What is Problem solving: Definition and 238 Discussions

Problem solving consists of using generic or ad hoc methods in an orderly manner to find solutions to problems. Some of the problem-solving techniques developed and used in philosophy, artificial intelligence, computer science, engineering, mathematics, medicine and societies in general are related to mental problem-solving techniques studied in psychology and cognitive sciences.

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  1. A

    Could Somebody Recommend Me a Mathematics Problem solving book ?

    I am having a hard time solving word problem like those that you have model an function to find the right answer. This would become very problematic in the next semester since I will take Calculus. I have taken pre-calculus,but the class didn't require me to solve modeling problems...
  2. Z

    Trigonometry Problem Solving Question

    Question: "A cat sitting on the edge of a straight river bank spots a bird sitting in a tree directly across the river's edge. The angle of elevation from the cat to the bird is 15°. The cat the moves 25m along the river bank, and now spots the same bird at an angle of elevation of 13°. How...
  3. M

    Improving problem solving skills

    I've often been plagued by the thought of being unintelligent and slow compared to others. I seem to take much longer to understand concepts and work out problems. With that said, I do really well at school (but also put in much more time than others). I'm also quite obsessive when it comes to...
  4. S

    A revelation regarding problem solving especially for tough contests.

    I have recently had a revelation and I have very few people to share it with. It would mean a lot to me if the experienced problem solvers in this forum can pitch in and add to/correct the following paragraph. I am thinking that in case there is more to it, then I would love to hear about it and...
  5. L

    Very hard modelling and problem solving Calculus Question

    A light-weight "pop-up" tent consists of six flexible plastic struts that are inserted into pockets sewn into the joins of the fabric panels. The resulting shape has hexagonal horizontal cross-sections, while vertical cross-sections through the centre are semi-circular. Derive a formula for...
  6. 1

    Homework Help 3D vectors problem solving

    Homework Help! 3D vectors problem solving! Homework Statement the vector v=(1,√2,c) makes an angle of 60° with the positive z-axis. Determine the angles that v makes with the positive x-axis and the positive y-axis. Explain how many answers there are. Homework Equations dot product...
  7. W

    Relativity problem solving help time dilation

    Relativity problem solving help! time dilation http://courses.physics.illinois.edu/phys225/sp2013/homework/225-hwk01.pdf Please click on the top link ^ to see the questions. I have already solved them and turned it in, however i would like to see how others would approach the questions and...
  8. T

    Problem solving equation system

    Homework Statement Solve this equation system for x, y and lambda. \left\{\begin{matrix} 2x = \lambda (2x-6y)\\ 2y = \lambda(-6x-14y)\\ x^2-6xy-7y^2+80=0 \end{matrix}\right. The Attempt at a Solution I really tried A LOT of things, but I can't solve it. I think it is not helpful to post...
  9. S

    Schools How to improve problem solving skills at pre college level

    I am preparing for olympiads ( though not actually giving) . I am first doing a theory book and then after completing theory and being satisfied that I have understood any particular topic I go on to solve a problem book of the same topic. I have just planned to do progress in this way but I...
  10. A

    [Problem Solving] See if you can answer my question.

    Here we go. Lets say SUBJECT 1 and SUBJECT 2 have a fight. They both have 990 Points. Each SUBJECT can hit a number from nothing (0) to 112. And they both take turns evenly. Let's say SUBJECT 1 starts to hit a number first and hits 20. Then the Subject 2 would be (990-20)= 970. And they all...
  11. O

    Solving Math Challenges with Art of Problem Solving

    I'm tutoring some high school kids right now, but I don't actually own any high-school level math books. We've just been working out of the books they use at school. But I'm getting very irritated with their books. One kid has this geometry book that makes me want to pull my hair out. It's...
  12. R

