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what's the best route to your new job how do you decide who to marry how do you satisfy your growling stomach each of these questions represents a problem that we sometimes face you may not even realize it but you are an excellent problem solver 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 a 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 well-defined problems have a clear starting and ending point such as how to make it bright in a room that's currently dark you know exactly what you're starting with and exactly how you want to end up ill-defined problems on the other hand have a more ambiguous starting and or ending point such as how to live a happy life 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 one method of solving problems is trial and error this means that you just take random guesses until something finally works for example imagine you're trying to log into 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 are using the trial and error method of problem solving then you would just try any random combination of letters and numbers until something works as you can probably tell that approach would take forever 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 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 1 2 3 4 5 6 eight if that doesn't work we'll change one number at a time 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 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 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 this drastically reduces the number of solutions we need to try because it eliminates any unlikely ones right off the bat here sticks don't guarantee a correct solution but they do simplify complex problems and reduce the total number of solutions that we'll try in order to get to a more manageable number since heuristics are so common let's talk about a few different ones that work for different types of problems one type of heuristic is means-end analysis 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 if you're planning a trip to another country then the biggest problem might be the distance between you in that country so your first step would be to book a plane ticket that creates another group of subproblems which you solve one at a time usually starting with the biggest one a second heuristic is working backwards 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 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 work your way backwards toward the beginning let's try to solve another problem what if I gave you these six matches and asked you to use them to draw four equilateral triangles go ahead give it a try if you had trouble solving that problem you're not alone most people get stuck on thinking about this problem in a two dimensional way this act of getting stuck is called fixation the answer though it 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 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 what probably happened is something called insight which is that set in a hot moment when the solution just pops into your head inside is tricky it's hard to predict and hard 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 often insight comes after a period of incubation 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