You may also have seen her around the M Center, as she has gotten involved in theater as well. Try Martin Gardner's article. Dallas Willis will be the speaker at the next C 4 meeting, on Tuesday, April 22 at 7 PM in CMC 206. NP-complete problems are even harder. In fact, people used to think that those problems were really hard to solve.
Investigations can be quite messy . . .
While trying to solve a problem that asks for a proof, for example, one might have to go back and change the problem to ask for a disproof. While looking for other solutions one might realize that the first solution was faulty. And so on. Investigation is an art, not an algorithm. But that makes the question of how to teach mathematical investigations very difficult.