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# Problem solving

Problem-solving skills are essential in our daily lives. The video explains different problem-solving methods, including trial and error, algorithm strategy, and heuristics. It also discusses concepts like means-end analysis, working backwards, fixation, and insight. These techniques help us tackle both well-defined and ill-defined problems effectively. Created by Carole Yue.

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• Would I be wrong if I went and cut all the matches in half and made those halves into equilateral triangles?
• Yes. That's not following the rules, and changing the objective silly.
• For the match problem... couldn't you do a square with an x in it for 4 equilateral triangles?
• you can't, the diagonal of the square is not the same as the side, so the matches in the x can never touch both corners.
• Why wouldn't means end analysis be considered a type of algorithm. You are essentially taking a logical step by step approach by breaking it down into little pieces and solving them aren't you?
• Because the means-end analysis is a mental shortcut that helps with breaking down larger problems into more manageable ones. The algorithm method is just a logical step-wise process to get an answer. For means-end analysis, the process might not be in the most logical format, but will get you to your goal.
(1 vote)
• At , "With trial and error you're not necessarily keeping track of what you have already done"?
Is she sure about that? I went to the Wikipedia page on this and although there's no specific mention of having to keep track, all examples and manifestations do keep track of the errors, and it's what I've always thought about trial and errors-that you could at least exclude previous errors on subsequent trials.
Is it by definition that with trial and error you could actually err in the same way for an unlimited number of trials?
• In a practical sense, trial and error is a way to find the most successful solution, and the best way to do that would be to not repeat the same error. So, she wasn't very clear about that. Unless she means somebody is putting in random passwords without thinking about what they're typing, then no, we wouldn't constantly make the same error since trial and error is about moving towards the best solution. We tend to learn from our mistakes and repeating the same error endlessly would go against this concept.
• our brain is just a big chunk of tissues. how does it do so much?
(1 vote)
• Nobody knows exactly how the brain works, even though a lot of people have spent a lot of time trying to figure it out. We do know some things though. For example, we know that the brain works by cells called neurons, and that these do (a bit simplified) one thing: fire off an electrical impulse, or not fire off an electrical impulse. The neurons are connected together, and if a neuron receives a lot of impulses, then it will fire off an impulse of its own. Some neurons connect to our senses, and receive impulses from for example light hitting the eyes, or something touching a part of the skin. Other neurons connect to the muscles, and when these neurons fire off an impulse, the muscle it connects to contracts. The way the brain does so much lies in how the connections between the neurons cause for example an impulse from neurons connected to the eyes to trigger a cascade of firings that end up causing the neurons connected to the muscles in the arm to contract, causing you to pull up your hand to catch a ball.

There is a whole lot more to the brain than this, but it captures the idea of how the individual neurons are pretty simple, but the whole, connected mass of neurons and other cells and chemicals called the brain is massively complex. Again using a simplification that can't really be taken too far, we can think of the brain as a computer. The individual components that make up a computer are very simple. However, when you connect them together in the right way, we can send an electrical impulse from our keyboard that will trigger a cascade of electrical impulses in the computer that end up causing a letter to appear on the screen. Since we built it, we know exactly how the computer does this, while we don't know exactly how the brain does all the things that it does, but the principle is the same.
• Why did she only make 3 triangles?
• What will video games do to a child mind? Will it cause their development to slow down?
• Quite the opposite actually. Studies have shown that video gamers are better problem solvers and perform well in academics.
• how does problem solving relate to cognition?
• Cognition is another word for thoughts, or the way we process information. So, problem solving is a large part of how we process information. For instance, I couldn't just write down random words to answer this question, I had to process your question and then with cognitions come up with a logical reply.
• Didn't quite understand working backwards ?
If we work our way back to the maze, as the given example, that would take take ages... ?
• A maze is the same distance from the start and the finish, no matter where you start
• What are the problem solving strategies in math!
(1 vote)
• There are a lot of different tricks for MCAT math. Sometimes it is just memorizing a different form of the equation that will get you straight to your answer (such as, for a weak acid, [H+}=sqrt(Ka*[HA]) where you assume HA is just your original molarity of the weak acid), but what seems to help me the most is finding different patterns to the math problem that make it easier to chunk everything together. For example, knowing the sine and cosine of different angles (0, 30, 45, 60, and 90) are very important for the MCAT so:
sin(0) = 0________cos(0) = 1
sin(30)=0.5_______cos(30) = ~0.9
sin(45)=~0.7______cos(45) = ~0.7
sin(60)=~0.9______cos(60) = 0.5
sin(90)=1_________cos(90) = 0
Notice that you are just counting upwards for the angles that you should know (0, 30, 45, 60, 90) and you are almost counting up by odd numbers (5, 7, 9) for the answer.
For cosine (since they are complementary) you are just going the opposite way.
*I am using the ( ~ ) sign to indicate rounding.
These numbers should get you close to the correct answer. Let me know if you have a more specific "problem solving strategy in math" question.