[/quote]
,
be a scalene triangle with incenter 
and incircle 
.
be 
respectively. Let the line 
intersect the circumcircle of 
.
lies between the points 
and 
.
be a circle that passes through 
and that is tangent to 
which lies on different semi-planes with 
with respect to the line 
at points 
and 
and let the second intersection point of the circumcircle of 
be 
.
and 
lies on the circumcircle of 
and 
lies on 
and 
are situated 
units apart on a level surface. Find the set of all points on the surface which are so situated that the angles of elevation of the tops of the poles are equal.
with 
odd, which satisfy the equation:
denote the set of all real numbers. Find all functions 
such that ![\[ f\left( x^{2}+f(y)\right) =y+\left( f(x)\right) ^{2}\hspace{0.2in}\text{for all}\,x,y\in \mathbb{R}. \]](http://latex.artofproblemsolving.com/8/5/c/85c37ee472f918eace12c8cd7bef6766e617d2aa.png)
(where 
are the digits and 
)
For example the permutation sum of 20253 is 
Let 
and 
be two fivedigit integers with the same permutation sum.
.
pairwise distinct positive integer numbers 
,![\[
\frac{a_i^2 + a_j^2}{a_i + a_j}
\]](http://latex.artofproblemsolving.com/3/5/3/3537ddec6d793d3831ba82a1e13b98d43b1c29bc.png)
is parallel to side 
and tangent to 
is parallel to side 
and tangent to 
,
satisfy all conditions below:
for all 
for all 
for all 
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The International Math Competition (IMC) is essentially the elementary and middle school equivalent of the IMO, with individual and team rounds featuring both short-answer and proof-based problems. See past problems here.
Team USA is looking for 6th graders and below with AIME qualification or AMC 8 DHR (or equivalent), and for 9th graders and below with JMO or Mathcounts Nationals qualification. If you think you meet said criteria, fill out the initial form here.
Here are a couple quick links for further information:
Team USA is looking for 6th graders and below with AIME qualification or AMC 8 DHR (or equivalent), and for 9th graders and below with JMO or Mathcounts Nationals qualification. If you think you meet said criteria, fill out the initial form here.
Here are a couple quick links for further information:
- Dr. Tao Hong's website, which contains a detailed recap of the 2024 competition (and previous years'), as well as Team USA's historical results. (You may recognize a couple names... @channing421 @vrondoS et al.: back me up here
) - My journal, which gives an insider's perspective on the camp
This post has been edited 1 time. Last edited by peace09, Aug 13, 2024, 2:41 PM
(So i was really confused why elementary and middle schoolers can join)
im cooked
