Chinese Dumbass Notation
by v_Enhance, Aug 7, 2012, 3:05 AM
![\[ \begin{tabular}{rccccccccccccc}
& & & & & & 0\\\noalign{\smallskip\smallskip}
& & & & & 0 & & 0\\\noalign{\smallskip\smallskip}
& & & & 1 & & -2 & & 1\\\noalign{\smallskip\smallskip}
& & & -2 & & 2 & & 2 & & -2\\\noalign{\smallskip\smallskip}
& & 1 & & 2 & & -6 & & 2 & & 1\\\noalign{\smallskip\smallskip}
& 0 & & -2 & & 2 & & 2 & & -2 & & 0\\\noalign{\smallskip\smallskip}
0 & & 0 & & 1 & & -2 & & 1 & & 0 & & 0\\\noalign{\smallskip\smallskip}
\end{tabular} \]](http://latex.artofproblemsolving.com/a/b/6/ab62a1e9fa61dcfac4d183a3e4af088a51dee4b3.png)
(I heard this was actually given as a problem at MOP '03.)
(I heard this was actually given as a problem at MOP '03.)
9 Comments
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by
dinoboy, Aug 7, 2012, 3:58 AM
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If this was a MOP '03 problem, then I probably would've cried during the test xD
If I'm not mistaken, this is equivalent to
(first time I tried standard Schur/AM-GM but realized the signs were switched).
If I'm not mistaken, this is equivalent to
(first time I tried standard Schur/AM-GM but realized the signs were switched).This post has been edited 1 time. Last edited by GlassBead, Aug 7, 2012, 1:20 PM
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Wait this problem is definitely not trivial ^^
The tip-off is that
leads to equality; you can see this by noting that the sum of the entries in each row is zero. Hence, if this problem is going to be true, 
had better divide the polynomial, and then cyclically for the others, and since this is degree six we see that this must be the factorization (possibly times a constant).
The tip-off is that
leads to equality; you can see this by noting that the sum of the entries in each row is zero. Hence, if this problem is going to be true, 
had better divide the polynomial, and then cyclically for the others, and since this is degree six we see that this must be the factorization (possibly times a constant).
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by
Mewto55555, Aug 8, 2012, 7:31 PM
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@bzprules haha are there people who actually cry during tests?
On a more serious note, it seems like not in the set of stuff of what people do when faced with an ineq is to plug in a=b (especially in a nice, refined symmetric one like this). BUt hey, if nothing else works, then you might just try that and hope for the best. v_Enhance, you probably had a similar experience with USAMO 2014 #3 hahaha
lolololol
On a more serious note, it seems like not in the set of stuff of what people do when faced with an ineq is to plug in a=b (especially in a nice, refined symmetric one like this). BUt hey, if nothing else works, then you might just try that and hope for the best. v_Enhance, you probably had a similar experience with USAMO 2014 #3 hahaha
lolololol
by
Konigsberg, Dec 24, 2014, 7:16 PM
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