USAMO tomorrow

by v_Enhance, Apr 23, 2012, 7:38 PM

Good luck everyone!

My ideal (semi-realistic) USAMO:
  1. Easy combo
  2. NT
  3. Something that starts with "Let ABC be a triangle"
  4. Easy inequality
  5. Something that starts with "Let ABC be a triangle"
  6. Immediate consequence of combo null
Well, I guess more realistically, NT/triangle geo (aka baryable geo) is good for anything that's not 1/4. Anything combo had better be easy or die instantly to Alon's nullstellensatz.
This post has been edited 3 times. Last edited by v_Enhance, Apr 23, 2012, 7:47 PM

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Hopefully we'll see each other at MOP!

GOOD LUCK!

:)

by yugrey, Apr 23, 2012, 7:48 PM

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Speaking of barybash, I'm working on the second half of the solutions, but the problems get a lot harder as they go on. Is there any really efficient way to find the intersection of two lines?

by pi37, Apr 23, 2012, 7:51 PM

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YOU WISH

by Mewto55555, Apr 23, 2012, 8:03 PM

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Good luck :) make Gree33e!1n

by AwesomeToad, Apr 23, 2012, 8:16 PM

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Good luck tomorrow! Make MOP again :D

by GlassBead, Apr 23, 2012, 8:25 PM

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Good luck! Although your ideal USAMO seems very different from mine :wink:

by MathTwo, Apr 23, 2012, 9:57 PM

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Quote:
Speaking of barybash, I'm working on the second half of the solutions, but the problems get a lot harder as they go on. Is there any really efficient way to find the intersection of two lines?
If one of them is the side of a triangle. Otherwise it's going to be a system of two equations, after scaling... so try and be smart with how you use the fact that the lines are homogenous equations. Also, scale the coefficients of the line as well, if you haven't already. :P

Yeah, I probably didn't include enough exercises between the medium-easy and hard range, so the difficulty escalates rapidly. I think one of them may have an intended ``hybrid'' solution; that is, you make quite a few synthetic observations before bringing out the coordinates. I suspect this general idea solves more problems than I've used it on.



Thanks for the good wishes! I'll try and make Green, but we'll see how that works out :)
This post has been edited 1 time. Last edited by v_Enhance, Apr 23, 2012, 11:00 PM

by v_Enhance, Apr 23, 2012, 11:00 PM

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Oh yeah I want that combo J3/J6/U1/U4 as well.

:)

But for the opposite reason. I like combo.

by yugrey, Apr 23, 2012, 11:19 PM

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