    Determining Step Size with Given Problem Solving

    Homework Statement I have some trouble understanding the following solved problem: http://img808.imageshack.us/img808/3340/euler2.jpg This is the solutions they have given us: E(32 \ steps) = 0.00097030 E(64 \ steps) = 0.00003202 32 steps has h=0.625 64 steps has h= 0.03125 The formula...
  13. T

    Calculating Concentrations and Dilutions in Titrations

    Homework Statement Kevin must prepare a solution of NaOH with a concentration of 0.2 mol.dm3. 1.1) What mass of solid must he dissolve in 1dm3 of water to make this solution. 1.2) Kevin dissolves too much solid and makes 1dm3 of solution with a concentration of 0.22 mol.dm3. How much water...
  14. H

    Mathematical induction problem solving question help

    hi this question i just cannot do. i have no idea where to start: a student is trying to recall the formula for the sum of cubes of consecutive numbers. she thinks it may be (n^3(n+1)^3) /8 or (n^2(n+1)^2)/4 . show by counter example one is incorrect and the other is correct by induction...
  15. K

    Problem Solving With Permutations

    Hi, I have the following questions 1) A coin is tossed 9 times. In how many ways could the results be six heads and three tails? 2) A man bought two vanilla ice cream cones, three chocolate ones, four strawberry, and one butterscotch. In how many ways could he distribute them among his 10...
  16. Saladsamurai

    Inequalities and Absolue Values: Problem Solving Approach

    Hello all! :smile: In my quest to re-teach myself the basics of mathematics in a more rigorous fashion, I have found out that inequalities and absolute values are a weak point if mine. So I am working to address that. I am getting much better at it (with help from PF), but I have recently...
  17. I

    Epsilon-delta in problem solving

    good day everyone: I just want to ask help from you guys on how I can use the epsilon-delta definition of limits in problem solving specially those involving quadratic expressions. Thanks.
  18. W

    Stuck on Math 11 Problem Solving questions.

    Homework Statement I've worked through and been able to understand each problem I've been given except for the following two, does anyone have a suggestion or an explanation on how to solve either of these problems? Thanks in advance. 1. "On the first part of a 317 mile trip, a sales...
  19. Ivan Seeking

    Creative problem solving at 3 AM

    Over the years I have noticed a pattern: I tend to do my best work after fixating on a problem for a very long time, and usually after getting far too little sleep and drinking way too much coffee. If I am well rested and working a sane schedule, I never seem to pop off with those OMG solutions...
  20. F

    Problem Solving about Archimedes' Principle

    Homework Statement A piece of metal weighs 50.0 N in air, 36.0 N in water and 41.0 N in oil. Find the densities of the metal and the oil.Homework Equations Density of Water is 1000 kg / m^{3} Density of Air is 0.00121 g / cm^{3}The Attempt at a Solution I really don't have any idea on how to...
  21. 1

    Which Lockers Stay Open in Percy's Locker Challenge?

    Percy went to a school with 900 students with exactly 900 lockers. His principal, who used to be a math teacher, met the students outside the building on the first day of school, and described the following weird plan. The first student is to enter the school and open all the lockers. The...
  22. X

    Problem solving Heat Diffusion Equation

    Homework Statement One face of a thick uniform layer is subject to a sinusoidal temperature variation of angular frequency ω. SHow that the damped sinusoidal temperature oscillation propagate into eh layer and give an expression for the decay length of the oscillation amplitude. A cellar...
  23. 2

    Problem Solving Physics students vs Non-science students

    I have to write a report and in one section I have to give the same problem to a bunch of physics students and a bunch of non-science majors to solve. Then I have to compare their techniques of solving it. I need help finding a problem to test problem solving skills that a non-math/science...
  24. M

    2 dimension forces - problem solving for parked car

    Problem of the day: Trying to find the formula to use for my 15 year old daughter. A 20,000N car is parked on an incline that makes an angle of 30 degrees with the horizontal. If the maximum force the brakes can withstand is 12,000N, will the car remain at rest? She is just learning how to...
  25. M

    Problem solving state change exercise

    Hi everybody, I'm having a problem with the following question: A piston-cylinder device originally contains 5 kg of saturated-liquid water at 100 kPa. Determine the heat addition required to bring the fluid to a saturated-vapor state. Using the first law.. i was thinking the following...
  26. X

    Correlation between problem solving skills and being able to derive theories.

