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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

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Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

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0 replies
jlacosta
Mar 2, 2025
0 replies
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Mathcounts state iowa
iwillregretthisnamelater   7
N 8 minutes ago by ericwengcn
Ok I’m a 6th grader in Iowa who got 38 in chapter which was first, so what are the chances of me getting in nats? I should feel confident but I don’t. I have a week until states and I’m getting really anxious. What should I do? And also does the cdr count in Iowa? Because I heard that some states do cdr for fun or something and that it doesn’t count to final standings.
7 replies
iwillregretthisnamelater
Yesterday at 4:55 AM
ericwengcn
8 minutes ago
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Basic Maths
JetFire008   4
N 12 minutes ago by kamuii
Find $x$: $\sqrt{9}x=18$
4 replies
JetFire008
22 minutes ago
kamuii
12 minutes ago
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state mathcounts colorado
aoh11   58
N 36 minutes ago by mickieani
I have state mathcounts tomorrow. What should I do to get prepared btw, and what are some tips for doing sprint and cdr?
58 replies
aoh11
Mar 15, 2025
mickieani
36 minutes ago
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squares in dots - MATHCOUNTS challenge problem
rrusczyk   6
N 3 hours ago by DhruvJha
. . . . .
. . . . .
. . . . .
. . . . .

(That should be a 4x5 grid of dots.) Assuming each point is exactly one unit from its nearest neighbors, how many squares can be formed by connecting groups of four points?
6 replies
rrusczyk
May 27, 2003
DhruvJha
3 hours ago
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No more topics!
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Tangent Spheres in a plane
ReticulatedPython   13
N Yesterday at 6:02 PM by ChaitraliKA
Three mutually tangent spheres with radius $6$ rest on a plane. A sphere with radius $10$ is tangent to all of them, but does not intersect nor lie on the plane. A sphere with radius $r$ lies on the plane, and is tangent to all three spheres with radius $6.$ Compute the shortest distance between the sphere with radius $r$ and the sphere with radius $10.$

Source: Own
13 replies
ReticulatedPython
Wednesday at 9:44 PM
ChaitraliKA
Yesterday at 6:02 PM
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Tangent Spheres in a plane
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Reveal topic tags
geometry
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sphere
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ReticulatedPython
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ReticulatedPython
#1 h  Wednesday at 9:44 PM
Y by
Three mutually tangent spheres with radius $6$ rest on a plane. A sphere with radius $10$ is tangent to all of them, but does not intersect nor lie on the plane. A sphere with radius $r$ lies on the plane, and is tangent to all three spheres with radius $6.$ Compute the shortest distance between the sphere with radius $r$ and the sphere with radius $10.$

Source: Own
This post has been edited 11 times. Last edited by ReticulatedPython, Yesterday at 10:27 AM
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ReticulatedPython
516 posts
ReticulatedPython
#2 h  Wednesday at 11:33 PM
Y by
Someone please try! This problem is not as monstrous as it looks! Hint if you need it
This post has been edited 1 time. Last edited by ReticulatedPython, Wednesday at 11:34 PM
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ChaitraliKA
972 posts
ChaitraliKA
#3 h  Wednesday at 11:34 PM
Y by
This doesn't need a bump in 2 hours :)
I am going to try it soon, I'll edit this message later if I do.
@op lol edited 9 times
Last time I saw this, the radius was 2
This post has been edited 1 time. Last edited by ChaitraliKA, Wednesday at 11:35 PM
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ReticulatedPython
516 posts
ReticulatedPython
#4 h  Wednesday at 11:37 PM
Y by
@above Thank you!
ChaitraliKAI wrote:
Last time I saw this, the radius was 2
I edited it so that the numbers inside the radicals will be integers.
This post has been edited 2 times. Last edited by ReticulatedPython, Wednesday at 11:38 PM
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aidan0626
1755 posts
aidan0626
#5 h  Wednesday at 11:45 PM
Y by
my answer doesn't match the extract oop
i got r=, which is prob wrong idk
i'm visualizing the diagram in my head
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ChaitraliKA
972 posts
ChaitraliKA
#6 h  Yesterday at 12:12 AM
Y by
I also got r=2
The question asks for the shortest distance between the spheres with radius 10 and r
I also got the double pyramid that was given in the hint, but I'm also not getting the same answer extraction.
Are a, b, and c allowed to have perfect squares in them? Either way, I don't understand how the answer can have minus sqrtb. Shouldn't it be sqrta+sqrtb-c ?
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ReticulatedPython
516 posts
ReticulatedPython
#7 h  Yesterday at 12:27 AM
Y by
I think it would be helpful if you use actual balls to visualize this problem.
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ChaitraliKA
972 posts
ChaitraliKA
#8 h  Yesterday at 12:54 AM
Y by
yes, i did draw the actual balls
but when it came to finding the distance, i drew the double pyramid and found the total height, then subtracted both radii (10 and 2)
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ReticulatedPython
516 posts
ReticulatedPython
#11 h  Yesterday at 1:10 AM
Y by
Click to reveal hidden text Also I changed the problem statement because I realized that the answer is not in the form $\sqrt{a}-\sqrt{b}+c.$
This post has been edited 3 times. Last edited by ReticulatedPython, Yesterday at 10:28 AM
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ChaitraliKA
972 posts
ChaitraliKA
#12 h  Yesterday at 11:59 AM • 1 Y
Y by ReticulatedPython
Quote:
I realized that the answer is not in the form $\sqrt{a}-\sqrt{b}+c.$
That's what I thought lol
Also yeah that's exactly what I did
I got Click to reveal hidden text
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ReticulatedPython
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ReticulatedPython
#13 h  Yesterday at 3:01 PM
Y by
ChaitraliKA wrote:
Quote:
I realized that the answer is not in the form $\sqrt{a}-\sqrt{b}+c.$
That's what I thought lol
Also yeah that's exactly what I did
I got Click to reveal hidden text

That is correct!
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aidan0626
1755 posts
aidan0626
#14 h  Yesterday at 3:06 PM
Y by
ReticulatedPython wrote:
ChaitraliKA wrote:
Quote:
I realized that the answer is not in the form $\sqrt{a}-\sqrt{b}+c.$
That's what I thought lol
Also yeah that's exactly what I did
I got Click to reveal hidden text

That is correct!

bro
that's what i got
and i didn't post it since i thought it was wrong
is it really that hard to do a basic thing like checking the answer extract??
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ReticulatedPython
516 posts
ReticulatedPython
#15 h  Yesterday at 3:13 PM
Y by
aidan0626 wrote:
bro
that's what i got
and i didn't post it since i thought it was wrong
is it really that hard to do a basic thing like checking the answer extract??

Yeah it was an error on my part, I miscalculated $r$ to be $6\sqrt{3}-6$, then I realized the mistake.
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ChaitraliKA
972 posts
ChaitraliKA
#16 h  Yesterday at 6:02 PM
Y by
you seem to be very obsessed with tangent spheres/circles after scrolling through your posts lolll
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