Archimedes leaped out of his bathtub and ran through the streets of Syracuse naked crying "Eureka!" (got it!) when he had at last understood why the irons sink an iron ships float (to be more precise, there were no iron ships at his times but he discovered the general law that can explain why they float).
People often believe that intellectual exercise is dull because they relate it to the learning (gaining the knowledge) and formal logic. However though these things are necessary they are not the essence of the intellectual exercise as the efforts to find your couple and everyday routine is not the essence of the happy family life. They are just the preparation and the cleaning out.
Intellectual exercises are the exercises for our conscious to control and direct our unconscious.
In the case of the regular intelligence (skills of problem solving as it defined by Howard Gardner), it is the training in getting the new solution to the problem from our subconscious when required. Of course we first should supply our unconscious with the facts, gain the knowledge, otherwise we hardly find the correct solution.
However the new creative solution does not results from the logic. The logic will be required later to evaluate and test the solution.
The new solution comes out of the blue, often when we turn away from the problem, and it is very exciting.
It is probably in the human nature, or "by design" to be happy getting new knowledge and understanding because otherwise we would have no motivation to build the human civilization and become much more powerful than any animal in the Earth.
It is also important that you may get knew knowledge and make your own small discoveries virtually at any age and this will help you to keep your wellness up because people who are deeply drawn into the researches easily forget their diseases and distress, living in their ivory towers.
The answer to the famous question "if you are so smart why are you so poor" is that getting new knowledge is so addictive that people, who practice it, often forget to exercise their emotional intelligence i.e. the ability of their conscious to control and understand their own and other people (unconscious) emotions. They especially need the wellness balance monitor. It can be literally vitally important.
For example Archimedes died actually because he evidently did not exercise his emotional intelligence. He probably knew that Roman general, Marcellus, when Romans captured Syracuse, issued the order that Archimedes was not to be harmed. Therefore Archimedes did not hide. He was so negligent in the emotional intelligence that even ordered to the soldier that found him not to touch his drawings ("Don't disturb my circles!"). However too many fellows of this soldier have died because of the Archimedes inventions for the Syracuse defense. Archimedes also could hardly expect from the soldier that he is intelligent enough to hold on his rage emotion. In short the soldier unfortunately violated the order (probably before even recognizing what he did) and killed the Archimedes.
As for businesspersons, we would like to note that though the scientists in general are not as rich as businesspersons, it may happen that they are actually happier.
Therefore even if you more businessperson than the scientists by nature it have sense to do intellectual exercises like a hobby to rest from your business and actually many wealthy people were scientist out of pleasure.
Nowadays the regular intelligence is also very important in the preserving the wellness and the business because the solutions that worked just yesterday often does not work now. Creative people become more and more important to business. Executives as well as share holders should have at least some practice in the creativity to understand and manage creative employees as well as manage the company as a whole.
For example, first popular personal computer Apple was initially built in Steve Job's parent's garage in 1976. IBM tried to do the same even earlier, but in spite or their power and resources failed with IBM 5100 in 1975. Some IBM executives, in particular William C. Lowe, understood that money is not enough, the intelligence is the key and IBM corporate culture did not work. Then IBM took really intelligent and new approach. In 1980 they made a kind of garage inside IBM, i.e. gave to the small group of twelve creative people led by Philip D. Estridge and William C. Lowe almost unlimited freedom and resources with the only condition: to develop a competitive personal computer in reasonably short time. After IBM PC or simply PC as we call it now hit the market and had success, IBM decided to return to their traditional methods to manage its production and distribution. It was an error. They evidently did not sufficiently exercise their intellectual dimension to make corrections for their established corporate culture, though they knew that their culture made impossible to develop IBM PC. In accordance with the universal wellness entropy law (if you do nothing you eventually get the disorder) since year 2005 IBM PC does not produce PC anymore though more creative companies like Dell continue to produce the IBM-compatible computers and flourish.
It is true that money allows hiring the best advisers and experts but the problem is to know who is the best, to what extend you may trust the experts and how you may test them. Without your own experience in researches and discoveries it is virtually impossible to keep up even your physical wellness and health.
For example, when it was discovered that there are plenty of the cholesterol in the eggs many people including some experts and physicians believed that the eggs are bad for you health. If you had believed them you would have excluded the healthy product from your meal. However if you had even small experience in the researches your first routine question would have been, "Are there direct evidence that eggs are not healthy? Has the practice confirmed this or it's just and idea (hypothesis)"? You would have quickly found out that there were no neither direct nor indirect evidences though most people always have been eating eggs. So the best solution for your wellness would have been to continue to eat the eggs until the scientists get more evidence. And it would have been correct solution because later it was discovered that though eggs indeed have plenty of the cholesterol the cholesterol in our blood originates mainly from the saturated and trans fats and not dietary egg cholesterol. The irony is that the fat in the eggs is mostly unsaturated i.e. actually healthy. In short in general there are no reasons to exclude the eggs from your meal.
