@ Humble, your statement about "they" (and by extension them, their, theirs) being inappropriate for the third person singular is right on target. However, I do have a quibble with your statement that "'He' serves that purpose aptly." The problem is that even though traditional grammar rules permit it, the use of "he" (and him, his) gives the distinct impression that the person being referred to is male. One possible strategy for avoiding this language trap is to avoid these pronouns when they might be confusing, if possible; and another is to make everything plural. For example, instead of saying "Each student must bring his own pencils and paper," which implies male students, we could say "Students must bring their own pencils and paper," or "Each student must bring pencils and paper."