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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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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 March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/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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0 replies
jlacosta
Mar 2, 2025
0 replies
AIME score for college apps
Happyllamaalways   56
N 5 hours ago by Countmath1
What good colleges do I have a chance of getting into with an 11 on AIME? (Any chances for Princeton)

Also idk if this has weight but I had the highest AIME score in my school.
56 replies
Happyllamaalways
Mar 13, 2025
Countmath1
5 hours ago
MIT Beaverworks Summer Institute
PowerOfPi_09   0
5 hours ago
Hi! I was wondering if anyone here has completed this program, and if so, which track did you choose? Do rising juniors have a chance, or is it mainly rising seniors that they accept? Also, how long did it take you to complete the prerequisites?
Thanks!
0 replies
PowerOfPi_09
5 hours ago
0 replies
Convolution of order f(n)
trumpeter   70
N 5 hours ago by HamstPan38825
Source: 2019 USAMO Problem 1
Let $\mathbb{N}$ be the set of positive integers. A function $f:\mathbb{N}\to\mathbb{N}$ satisfies the equation \[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]for all positive integers $n$. Given this information, determine all possible values of $f(1000)$.

Proposed by Evan Chen
70 replies
trumpeter
Apr 17, 2019
HamstPan38825
5 hours ago
k HOT TAKE: MIT SHOULD NOT RELEASE THEIR DECISIONS ON PI DAY
alcumusftwgrind   8
N Today at 10:13 AM by maxamc
rant lol

Imagine a poor senior waiting for their MIT decisions just to have their hopes CRUSHED on 3/14 and they can't even celebrate pi day...

and even worse, this year's pi day is special because this year is a very special number...

8 replies
alcumusftwgrind
Today at 2:11 AM
maxamc
Today at 10:13 AM
No more topics!
Repeating Decimals of Different Lengths
Happytycho   10
N Dec 31, 2019 by V10599116111114
Source: Problem #22 2016 AMC 12B
For a certain positive integer $n$ less than $1000$, the decimal equivalent of $\frac{1}{n}$ is $0.\overline{abcdef}$, a repeating decimal of period $6$, and the decimal equivalent of $\frac{1}{n+6}$ is $0.\overline{wxyz}$, a repeating decimal of period $4$. In which interval does $n$ lie?

$\textbf{(A)}\ [1,200] \qquad
\textbf{(B)}\ [201,400] \qquad
\textbf{(C)}\ [401,600] \qquad
\textbf{(D)}\ [601,800] \qquad
\textbf{(E)}\ [801,999] $
10 replies
Happytycho
Feb 21, 2016
V10599116111114
Dec 31, 2019
Repeating Decimals of Different Lengths
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Source: Problem #22 2016 AMC 12B
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Happytycho
661 posts
#1 • 2 Y
Y by Adventure10, Mango247
For a certain positive integer $n$ less than $1000$, the decimal equivalent of $\frac{1}{n}$ is $0.\overline{abcdef}$, a repeating decimal of period $6$, and the decimal equivalent of $\frac{1}{n+6}$ is $0.\overline{wxyz}$, a repeating decimal of period $4$. In which interval does $n$ lie?

$\textbf{(A)}\ [1,200] \qquad
\textbf{(B)}\ [201,400] \qquad
\textbf{(C)}\ [401,600] \qquad
\textbf{(D)}\ [601,800] \qquad
\textbf{(E)}\ [801,999] $
Z K Y
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rkm0959
1721 posts
#2 • 6 Y
Y by eyzhang, DominicanAOPSer, dantx5, dram, Adventure10, Mango247
Solution
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YumaT
100 posts
#3 • 1 Y
Y by Adventure10
why does 27 fail
Z K Y
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YumaT
100 posts
#4 • 2 Y
Y by Adventure10, Mango247
^without the use of a calculator
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Mudkipswims42
8867 posts
#5 • 2 Y
Y by Adventure10, Mango247
YumaT wrote:
why does 27 fail

$\frac{1}{33}$ clearly has period 2
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shiningsunnyday
1350 posts
#6 • 2 Y
Y by Adventure10, Mango247
Here's my full solution. #Shamelessadvertising
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YumaT
100 posts
#7 • 2 Y
Y by Adventure10, Mango247
oh ok I get it now. Thanks!
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YumaT
100 posts
#8 • 2 Y
Y by Adventure10, Mango247
Can you explain mod's? I've been trying to understand it on my own, but I only get the basics. Also, can you mention how to use it effectively on AMC's?
This post has been edited 1 time. Last edited by YumaT, Sep 5, 2016, 2:56 PM
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velraman
105 posts
#9 • 2 Y
Y by Adventure10, Mango247
rkm0959 wrote:
$n|10^6-1=999999$ and $n+6|10^4-1=9999$.

Why $n+6$ should divide $10^4-1$ ?
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ayushk
362 posts
#10 • 11 Y
Y by velraman, shaletome, Binomial-theorem, Gibby, dram, bhatman, GoodMorning, bowenying24, Adventure10, Mango247, Math4Life7
Short Answer
Long Answer

As for mods, heres a quick summary of what you would want to know for the AMC and AIME (more so for AIME though) and a few problems that can be solved using mods.
This post has been edited 1 time. Last edited by ayushk, Sep 15, 2016, 4:06 AM
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V10599116111114
7 posts
#11 • 2 Y
Y by Adventure10, Mango247
velraman wrote:
rkm0959 wrote:
$n|10^6-1=999999$ and $n+6|10^4-1=9999$.

Why $n+6$ should divide $10^4-1$ ?


well, 1/(n+6) = (1000w+100x+10y+z)/9999, the numerator is an integer. So its clear that n+6|10^4 -1
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