If all the conjectures made in this paper are intractable, where would one begin to do research on this deceptively simple problem? As a guide to doing research, I ask questions. Here are a few that occur to me: For the 3x+1 problem, what restrictions are there on the growth in size of members of a divergent trajectory assuming that one exists? What interesting properties does the function have? Is there some direct characterization of other than the recursive definition (2.33)?