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Contests & Programs AMC and other contests, summer programs, etc.

AMC and other contests, summer programs, etc.

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k a June Highlights and 2025 AoPS Online Class Information

jlacosta 0

Yesterday at 3:57 PM

Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have a transformative summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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Prealgebra 1 Self-Paced

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0 replies

jlacosta

Yesterday at 3:57 PM

0 replies

k i Adding contests to the Contest Collections

dcouchman 1

N Apr 5, 2023 by v_Enhance

Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add

1 reply

dcouchman

Sep 9, 2019

v_Enhance

Apr 5, 2023

k i Zero tolerance

ZetaX 49

N May 4, 2019 by NoDealsHere

Source: Use your common sense! (enough is enough)

Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:

To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.

More specifically:

For new threads:

a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"

b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".

c) Good problem statement:
Some recent really bad post was:
[quote] $lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$ [/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.

For answers to already existing threads:

d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$ , do not answer with " $x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like " $x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.

To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!

Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.

49 replies

ZetaX

Feb 27, 2007

NoDealsHere

May 4, 2019

Why does π+i^2+ log10(π) + 1/(4π)-sin(1.21 × 10^-5π) yield a value close to e?

Nithish_kumar 0

7 minutes ago

Why does π+i^2+ log10(π) + 1/(4π)-sin(1.21 × 10^-5π) yield a value close to e?

0 replies

Nithish_kumar

7 minutes ago

0 replies

I could have used these three minutes on #10...

sub_math 43

N 24 minutes ago by mahyar_ais

Source: 2020 AIME I #2

There is a unique positive real number $x$ such that the three numbers $\log_8(2x),\log_4x,$ and $\log_2x,$ in that order, form a geometric progression with positive common ratio. The number $x$ can be written as $\tfrac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

43 replies

1 viewing

sub_math

Mar 12, 2020

mahyar_ais

24 minutes ago

Zsigmondy's theorem

V0305 19

N 2 hours ago by CatCatHead

Is Zsigmondy's theorem allowed on the IMO, and is it allowed on the AMC series of proof competitions (e.g. USAJMO, USA TSTST)?

19 replies

+1 w

V0305

May 24, 2025

CatCatHead

2 hours ago

Four Variable System

P_Groudon 29

N 2 hours ago by lakshya2009

Source: 2021 AIME II #7

Let $a, b, c,$ and $d$ be real numbers that satisfy the system of equations
$\begin{align*} a+b&=-3\\ ab+bc+ca&= -4\\ abc+bcd+cda+dab&=14\\ abcd&=30. \end{align*}$ There exist relatively prime positive integers $m$ and $n$ such that
$a^2 + b^2 + c^2 + d^2 = \frac{m}{n}.$ Find $m + n$ .

29 replies

P_Groudon

Mar 19, 2021

lakshya2009

2 hours ago

Problem 4 of RMO 2006 (Regional Mathematical Olympiad-India)

makar 7

N May 24, 2025 by SomeonecoolLovesMaths

Source: Combinatorics (Box Principle)

A $6\times 6$ square is dissected in to 9 rectangles by lines parallel to its sides such that all these rectangles have integer sides. Prove that there are always two congruent rectangles.

7 replies

makar

Sep 13, 2009

SomeonecoolLovesMaths

May 24, 2025

Rectangles of grid cells

tapir1729 11

N May 23, 2025 by Mathandski

Source: TSTST 2024, problem 9

Let $n \ge 2$ be a fixed integer. The cells of an $n \times n$ table are filled with the integers from $1$ to $n^2$ with each number appearing exactly once. Let $N$ be the number of unordered quadruples of cells on this board which form an axis-aligned rectangle, with the two smaller integers being on opposite vertices of this rectangle. Find the largest possible value of $N$ .

Anonymous

11 replies

tapir1729

Jun 24, 2024

Mathandski

May 23, 2025

Tangents to a cyclic quadrilateral

v_Enhance 24

N May 15, 2025 by hectorleo123

Source: ELMO Shortlist 2013: Problem G9, by Allen Liu

Let $ABCD$ be a cyclic quadrilateral inscribed in circle $\omega$ whose diagonals meet at $F$ . Lines $AB$ and $CD$ meet at $E$ . Segment $EF$ intersects $\omega$ at $X$ . Lines $BX$ and $CD$ meet at $M$ , and lines $CX$ and $AB$ meet at $N$ . Prove that $MN$ and $BC$ concur with the tangent to $\omega$ at $X$ .

