be the n-th prime number in increasing order for 
.
satisfying 
for all 
be an acute triangle. Let 
be the midpoint of side 
,
and 
be the feet of the altitudes from 
and 
,
and 
intersect at a point 
,
is perpendicular to line 
such that ![\[f(f(x)) + xf(xy) = x + f(y)\]](http://latex.artofproblemsolving.com/a/6/f/a6f84dd53eec985b90bad3df6580eeaf29d73195.png)
for all positive real numbers 
and 
.
,
with center 
and radius 
.
intersects the circle 
.
and 
.
.
such that for any real value of 
we have:
and 
are points, such that 
,
= 
and 
and 
passes through the fix point.
Consider an 
-
in the plane. An eligible set is a non-empty set of the form 
where 
determine the smallest possible number of eligible subsets 
such that :
Y by ahaanomegas, dantx5, droid347, ABCDE, Amir Hossein, TheMaskedMagician, MSTang, mathleticguyyy, HamstPan38825, Adventure10
16th Ego Loss May Occur
June 15, 2013 and June 21, 2013
Lincoln, Nebraska
A total of 411 points were given out to 27 contestants (compared to 410 points over 29 last year), for an average score of 15.22 (compared to 14.14 last year). The problems and solutions for the ELMO, as well as the ELSMO, have been attached to this post. The shortlist will be coming out sometime soon.
This year, the gold medalists were LIU2 Michael Ma, WWP3 Calvin Lee, and WWP4 Ashwin Sah, each with 29 points. The winning team was We Won't Phail WWP, with leaders Ryan Alweiss, Brice Huang, Kevin Li, and Michael Seaman. The complete MOP results are at the ELMO website, http://web.mit.edu/~evanchen/www/elmo/.
The top scores on AoPS were:
Avengers, 28 points
mssmath, 21 points
AndrewKwon97, 16 points
In addition, ABCDE, msinghal, and explogabloger each earned 14 points.
The highest D1 score was 7, achieved by Avengers, mssmath, and msinghal. The highest D2 score was 21, achieved by Avengers.
Thank you to everyone who participated!
---
Good morning from ARML Las Vegas! Due to popular request, like last year we will be letting AoPS-ers compete unofficially alongside the MOP attendees at the 16th ELMO.
For those of you that don't already know, the ELMO is an IMO-style exam prepared by returning MOPpers for the new MOPpers. You can see links for the ELMO in 2009, 2010, 2011, 2012 and 2013. The ELMO and its shortlist are also available in the USA contest section. The name of the acronym changes every year.
The proceedings are otherwise similar to last year.
We look forward to your participation!
June 15, 2013 and June 21, 2013
Lincoln, Nebraska
A total of 411 points were given out to 27 contestants (compared to 410 points over 29 last year), for an average score of 15.22 (compared to 14.14 last year). The problems and solutions for the ELMO, as well as the ELSMO, have been attached to this post. The shortlist will be coming out sometime soon.
This year, the gold medalists were LIU2 Michael Ma, WWP3 Calvin Lee, and WWP4 Ashwin Sah, each with 29 points. The winning team was We Won't Phail WWP, with leaders Ryan Alweiss, Brice Huang, Kevin Li, and Michael Seaman. The complete MOP results are at the ELMO website, http://web.mit.edu/~evanchen/www/elmo/.
The top scores on AoPS were:
Avengers, 28 points mssmath, 21 points AndrewKwon97, 16 pointsIn addition, ABCDE, msinghal, and explogabloger each earned 14 points.
The highest D1 score was 7, achieved by Avengers, mssmath, and msinghal. The highest D2 score was 21, achieved by Avengers.
Thank you to everyone who participated!
---
Good morning from ARML Las Vegas! Due to popular request, like last year we will be letting AoPS-ers compete unofficially alongside the MOP attendees at the 16th ELMO.
For those of you that don't already know, the ELMO is an IMO-style exam prepared by returning MOPpers for the new MOPpers. You can see links for the ELMO in 2009, 2010, 2011, 2012 and 2013. The ELMO and its shortlist are also available in the USA contest section. The name of the acronym changes every year.
The proceedings are otherwise similar to last year.
- Sign-up in thread. This sign-up is non-binding and non-mandatory, it's just so I have a rough idea of how many people are submitting.
- You may participate in either Day 1, Day 2, or both. I will post the top scores from each day as well as the top total scores.
- Both days are due 72 hours after Day 2 is posted.
- Each day should be taken under the same conditions as the USAMO, with one exception: you can type up your solutions in LaTeX if you prefer.
- Submit your solutions as a PDF, either scanned or LaTeX-ed, to mockjmo.solutions@gmail.com. Do not send solutions by PM.
- Please do not discuss the problems with others who have not taken the contest until the solutions are posted here. If you want to chat about the problems with people who have already seen the test that is perfectly okay, but please do not spoil the problems for others.
We look forward to your participation!
(It takes me anywhere from 20 to 50 minutes to grade each ELMO submission since I include feedback.)
