If you want to sharpen your mental ability to solve new problems outside your area of expertise, you should train your working memory, according to The New York Times article “Memory Training Shown to Turn Up Brainpower” by Nicholas Bakalar.
Fluid intelligence refers to the ability to reason and solve new problems independently of previously acquired knowledge:
"Until now, it had been widely assumed that the kind of mental ability that allows us to solve new problems without having any relevant previous experience — what psychologists call fluid intelligence — is innate and cannot be taught (though people can raise their grades on tests of it by practicing).
But in the new study, researchers describe a method for improving this skill, along with experiments to prove it works."
This method was a structured training in working memory:
"The four groups underwent a half-hour of training daily for 8, 12, 17 and 19 days, respectively. At the end of each training, researchers tested the participants’ fluid intelligence again. To make sure they were not just improving their test-taking skills, the researchers compared them with control groups that took the tests without the training.
The results … were striking. Although the control groups also made gains, presumably because they had practice with the fluid intelligence tests, improvement in the trained groups was substantially greater. Moreover, the longer they trained, the higher their scores were. All performers, from the weakest to the strongest, showed significant improvement.
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The authors suggest several aspects of the exercise relevant to solving new problems: ignoring irrelevant items, monitoring ongoing performance, managing two tasks simultaneously and connecting related items to one another in space and time."
