How To Solve Problems Creatively?

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 the problems?

• Answer:

  There is a lot of good advice and discussion at the links at the Stat 110 Quora blog: https://stat110.quora.com. Here are some additional suggestions about Stat 110 practice problems. The strategic practice problems are meant to be challenging, so don't get discouraged. You can't learn probability well unless you work hard on practice problems, especially problems that require real thinking rather than mindless plug-and-chug. So it's great that you are working on these. A lot of beautiful and important statistical ideas appear in the strategic practice problems, and they are organized thematically so you can practice particular concepts such as thinking conditionally.  As I discuss in , the reading process (I'm including both reading a book and watching a lecture video as "reading" here) should be interwoven with the problem-solving process. Practice, practice, practice -- this will help build up your pattern-recognition skills, and gradually the ideas will make more and more sense. Students often struggle with probability concepts at first since there are so many new and counterintuitive ideas, but when they work very hard at solving the strategic practice problem, it is common that they look back a month later at what they were struggling with earlier and can't believe how much easier they now find things that they found extremely difficult before! The natural tendency after solving a problem is to move on to another problem. Because of limited time that is sometimes necessary, but when possible I recommend doing the following before moving on, or on a revisit of the problem: Miracle checks: Does your answer seem intuitively plausible? Is there a category error? Is your answer correct in simple and extreme cases? Did asymmetry appear out of nowhere? Alternative approaches: Polya said that "It is better to solve one problem five different ways than to solve five problems one way." Solving a problem in more than one way not only gives more confidence in the answer, but also strengthens one's general problem-solving skills and intuition into when one method may be better than another. Connections, structure, and applications: How is the problem related to other problems that you've seen? What is the essential structure of the problem? What are some possible applications of the result to other problems or other fields? Reflection: Explain the result intuitively, and whether it is surprising. What are some examples? Can the proof be simplified? Can the result be generalized readily? Are there natural variations on the theme of the problem? So what if you are just completely stuck on a strategic practice problem, after working hard to try to solve it? Then I would suggest working with a friend on it (or posting it on Quora for discussion!), and studying the solutions (sometimes a quick glance at the solutions is enough to get a good hint, then you can try to work it out for yourself without having the solutions open). Then try to solve some similar problems, and in a couple weeks revisit the problems you solved (or couldn't solve). Re-solving problems often resolves conceptual issues! Doing these things takes a lot of dedication and patience, but my experience is that it is utterly worth the effort.