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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Jul 1, 2025
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
and train with the best! Please note that early bird pricing ends August 19th!
Are you tired of the heat and thinking about Fall? You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US.

Our full course list for upcoming classes is below:
All classes start 7:30pm ET/4:30pm PT unless otherwise noted.

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0 replies
jwelsh
Jul 1, 2025
0 replies
k i Peer-to-Peer Programs Forum
jwelsh   157
N Dec 11, 2023 by cw357
Many of our AoPS Community members share their knowledge with their peers in a variety of ways, ranging from creating mock contests to creating real contests to writing handouts to hosting sessions as part of our partnership with schoolhouse.world.

To facilitate students in these efforts, we have created a new Peer-to-Peer Programs forum. With the creation of this forum, we are starting a new process for those of you who want to advertise your efforts. These advertisements and ensuing discussions have been cluttering up some of the forums that were meant for other purposes, so we’re gathering these topics in one place. This also allows students to find new peer-to-peer learning opportunities without having to poke around all the other forums.

To announce your program, or to invite others to work with you on it, here’s what to do:

1) Post a new topic in the Peer-to-Peer Programs forum. This will be the discussion thread for your program.

2) Post a single brief post in this thread that links the discussion thread of your program in the Peer-to-Peer Programs forum.

Please note that we’ll move or delete any future advertisement posts that are outside the Peer-to-Peer Programs forum, as well as any posts in this topic that are not brief announcements of new opportunities. In particular, this topic should not be used to discuss specific programs; those discussions should occur in topics in the Peer-to-Peer Programs forum.

Your post in this thread should have what you're sharing (class, session, tutoring, handout, math or coding game/other program) and a link to the thread in the Peer-to-Peer Programs forum, which should have more information (like where to find what you're sharing).
157 replies
jwelsh
Mar 15, 2021
cw357
Dec 11, 2023
k i C&P posting recs by mods
v_Enhance   0
Jun 12, 2020
The purpose of this post is to lay out a few suggestions about what kind of posts work well for the C&P forum. Except in a few cases these are mostly meant to be "suggestions based on historical trends" rather than firm hard rules; we may eventually replace this with an actual list of firm rules but that requires admin approval :) That said, if you post something in the "discouraged" category, you should not be totally surprised if it gets locked; they are discouraged exactly because past experience shows they tend to go badly.
-----------------------------
1. Program discussion: Allowed
If you have questions about specific camps or programs (e.g. which classes are good at X camp?), these questions fit well here. Many camps/programs have specific sub-forums too but we understand a lot of them are not active.
-----------------------------
2. Results discussion: Allowed
You can make threads about e.g. how you did on contests (including AMC), though on AMC day when there is a lot of discussion. Moderators and administrators may do a lot of thread-merging / forum-wrangling to keep things in one place.
-----------------------------
3. Reposting solutions or questions to past AMC/AIME/USAMO problems: Allowed
This forum contains a post for nearly every problem from AMC8, AMC10, AMC12, AIME, USAJMO, USAMO (and these links give you an index of all these posts). It is always permitted to post a full solution to any problem in its own thread (linked above), regardless of how old the problem is, and even if this solution is similar to one that has already been posted. We encourage this type of posting because it is helpful for the user to explain their solution in full to an audience, and for future users who want to see multiple approaches to a problem or even just the frequency distribution of common approaches. We do ask for some explanation; if you just post "the answer is (B); ez" then you are not adding anything useful.

You are also encouraged to post questions about a specific problem in the specific thread for that problem, or about previous user's solutions. It's almost always better to use the existing thread than to start a new one, to keep all the discussion in one place easily searchable for future visitors.
-----------------------------
4. Advice posts: Allowed, but read below first
You can use this forum to ask for advice about how to prepare for math competitions in general. But you should be aware that this question has been asked many many times. Before making a post, you are encouraged to look at the following:
[list]
[*] Stop looking for the right training: A generic post about advice that keeps getting stickied :)
[*] There is an enormous list of links on the Wiki of books / problems / etc for all levels.
[/list]
When you do post, we really encourage you to be as specific as possible in your question. Tell us about your background, what you've tried already, etc.