    From my understanding the job of a theoretical physicist is to derive theories to explain phenomena in nature. But let's say you aren't the best problem solver in the world. You are good enough in your physics class to get the 3.5 GPA but you are never able to solve those extra credit problems...
  27. M

    Ideas and techniques to improve problem solving skills

    Hey there I’m currently in year 11 and I’m in physics. This year, we have been doing some basic math which relates to projectiles and conservation of momentum ect, it was pretty much just sub a whole bunch of knowns into a formula and solve for x or something, anyway, this term we have...
  28. L

    Air wedge problem solving (single interference)

    Homework Statement 8 bright fringes are counted across 1.06 cm in the air wedge. Homework Equations Δx = L (λ/2t) The Attempt at a Solution i don't understand whether Δx is: 8Δx = 1.06cm or 7Δx = 1.06cm it said 8 bright fringes but Δx = the distance between...
  29. L

    Waves and light (problem solving)

    Homework Statement two speakers producing exactly the same frequency and always in phase are located on an east-west line emitting sound toward the north. the speakers are 30cm apart and a microphone is loacted 40cm due north of one speaker. which of the following wavelengths would produce...
  30. T

    Having problem solving a limit

    having problem solving a limit! Homework Statement Solve the following limits algebraically. lim x->5 x^2 - 25 / √(2x+6) -4 Homework Equations The Attempt at a Solution i've tried a different few ways. so by factoring the top i have (x+5)(x-5) so i get x=5 or x=-5...
  31. C

    Improve Math Problem Solving - 15yo University Student

    Hi, I'm 15 and currently in the highest mathematics class at school - And being lectured at a university every Friday as an enrichment. Though, I am very good at problem solving in physics, but very bad at mathematics. I find it hard because I don't get told what area of mathematics I should be...
  32. J

    Solve SHM Problem: 1 Initial Condition

    What is the best way to go about solving a SHM problem that asks for amplitude and phase constant when only one initial condition (x(0)) is given? I'm a little confused because I read that to find A and the phase constant you must use the initial conditions - but I've encounter a few problems...
  33. D

    Problem solving with quadratic functions.

    Homework Statement okay I know understand that I should get a reasonable understanding about the questions I post before I post them sorry about before. An Illinois farmer will plant from 800 to 2000 acres of soybeans. The number of acres q that he will plant depends on the selling price...
  34. A

    Why Does Coulomb's Law Give Different Results for the Same Charges?

    Homework Statement three objects carrying charges of (a)-4x10^-6 C, (B)-6x10^-6 C, and (c)+9x10^-6 C are placed in a line equally spaced from left to right by a distance of 0.5m. calculate the magnitude and direction of the net force acting on each. Homework Equations Force of the magnitude...
  35. D

    Problem solving with quadratic functions.

    Homework Statement Eastern Ceramics can sell up to 200 of its flower pots per day in accordance with the demand function. p=13 -.04q write revenue as a function of the quantity sold q. find the output level q that maximizes R and the selling price at this output level.Homework Equations The...
  36. D

    Problem solving with linear functions 2.

    Homework Statement Suppose the selling price p of a product is linearly related to the quantity demanded q. If p=$15 when q=25, and p=$10 when q=100, and if q is at least 20 but not more than 150, find p as a function of q. Homework Equations The Attempt at a Solution I...
  37. D

    Problem solving with linear functions.

    Homework Statement The daily operation of a plant that produces LCD clocks entails a fixed cost of $150. Furthermore, the production of one clock requires $3.00 in raw materials,$0.25 in electricity and $1.50 in labor. If these are the only variable costs and the plant can produce up to 400...
  38. D

    Problem solving radius and area.

