Should You Mentor High School Students?

I have mentored many high school students on projects (21 in the past, 6 right now). Is this a good use of ones time? I note my experiences and advice- if you have different experiences and advice, feel free to share.

1. Unlike PhD students you don't have to worry about the job market, support money, or if they prove something original.
2. I have not gotten papers out of it. Even very good students lack a certain maturity for paper writing. (There have been exceptions.)
3. It is good of society. (The most important problem facing society today, that I can do something about, is that not enough high school students know Ramsey Theory.)
4. By explaining material to them it has helped me sharpen my own understanding.
5. Most of the students I have advised have been pretty good mathematically (they already know discrete math and induction and how to prove things). Some have been good at coding which also comes in handy. Most have come from Blair High School's Magnet Program. (They have a very strong physics department which specializes in Magnetism.)
6. Having students do a project where they can code some stuff is good in that SOMETHING will come of it. Also, this may be something you wouldn't normally do so it may help you.
7. The standards of what is original are different on this level. The project does not have to really be original in the sense we would mean it. If they work out something that you already know the answer to and write it up that's fine. It may be more accurate to call it a research experience.
8. The mostly did projects that DID NOT require a lot of background. Even if they are very good, they are unlikely to have a lot of background. This is why many of them have worked in Ramsey Theory. You may be saying but bill, you like Ramsey Theory anyway. True- but one of the reasons I got interested in it was to help mentor high school students. Its a chicken-and-egg thing. (This metaphor may die soon as scientists now think the chicken came first.)
9. The student of mine who has gone the furthest in Math is Jacob Lurie. who is now a full professor at Harvard (in Math). He didn't need much help; however, I did help him learn some recursion theory (we went through all of Soare's book) His project was on Recursive Surreal Numbers.
10. Many of my students enter various contests. For every thousand dollars they win, I get a free lunch. (If Jacob wins the Fields Medal I'll get 15 free lunches!)
11. Recruitment. Some of my mentorees have come to UMCP, though that is not really on my mind when I agree to be a mentor.
12. Why have I mentored so many? I have never sought them out--- they find me since I have mentored people in the past. Also, if a HS student comes around and wants a mentor they are often pointed to me.
13. Should you mentor high school students? It is unlikely to help you with your research program (there are exceptions). But if you do mentor high school student then (1) make sure its not a big time sink, and (2) use it to learn or relearn results you've forgotten (Recently I was forced to relearn the Erdos-Szekeres Theorem).
14. So, what have they worked on. Including this years gang and their tentative projects here is the breakdown:
    1. 11 worked on Ramsey Theory (3 of these worked together).
    2. 3 worked on Duplicator-Spoiler Games (together).
    3. 3 worked on Empirical Algorithms (2 of these worked together).
    4. 3 worked on Crypto.
    5. 2 analyzed some Simple Games.
    6. 1 worked on Recursive Surreal Numbers.
    7. 1 worked on Graph Isomorphism.
    8. 1 worked on Monotone Circuits.
    9. 1 worked on the Prob Method.