Actually, the absolute best way to get a helpful response is to take a few examples of problems that you tried to solve but couldn't, and explain what you tried on them / why you couldn't solve them. Here is a great example of a specific question.
-----------------------------
5. Publicity: use P2P forum instead
See https://artofproblemsolving.com/community/c5h2489297_peertopeer_programs_forum.
Some exceptions have been allowed in the past, but these require approval from administrators. (I am not totally sure what the criteria is. I am not an administrator.)
-----------------------------
6. Mock contests: use Mock Contests forum instead
Mock contests should be posted in the dedicated forum instead:
https://artofproblemsolving.com/community/c594864_aops_mock_contests
-----------------------------
7. AMC procedural questions: suggest to contact the AMC HQ instead
If you have a question like "how do I submit a change of venue form for the AIME" or "why is my name not on the qualifiers list even though I have a 300 index", you would be better off calling or emailing the AMC program to ask, they are the ones who can help you :)
-----------------------------
8. Discussion of random math problems: suggest to use MSM/HSM/HSO instead
If you are discussing a specific math problem that isn't from the AMC/AIME/USAMO, it's better to post these in Middle School Math, High School Math, High School Olympiads instead.
-----------------------------
9. Politics: suggest to use Round Table instead
There are important conversations to be had about things like gender diversity in math contests, etc., for sure. However, from experience we think that C&P is historically not a good place to have these conversations, as they go off the rails very quickly. We encourage you to use the Round Table instead, where it is much more clear that all posts need to be serious.
-----------------------------
10. MAA complaints: discouraged
We don't want to pretend that the MAA is perfect or that we agree with everything they do. However, we chose to discourage this sort of behavior because in practice most of the comments we see are not useful and some are frankly offensive.
[list] [*] If you just want to blow off steam, do it on your blog instead.
[*] When you have criticism, it should be reasoned, well-thought and constructive. What we mean by this is, for example, when the AOIME was announced, there was great outrage about potential cheating. Well, do you really think that this is something the organizers didn't think about too? Simply posting that "people will cheat and steal my USAMOO qualification, the MAA are idiots!" is not helpful as it is not bringing any new information to the table.
[*] Even if you do have reasoned, well-thought, constructive criticism, we think it is actually better to email it the MAA instead, rather than post it here. Experience shows that even polite, well-meaning suggestions posted in C&P are often derailed by less mature users who insist on complaining about everything.
[/list]
-----------------------------
11. Memes and joke posts: discouraged
It's fine to make jokes or lighthearted posts every so often. But it should be done with discretion. Ideally, jokes should be done within a longer post that has other content. For example, in my response to one user's question about olympiad combinatorics, I used a silly picture of Sogiita Gunha, but it was done within a context of a much longer post where it was meant to actually make a point.

On the other hand, there are many threads which consist largely of posts whose only content is an attached meme with the word "MAA" in it. When done in excess like this, the jokes reflect poorly on the community, so we explicitly discourage them.
-----------------------------
12. Questions that no one can answer: discouraged
Examples of this: "will MIT ask for AOIME scores?", "what will the AIME 2021 cutoffs be (asked in 2020)", etc. Basically, if you ask a question on this forum, it's better if the question is something that a user can plausibly answer :)
-----------------------------
13. Blind speculation: discouraged
Along these lines, if you do see a question that you don't have an answer to, we discourage "blindly guessing" as it leads to spreading of baseless rumors. For example, if you see some user posting "why are there fewer qualifiers than usual this year?", you should not reply "the MAA must have been worried about online cheating so they took fewer people!!". Was sich überhaupt sagen lässt, lässt sich klar sagen; und wovon man nicht reden kann, darüber muss man schweigen.
-----------------------------
14. Discussion of cheating: strongly discouraged
If you have evidence or reasonable suspicion of cheating, please report this to your Competition Manager or to the AMC HQ; these forums cannot help you.
Otherwise, please avoid public discussion of cheating. That is: no discussion of methods of cheating, no speculation about how cheating affects cutoffs, and so on --- it is not helpful to anyone, and it creates a sour atmosphere. A longer explanation is given in Seriously, please stop discussing how to cheat.
-----------------------------
15. Cutoff jokes: never allowed
Whenever the cutoffs for any major contest are released, it is very obvious when they are official. In the past, this has been achieved by the numbers being posted on the official AMC website (here) or through a post from the AMCDirector account.

