[/quote]
,
atoms called usamons. Each usamon either has one electron or zero electrons, and the physicist can't tell the difference. The physicist's only tool is a diode. The physicist may connect the diode from any usamon 
to any other usamon 
.
.
Let 
.![$$ \frac{1}{2}\geq \frac{a}{a^2+3 }+ \frac{b}{b^2+3} \geq \frac{1}{4}(\frac{1}{\sqrt[3]{3}}+\sqrt[3]{3}-1)$$](http://latex.artofproblemsolving.com/f/9/1/f9119e071c12778037616c624c7b9ca75356e8e3.png)
![$$ \frac{1}{2}\geq \frac{a}{a^3+3 }+ \frac{b}{b^3+3} \geq \frac{1}{2\sqrt[3]{9}}$$](http://latex.artofproblemsolving.com/2/b/2/2b2d8a011229fe88a81cb75f9b018ad3a6245faa.png)
![$$ \frac{1}{2}\geq \frac{a}{a^2+ab+2}+ \frac{b}{b^2+ ab+2} \geq \frac{4\sqrt[3]{3}+3\sqrt[3]{9}-6}{17}$$](http://latex.artofproblemsolving.com/5/f/6/5f673cd494b1909ca237db63e96f949c24b6f2ad.png)
![$$ \frac{1}{2}\geq \frac{a}{a^3+ab+2}+ \frac{b}{b^3+ ab+2} \geq \frac{\sqrt[3]{3}}{5}$$](http://latex.artofproblemsolving.com/b/c/3/bc343a07c88dbd98ebffdfb78f311b7b82683d65.png)
-
be a unit square. Points 
are chosen outside 
. Let 
,
.
is at most 
.
.
and 
lie on segments 
and 
,
and 
intersect at point 
.
and 
intersect at a second point 
.
intersect at a second point 
.
lies on segment 
such that 
.
and 
are similar.
from the non-zero reals to the non-zero reals, such that ![\[f(x+y) \left(f(x) + f(y)\right) = f(xy)\]](http://latex.artofproblemsolving.com/2/f/e/2fe8a09e628f60faedaa07ceb154891375763a83.png)
for all non-zero reals 
such that 
.
.
Let 
.
Let 
.
.
Y by
Hi,
I just received my USAJMO score distribution: 000 701 (very cursed I know)
The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
I just received my USAJMO score distribution: 000 701 (very cursed I know)
The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
