What is problem: Definition and 30 Discussions

Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices.Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, and consultants are largely problem solvers for issues which require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution.
There are many specialized problem-solving techniques and methods in fields such as engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences. Additionally, the mental obstacles preventing people from finding solutions is a widely researched topic: problem solving impediments include confirmation bias, mental set, and functional fixedness.

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1. Block and wedge problem -- Where am I going wrong?

This question is from the book Kleppner and Kolenkow Q 3.8: ___________________________________ My attempt is posted here: ___________________________________ The value of a(minimum) that I'm getting is different from the official solution. The official solution is posted here...
2. Solve the given trigonometry problem

My question is on the highlighted part (circled in red); Why is it wrong to pre-multiply each term by ##e^x##? to realize , ##5e^{2x} -2-9e^x=0## as opposed to factorising by ##e^{-x} ## ? The other steps to required solution ##x=\ln 2## is quite clear and straightforward to me.
3. Find ##\tan \theta ## in the form of ##a+b\sqrt {2}##

There is an error on ms ...unless i am missing something.
4. Other A problem in my transcript

Hello esteemed members I hope this message finds you all well. I am writing to you to address what I think are inaccuracies in my English transcript of the courses I have studied in my university, which is my courses’ titles are not correct. For example, "General Mathematics 1" should actually...
5. HI!

I was looking for videos, or post on how to do a physics home work problem. Ended up finding a similar post on this website. It didn't quite answer my question, but I thought I could post here to figure it out.
6. I Post your favorite real analysis problem

I figure one can dig around for plenty of quality problems online, but I'm hoping to skip right to the good stuff by you posting your favorite real analysis problems from college, internet, textbook, dream, imagination, etc. It would be so helpful to get some comments this time, and please don't...
7. Necroposts

Is necroposting seen as a problem here on PF? Screenshot below from another forum shows an approach to avoiding necroposts, at least those unintentional ones.
8. Solve the given word problem: Selecting 2 numbers from a watch face

I honestly do not understand this question, my thoughts; ignoring the diagram and using algebra i can see that the step size [1,5] → [2,6] can be found by adding 1 (common difference) to each number meaning that the answer is A... ...the other options B,C,D and E can not be related by a...
9. Flow discharge between 2 open water bodies connected by a concrete sluice

Hello, Looking for help with a physics problem. I am dealing with a problem regarding the flow discharge between 2 open water bodies connected by a concrete sluice with gates. The issue is that the channel is not straight but rather a trapezoid (image of the cross-section below). The discharge...
10. I Feynman discussion of electron diffraction

Feynman, in the third volume of his Lectures on Physics, chapter 1, presents bullets and waves in two different diagrams, Fig 1-1 and 1-2 respectively. https://www.feynmanlectures.caltech.edu/III_01.html It is obvious that bullets are counted individually, the detector registering each hit...
11. I Interesting Thermodynamics Problem deleted in PhysicsStackExchange

I came across this very interesting Thermodynamics problem in PhysicsStackExchange. It was deleted by the OP because the moderators, in their infinite wisdom, gave him a hard time about its being a homework problem which was, in their opinion, a "check my work" post, rather than a "I'm having...
12. Solving a Non-Equilibrium Pully System with a Fixed Length Rope at a 154 Degree Angle

Please note that the system is not in equilibrium, and that tension must be solved for the instant where the angle is 154 degrees. My attempt (correct ans is Ft = 626N)
13. How can I fix the illegal data signal error in my FMESH tally code in MCNP6?

Hi everyone, I would help in such problem. i have tried to use a fresh card, but it always gives an illegal data signal am using mcnp6. here is my fmesh code. thanks FMESH44:n GEOM=X Y Z ORIGIN=-10 -10 -10 IMESH=-50 IINTS=5 JMESH=50 JINTS=11 KMESH=50 KINTS=8 EMESH= 1e-7...
14. Create a physics problem for me!

