These are run-of-the-mill mathematical and word problems. The vast majority of problems on Khan Academy are of this type.
These are problems that are generally unfamiliar. They might pose a familiar problem in an unusal way, or they might require a creative step, such as a geometric construction. Most challenges are complex enough to cause the student to think about more specific or more general instances of the problem. Khan Academy has very few challenge problems, which is a huge detriment.
These are the deepest types of problems. For investigations, there are often many questions to ask and many answers to be found. The teacher will likely know how to answer many of the simple questions, but understanding the space of questions and answers entirely is unlikely for both the student and teacher. Most investigations are provided by MathPickle and JRMF. Because these problems are so deep, many of the problems offered by MathPickle for K-12 will also interest undergraduates.