You must never post fake cutoffs, even as a joke. You should also refrain from posting cutoffs that you've heard of via email, etc., because it is better to wait for the obvious official announcement. A longer explanation is given in A Treatise on Cutoff Trolling.
-----------------------------
16. Meanness: never allowed
Being mean is worse than being immature and unproductive. If another user does something which you think is inappropriate, use the Report button to bring the post to moderator attention, or if you really must reply, do so in a way that is tactful and constructive rather than inflammatory.
-----------------------------

Finally, we remind you all to sit back and enjoy the problems. :D

-----------------------------
(EDIT 2024-09-13: AoPS has asked to me to add the following item.)

Advertising paid program or service: never allowed

Per the AoPS Terms of Service (rule 5h), general advertisements are not allowed.

While we do allow advertisements of official contests (at the MAA and MATHCOUNTS level) and those run by college students with at least one successful year, any and all advertisements of a paid service or program is not allowed and will be deleted.
0 replies
v_Enhance
Jun 12, 2020
0 replies
k i Stop looking for the "right" training
v_Enhance   50
N Oct 16, 2017 by blawho12
Source: Contest advice
EDIT 2019-02-01: https://blog.evanchen.cc/2019/01/31/math-contest-platitudes-v3/ is the updated version of this.

EDIT 2021-06-09: see also https://web.evanchen.cc/faq-contest.html.

Original 2013 post
50 replies
v_Enhance
Feb 15, 2013
blawho12
Oct 16, 2017
2000 TAMU - Best Student Exam - Texas A&M University HS Mathematics Contest
parmenides51   14
N 17 minutes ago by imtiyas1
p1. Simplify the expression $(x-1)^4 + 4(x-1)^3 + 6(x-1)2 + 4(x-1) + 1$.


p2. Find the minimum value of $\sqrt{x^2 + y^2}$ if $6x-5y = 4$.


p3. Suppose $x, b > 0$ and $\log_{b^2} x + \log_{x^2} b = 1$.Find x.


p4. The sum of $n$ terms in an arithmetic progression is $153$, and the common difference is $2$. If the fist term is an integer, and $n > 1$, then what is the number of all possible values for $n$?


p5. Let $f$ be a function such that $f(3) = 1$ and $f(3x) = x+f (3x- 3)$ for all $x$. Find $f(300)$.


p6. Suppose $\vartriangle ABC$ is an equilateral triangle and $P$ is a point interior to $\vartriangle ABC$. If the distance from P to sides $AB$, $BC$ and $AC$ is $6$, $7$ and $8$ units respectively, what is the area of $\vartriangle ABC$?


p7. If $A =\begin{pmatrix}
a & b\\
c & d
\end{pmatrix}$ and $B =\begin{pmatrix}
w & x\\
y & z
\end{pmatrix}$ then the product $A \cdot B$ is defined to be $AB =\begin{pmatrix}
aw + by & ax + bz\\
cw + dy & cx + dz
\end{pmatrix}$.
Furthermore, $A^2 = A \cdot A$, $A^3 = A \cdot A \cdot A$, etc $...$ If $A =\begin{pmatrix}
0 & a\\
b & 0
\end{pmatrix}$, find $A^{241}$.


