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Most people get stuck on thinking about this problem in a two-dimensional way. The answer, though, requires you to think about the problem in three dimensions.You need to create a triangle pyramid with the six matches in order to form four equilateral triangles.If you did solve that problem, try to think about how the solution came to you.
It's something you can still try to solve, but you may not know exactly what the outcome will look like.
Because you face such a variety of problems each day from the simple to the complex, your brain has several different ways of solving problems. This means that you just take random guesses until something finally works.
This strategy is commonly used in mathematical proofs.
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.
Problems can be generally broken down into two categories; well-defined problems and ill-defined problems.
Well-defined problems have a clear starting and ending point, such as how to make it bright in a room that's currently dark.
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.
that all students need to learn more, and often different, mathematics and that instruction in mathematics must be significantly revised." (, page 1).
What probably happened is something called insight, which is that sudden aha moment when the solution just pops into your head.
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.