[TEST RELEASED] OMMC Year 5
by DottedCaculator, Apr 26, 2025, 5:40 PM
Test portal: https://ommc-test-portal-2025.vercel.app/
Hello to all creative problem solvers,
Do you want to work on a fun, untimed team math competition with amazing questions by MOPpers and IMO & EGMO medalists?
Do you want to have a chance to win thousands in cash and raffle prizes (no matter your skill level)?
Check out the fifth annual iteration of the
Online Monmouth Math Competition!
Online Monmouth Math Competition, or OMMC, is a 501c3 accredited nonprofit organization managed by adults, college students, and high schoolers which aims to give talented high school and middle school students an exciting way to develop their skills in mathematics.
Our website: https://www.ommcofficial.org/
This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read carefully and thoroughly. Join our Discord or monitor this thread for updates and test releases.
We plan to raffle out a TON of prizes over all competitors regardless of performance. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!
You can check out our past problems and sample problems here:
https://www.ommcofficial.org/sample
https://www.ommcofficial.org/2022-documents
https://www.ommcofficial.org/2023-documents
https://www.ommcofficial.org/ommc-amc
Timeline:
Main Round: May 17th - May 24th
Test Portal Released. The Main Round of the contest is held. The Main Round consists of 25 questions that each have a numerical answer. Teams will have the entire time interval to work on the questions. They can submit any time during the interval. Teams are free to edit their submissions before the period ends, even after they submit.
Final Round: May 26th - May 28th
The top placing teams will qualify for this invitational round (5-10 questions). The final round consists of 5-10 proof questions. Teams again will have the entire time interval to work on these questions and can submit their proofs any time during this interval. Teams are free to edit their submissions before the period ends, even after they submit.
Conclusion of Competition: Early June
Solutions will be released, winners announced, and prizes sent out to winners.
We hope for your participation, and good luck!
OMMC staff
OMMC’S 2025 EVENTS ARE SPONSORED BY:
Hello to all creative problem solvers,
Do you want to work on a fun, untimed team math competition with amazing questions by MOPpers and IMO & EGMO medalists?
Do you want to have a chance to win thousands in cash and raffle prizes (no matter your skill level)?
Check out the fifth annual iteration of the
Online Monmouth Math Competition!
Online Monmouth Math Competition, or OMMC, is a 501c3 accredited nonprofit organization managed by adults, college students, and high schoolers which aims to give talented high school and middle school students an exciting way to develop their skills in mathematics.
Our website: https://www.ommcofficial.org/
This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read carefully and thoroughly. Join our Discord or monitor this thread for updates and test releases.
We plan to raffle out a TON of prizes over all competitors regardless of performance. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!
You can check out our past problems and sample problems here:
https://www.ommcofficial.org/sample
https://www.ommcofficial.org/2022-documents
https://www.ommcofficial.org/2023-documents
https://www.ommcofficial.org/ommc-amc
Timeline:
Main Round: May 17th - May 24th
Test Portal Released. The Main Round of the contest is held. The Main Round consists of 25 questions that each have a numerical answer. Teams will have the entire time interval to work on the questions. They can submit any time during the interval. Teams are free to edit their submissions before the period ends, even after they submit.
Final Round: May 26th - May 28th
The top placing teams will qualify for this invitational round (5-10 questions). The final round consists of 5-10 proof questions. Teams again will have the entire time interval to work on these questions and can submit their proofs any time during this interval. Teams are free to edit their submissions before the period ends, even after they submit.
Conclusion of Competition: Early June
Solutions will be released, winners announced, and prizes sent out to winners.
We hope for your participation, and good luck!
OMMC staff
OMMC’S 2025 EVENTS ARE SPONSORED BY:
- Nontrivial Fellowship
- Citadel
- SPARC
- Jane Street
- And counting!
This post has been edited 4 times. Last edited by AoPSSheriff, May 21, 2025, 6:34 PM
Reason: Removed social link.
Reason: Removed social link.