p8. A circle and a parabola are drawn in the $xy$-plane. The circle has its center at $(0, 5)$ with a radius of $4$, and the parabola has its vertex at $(0, 0)$ . If the circle is tangent to the parabola at two points, give the equation of the parabola.


p9. The triangle $PQR$ sits in the $xy$-plane with $P = (0, 0)$, $Q = (3, 12)$ and $R = (6, 0)$ . Suppose the x-axis represents the horizontal ground and the triangle is rotated counter clockwise around the origin (note that $P$ will stay fixed) until it reaches a position where it balances perfectly on the vertex $P$. What is the y-coordinate of the point $Q$ when the triangle is balanced?


p10. A circle is placed in the $xy$-plane and a line $L$ is drawn through the center of the circle. Suppose $P$ is a point interior to the circle which is $6$ units from the circle, $6$ units from the line $L$ and $10$ units from the closest intersection point of the line $L$ with the circle. What is the area of the circle?


p11. Five people are asked (individually) to choose a random integer in the interval $[1, 20]$. What is the probability that everyone chooses a different number?


p12. A matrix $\begin{pmatrix}
a & b\\
c & d
\end{pmatrix}$ is said to be singular if $ad - bc = 0$. If the matrix $\begin{pmatrix}
a & b\\
c & d
\end{pmatrix}$ is created at random by choosing integer values $a, b, c, d$ at random from the interval $[-3, 3]$ , what is the probability that the matrix will be singular?


p13. Consider the table of values shown below $\begin{tabular}{ | l | c | c | r| }
    \hline
    2 & a & b & 2 \\ \hline
    c & 2 & 2 & d \\ \hline
       e & 2 & 2 & f\\ \hline
 2 & g & h & 2\\
    \hline
  \end{tabular}$.
All rows and columns of this table sum to $0$. In addition, $a + c = 5$ and $eg = 22$. Find all possible solutions $(a, b, c, d, e, f, g, h)$.


p14. Let $P > 0$ and suppose $\vartriangle ABC$ is an isosceles right triangle with area $P$ square inches. What is the radius of the circle that passes through the points $A, B$ and $C$?


p15. How must the numbers $a, b$ and $c$ be related for the following system to have at least one solution?
$$x - 2y + z = a$$$$2x + y - 2z = b$$$$x + 3y-3z = c$$

p16. Let $x$ be a real number and create a triangle having vertices $(-2, 1)$ , $(1, 3)$ and $(3x, 2x- 3)$ : Give a formula for the area of this triangle.


p17. The final race in a swimming event involves $8$ swimmers. Three of the swimmers are from one country and the other five are from different countries. Each is to be given a lane assignment between $1$ and $8$ for the race. Aside from the obvious rule that no two swimmers can be assigned to the same lane, there are two other restrictions. The first is that no two swimmers from the same country can be in adjacent lanes. The second is that the two outside lanes cannot be occupied by swimmers from the same country. With these rules, how many different lane assignments are possible for this race?


p18. Let $r > 0$. Four circles of radius $2r$ are placed in the xy-plane so that their centers are located at $(-r,-r)$ , $(-r, r)$ , $(r, r)$ and $(r,-r)$ . What is the area of the region of intersection of these circles?