    Homework Statement A circular garden is surrounded by fencing costing $5 per meter. If the total cost of the fencing is $100, find: a)the radius of the garden b)the area of the garden Homework Equations The Attempt at a Solution all I know is that it would make sense if...
  39. D

    Solving for the Sides of a Triangle with Given Perimeter and Side Relationships

    Homework Statement The perimeter of a triangle is 14 meters. One of the sides is one meter less than twice the shortest side. If the remaining side is 3 meters longer than the shortest side, what are the lengths of the sides of the triangle? Homework Equations The Attempt at a...
  40. D

    Problem solving Periodic Function

    Homework Statement Hello, I am having problem solving this problem (picture below). The figure IS drawn to scale. A = 70 Volts Q1. What is the numerical value of V(2) on the graph (in volts)? Q2. What is the numerical value of point B on the graph (in volts)? Q3. What is the period for...
  41. D

    Fourier series problem solving for an,bn

    Homework Statement let f(x)={0;-2\leqx\leq0. x;0\leqx\leq2 find a0 an bn given the period is 4 Homework Equations a0=1/L\intf(x)dx an=1/L\intf(x)cos(n\pix/L) bn=1/L\intf(x)sin(n\pix/L) The Attempt at a Solution so I can get a0 = 1 but I run into trouble with an. so I plug...
  42. U

    What Is the Initial Velocity Required for a Cannonball to Hit a Moving Target?

    Homework Statement A cannon which is at the top of a 99 m high cliff fires in a horizontal direction to a dog. The initial position of the dog is 1000 m from the cliff's base. What should be the initial velocity of the cannon if the dog is moving at constant speed of 9 m/s to the cliff...
  43. A

    Momentum - Hit and stick problem solving

    Momentum - "Hit and stick" problem solving Homework Statement 6. A 75.0 kg hockey player moving at +10.0 m/s crashes into a second, stationary hockey player. After the collision, the two skaters move as a unit at +4.50 m/s. In the collision, the impulse received by the second hockey player...
  44. C

    Kinetic and Potential Energy Problem Solving

    Homework Statement Doing some homework with kinetic energy and potential energy. I came across 3 questions that I am struggling with. Basically we have a mass attached to the end of a string. The string is hanging straight down to start off these questions. The following questions assume that...
  45. U

    Year 12 Maths B problem solving

    Homework Statement http://s1183.photobucket.com/albums/x477/mathsscholar/ This photo just show equations which define the boundaries, note there is no eastern boundary but the domain is 0-20. After further discussions with his accountant, Mr X is not satisfied that he will make enough profit on...
  46. N

    Do You Need a Website for Problem Solving?

    I would like a site that would challenge my mind. So far I have taken pre-calculus and I took physics I back in high school. I have to take physics again after this semester though -.-. Specifically something that could challenge me with math and physics. Please, I'm dying to problem solve...
  47. C

    Pulley problem solving for mass

    Movers have to haul a piano up to a window that is 5 floors above the ground. They decide to use a pulley system with 6 strands of rope. if the movers can exert a total force of 1111 N, how heavy a piano can they hoist? It doesn't say where the movers are standing but I'm assuming on the...
  48. L

    Solved it Myself to Self-Help Problem Solving

    figured it out myself, thanks
  49. Z

    Problem solving for time when average power and total energy is given

    Homework Statement A student spends part of her day walking between classes or for recreation, during which time she expends energy at an average rate of 280 W. The remainder of the day she is sitting in class, studying, or resting; during these activities, she expends energy at an average rate...
  50. G

    Excellent Physics Book to Enhance Problem Solving Skills?

    I'm a High School Student and I love studying Physics, but my main problem is, I sometimes get careless and sometimes uncritical to the word problems given in our Physics class, though, I get decent grades in Physics, I feel that I'm not yet satisfied with my skills in it, its seems that I still...
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