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.
If you're planning a trip to another country then, the biggest problem might be the distance between you and that country, so your first step would be to book a plane ticket.
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.
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.
This drastically reduces the number of solutions we need to try because it eliminates any unlikely ones right off the bat.
Heuristics 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.
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.