be the orthocenter of acute triangle 
,
be the foot of the altitude from 
to 
,
be the reflection of 
.
intersects line 
and 
.
.
and 
be positive integers, and let 
be a 
grid of unit squares.
or 
rectangle. A subset 
of grid squares in 
edges of the grid squares.
.
and 
,
.
,
is composite, then all positive divisors of 
be positive integers with 
.
be a polynomial of degree 
such that the polynomial 
divides 
is zero. Prove that 
be nonnegative integers such that 
Prove that![\[
\sum_{i=0}^n i\binom{a_i}{2}\le\frac{1}{2}\binom{a_0+a_1+\dots+a_n}{2}.
\]](http://latex.artofproblemsolving.com/c/4/9/c49d0ccfef69402d05dc44d721172498c605cf7e.png)
Note: 
for all nonnegative integers 
be the set of integers, and let 
be a function. Prove that there are infinitely many integers 
such that the function 
defined by 
is not bijective.
,
such that 
.
.
.
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Satisfactory. Keep cooking.
Problems are posted at https://web.evanchen.cc/mockaime.html#current now!
Like last year, we're running the OTIS Mock AIME 2025 again, except this time there will actually be both a I and a II because we had enough problems to pull it off. However, the two versions will feel quite different from each other:
Details are written out at https://web.evanchen.cc/mockaime.html, but to highlight important info:
Problems are posted at https://web.evanchen.cc/mockaime.html#current now!
Like last year, we're running the OTIS Mock AIME 2025 again, except this time there will actually be both a I and a II because we had enough problems to pull it off. However, the two versions will feel quite different from each other:
- The OTIS Mock AIME I is going to be tough. It will definitely be harder than the actual AIME, by perhaps 2 to 4 problems. But more tangibly, it will also have significant artistic license. Problems will freely assume IMO-style background throughout the test, and intentionally stretch the boundary of what constitutes an “AIME problem”.
- The OTIS Mock AIME II is meant to be more practically useful. It will adhere more closely to the difficulty and style of the real AIME. There will inevitably still be some more IMO-flavored problems, but they’ll appear later in the ordering.
Details are written out at https://web.evanchen.cc/mockaime.html, but to highlight important info:
- Free, obviously. Anyone can participate.
- Both tests will release sometime Dec 19th. You can do either/both.
- If you'd like to submit for scoring, you should do so by January 20th at 23:59 Pacific time (same deadline for both). Please hold off on public spoilers before then.
- Solutions, statistics, and maybe some high scores will be published shortly after that.
This post has been edited 1 time. Last edited by v_Enhance, Dec 19, 2024, 6:43 PM
, yeah AIME I is very olympiad-focused. The raw "difficulty" of AIME II is actually very similar to a harder AIME like 2023, but demands more knowledge towards the end.
[14 points] Yonghao Jin
[13 points] Michael Zhao, person1324.990, tenth
[12 points] Advaith Tumiki, Eric Dai, lethan3, sami
