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From: Graven Water on 21 Jun 2010 17:34
I was solving problems from the 2006 Math Olympiad, and I came across this
one, which puzzled me for many days:

Assign to each side b of a convex polygon P the maximum area of a triangle
that has b as a side and is contained in P. Show that the sum of the
areas assigned to the sides of P is at least twice the area of P.

It was very frustrating! But I knew from past experience that when I
finally solve problems that have cost long struggle, the result is very
nice. So with this prospect dangling before me, EVENTUALLY, I solved it!

WHen I watched the Youtube video that I thought had the solution, it
turned out nobody in the Math Olympiad had solved it! So after feeling
stupid for days, I felt better.

I didn't see the short, clever solution online in a quick search, only a
horribly laborious version. So here's the clever proof:

http://camoo.freeshell.org/IMO_2006_6.pdf

Laura

From: Henry on 22 Jun 2010 05:04
On 21 June, 22:34, p...(a)grex.org (Graven Water) wrote:
>
> WHen I watched the Youtube video that I thought had the solution, it
> turned out nobody in the Math Olympiad had solved it!  So after feeling
> stupid for days, I felt better.  

That is not quite correct. 8 people seem to have solved it in the IMO
(2 each from China and Russia, and 1 each from Moldova, Poland,
Germany, and France) and 1 almost did (South Korea).

See http://imo2006.dmfa.si/results_itd.html
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