<p>Sorry for the late response, UMTYMP!</p>
<p>Normally, if the student neglected a critical problem (typically a proof) that is necessary to prove later theorems, the counselors will sit with the student and offer direction/guidance/suggestions if necessary. The amount of counselor interference varies from counselor to counselor and student to student, but generally, counselors offer feedback on completed proofs (eg where to be more rigorous) and maybe some suggestions on approaches for difficult proofs (eg "have you tried a graphical approach?).</p>
<p>By the end, most students will be working on problems related to one or two threads and sampling problems from other threads. This is normally accidental, but students generally gravitate towards to some topics over others. Of course, some boss students will complete most of the problems on each problem sets, although this is normally rare.</p>