*Two, two, three, four, five, six, seven, eight, then three, two, three, four, five, six, seven, eight, and so on.This could still take a really long time, but you are guaranteed to find the right solution eventually.What probably happened is something called insight, which is that sudden aha moment when the solution just pops into your head.*

And that creates another group of subproblems, which you solve one at a time, usually starting with the biggest one. Now, with means-end analysis, we were trying to work from our current state toward our goal state.

With working backwards however, you start with your goal state and use it to suggest connections back to your current state.

And with trial and error, you're not necessarily keeping track of what you've already done, so you could get lucky and hit on the right password early, or it could take a very, very long time.

A more methodical approach would be to use the algorithm strategy.

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.For example, imagine you're trying to log in to an email account you haven't accessed in a while.You know that the password is eight numbers long, but you don't remember what it is.If you did solve that problem, try to think about how the solution came to you.You probably didn't do a series of step-by-step arrangements of matches, and the heuristics we've talked about don't quite work.An algorithm is a logical, step-by-step procedure of trying solutions until you hit on the right one.So if we're still trying to get into our email account, we might start with one, two, three, four, five, six, seven, eight, and if that doesn't work, we'll change one number at a time.Usually though, we don't have time to try every possible solution, so a more common method of solving problems is to use some sort of heuristic.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.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." ([1], page 1).

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