How Important is Intuition in Problem Solving?

The Complete Method of Problem Solving, at http://www.problemsolving.net/ps7-1of4-intuition.html, lists intuition one of "major problem solving strategies." The guide discusses what intuition is, what it does for our problem solving process, how to develop better problem solving intuition, and what the "peril[s]" may be when intuition without justification is used to solve problems. Interesting read that gives me more license to continue surfing the web to help my intuition development! :)