[/quote]
,
for which the following statement holds: there exists at least one triple 
of integers such that
and all triples 
are integers.
be a triangle, 
its circumcircle and 
the center of 
be a point on the segment 
.
the second intersection point of the circumcircles of triangles 
and 
.
and the tangent to 
intersect on the circumcircle of triangle 
.
,
,
.![\[\frac{1}{(2a+b+c)^2}+\frac{1}{(a+2b+c)^2}+\frac{1}{(a+b+2c)^2}\leq \frac{3}{16}.\]](http://latex.artofproblemsolving.com/d/1/8/d18152c5635ee2f2059a860bf2fa362fe525ebb3.png)
satisfying the following two conditions:
such that, for all indices 
,
.
and for any index ![\[
a_n a_{n+1} \cdots a_{n+p-1} - a_{n+p}
\]](http://latex.artofproblemsolving.com/5/4/a/54ac17063104439114f3c7b07de8fd27450ea1eb.png)
is a multiple of 
and 
be two fixed points on the circle 
the intersection point of lines 
and 
,
.
be the circumcircle of triangle 
.
be the second intersection point of 
.
intersects 
.
intersects line 
at 
,
intersects 
the second intersection point of the circumcircle of triangle 
with 
into two regions, two parallel planes divide it into three regions, and two intersecting planes divide space into four regions. Consider the six planes which the faces of the cube 
lie on, and the four planes that the tetrahedron 
lie on. How many regions do these ten planes split the space into?
such that 
.
on the board. Charlotte has two operations available: the GCD operation and the LCM operation.
.
.
is called a winning number if there exists a sequence of operations such that, at the end, the only integer left on the board is 
and, for each of them, determine the minimum number of GCD operations Charlotte must use.
be an integer. We consider a square grid of size 
divided into 
unit squares. The grid is called balanced if:
,
or 
.
.
,
such that any balanced grid always contains an 
square whose absolute sum of the 
cells is less than or equal to 
.
Y by Exponent11, Alex-131, Pengu14, squareman, Danielzh, NaturalSelection, EpicBird08, ESAOPS, Everestbaker, scannose, KenWuMath, DhruvJha, crazyeyemoody907
Hello to all creative problem solvers,
Do you want a life changing math experience?
Do you want to see me in real life?
Check out the
Rutgers Expo in Problem Solving (REPS) by OMMC!
OMMC is presenting to you its next major event: in-person this time! This spring, OMMC is hosting its THIRD IN-PERSON event, where we will be presenting various speakers of math, holding breakout sessions, games and friendly competitions, and providing a math hub for people all over to learn and enjoy. No math experience is needed, and elementary, middle and high schoolers can all register!
The Rutgers Expo in Problem Solving will take place on DATE TBD.
The venue is the Science Engineering Complex at Rutgers New-Brunswick. This is 96 Frelinghuysen Rd, Piscataway, NJ 08854.
Event includes:
This event is completely FREE to all students!
Fill out the registration form linked below to sign-up for this event and answer some important questions.
https://docs.google.com/forms/d/e/1FAIpQLSeAr2Nul9MBO_adVzHN9Rsrc8yQEjzxPXZHZ-LUFf-zWcwR7A/viewform?usp=preview
Students from anywhere can attend, as long as you can commute to the venue. Email us at ommcofficial@gmail.com for any questions or concerns.
We can’t wait to see you there!
- REPS Team
OMMC’S 2025 EVENTS ARE SPONSORED BY:
Do you want a life changing math experience?
Do you want to see me in real life?
Check out the
Rutgers Expo in Problem Solving (REPS) by OMMC!
OMMC is presenting to you its next major event: in-person this time! This spring, OMMC is hosting its THIRD IN-PERSON event, where we will be presenting various speakers of math, holding breakout sessions, games and friendly competitions, and providing a math hub for people all over to learn and enjoy. No math experience is needed, and elementary, middle and high schoolers can all register!
The Rutgers Expo in Problem Solving will take place on DATE TBD.
The venue is the Science Engineering Complex at Rutgers New-Brunswick. This is 96 Frelinghuysen Rd, Piscataway, NJ 08854.
Event includes:
- Math speakers, including university professors
- Activities including estimathon and mini math competition WITH PRIZES
- Itinerary coming soon!
This event is completely FREE to all students!
Fill out the registration form linked below to sign-up for this event and answer some important questions.
https://docs.google.com/forms/d/e/1FAIpQLSeAr2Nul9MBO_adVzHN9Rsrc8yQEjzxPXZHZ-LUFf-zWcwR7A/viewform?usp=preview
Students from anywhere can attend, as long as you can commute to the venue. Email us at ommcofficial@gmail.com for any questions or concerns.
We can’t wait to see you there!
- REPS Team
OMMC’S 2025 EVENTS ARE SPONSORED BY:
- Nontrivial Fellowship
- Citadel
- Jane Street
This post has been edited 2 times. Last edited by AoPSSheriff, Apr 15, 2025, 9:54 PM
Reason: Removed social link.
Reason: Removed social link.
