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Analytical and creative problem solving abilities rely on different skill sets. Analytical thinking is also referred to as logical thinking, while creative thinking can also be called "lateral" thinking. Sometimes the difference is described in terms of left-brain, or analytical, and right brain, or creative, thinking. Analytical thinking is useful in solving convergent problems, ones to which there is only one correct answer. Creative thinking works better in solving divergent problems, where there may be many or even infinite solutions. Many problems respond best to a mix of both.

Analytical thinking is essential in solving logistical problems, such as, "What's the best way to ship this load of widgets to Muncie, Indiana?" or "How do I make a week's worth of meals on my limited food budget?" For either of these, you will need a knowledge of facts and the ability to put them together in the right way: shipping prices and speeds, for example, or what ingredients you'll need to make a meatloaf.

Analytical thinking depends on the ability to recall or research facts and figures that are relevant to the problem. Being able to categorize these facts, use the right ones in the right ways and think logically about the probable outcomes of various options is key to analytical problem solving. So is the ability to narrow down options, eliminating irrelevant data or unworkable choices. Analytical problem solving also calls for the ability to observe trends and tendencies and use what has happened in the past to predict probable outcomes.

Creative thinking is essential in finding solutions to problems with complex or abstract elements, such as, "What's the best way to govern a city?" or "Why don't my children get along better?" These kinds of problems have no correct answer that applies in every situation, so generating creative ideas is a must. Most of the bigger questions in life call for at least some creative thinking.

Creative thinking involves the ability to see not just what is evident but also what may be the missing pieces of a solution. One common creative problem-solving technique is brainstorming, in which numerous ideas are collected before any of them are criticized or discarded. Another important skill in creative problem solving is the ability to suspend judgment and follow a train of thought imaginatively to see where it may lead. And sometimes it is helpful to lay a problem aside, allowing its elements to percolate in the subconscious mind, and return to it later to see what new angles or solutions may emerge.