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2025 USA IMO
john0512 68
N
by NicoN9
Congratulations to all of you!!!!!!!
Alexander Wang
Hannah Fox
Karn Chutinan
Andrew Lin
Calvin Wang
Tiger Zhang
Good luck in Australia!
Alexander Wang
Hannah Fox
Karn Chutinan
Andrew Lin
Calvin Wang
Tiger Zhang
Good luck in Australia!
68 replies
Inequality with a^2+b^2+c^2+abc=4
cn2_71828182846 71
N
by Novmath
Source: USAMO 2001 #3
Let 
and satisfy ![\[ a^2+b^2+c^2 +abc = 4 . \]](//latex.artofproblemsolving.com/d/3/a/d3ac01295b077425b5eaae556faa4cd678bce32a.png)
Show that ![\[ 0 \le ab + bc + ca - abc \leq 2. \]](//latex.artofproblemsolving.com/2/0/9/209b3fcb56c01c335bbcb8d5fb781e28e49a0798.png)
and satisfy ![\[ a^2+b^2+c^2 +abc = 4 . \]](http://latex.artofproblemsolving.com/d/3/a/d3ac01295b077425b5eaae556faa4cd678bce32a.png)
Show that ![\[ 0 \le ab + bc + ca - abc \leq 2. \]](http://latex.artofproblemsolving.com/2/0/9/209b3fcb56c01c335bbcb8d5fb781e28e49a0798.png)
71 replies
AIME I 2025 Problem 6
PaperMath 38
N
by NicoN9
Source: 2025 AIME 1 #6
An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 
, and the area of the trapezoid is 
. Let the parallel sides of the trapezoid have lengths 
and 
, with 
. Find 
, and the area of the trapezoid is 
. Let the parallel sides of the trapezoid have lengths 
and 
, with 
. Find 
38 replies
+1 w
PROMYS Europe
Taxicab-1211729 1
N
by Taxicab-1211729
Is anyone attending Promys Europe this summer?
1 reply
do NOT double count (0,0)
bobthegod78 40
N
by NicoN9
Source: 2025 AIME I P4
Find the number of ordered pairs 
, where both 
and 
are integers between 
and 
inclusive, such that 
.
, where both 
and 
are integers between 
and 
inclusive, such that 
.
40 replies
Stressed spelled backwards
centslordm 25
N
by NicoN9
Source: AIME 2025 #3
The 9 members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let 
be the number of different assignments of flavors to players that meet these conditions. Find the remainder when is divided by 
be the number of different assignments of flavors to players that meet these conditions. Find the remainder when is divided by 
25 replies
Heptagon
StressedPineapple 22
N
by NicoN9
Source: 2025 AIME I P2
In 
points 
and 
lie on 
so that 
, while points 
and 
lie on 
so that 
. Suppose 
, 
, 
, 
, 
, and 
. Let 
be the reflection of through , and let be the reflection of through . The area of quadrilateral 
is 
. Find the area of heptagon 
, as shown in the figure below.
IMAGE
points 
and 
lie on 
so that 
, while points 
and 
lie on 
so that 
. Suppose 
, 
, 
, 
, 
, and 
. Let 
be the reflection of through , and let be the reflection of through . The area of quadrilateral 
is 
. Find the area of heptagon 
, as shown in the figure below.IMAGE
22 replies
basic nt
zhoujef000 39
N
by NicoN9
Source: 2025 AIME I #1
Find the sum of all integer bases 
for which 
is a divisor of 
for which 
is a divisor of 
39 replies
USA Canada math camp
Bread10 53
N
by FructosePear
How difficult is it to get into USA Canada math camp? What should be expected from an accepted applicant in terms of the qualifying quiz, essays and other awards or math context?
53 replies
Tennessee Math Tournament (TMT) Online 2025
TennesseeMathTournament 74
N
by Inaaya
Hello everyone! We are excited to announce a new competition, the Tennessee Math Tournament, created by the Tennessee Math Coalition! Anyone can participate in the virtual competition for free.
The testing window is from March 22nd to April 12th, 2025. Virtual competitors may participate in the competition at any time during that window.
The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.
To register and see more information, click here!
If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!
Thank you to our lead sponsor, Jane Street!
IMAGE
The testing window is from March 22nd to April 12th, 2025. Virtual competitors may participate in the competition at any time during that window.
The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.
To register and see more information, click here!
If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!
Thank you to our lead sponsor, Jane Street!
IMAGE
74 replies
