10] Burns, Marilyn (April 30, 1982). Math for Smarty Pants. Martha Weston, illustrator.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
Image credits: TheBurn1nator No doubt about it, it’s a fact that humans are the most intelligent creatures on the planet. But, while we have a rich history of adapting to and comprehending the ...