I brought home with me a copy of the Fairfax County Math League challenge problems that a student had shown me. Feast your eyes:
I've already answered 2-1 and 2-4 here on the blog. Since I first received the sheet, I've also successfully answered all the other problems except 2-6, the final one. Goddamn combinatorial math!
Feel free to try your hand at this set, and if you're especially brave, try to answer all the problems in the allotted time (36 minutes). I'll admit here and now that there's no way I could have managed that feat. For me, the major obstacle was my inability to envision how to set some of these problems up. I did manage to figure out 2-1 without help, but it took a colleague to make me see how to approach 2-4. I arrived at the solution to 2-2 through a sloppy combination of intuitive leaps, a student's hint, and sheer luck. 2-3 wasn't too hard to figure out; in fact, it may be the easiest problem on that sheet.
2-5 deserves a separate paragraph for its sheer awesomeness. It's a really fascinating problem (for us math losers, I mean-- not for math geniuses), and not as difficult as it might look at first blush. If you've been away from a math class for a long time, as I have, you may have forgotten that the phrase "center of symmetry" is not the same as "axis of symmetry." In other words, the FCML problem is asking for the coordinates of a point, not the formula for a line. If you're good at doing algebra in your head, you might even be able to figure this one out without writing a single thing down. Once I did all my figuring, I looked back at everything I had written and saw that there's a very easy way to figure the solution.
2-6 scares the crap out of me. The student who gave me this copy of the FCML questions told me what the answer was after I had given up, but I still don't know how to get to the answer. That student didn't know, either; I asked him. He said he'd managed to figure out only two of the six problems by the end of the allotted time, and 2-6 wasn't one of them.
Good luck!
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