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.
Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)
Please hide solutions and answers, hints are fine though! :)
Problems usually get harder throughout the week, so Sunday is the easiest and Saturday is the hardest!
Past Problems!
[quote=March 21st Problem]Alice flips a fair coin until she gets 2 heads in a row, or a tail and then a head. What is the probability that she stopped after 2 heads in a row? Express your answer as a common fraction.[/quote] Answer
[quote=March 22nd Problem]In a best out of 5 math tournament, 2 teams compete to solve math problems, with each of the teams having a 50% chance of winning each round. The tournament ends when one team wins 3 rounds. What is the probability that the tournament will end before the fifth round? Express your answer as a common fraction.[/quote] Answer
[quote=March 23rd Problem]The equations of and intersect at the point . What is the value of ?[/quote] Answer
[quote=March 24th Problem]Anthony rolls two fair six sided dice. What is the sum of all the different possible products of his rolls?[/quote] Answer
[quote=March 25th Problem]If , find the value of .[/quote] Answer
[quote=March 26th Problem]There is a group of 6 friends standing in line. However, 3 of them don't want to stand next to each other. In how many ways can they stand in line?[/quote] Answer
[quote=March 27th Problem]Two real numbers, and are chosen from 0 to 1. What is the probability that their positive difference is more than ?[/quote] Answer
[quote=March 28th Problem]What is the least possible value of the expression ?[/quote] Answer
[quote=March 29th Problem]How many integers from 1 to 2025, inclusive, contain the digit “1”?[/quote] Answer
[quote=April 3rd Problem]In families, there are children respectively. If a random child from any of the families is chosen, what is the probability that the child has siblings? Express your answer as a common fraction.[/quote] Answer
[quote=April 5th Problem]A circle with a radius of 3 units is centered at the point (0,0) on the coordinate plane. How many lattice points, points which both of the coordinates are integers, are strictly inside the circle?[/quote] Answer
[quote=April 6th Problem]If the probability that someone asks for a problem is , find the probability that out of people, exactly of them ask for a problem.[/quote] Answer
[quote=April 8th Problem]Find the value of such that .[/quote] Answer
[quote=April 9th Problem]In unit square , point lies on diagonal such that . Find the area of quadrilateral .[/quote] Answer
[quote=April 10th Problem]An function in the form has ,, and . Find the value of .[/quote] Answer
We say that a finite set of points in the plane is balanced if, for any two different points and in , there is a point in such that . We say that is centre-free if for any three different points , and in , there is no points in such that .
(a) Show that for all integers , there exists a balanced set consisting of points.
(b) Determine all integers for which there exists a balanced centre-free set consisting of points.
Let ,,, be four points such that no three are collinear and is not the orthocenter of . Let ,, be the orthocenters of ,,, respectively. Suppose that the lines ,, are pairwise distinct and are concurrent. Show that the four points ,,, lie on a circle.
Let and be the circumcenter and orthocenter, respectively, of an acute scalene triangle . The perpendicular bisector of intersects and at and respectively. Let denote the intersection of the circumcircles of triangles and other than .
Define and analogously by repeating this construction two more times. Prove that ,,, and are concyclic.
Find the number of different ways to arrange seven people around a circular meeting table if A and B must sit together and C and D cannot sit next to each other. (Note: the order for A and B might be A,B or B,A)
Solved with resources, greendivisors, eg4334, lpieleanu, SigmaPiE, Arcticturn, and CoolJupiter.
Here, having several continguous characters as a variable name is absurd! A clear counterexample is in programming, a variable name is invalid if it contains spaces. Thus, the only reasonable explanation is a multiplication using the symbol standard. We want to solve: But this is just . Since we are in Middle School Math, we will not consider the case of as surely outrage will spark. Now if you are not experienced in the dark arts, a feeble-minded individual would simply plug in and sum it up. How absurd! Instead, we explore the more reasonable path of multiplying the "normal" sum of by , as every unit in the sum is replaced by the embedded within the sequence, clearly the intended path of the creator.
Now suppose it is thousands of years ago and we do not have a calculator. We instead use the approximation written by Euclid himself on a humble rock. Multiplying with our fingers, we obtain Since has significant figures, we round our answer accordingly to scientific procedure to obtain .
This post has been edited 2 times. Last edited by blueprimes, Apr 2, 2025, 2:37 AM
Solved with resources, greendivisors, eg4334, lpieleanu, SigmaPiE, Arcticturn, and CoolJupiter.
Here, having several continguous characters as a variable name is absurd! A clear counterexample is in programming, a variable name is invalid if it contains spaces. Thus, the only reasonable explanation is a multiplication using the symbol standard. We want to solve: But this is just . Since we are in Middle School Math, we will not consider the case of as surely outrage will spark. Now if you are not experienced in the dark arts, a feeble-minded individual would simply plug in and sum it up. How absurd! Instead, we explore the more reasonable path of multiplying the "normal" sum of by , as every unit in the sum is replaced by the embedded within the sequence, clearly the intended path of the creator.
Now suppose it is thousands of years ago and we do not have a calculator. We instead use the approximation written by Euclid himself on a humble rock. Multiplying with our fingers, we obtain Since has significant figures, we round our answer accordingly to scientific procedure to obtain .
Solved with resources, greendivisors, eg4334, lpieleanu, SigmaPiE, Arcticturn, and CoolJupiter.
Here, having several continguous characters as a variable name is absurd! A clear counterexample is in programming, a variable name is invalid if it contains spaces. Thus, the only reasonable explanation is a multiplication using the symbol standard. We want to solve: But this is just . Since we are in Middle School Math, we will not consider the case of as surely outrage will spark. Now if you are not experienced in the dark arts, a feeble-minded individual would simply plug in and sum it up. How absurd! Instead, we explore the more reasonable path of multiplying the "normal" sum of by , as every unit in the sum is replaced by the embedded within the sequence, clearly the intended path of the creator.
Now suppose it is thousands of years ago and we do not have a calculator. We instead use the approximation written by Euclid himself on a humble rock. Multiplying with our fingers, we obtain Since has significant figures, we round our answer accordingly to scientific procedure to obtain .
Best solution so far but this makes a slight assumption which seems trivial but is actually incorrect. However, this would probably still get partials.
Intended sol (according to some moppers): Click to reveal hidden text
Let be the group with set and operation of multiplication. Suppose, furthermore, that . We obtain with as an identity, that the distributive property only applies to the terms of within the notation . In particular, ,,, and are not considered. Therefore the correct radical form is , or
Remark: I don't know how it would be expected in contest for anyone to actually be able to evaluate within a reasonable timing even after finding the (already hard) cruxes of considering and finding , so this problem is probably best just to be posted here for us to speculate and not used within a timed contest.
This post has been edited 6 times. Last edited by arfekete, Apr 2, 2025, 2:53 AM
For clarity, we will write any " " in our math as "space". Then spacespacespacespace so space=
We aim to compute spacespacespacespacespacespacespacespacespacespacespace This is simply: We will now estimate to the nearest integer, because every number in the problem is an integer. we have 1.6^4=6.5536<7 but 1.7^4=8.3521 so Similarly, Thus, the first part is
for the second part, finitely many nested roots bad. infinitely many better. assume infinitely many. let it be then so Now, use newton's method on Guess Then Close enough.
Finally, Our sum is which fittingly enough is the last two digits of the year. Also, the sum of the first two parts and the last part are, when rounded, are the two squares that when combined with the three in the date, make the first five squares, which is a beautiful easter egg in memorium for easter being in (last two digits of year)-(month number) days.