PS. You should use hide for answers. Collected here.
14 replies
parmenides51
Mar 22, 2022
imtiyas1
17 minutes ago
Simple Angle Chasing Problem Stumping Me
WheatNeat   6
N 23 minutes ago by Sid-darth-vater
Isoceles triangle $ABC$ with $AC = BC$, has angle $CAB$ as $80$ degrees. Let points $E$ and $D$ be on sides $BC$ and $AC$ respectively, such that angle $CBD$ is 20 degrees and angle $CAE$ is 10 degrees. Find angle $DEA$.
6 replies
WheatNeat
Yesterday at 8:54 AM
Sid-darth-vater
23 minutes ago
Inequalities
sqing   8
N 2 hours ago by sqing
Suppose that $x$ and $y$ are nonzero real numbers such that $\left(x + \frac{1}{y} \right) \left(y + \frac{1}{x} \right) = 5$. Prove that
$$\left( x^2-y^2 + \frac{1}{y^2} \right) \left(y^2-x^2 + \frac{1}{x^2} \right)\leq  \frac{7+3\sqrt{5}}{2}$$$$\left( x^3 -y^3+ \frac{1}{y^3} \right) \left(y^3 -x^3+ \frac{1}{x^3} \right)\leq  9+4\sqrt{5}$$
8 replies
sqing
Wednesday at 11:54 AM
sqing
2 hours ago
2v2 (bob lost the game)
GoodMorning   87
N 3 hours ago by eg4334
Source: 2023 USAJMO Problem 5/USAMO Problem 4
A positive integer $a$ is selected, and some positive integers are written on a board. Alice and Bob play the following game. On Alice's turn, she must replace some integer $n$ on the board with $n+a$, and on Bob's turn he must replace some even integer $n$ on the board with $n/2$. Alice goes first and they alternate turns. If on his turn Bob has no valid moves, the game ends.

After analyzing the integers on the board, Bob realizes that, regardless of what moves Alice makes, he will be able to force the game to end eventually. Show that, in fact, for this value of $a$ and these integers on the board, the game is guaranteed to end regardless of Alice's or Bob's moves.
87 replies
GoodMorning
Mar 23, 2023
eg4334
3 hours ago
Goals for 2025-2026
Airbus320-214   297
N 4 hours ago by pingpongmerrily
Please write down your goal/goals for competitions here for 2025-2026.
297 replies
Airbus320-214
May 11, 2025
pingpongmerrily
4 hours ago
Sad Algebra
tastymath75025   47
N 4 hours ago by ihategeo_1969
Source: 2019 USAMO 6, by Titu Andreescu and Gabriel Dospinescu
Find all polynomials $P$ with real coefficients such that $$\frac{P(x)}{yz}+\frac{P(y)}{zx}+\frac{P(z)}{xy}=P(x-y)+P(y-z)+P(z-x)$$holds for all nonzero real numbers $x,y,z$ satisfying $2xyz=x+y+z$.

Proposed by Titu Andreescu and Gabriel Dospinescu
47 replies
tastymath75025
Apr 18, 2019
ihategeo_1969
4 hours ago
min m such m2^5x 3^6x4^3x5^3x6^7 perfect square - IOQM 2020-21 p6
parmenides51   4
N 6 hours ago by SomeonecoolLovesMaths
What is the least positive integer by which $2^5 \cdot  3^6 \cdot  4^3 \cdot  5^3 \cdot 6^7$ should be multiplied so that, the product is a perfect square?
4 replies
parmenides51
Jan 18, 2021
SomeonecoolLovesMaths
6 hours ago
Congruent Incircles
worthawholebean   31
N Yesterday at 8:43 PM by Kempu33334
Source: AIME 2010I Problem 15
In $ \triangle{ABC}$ with $ AB = 12$, $ BC = 13$, and $ AC = 15$, let $ M$ be a point on $ \overline{AC}$ such that the incircles of $ \triangle{ABM}$ and $ \triangle{BCM}$ have equal radii. Let $ p$ and $ q$ be positive relatively prime integers such that $ \tfrac{AM}{CM} = \tfrac{p}{q}$. Find $ p + q$.
31 replies
worthawholebean
Mar 17, 2010
Kempu33334
Yesterday at 8:43 PM
USAJMO problem 3: Inequality
BOGTRO   109
N Yesterday at 8:32 PM by SomeonecoolLovesMaths
Let $a,b,c$ be positive real numbers. Prove that $\frac{a^3+3b^3}{5a+b}+\frac{b^3+3c^3}{5b+c}+\frac{c^3+3a^3}{5c+a} \geq \frac{2}{3}(a^2+b^2+c^2)$.
109 replies
BOGTRO
Apr 24, 2012
SomeonecoolLovesMaths
Yesterday at 8:32 PM
hardest subject on amc 10?
hgmium   21
N Yesterday at 6:14 PM by hgmium
amc 10 is coming in a few months, and I'm not sure what to spent most of my time on
what topic should i focus on the most?
21 replies
hgmium
Jun 26, 2025
hgmium
Yesterday at 6:14 PM
Find BE
TheMaskedMagician   6
N Yesterday at 5:44 PM by SomeonecoolLovesMaths
Source: AHSME 1963 Problem 38
Point $F$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BF$ intersects diagonal $AC$ at $E$ and side $DC$ at $G$. If $EF = 32$ and $GF = 24$, then $BE$ equals:


