Do you think it was more challenging than the previous years?

Not for me, but this test played to my strengths and mostly avoided my biggest weakness (number theory). I have a hard time judging difficulty. I felt like the #1 and #4 were more approachable than some of the 1s and 4s I've seen in recent years.

I liked this test a lot :O except for #3/#6... combo/nt?

I liked both #3 and #6 a lot, though I haven't solved the latter. This is the first USAMO in a while on which I found all six problems appealing. (I'm also glad that they seem to be moving away from bash-it-out inequalities.)

Hmm...

I liked 3, but I thought that 6 was WAY TOO EASY to be a 6.

I just took a look at this. I'm rather surprised that they included #2, actually. This problem actually appeared in the Monthly in early 2008 -- number 11351 if you are interested -- and surely the solution has been published by now as well.

I like #6; it's a nice problem, though it's easier than what I'd expect on a #6. This is the sort of problem I'd expect to see as a #3 or #4 on the Putnam, not as a #6 on the USAMO. Still, it has a nice solution and reminds me of why I liked these sorts of contests in HS and undergrad.

Hmm, I actually disagree with you on 1 and 4 - I think they were less approachable in that they required more experience to solve, and in the case of #1, a "non-trivial" concept (radical axes). At least, I think it does, I haven't seen a solution that doesn't use radical axes or something equivalent (I mean, I see no other way to deal with XY). As for #4, I think someone who doesn't have at least a little bit of experience dealing with inequalities might struggle with this problem, although I may be wrong. I probably wouldn't have solved it last year, but I think I got better at inequalities.

I feel like last year's 1 and 4 were better problems in that they were sort of "see the trick and you're done" type things. To some extent 1 and 4 were like this this time, but I think they more tested general creative problem solving skills rather than problem solving skills in a particular area. I don't know.

I thought the test was pretty good, anyway, in that the problems were nice. 2 and 4 were fun, and 5 probably would have been if I was actually good at geometry (though I think I made some progress?), 3 also looked like fun even though I didn't look at it. Unfortunately, on day 1 I never focused on one problem; 1 looked like pain and 2 looked like fun, but 1 was supposed to be easier (which I now don't actually think is true). This turned out to be a huge mistake and costed me all my chances for MOP.

@CatalystOfNostalgia: I've seen a solution using only Pythagorean theorem (but it was basically the translation of the Carnot proof of radical center)

My solutions to #1 and #4 used very simple tools. (To be sporting, I found a non-radical axis solution to number 1, which is probably the solution pythag refers to.) For #4, I think knowing lots of fancy tools might be a hindrance -- I solved it by just seeing that 1,2,4 and 1,2,2,4 worked. Then, the rest was pretty clear how to handle. The fanciest tool there was 2-variable AM-GM. In general, when I look at #1 and #4 I purposely try to forget all the fancy stuff -- they're not going to put a problem in those positions that require it. I mainly think these were easier than those in the recent past because they were not "process" problems (like the dinosaur problem a couple years back or the triangles problem last year), which are very outside the experience of most beginners. The difficulty with process problems is that newcomers won't even be able to tell if they have a valid solution.

Actually, thinking about it more, I'm coming around to your view on #1. I think of some things as "simple" now in geometry that really aren't. I don't think I have a great handle on how hard geometry problems are. I used power of a point and Pythagorean Theorem, but relating the power of a point to the radius of a circle is not an elementary observation in most geometry classes (although it is Problem 13.22 in our Intro Geometry book )

Yeah, I was expecting a #1 geometry but was hoping it would be a more angle/side chasing thing, something like USAMO 1994.3. As evidenced by the fact that I didn't get #1, I'm probably better at these types of geometry problems (funny story: a former red MOPper and probably someone who will be a 2009 blue MOPper were talking last Sunday at ARML practice, he told me about how he was the reverse of me in terms of geometry - he said he was hoping for a geometry problem on the USAMO that involved saying "oh man there's an orthocenter". i would guess that he was pretty happy about #1...)

Anyway on #4 I don't think it would have been harder for a beginning olympiad problem solver in that it required fancy tools, which I agree, it didn't (I think I had the same solution as you, which I liked because I found it by playing with equality cases), rather I think with any inequalities they take at least some inequality experience in solving them. That's just me; there were no ideas/facts/techniques in previous inequality problems I had done that helped me solve that particular problem, but I felt that just doing inequalities allowed me to solve it more efficiently.

That's a fair comment on #4 -- someone who knows a little AM-GM and Cauchy and a couple other "named" inequalities but is inexperienced probably is in a worse position than someone who doesn't have any experience at all, since the former person might try to jam their fancy tools into the problem. The 8th grader who is just messing around might be more likely to find the solution we found.

Blah, I found this USAMO far more challenging than the ones I took in practice. For one, there was no number theory before 3/6, which hurts me tremendously. Additionally, #2 (which I had time to work on) was combinatorics and #4 was inequalities (which I didn't solve, leaving no time to work on 5). I walked out of day two stunned that I hadn't been able to solve anything.

I realize that I should be happy about solving one problem, and I don't want to come across as another one of those jerks who complains about getting what are by all accounts good scores, but my performance was really far below my expectations.

I also got one problem, #4. I could have also solved #1 if I had just tried my idea to coordinate bash (and it would have worked), but I thought it unfeasible. On #2, I read the problem wrong, so I got confused (but I think I would have gotten confused anyway). #3, #5, and #6 were clearly beyond me.
I wish I could have done more preparation for USAMO, but school, especially my school, is demanding. It calls itself a math and science magnet, but I would venture to say it's more of a humanities one...

Where can I get the problems?