'Problem solving' is a broad and somewhat abstract term that can refer to a range of different situations. Of course any situation that you are unhappy with or that prevents you from accomplishing your intended goals can be considered a problem, and so solving any of these problems could be considered 'problem solving'. Deep I know...
Generally the term is used to refer to applying logic, lateral thinking, or general mental dexterity in order to solve a problem. In other words these are problems with a direct cause and a clearly defined end goal, rather than the more abstract or emotional problems like 'which person should I date?' or 'how can I achieve happiness?'.
In other words problem solving skills are the kinds of skills that might apply if you were trying to work out how to fit a number of objects into a small space, or if you were trying to work out how to afford a trip on a short budget, or if you were trying to get your keys out of a locked house. Problem solving skills are also highly useful in business and certainly in programming or design where you can use them in order to achieve better results with lower overheads or to get around shortages of resources or other issues.
In short then, problem solving skills are highly useful, and they can help you in a large range of circumstances and even help you to improve your career or your finances. Practicing and developing these skills is highly useful and fortunately they can be trained just like any other skills.
Training Your Problem Solving Abilities
Problem solving is not a single skill but rather a set of skills and traits that can be applied to various situations. These abilities include: resourcefulness, lateral thinking, memory, observation, attention to detail, originality, imagination, forward planning, maths, theory of mind and more; and all of them are trained simply through attempting tasks that require those skills and doing so regularly. Fortunately there are many tasks you can practice that will employ these traits. Here are a few suggestions that you can use:
Computer Games: Computer games are very useful for testing your problem solving. Here you should look not so much at the 'brain training' tasks which test a more crystalized form of intelligent, but rather the 'puzzle platformers' which include puzzles such as flipping switches in the right order or pushing boxes to form paths. Something like the Portal games for instance is brilliant for testing your problem solving, as is the Android game Germination and the Indie PC game Q.U.B.E. Other examples are the point and click adventures of yore that once populated PCs.
Programming: Programming is fantastic for testing your ability to solve problems and to think logically. This involves using variables and equations in order to make a range of input and output scenarios that achieve the desired result. When you start with a couple of basic lines of code and manage to build a 3D world out of it, that's some pretty great thinking power there.
Physical Puzzles: I'm not talking the 3,000 piece puzzles here (though they will help your observation skills), but rather the kinds of puzzles you get given for Christmas – like a Rubix Cube, or that old 'Lights Out' thing, or those linked up pieces of metal. These force you to engage with the media in a new way in order to solve a simple problem and provide a very special task.
Business Scenarios: You can get a range of business problems and many of these are available online – for instance as example interview questions. Practice going through these and thinking about what you would do if for instance – you lost funding. You can also invent your own scenarios and they don't even need to relate to business. This is called 'counterfactual simulation' and it's a good way to plan for every eventuality as well as to test your ability to come up with solutions.
Chess: Chess means planning ahead and setting traps to capture the enemy and outsmart them. Here the problem is the opponent, and you can only solve it with planning.
Riddles: Riddles like 'A man rides into a bar on Wednesday... ' are fantastic for testing your mental mettle and even if some of the answers are a little cheap sometimes, the simple fact that you spend so long thinking about them is very good for you. Here is my favorite examples to leave you with:
You are hunting for treasure when you come to a fork in the road, and each of the two routes is guarded by one man. One of these men always tells the truth, and one of them always lies – the problem is that you don't know which is which and you can only ask one question. What question do you ask to whom to work out which way you need to go?