Hello! Using concepts of physics 1 like kinamatics, dynamics, circular motion, pressure, newton's laws. Make me a physics question that needs basic calculus like integrals and derivaties to solve!
15. Basic Simultaneous Equations Problem

I got c=13, but I'm using an app that, at the 'diagnostic' stage, doesn't tell you if you're correct or not (I multiplied the first equation by 4, and the second by 2, then subtracted the second from the first)
16. Conservation Laws and Velocity Reversal in 1D Collisions

i dont know how
17. Two dimensional motion problem (kicking a soccer ball into the goal)

I did this too fast idk if I'm wrong So for the x component use the formula d = rt / delta x = v*t 26 = vcos(theta) y component use the displacement formula 19.6 = vsin(theta) tan^-1(19.6/26) = 36.5 degrees the answer key says 20.2 degrees idk whats wrong
18. I Work done in cycle of a refrigerator (in Heat and Thermodynamics by Zemansky)

I guess the first one is wrong. Because in this cycle we have ##|Q_H| > |Q_L|## then ## |Q_L| - |Q_H| ## is negative and caanot be equal with ##|W|##. Am I right?
19. Why Do I Get Negative Values Solving the SHM Spring Problem?

m1 = unknown m2 = 0.05 kg x = 0.38 m T = 0.8s Tried to plug in values into the above equations: 0.8 = 2pi*sqrt(m1+0.05/k) k = ((m1+0.05)*9.8)/0.38 Got negative values for both k and m which doesn't make sense

21. Indentations in the contact surface of the clutch drum and the circula

Hello guys, in my work we have a problem detected in the clutch drum (automatic gearbox) : indentations in the contact of the clutch drum and the circular plate, wefound that the hardness of the circular plate is higher than the clutch drum, do you guys have some propositions to solve this?
22. Challenge: Find the minimum amount of draws possible for a list of integers

Hello. Sorry if the title is a bit vague. I'm doing this challenge (google foobar) and even though it's not very elegant to ask for help, it's not like I'm going to win any kind of prize for it. In any case I'd like some suggestions since my current solution fails 2 tests on 5. The most...
23. Newton's law problem: Pushing 2 stacked blocks on a horizontal table

Would anyone be able to help with this Newtons law problem Block A rests on top of block B as shown in (Figure 1). The table is frictionless but there is friction (a horizontal force) between blocks A and B. Block B has mass 6.00 kg and block A has mass 2.00 kg. If the horizontal pull applied to...
24. Solve the problem that involves diameter of the Bullseye

I really do not understand what they are asking here...wording here in english is a bit confusing to me...but from similar examples, i made use of the approach below (which i still do not understand) hence my post. ##\dfrac{30π}{60 ×180} = \dfrac{0.0254}{d}## ##d = \dfrac{274.32}{30π}## ##d=...
25. I need feedback on MCQ test in IJSO style

Solutions are also attached as a file

27. Running princess and spider - time problem

If the veil stretches prefectly, then when the princess moves by ##\Delta x##, then if the spider was not moving, he would also move by ##\Delta x## from the door, so he would be in the same distance from the princess. So assuming it, the time would be ##t_f=\frac {l_0}{u}## but that is no...
28. Problem with FireFox browser (BUT, it turns out, not with PF)

I get PF to work just fine with Chrome and Edge but it's a mess with Firefox. I've cleared the cache, closed Firefox and opened it again. No joy. Anyone else using Firefox here and NOT having problems? Also, FYI, I'm using Windows 10 and Firefox says I have the latest version
29. I Solve the problem involving Rings

Its a bit clear; i can follow just to pick another polynomial say ##(x+1)^3## are we then going to have ##(2x-2)+ x+3##? or it has to be a polynomial with ##x^2+1## being evident? cheers...
30. Confusion on mechanics problem involving cart, blocks, and pulley

[Mentor Note -- Two threads on the same by the OP have been merged into one] I'm having trouble understanding the solution my professor gave me, in particular, the accelerations of m_2 and m_1. When my professor solved for the acceleration of m_2, he used a as the acceleration but when I look...