How To Solve Problems Creatively?

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There are ten answers to this question.

Best solution

How do you make the leap from proving things with standard techniques (like proof by contradiction, induction, etc.) to coming up with lemmas to solve problems?

I understand that the answer to all of these questions is practice.However, it has been my observation that simply practicing for a large amount of time is of no great consequence if you don't do it the right way. In particular, I have 'seen' through a problem before and just knew that I had to prove a lemma, and from toying around with the problem arrived at a statement which I had to prove that would make the previous problem almost trivial. My question is therefore in a sense misworded but really...

Answer:

The short answer is: Read lots and lots of papers. Read lots and lots of proofs. Solve lots and lots...

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Obinna Okechukwu at Quora Mark as irrelevant Undo

Other solutions

How are companies using data and analytics to solve HR problems?

I wanted to hear from experts on Quora regarding using data and analytics to solve HR problems. Its common knowledge that Google has a big team called People Operations that dig into data to solve HR problems for the company. Some of the problems that...

Answer:

1. Absolutely. HR analytics is growing extremely quickly. Both the scope and frequency of data is increasing...

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Jon Williams at Quora Mark as irrelevant Undo

Common Good: How (and where) can entrepreneurs and designers find meaningful problems to solve?

Broadly, I define "meaningful" as having a profound, recurring and/or long-lasting impact on the lives of a large number of people (or having an even more profound impact on the lives of a small number of people). More specifically, I define...

Answer:

I don't think it works that way.  There are lots of unsolved problems out there.  Quite often they are...

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Miguel Valdespino at Quora Mark as irrelevant Undo

How can I improve my ability to solve hard problems?

(Note: This question is specifically asking about problems in the fields of math/physics/CS and related domains.) I find that, while I am exceptional in solving easy problems (such as SAT and some problems on college tests) or medium-difficulty problems...

Answer:

Take one month of your life- solve the hardest problems you can find. There is nothing that I can tell...

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Kyle Certiorari at Quora Mark as irrelevant Undo

How likely is it that a mathematics student can't solve IMO problems?

A better way of phrasing this question might be, how far removed are problems at math contests like IMO from problems that college and graduate students are faced with? It seems like the tricks and techniques used to solve competition problems is very...

Answer:

I didn't do many math competitions before college. While I was at Caltech, I took the Putnam twice....

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Timothy Johnson at Quora Mark as irrelevant Undo

How do you solve these algebra problems?

please help me!! i don't understand this at all... It would be greatly appreciated if you did it step by step so I can try to learn how to do it. thank-you so much =) Simplify each expression: 13) (7 - 4i)(10 - 2i) Solve each Quadratic equation: 32)...

Answer:

13) To simplify the expression (7 - 4i)(10 - 2i) all you have to do is multiply the binomials together...

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Jules at Yahoo! Answers Mark as irrelevant Undo

How can I build my basics to solve the Harvard Stat 110 strategic practice problems and homework?

I watched the first 6 videos from the Harvard Stat 110 youtube link and understood the concepts while watching the videos. As I sat down to solve the Strategic problems and homework, I could only solve 1-2 questions. How can I build my basics to solve...

Answer:

There is a lot of good advice and discussion at the links at the Stat 110 Quora blog: Stat 110 - Introduction...

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Joe Blitzstein at Quora Mark as irrelevant Undo

Answer:

The best way to start is to make a drawing and go from there.

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Erica at Yahoo! Answers Mark as irrelevant Undo

How can and do we use historical knowledge to solve problems in the present?

I have a short essay to write for History that is due thursday the 17th of may. I have a few of my own ideas to answer the question, but I would like a little more help in fully answering the question. Any ideas? Here's the full essay question: History...

Answer:

Since history is an agreed fiction* we might not set too much store by it as a teacher. There is also...

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Laura at Yahoo! Answers Mark as irrelevant Undo

How to solve these difficult AP Calculus problems?

I took a practice AP Calculus AB test from my Kaplan study guide (2007) and couldn't figure out these two explanations (some study guide...) These are from the free response section. How to solve 160=integral from 0 to S: 10 + 6sin((t^2)/3)dt for S....

Answer:

X-1+2*cos(pi*x/2)-cos^2(pi*x/2) .5x^2-x+4/pi*sin(pi*x/2)-integral cos^2(pi*x/2) integral cos^2(pi*x...

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bill b at Yahoo! Answers Mark as irrelevant Undo

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