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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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All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Apr 2, 2025
0 replies
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Inequalities
sqing   15
N 2 hours ago by lbh_qys
Let $ a,b,c> 0 $ and $ ab+bc+ca\leq 3abc . $ Prove that
$$ a+ b^2+c\leq a^2+ b^3+c^2 $$$$ a+ b^{11}+c\leq a^2+ b^{12}+c^2 $$
15 replies
sqing
Yesterday at 1:54 PM
lbh_qys
2 hours ago
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CHINA TST 2017 P6 DAY1
lingaguliguli   0
2 hours ago
When i search the china TST 2017 problem 6 day I i crossed out this lemme, but don't know to prove it, anyone have suggestion? tks
Given a fixed number n, and a prime p. Let f(x)=(x+a_1)(x+a_2)...(x+a_n) in which a_1,a_2,...a_n are positive intergers. Show that there exist an interger M so that 0<v_p((f(M))< n + v_p(n!)
0 replies
lingaguliguli
2 hours ago
0 replies
J
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How many ways can we indistribute n different marbles into 6 identical boxes
Taiharward   7
N 3 hours ago by MathBot101101
How many ways can we distribute n indifferent marbles into 6 identical boxes and one jar?
7 replies
Taiharward
Today at 2:14 AM
MathBot101101
3 hours ago
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Math and physics camp
Snezana242   0
3 hours ago
Discover IMPSC 2025: International Math & Physics Summer Camp!

Are you a high school student (grades 9–12) with a passion for Physics and Math?
Join the IMPSC 2025, an online summer camp led by top IIT professors, offering a college-level education in Physics and Math.

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Learn advanced topics from renowned IIT professors

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https://www.imc-impea.org/IMC/index.php

Don't miss out on this opportunity to elevate your academic journey!
Apply now and take your education to the next level.
0 replies
Snezana242
3 hours ago
0 replies
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distance of tangent spheres externally inside a cube (Chile 2011 L1 p2)
parmenides51   1
N May 26, 2019 by sotpidot
Inside a cube of side $1$, two spheres are introduced that are tangent externally to each other and such that each is tangent to three faces of the cube. Determine the greater distance to which the centers of the spheres can be found.
1 reply
parmenides51
May 26, 2019
sotpidot
May 26, 2019
J
distance of tangent spheres externally inside a cube (Chile 2011 L1 p2)
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Reveal topic tags
geometry
3D geometry
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parmenides51
30630 posts
parmenides51
#1 h  May 26, 2019, 7:04 PM • 1 Y
Y by Adventure10
Inside a cube of side $1$, two spheres are introduced that are tangent externally to each other and such that each is tangent to three faces of the cube. Determine the greater distance to which the centers of the spheres can be found.
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sotpidot
290 posts
sotpidot
#2 h  May 26, 2019, 7:10 PM • 2 Y
Y by Adventure10, Mango247
is it $(3-sqrt(3))/2$
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