Proposed by Allen Liu

24 replies

v_Enhance

Jul 23, 2013

hectorleo123

May 15, 2025

subsets of {1,2,...,mn}

N.T.TUAN 11

N May 15, 2025 by MathLuis

Source: USA TST 2005, Problem 1

Let $n$ be an integer greater than $1$ . For a positive integer $m$ , let $S_{m}= \{ 1,2,\ldots, mn\}$ . Suppose that there exists a $2n$ -element set $T$ such that
(a) each element of $T$ is an $m$ -element subset of $S_{m}$ ;
(b) each pair of elements of $T$ shares at most one common element;
and
(c) each element of $S_{m}$ is contained in exactly two elements of $T$ .

Determine the maximum possible value of $m$ in terms of $n$ .

11 replies

N.T.TUAN

May 14, 2007

MathLuis

May 15, 2025

Problem 3 (First Day)

Valentin Vornicu 47

N May 13, 2025 by cj13609517288

Define a "hook" to be a figure made up of six unit squares as shown below in the picture, or any of the figures obtained by applying rotations and reflections to this figure.

IMAGE
Determine all $m\times n$ rectangles that can be covered without gaps and without overlaps with hooks such that

- the rectangle is covered without gaps and without overlaps
- no part of a hook covers area outside the rectangle.

47 replies

Valentin Vornicu

Jul 12, 2004

cj13609517288

May 13, 2025

Jbmo 2011 Problem 4

Eukleidis 13

N May 5, 2025 by Adventure1000

Source: Jbmo 2011

Let $ABCD$ be a convex quadrilateral and points $E$ and $F$ on sides $AB,CD$ such that
$\tfrac{AB}{AE}=\tfrac{CD}{DF}=n$

If $S$ is the area of $AEFD$ show that ${S\leq\frac{AB\cdot CD+n(n-1)AD^2+n^2DA\cdot BC}{2n^2}}$

13 replies

Eukleidis

Jun 21, 2011

Adventure1000

May 5, 2025

HK bisect QS

lssl 24

N May 5, 2025 by LeYohan

Source: 1998 HK

In a concyclic quadrilateral $PQRS$ , $\angle PSR=\frac{\pi}{2}$ , $H,K$ are perpendicular foot from $Q$ to sides $PR,RS$ , prove that $HK$ bisect segment $SQ$ .

24 replies

lssl

Jan 5, 2012

LeYohan

May 5, 2025

foldina a rectangle paper 3 times

parmenides51 1

N May 4, 2025 by TheBaiano

Source: 2023 May Olympiad L2 p4

Matías has a rectangular sheet of paper $ABCD$ , with $AB<AD$ .Initially, he folds the sheet along a straight line $AE$ , where $E$ is a point on the side $DC$ , so that vertex $D$ is located on side $BC$ , as shown in the figure. Then folds the sheet again along a straight line $AF$ , where $F$ is a point on side $BC$ , so that vertex $B$ lies on the line $AE$ ; and finally folds the sheet along the line $EF$ . Matías observed that the vertices $B$ and $C$ were located on the same point of segment $AE$ after making the folds. Calculate the measure of the angle $\angle DAE$ .
IMAGE

1 reply

parmenides51

Mar 24, 2024

TheBaiano

May 4, 2025

Generalized mirror problem

Taha1381 8

N May 2, 2025 by Lemmas

Source: Iranian second round/day1/problem1

We have a rectangle with it sides being a mirror.A light Ray enters from one of the corners of the rectangle and after being reflected several times enters to the opposite corner it started.Prove that at some time the light Ray passed the center of rectangle(Intersection of diagonals.)

8 replies

Taha1381

May 2, 2019

Lemmas

May 2, 2025

Rectangle EFGH in incircle, prove that QIM = 90

v_Enhance 64

N Apr 30, 2025 by lpieleanu

Source: Taiwan 2014 TST1, Problem 3

Let $ABC$ be a triangle with incenter $I$ , and suppose the incircle is tangent to $CA$ and $AB$ at $E$ and $F$ . Denote by $G$ and $H$ the reflections of $E$ and $F$ over $I$ . Let $Q$ be the intersection of $BC$ with $GH$ , and let $M$ be the midpoint of $BC$ . Prove that $IQ$ and $IM$ are perpendicular.

64 replies

v_Enhance

Jul 18, 2014

lpieleanu

Apr 30, 2025

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