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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 ...
For example: 150,000 rupees is "1.5 lakh rupees" which can be written as "1,50,000 rupees", and 30,000,000 (thirty million) rupees is referred to as "3 crore rupees" which is can be written as "3,00,00,000 rupees". There are names for numbers larger than crore, but they are less commonly used.
The Centre for Education in Mathematics and Computing (CEMC) based out of the University of Waterloo hosts long-standing national competitions for grade levels 7–12 [2] [3] MathChallengers (formerly MathCounts BC) — for eighth, ninth, and tenth grade students
Purdue University prohibits students soliciting answers using Chegg's homework help: "While Chegg can be helpful to access textbooks and more practice problems, using this resource to find assignment answers is considered academic dishonesty because it is a form of copying and plagiarism.". [55]
For example 150,000,000 (one hundred and fifty million) rupees is written as "fifteen crore rupees", "₹ 15 crore". [1] In the abbreviated form, usage such as "₹ 15 cr" is common. [3] Trillions (in the short scale) of money are often written or spoken of in terms of lakh crore. For example, one trillion rupees is equivalent to: ₹ 1 lakh ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
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In the abbreviated form, usage such as "₹ 5L" or "₹ 5 lac" (for "5 lakh rupees") is common. [4] In this system of numeration, 100 lakh is called one crore [ 3 ] and is equal to 10 million. Formal written publications in English in India tend to use lakh/ crore for Indian currency and Western numbering for foreign currencies, such as dollars ...