Alcumus vs books
by UnbeatableJJ, Apr 23, 2025, 12:58 PM
This post has been edited 1 time. Last edited by UnbeatableJJ, May 15, 2025, 2:32 AM
what the yap
by KevinYang2.71, Mar 20, 2025, 12:00 PM
Alice the architect and Bob the builder play a game. First, Alice chooses two points 
and 
in the plane and a subset 
of the plane, which are announced to Bob. Next, Bob marks infinitely many points in the plane, designating each a city. He may not place two cities within distance at most one unit of each other, and no three cities he places may be collinear. Finally, roads are constructed between the cities as follows: for each pair 
of cities, they are connected with a road along the line segment 
if and only if the following condition holds:
Note:
is directly similar to 
if there exists a sequence of rotations, translations, and dilations sending 
to 
, 
to 
, and 
to 
.
and 
in the plane and a subset 
of the plane, which are announced to Bob. Next, Bob marks infinitely many points in the plane, designating each a city. He may not place two cities within distance at most one unit of each other, and no three cities he places may be collinear. Finally, roads are constructed between the cities as follows: for each pair 
of cities, they are connected with a road along the line segment 
if and only if the following condition holds:
For every city 
distinct from 
and 
, there exists 
such
distinct from 
and 
, there exists 
such
that 
is directly similar to either 
or 
.
Alice wins the game if (i) the resulting roads allow for travel between any pair of cities via a finite sequence of roads and (ii) no two roads cross. Otherwise, Bob wins. Determine, with proof, which player has a winning strategy.
is directly similar to either 
or 
.
Note:
is directly similar to 
if there exists a sequence of rotations, translations, and dilations sending 
to 
, 
to 
, and 
to 
.Special Points on $BC$
by tenniskidperson3, May 1, 2013, 10:01 PM
Let 
be a triangle. Find all points on segment 
satisfying the following property: If and are the intersections of line 
with the common external tangent lines of the circumcircles of triangles 
and 
, then ![\[\left(\frac{PA}{XY}\right)^2+\frac{PB\cdot PC}{AB\cdot AC}=1.\]](//latex.artofproblemsolving.com/0/8/0/080a689aea002f1b997294cb6aa48d3334881be7.png)
be a triangle. Find all points on segment 
satisfying the following property: If and are the intersections of line 
with the common external tangent lines of the circumcircles of triangles 
and 
, then ![\[\left(\frac{PA}{XY}\right)^2+\frac{PB\cdot PC}{AB\cdot AC}=1.\]](http://latex.artofproblemsolving.com/0/8/0/080a689aea002f1b997294cb6aa48d3334881be7.png)
USAJMO problem 3: Inequality
by BOGTRO, Apr 24, 2012, 9:57 PM
Let 
be positive real numbers. Prove that 
.
be positive real numbers. Prove that 
.Inequality with a^2+b^2+c^2+abc=4
by cn2_71828182846, Jun 27, 2004, 5:54 PM
Let 
and satisfy ![\[ a^2+b^2+c^2 +abc = 4 . \]](//latex.artofproblemsolving.com/d/3/a/d3ac01295b077425b5eaae556faa4cd678bce32a.png)
Show that ![\[ 0 \le ab + bc + ca - abc \leq 2. \]](//latex.artofproblemsolving.com/2/0/9/209b3fcb56c01c335bbcb8d5fb781e28e49a0798.png)
and satisfy ![\[ a^2+b^2+c^2 +abc = 4 . \]](http://latex.artofproblemsolving.com/d/3/a/d3ac01295b077425b5eaae556faa4cd678bce32a.png)
Show that ![\[ 0 \le ab + bc + ca - abc \leq 2. \]](http://latex.artofproblemsolving.com/2/0/9/209b3fcb56c01c335bbcb8d5fb781e28e49a0798.png)
This post has been edited 1 time. Last edited by v_Enhance, May 11, 2014, 3:38 PM
Reason: Added left bound from original problem statement
Reason: Added left bound from original problem statement
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