hlsat180, this isn't necessarily important to the point at issue here but I think you had a biased hand in emphasizing certain definitions of terms to fit your conclusion that "intuitive skill" is contradictory. Using your intuition means doing something without conscious reasoning; in other words something that's second nature or instinctive. A skill is just something you do well. So an intuitive skill would be in the sense of a skill that's fundamental and natural, as opposed to necessarily contrived or based on specific rules. So OP is talking about using the right intuitive approach.