usamo

by pythag011, Apr 30, 2009, 4:48 PM

Well, my (expected) results:

Expected: 7/7/3/7/0/7.

Hopefully I'll make MOP?

Blah I might lose quite a few points for bad proofwriting...

Anyways, thoughts on the problems:

1. Mieh, ok for a 1, but it's just orthocenter, radical center qed.
2. Apparently this was really well known.
3a. Not that hard, somewhat straightfoward induction (not entirely straightfoward though).
3b. I don't know how to solve this, so I can't say. Looks like a pretty good 3b.
4. Simple inequality.
5. Apparently ratio bash kills this.
6. WAY TOO EASY TO BE A 6. (I solved this before I solved 4...)

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7 Comments

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Um on #3 do note that polygon != rectangle. But I dont' know what you did.

by solafidefarms, Apr 30, 2009, 5:32 PM

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I didn't assume it was a rectangle.

by pythag011, Apr 30, 2009, 5:34 PM

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are you sure your solution to #6 works? from what i hear several (very good) people thought they solved it but there was a hole. but nice job anyhow.

by CatalystOfNostalgia, Apr 30, 2009, 9:03 PM

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what 3a is worth either 1 or 2 points probably :O

by not_trig, May 1, 2009, 7:45 PM

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Just curious, what was your solution to #6 on the USAMO?

by Yongyi781, May 4, 2009, 1:36 AM

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Huh I thought radical center does NOT kill the problem when triangle is degenerate??

by serialk11r, May 6, 2009, 5:02 AM

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Hmm I later found out about that unfortunately which is pretty unfortunate.

by pythag011, May 10, 2009, 5:25 PM

Click here if you did not make white MOP (Fake copy of pythag's blog)

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