IMAGE



$\textbf{(A)}\ 4 \qquad
\textbf{(B)}\ 8\qquad
\textbf{(C)}\ 10 \qquad
\textbf{(D)}\ 12 \qquad
\textbf{(E)}\ 16$
6 replies
TheMaskedMagician
Jan 13, 2014
SomeonecoolLovesMaths
Yesterday at 5:44 PM
LTE or Binomial Theorem
P_Groudon   111
N Yesterday at 5:34 PM by eg4334
Source: 2020 AIME I #12
Let $n$ be the least positive integer for which $149^n - 2^n$ is divisible by $3^3 \cdot 5^5 \cdot 7^7$. Find the number of positive divisors of $n$.
111 replies
P_Groudon
Mar 12, 2020
eg4334
Yesterday at 5:34 PM
MAA likes misplacing problems this year
math31415926535   42
N Yesterday at 4:52 PM by Kempu33334
Source: 2022 AIME II Problem 11
Let $ABCD$ be a convex quadrilateral with $AB=2, AD=7,$ and $CD=3$ such that the bisectors of acute angles $\angle{DAB}$ and $\angle{ADC}$ intersect at the midpoint of $\overline{BC}.$ Find the square of the area of $ABCD.$
42 replies
math31415926535
Feb 17, 2022
Kempu33334
Yesterday at 4:52 PM
A lot of integer lengths: JMO #6 or USAMO Problem 4
BarbieRocks   83
N Yesterday at 3:30 PM by Kempu33334
Let $ABC$ be a triangle with $\angle A = 90^{\circ}$. Points $D$ and $E$ lie on sides $AC$ and $AB$, respectively, such that $\angle ABD = \angle DBC$ and $\angle ACE = \angle ECB$. Segments $BD$ and $CE$ meet at $I$. Determine whether or not it is possible for segments $AB$, $AC$, $BI$, $ID$, $CI$, $IE$ to all have integer lengths.
83 replies
BarbieRocks
Apr 29, 2010
Kempu33334
Yesterday at 3:30 PM
book/resource recommendations
walterboro   3
N May 13, 2025 by Konigsberg
hi guys, does anyone have book recs (or other resources) for like aime+ level alg, nt, geo, comb? i want to learn a lot of theory in depth
also does anyone know how otis or woot is like from experience?
3 replies
walterboro
May 11, 2025
Konigsberg
May 13, 2025
book/resource recommendations
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walterboro
4 posts
#1
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hi guys, does anyone have book recs (or other resources) for like aime+ level alg, nt, geo, comb? i want to learn a lot of theory in depth
also does anyone know how otis or woot is like from experience?
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Konigsberg
2239 posts
#2
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Since your question is quite general, I’d first link this guide: https://tinyurl.com/ContestGuideIntlGDrive.

OTIS and WOOT are both good programs if you’d want more structure in your training.
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walterboro
4 posts
#3
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could u link it again pls? the link doesn't work
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Konigsberg
2239 posts
#4
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this link works: https://tinyurl.com/ContestGuideIntlGDrive

are you not able to open it due to restrictions on google drive?
This post has been edited 1 time. Last edited by Konigsberg, May 13, 2025, 5:40 AM
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