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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
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)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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Intermediate Counting
RenheMiResembleRice   1
N 16 minutes ago by The5within
A coin is flipped, a 6-sided die numbered 1 through 6 is rolled, and a 10-sided die numbered 0
through 9 is rolled. What is the probability that the coin comes up heads and the sum of the
numbers that show on the dice is 8?
1 reply
RenheMiResembleRice
42 minutes ago
The5within
16 minutes ago
J
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Eazy equation clap
giangtruong13   1
N 3 hours ago by iniffur
Find all $x,y,z$ satisfy that: $$\frac{x}{y+z}=2x-1; \frac{y}{x+z}=3y-1;\frac{z}{x+y}=5z-1$$
1 reply
giangtruong13
Yesterday at 4:03 PM
iniffur
3 hours ago
J
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Inequalities
nhathhuyyp5c   0
4 hours ago
Prove that for all positive real numbers \( a, b, c \), the following inequality holds:

\[ \sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}} \]
0 replies
nhathhuyyp5c
4 hours ago
0 replies
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Inequalities
hn111009   3
N 6 hours ago by James4623009
Let $a,b,c>0$ satisfied $a^2+b^2+c^2=9.$ Find the minimum of $$P=\dfrac{a}{bc}+\dfrac{2b}{ca}+\dfrac{5c}{ab}.$$
3 replies
hn111009
Today at 1:25 AM
James4623009
6 hours ago
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restore one vertex of triangle 2021 SPbU finals 6-7 p3
parmenides51   0
May 29, 2022
In triangle $ABC$, point $D$ is the midpoint of side $AB$, $E$ is the midpoint of side $AC$, $F$ is the midpoint bisector $AL$, and $DF = 1$, $EF = 2$. Points $D, E, F$ are drawn on the plane so that the line $DF$ horizontal, and the rest of the drawing elements are erased. Is it possible to restore the position of at least one from the vertices of the triangle, if it is known that the vertex $A$ was above the line $DF$ ?
0 replies
parmenides51
May 29, 2022
0 replies
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restore one vertex of triangle 2021 SPbU finals 6-7 p3
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parmenides51
30629 posts
parmenides51
#1 h  May 29, 2022, 8:30 AM • 1 Y
Y by Mango247
In triangle $ABC$, point $D$ is the midpoint of side $AB$, $E$ is the midpoint of side $AC$, $F$ is the midpoint bisector $AL$, and $DF = 1$, $EF = 2$. Points $D, E, F$ are drawn on the plane so that the line $DF$ horizontal, and the rest of the drawing elements are erased. Is it possible to restore the position of at least one from the vertices of the triangle, if it is known that the vertex $A$ was above the line $DF$ ?
This post has been edited 2 times. Last edited by parmenides51, May 29, 2022, 9:26 AM
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