# System Problem Solving

Since heuristics are so common, let's talk about a few different ones that work for different types of problems. This heuristic means that we analyze the main problem and break it down into smaller problems.Then we attack the biggest subproblem in order to reduce the most difference between our current state and the goal state.You need to create a triangle pyramid with the six matches in order to form four equilateral triangles.

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This strategy is commonly used in mathematical proofs.

Just a few seconds ago, you figured out how to start this video, and that may not feel like a huge accomplishment compared to, say, coming up with the theory of relativity, but every time you engage in an action or thought pattern to move from your current state toward a goal state, you're solving a problem.

Problems can be generally broken down into two categories; well-defined problems and ill-defined problems.

Insight is tricky, it's hard to predict, and harder to encourage, particularly when you're fixated on seeing a problem from the same ineffective perspective.

If you do get stuck on a problem, you can let it incubate, or just sit in your mind while you're not really thinking about it. It's like when you're trying to think of the name of that actor in a movie you saw, but it only comes to you later that night after you thought you stopped thinking about it.

A heuristic is a mental shortcut that allows us to find a solution more quickly than the other two methods we've talked about so far.

For example, you probably made a password out of familiar number combinations, so you might try something that includes your birthday or something else that stands out in your mind.

Another example of it is if you've ever done a maze and started at the end and worked your way backwards toward the beginning. What if I gave you these six matches and asked you to use them to draw four equilateral triangles? If you had trouble solving that problem, you're not alone.

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