ka May Highlights and 2025 AoPS Online Class Information
jlacosta0
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.
Introduction to Algebra A
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28
Introduction to Counting & Probability
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19
Introduction to Number Theory
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30
Introduction to Algebra B
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14
Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19
Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)
Intermediate: Grades 8-12
Intermediate Algebra
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22
MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21
AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22
Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22
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][/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 , do not answer with " is a solution" only. Either you post any kind of proof or at least something unexpected (like " is the smallest solution). Someone that does not see that 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.
Let be a triangle with incenter and let be an arbitrary point on the side . Let the line through perpendicular to intersect at . Let the line through perpendicular to intersect at . Prove that the reflection of across the line lies on the line .
Source: At the time of posting the problem I do not know the source if any
Let be a positive integer and consider the set .
Two players alternate moves. On each turn, the current player must select a nonempty subset of numbers not previously chosen such that for every distinct , neither divides nor divides .
After selecting , all multiples of every element in , including those in itself, are removed from .
The game continues with the reduced set until no moves are possible.
Determine, for each , which player has a winning strategy if any
Source: Serbian selection contest for the IMO 2025
Let be an acute triangle. Let be the reflection of point over the line . Let and be the circumcenter and the orthocenter of triangle , respectively, and let be the midpoint of segment . Let and be the points where the reflection of line with respect to line intersects the circumcircle of triangle , where point lies on the arc not containing . If is a point on the line such that , prove that .
Let be a triangle. Circle passes through , meets segments and again at points and respectively, and intersects segment at and such that lies between and . The tangent to circle at and the tangent to circle at meet at point . Suppose that points and are distinct. Prove that line is parallel to .
In triangle with circumcircle and incenter , point bisects arc and line meets at . The excircle opposite to touches at point . Point on the circumcircle of is such that . Prove that the lines and meet on .
Let be an inscribed circle of and touching ,, at ,, respectively. Let and be diameters of . Let and be the pole of and with respect to , respectively. cuts again at . cuts again at . The tangent at of cuts at . The tangent at of cuts at . Let and be midpoint of and , respectively.
Show that : , and perpendicular bisector of are concurrent.
A hunter and an invisible rabbit are playing again...
Phorphyrion1
Nan hour ago
by JARP091
Source: 2021 Discord CCCC P4
A hunter and an invisible rabbit play a game in a grid. The rabbit's starting square is (unknown to the hunter), and after rounds, the rabbit is at square . In the -th round of the game, two things occur in order:
(i) The rabbit moves invisibly to a square which shares a point with (There are up to eight of these).
(ii) A tracking device searches squares of the hunter's choosing. If the rabbit is in one of these squares, the rabbit is captured and the game ends.
For what can the rabbit avoid capture indefinitely?
Let be an acute triangle with orthocenter . Let be the point such that the quadrilateral is a parallelogram. Let be the point on the line such that bisects . Suppose that the line intersects the circumcircle of the triangle at and . Prove that .
Let , where is rational for . A vector is called a rational point in -dimensional space. Denote the set of all such vectors as . For and in , define the distance between points and as . We say that point can move to point if and only if there is a unit distance between two points in .
Prove:
(1) If , there exists a point that cannot be reached from the origin via a finite number of moves.
(2) If , any point in can be reached from any other point via moves.
Claim 1. The problem reduces to the case when is connected.
Indeed, if consists of the connected components then there must be some such that Otherwise, contradiction.
Claim 2. The problem reduces to the case when each vertex has degree at least
Indeed, by removing all the vertices of degree or we end up with a graph for which (this is because each vertex removal causes at most one edge removal).
Claim 3. A connected graph in which every vertex has degree is cyclic.
We pick a vertex. There are two edges emerging from it; we choose one of them. This sends us to a new vertex, which again has two edges emerging from it: the one which we have just crossed and another one. We keep walking by always choosing the new edge. Since the graph is finite, at some point we must reach a vertex that we have already visited. This proves the existence of a cycle. Since this cycle forms a connected component, it must be the entire graph.
Now let's consider a connected graph whose vertices have degree at least with and By the handshaking lemma, the sum of the degrees of the vertices is The only ways this is achieved are: 1. all the vertices have degree except for one which has degree ; or 2. all the vertices have degree except for two which have degree
Case 1. All the vertices have degree except for one which has degree
From Claim 3 we know that the graph contains a cycle. This cycle must contain the -degree vertex because otherwise the graph is disconnected. By removing all the vertices from this cycle, except for the -degree vertex, we obtain a connected graph in which every vertex has degree According to Claim 3, this is a cycle, so we just found a second cycle in
Case 2. All the vertices have degree except for two which have degree
Since is connected, there is a path between the two -degree vertices. We remove all the vertices from this path, except for the -degree vertices. In this way we obtain a graph in which every vertex has degree so according to Claim 3 it is a cycle. Now by putting the removed path back, we prove that we obtain at least two cycles (in fact at least three).
Let's say the cycle obtained after removing that path is where and are the -degree vertices. Let be the removed path. Then we also have the cycles and (overline to indicate that it is crossed backwards)