"I didn't solve too many of them"

you solved everything but #4 -_-

Subtract a bit and everything goes away magically!, and we get f = 1 and e = -11.
Then we get that 4e+426f=382, so c+2d+8e+504f=424, b+6c+11d+16e+600f=466, so a+6b+21c+36d+32e+720f=508.

^darn I got 510 on the actual contest. /sulk
Handwaving ftw

lol @ power round #4. That was me thinking "Crap this 'tangent to all rational points' proof is way too hard and there seems to be no geometric way to do it. Let me just tell them what the needed technical lemma is so they can cite it, though I don't expect many people to try to prove it." And then come test time I find #4 had way more attempts than #5 (and way, way less points given out). Also, congratulations to your team for getting the only positive score on 7b.

Glad you liked the problems in general. Seeing as how I wrote all of them. I only heard secondhand reports about how tiebreaker went, but it sounds like things might have been much better if I had put an easier problem in place of the octahedron one. I didn't realize that one was going to be that hard. #1 on the other hand was as hard as I intended it to be.

most of the people in the tiebreakers had the correct idea for TB #2 but had silly errors (forgot to divide by 3, found maximum instead of minimum, etc.)

I felt proud of myself for dividing by 3 until I realized that the question said minimize. ._.

Mind. Blown.

@MellowMelon: I'm still amazed at how you managed to incorporate the 42 seamlessly. That was simply amazing.

^ Seconded.

I have no particular attachment to 42. I was trying to figure out what numbers to put on the right side, and decided that making a bunch of them 0 and having one of the variables come out to 1 would make the arithmetic easier. Just so happened that making the last one 42 pulled that off. I didn't think anything of it when I put it in.

123456789