ka April Highlights and 2025 AoPS Online Class Information
jlacosta0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.
WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.
Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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)!
Prealgebra 1
Sunday, Apr 13 - Aug 10
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Introduction to Algebra A
Monday, Apr 7 - Jul 28
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Introduction to Counting & Probability
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Introduction to Number Theory
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Introduction to Algebra B
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Introduction to Geometry
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Intermediate: Grades 8-12
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Introduction to Programming with Python
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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.
Given points in the plane such that all pairwise distances between them are distinct, prove that there exist two points , among them such that the perpendicular bisector of segment has at least two points on each of its sides (i.e., each side contains at least one point other than and ).
Let be natural numbers. As the New Year arrives, it is a cherished tradition among Iranian families to call their relatives and exchange Nowruz greetings. Just moments after the New Year begins, a family with members calls a related family with members to celebrate the occasion. Since the two families are close, every member of one family wishes to speak with every member of the other family to exchange greetings. Thus, during this single call, all distinct one-on-one conversations must take place exactly once.
Each family has only one telephone in their home, meaning the phone must be passed between family members as needed. For example, if the mothers of both families start the conversation, and then the mother from one family wants to speak with a child from the other family, only one phone needs to be passed. However, if after the mothers' conversation, the fathers from both families wish to speak with each other, then both phones must be handed over — once in each household — resulting in two phone passes.
What are the minimum and maximum possible numbers of times the telephones are passed in total (across both families) during the entire process?
Given . Let the perpendicular line from to meets at points , respectively, and the foot from to is . intersects line at , intersects line at , and lines intersect at .
i wanted to do one for 1000, then 1111, then 1234, then 1500, then 2000, then 2222 and i forgot about all of those lol
2500 is cool.
i am not very sentimental so im not going to post a math story or anything.
here are some problems though
p1
You roll 5 -sided regular dice. What is the minimum value of such that the expected value of the sum of all five rolls is at least ?
p2
students want to share pencils. If every student gets at least one pencil, how many ways are there to distribute the pencils?
p3
How many diagonals can a -sided regular polygon have such that the diagonals only meet at the vertices?
p4
Johnny buys a pet lobster named Pinchy. If Pinchy can eat water balloons at a rate of 69 pounds/nanogram, how tall is Johnny? Assume that it is not a leap year.
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
Ali and Shayan are playing a turn-based game on an infinite grid. Initially, all cells are white. Ali starts the game, and in the first turn, he colors one unit square black. In the following turns, each player must color a white square that shares at least one side with a black square. The game continues for exactly 2808 turns, after which each player has made 1404 moves. Let be the set of black cells at the end of the game. Ali and Shayan respectively aim to minimize and maximise the perimeter of the shape by playing optimally. (The perimeter of shape is defined as the total length of the boundary segments between a black and a white cell.)
What are the possible values of the perimeter of , assuming both players play optimally?
number of separated partitions for n+1 is equal the number of partitions for n
YLG_1235
Nan hour ago
by Victor23TT
Source: Brazilian Mathematical Olympiad 2024, Level 3, Problem 2
A partition of a set is a family of non-empty subsets of , such that any two distinct subsets in the family are disjoint, and the union of all subsets equals . We say that a partition of a set of integers is separated if each subset in the partition does not contain consecutive integers. Prove that, for every positive integer , the number of partitions of the set is equal to the number of separated partitions of the set .
For example, is a separated partition of the set . On the other hand, is a partition of the same set, but it is not separated since contains consecutive integers.
yeah, bruh you cant call the three that you got wrong on target sillies. maybe like 1 or 2
I put 2025 for subset problem cuz I was being goofy, I put 13.5 instead of 27/2, and I got both leg lengths correct on the right triangle I just Pythagorean theoremed wrong
Didn't want to judge before I got the test, but here is every silly I made, or questions that I could have easily gotten right
Sprint:
11) I forgot that that
14) I honestly don't know how I sillied this, but I think I put that or smth
24) I forgot to read "odd"
28) not a silly, but a genuine mistake
30) Rushing at the end of the test with little scratch paper, and probably like 10 arithmetic mistakes caused me to get this wrong, although it was easy in concept
Target
6) I had the correct answer, but I doubted myself, and I didn't want to check with like 5 seconds left. In an alternate universe, I could have easily gotten this one right
8) Overthought it and put 81/2, thought that I had to multiply by 3 since it was a group of three, but I forgot that you could take a running probability, and it doesn't have to be in packages of three. Borderline if you count this as a silly, but I'll count it, since I could have seen myself getting in right.
VERY disappointed in my performance in state, since I did so well in chapter 43), with only 1 SILLY (not necessarily a silly per se, but a question that I could have easily gotten right)!!! Most math contests I make like 3-4 sillies, so I thought if I continue my performance, I could have a decent shot at making nationals (I live in cali, so a "decent" shot for me is <5%). Nevertheless, my performance at state was very bad (for me), and I did not even make cdr. I got first in my chapter, and 2 people from my chapter made top 10, and one even got third! If I had the best possible score I could have gotten I would have gotten a 42, which would have putten me comfortably for cdr, although I still wouldn't have made nationals, but my main goal (realistic) goal was cdr. And before you say it's unrealistic to score almost the same in target and chapter, I know some people who boosted their score by like 5 points (I think). And even I went from a 41 (I think) on school to a 43 on chapter. Now, all of these things wouldn't really matter besides one crucial factor, I am in 8th grade, and this is my last year doing mathcounts. Mathcounts is what has gotten me into comp math, and I am forever grateful for the problems and experiences Mathcounts has provided me. I didn't do it as a sixth grader because I had never heard of comp math before, and I thought it was just another one of those "challenging" middle school math programs that ask, "WHaT iS ThE GreATeST 3 DiGiT INTeGer????!!?!!!" But when I saw my friend doing some mathcounts problems that were legitamately challenging, I decided to got, and oh boy did I love it. I tried out for the team in 7th grade, and I made it (partially my taking every test and memorizing all the solutions because my coach uses old tests for selection). I made it to chapter, where I won CDR!!!!! Winning CDR in chapter my first year was by far my proudest accomplishment in my comp math career, since I only just barely made CDR. But in 8th grade, I didn't practice as much as I did in 7th, so I guess I shouldn't be too disappointed in my score. But, I'm not really mad at how I did, but more of the fact that i don't get another shot to prove myself. So, to any seventh graders who are disappointed in their score in mathcounts, please remember that you have a whole year to practice and improve. But, I've met some of my best friends in mathcounts, so I guess I could say:
"The real mathcounts is the friends we made along the way"
- Abraham Lincoln
This post has been edited 1 time. Last edited by Existing_Human1, Apr 5, 2025, 6:14 PM