The situation when obvious does not stand the test of the practice is so common in science that there used to be old joke among the scientists, "every complex problem has at least one simple, attractive, obvious and wrong solution". Since the wellness problems are often complex it is virtually impossible to solve them without intellectual exercises.
Training in the regular intelligence is the training to solve the problems yourself, without the help of the experts. More exactly, you may get the facts or answers to the questions of the type, "Is it true that..., Is it proven that?" from any sources, including the experts, however to train your intelligence you should try first to find the solution yourself.
You should clearly understand that intelligence exercises is the exercises for our conscious to control and direct our subconscious. In the case of the traditional intelligence it is ability to get the solution from our subconscious. In the simplified and idealized picture you first feed the subconscious with the facts. Than you try some time to guess the answer intuitively. If you failed and tried enough subconscious will continue to look for the solution independently after you already have turned away from the problem. Subconscious may output the solution to your conscious quite unexpectedly at any time like to Archimedes in the bathtub. The solution however may be wrong or tentative. You should compare it with the known facts. The logic and reasoning are quit useful and even required to check whether the solution is valid but they hardly help you to find the solution. You may also fail to find the solution if you lack the facts to find it.
We see that there are three types of the exercises in the problem solving intelligence: getting knowledge, getting intuitive solution of the problem and checking the solution, comparing it with the known facts. All three are important but the most important and hard part is the intuition i.e. getting the solution from our unconscious.
Since we often don't know when we will need the particular knowledge, all that we can do is to watch the news every day and learn all our life. Use the wellness monitor; otherwise you almost for sure forget to make it regularly. Naturally we should select the news related to our occupation, wellness and simply interesting for us. If we like our work and care about our wellness all the relevant news are usually interesting. However, though we need the knowledge to get the correct solution the most important part in the getting "new" solution is the intuition.
Since we never know exactly whether we have enough knowledge to solve the problem, it usually worth first to try to find the solution yourself, using your intuition. Our subconscious works fast, so if you have not enough time you may try just a few minutes or even a few seconds. You nevertheless should try because neither the knowledge by itself nor the logic by itself is the intelligence.
After your intuition has given you the answer you may use the expert or books to check whether it is correct, comparing not with the ready answers but with the known facts and applying the logic. If your solution is not correct (you intuition always give your some answer) and you have no time to iterate more through learning-intuition-verifying you may ask or read the ready solution but you still have to compare it with the facts that you know and try to understand why your intuition failed and what facts you lacked to find the correct solution.
At the end of the day or next morning try to remember how much time you spend to solve the problems yourself (not looking or asking the ready answer) and enter it into Activities and Priorities. Otherwise it is very easy to forget to exercise because in nowadays we have plenty of ready solutions suggested to us by numerous services and advertisements, though they unfortunately often are wrong or not suited to us.
Include the time for checking whether the solution agrees with the facts and practice, i.e. time when you use the logic. You should always check your solution after you get it; otherwise it will be exercises in the dreaming and not the intelligence. But you should count only the cases where you tried to get your own answer from your subconscious before checking (even if the answer was not correct).
According to general rule, you need about 45 minutes three times a week for news and the same amount of time for the finding the solution and testing it. Here we take into account that intuition (unconscious) works quickly and even may work in parallel with conscious so it does not need the separate time from the testing. You may see the time for both of the intellectual exercise types as well as for the other wellness "exercises" in Typical Wellness Exercise Program table.
As for the problems to exercise it may be any problem at work or at home that you encounter, even small. The most important is to try to solve it yourself first.
For the comprehensive and useful exercise you may select a problem that is important but not urgent, i.e. one relatively simple wellness problem and try to solve it first applying your intuition and then comparing with facts or ready answers. For example should you always restrict the salt consumption? In this cases we simply have to give you the answer because if it is very hot and you have no the air-conditioning, in short when you sweat long time, the absence of the slightly salt water may kill you. I.e. when you sweat long time it is better to drink the slightly solty water. On the other hand if you eat too much salt regularly it is also of no good. But how may you determine the amount of salt you should consume? We are sure you will find the solution somewhere but try to get your own guess first. When you get the solution,- either yourself or the ready one,- don't forget to check that it is confirmed by the experiments, facts and the practice. The salt is just an example. Select what is important and interesting to you personally.
If the problem is urgent as well as important it is naturally not for the long exercises and in most cases you will have to ask an expert. However even in this case think a few minutes or seconds before calling the expert. Never miss the opportunity to train your intelligence and ask you subconscious. Sometimes there are no experts around, you have no time and all depends on how well your subconscious is trained to bring the quick and right answer to your conscious. If you never missed the opportunity to gain the knowledge, read or watch news and exercise your intuition your subconscious may be more powerful then you expect.