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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next 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 an enriching 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][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/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
May 1, 2025
0 replies
schur weighted
Ducksohappi   3
N 5 minutes ago by ariopro1387
Schur-weighted:
let a,b,c be positive. Prove that:
$a^3+b^3+c^3+3abc\ge \sum ab\sqrt{a^2+b^2}$
3 replies
Ducksohappi
Yesterday at 11:47 PM
ariopro1387
5 minutes ago
Cheesy's math casino and probability
pithon_with_an_i   0
23 minutes ago
Source: Revenge JOM 2025 Problem 4, Revenge JOMSL 2025 C3
There are $p$ people are playing a game at Cheesy's math casino, where $p$ is a prime number. Let $n$ be a positive integer. A subset of length $s$ from the set of integers from $1$ to $n$ inclusive is randomly chosen, with an equal probability ($s \leq  n$ and is fixed). The winner of Cheesy's game is person $i$, if the sum of the chosen numbers are congruent to $i \pmod p$ for $0 \leq i \leq p-1$.
For each $n$, find all values of $s$ such that no person will sue Cheesy for creating unfair games (i.e. all the winning outcomes are equally likely).

(Proposed by Jaydon Chieng, Yeoh Teck En)

Remark
0 replies
pithon_with_an_i
23 minutes ago
0 replies
Partitioning coprime integers to arithmetic sequences
sevket12   4
N 24 minutes ago by bochidd
Source: 2025 Turkey EGMO TST P3
For a positive integer $n$, let $S_n$ be the set of positive integers that do not exceed $n$ and are coprime to $n$. Define $f(n)$ as the smallest positive integer that allows $S_n$ to be partitioned into $f(n)$ disjoint subsets, each forming an arithmetic progression.

Prove that there exist infinitely many pairs $(a, b)$ satisfying $a, b > 2025$, $a \mid b$, and $f(a) \nmid f(b)$.
4 replies
sevket12
Feb 8, 2025
bochidd
24 minutes ago
Coaxal Circles
fattypiggy123   30
N 26 minutes ago by Ilikeminecraft
Source: China TSTST Test 2 Day 1 Q3
Let $ABCD$ be a quadrilateral and let $l$ be a line. Let $l$ intersect the lines $AB,CD,BC,DA,AC,BD$ at points $X,X',Y,Y',Z,Z'$ respectively. Given that these six points on $l$ are in the order $X,Y,Z,X',Y',Z'$, show that the circles with diameter $XX',YY',ZZ'$ are coaxal.
30 replies
fattypiggy123
Mar 13, 2017
Ilikeminecraft
26 minutes ago
No more topics!
d | \overline{aabbcc} iff d | \overline{abc} where d is two digit number
parmenides51   1
N Apr 29, 2025 by luphuc
Source: Czech-Polish-Slovak Junior Match 2013, Individual p4 CPSJ
Determine the largest two-digit number $d$ with the following property:
for any six-digit number $\overline{aabbcc}$ number $d$ is a divisor of the number $\overline{aabbcc}$ if and only if the number $d$ is a divisor of the corresponding three-digit number $\overline{abc}$.

Note The numbers $a \ne 0, b$ and $c$ need not be different.
1 reply
parmenides51
Mar 14, 2020
luphuc
Apr 29, 2025
d | \overline{aabbcc} iff d | \overline{abc} where d is two digit number
G H J
G H BBookmark kLocked kLocked NReply
Source: Czech-Polish-Slovak Junior Match 2013, Individual p4 CPSJ
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parmenides51
30652 posts
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Determine the largest two-digit number $d$ with the following property:
for any six-digit number $\overline{aabbcc}$ number $d$ is a divisor of the number $\overline{aabbcc}$ if and only if the number $d$ is a divisor of the corresponding three-digit number $\overline{abc}$.

Note The numbers $a \ne 0, b$ and $c$ need not be different.
Z K Y
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luphuc
23 posts
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Do you have answer ?
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