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Behind three closed doors a car, the car keys and a goat are randomly distributed. There are two players: the first player has to find the car, the second player the keys to the car. Only if both players are successful they may drive the car home. The first player enters the room and may consecutively open two of the three doors.
Use of the odds form of Bayes' theorem, often called Bayes' rule, makes such a derivation more transparent. [34] [53] Initially, the car is equally likely to be behind any of the three doors: the odds on door 1, door 2, and door 3 are 1 : 1 : 1. This remains the case after the player has chosen door 1, by independence.
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 ...
T1000-37 Tesuto Breakout box employing commonly used 37 position D-sub connectors that break out to banana jack test points. A four-port serial (RS-232) PCI Express ×1 expansion card with an octopus cable that breaks the card's DC-37 connector into four standard DE-9 connectors Example of a pocket-sized RS-232 breakout box that features switches to reconfigure or patch any or all the active ...
de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]
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.
Trivial may also refer to any easy case of a proof, which for the sake of completeness cannot be ignored. For instance, proofs by mathematical induction have two parts: the "base case" which shows that the theorem is true for a particular initial value (such as n = 0 or n = 1), and the inductive step which shows that if the theorem is true for a certain value of n, then it is also true for the ...
A decision-forcing case is also a kind of case study. That is, it is an examination of an incident that took place at some time in the past. However, in contrast to a retrospective case study, which provides a complete description of the events in question, a decision-forcing case is based upon an "interrupted narrative."