G
Topic
First Poster
Last Poster
and 
Prove tha
![\[\sum_{n=1}^{2025}n^5\]](http://latex.artofproblemsolving.com/0/8/3/08334297eaac7610645549ede6434e399000e480.png)
max area of triangle of centroids of PBC, PAC,PAB 2017 BMT Individual 16
parmenides51 4
N
by Rice_Farmer
Let 
be a triangle with 
, 
, 
, and let 
be a point in its interior. If 
, 
, 
are the centroids of 
, 
, 
, respectively, find the maximum possible area of 
.
be a triangle with 
, 
, 
, and let 
be a point in its interior. If 
, 
, 
are the centroids of 
, 
, 
, respectively, find the maximum possible area of 
.
4 replies
Daily Problem Writing Practice
KSH31415 16
N
by Vivaandax
I'm trying to get better at writing problems so I decided to challenge myself to write one problem for every day this month (June 2025). I will post them in this thread as well as edit this post with all of them in hide tags. If I can, I'll include a difficulty level in the form of AIME placement. If anybody wants to solve them and give feedback on the problem and/or my difficulty rating, please do!
June 1 (AIME P4)
A bag contains
red balls and blue balls. A draw consists of randomly selecting 
of the remaining balls from bag without replacement, and then setting them aside. A draw is called a match if the two balls have the same color. Compute the expected number of draws until either a match occurs or the bag is empty.
and 
,
in degrees as 
ranges over all real numbers.
and let 
(ie. 
with 
removed). Determine the number of injective* functions 
such that 
for all 
.
for all distinct 
and 
in the domain of 
possible triangles instead of 
)
be the centroid of 
.
as the centroid of 
and define 
and 
similarly. Points 
and 
,
,
,![$\frac{[G_AG_BG_c]}{[ABC]}.$](http://latex.artofproblemsolving.com/d/3/8/d38c1ec527c34f1e1519bba772a0765849e6fe7d.png)
chessboard, 
white knights and 
square vertically from the other, or one knight is June 1 (AIME P4)
A bag contains
red balls and blue balls. A draw consists of randomly selecting 
of the remaining balls from bag without replacement, and then setting them aside. A draw is called a match if the two balls have the same color. Compute the expected number of draws until either a match occurs or the bag is empty.
16 replies
Geometry
Exoticbuttersowo 0
In an isosceles triangle ABC with base AC and interior cevian AM, such that MC = 2 MB, and a point L on AM, such that BLC = 90 degrees and MAC = 42 degrees. Determine LBC.
0 replies
(own problem) polynomials
nithish_kumar138 2
N
by Mathelets
When x^4-2x^2-3x^2+7x-2 is divided by x-2 the remainder is 'K'.
By using K find α,β,γ.
Let K= α²+β²+γ²
N=(α+β)²+(β+ γ)²+(γ+α)²
K'= α*β*γ/α+β.
Find K+N+K'....~Nithish
By using K find α,β,γ.
Let K= α²+β²+γ²
N=(α+β)²+(β+ γ)²+(γ+α)²
K'= α*β*γ/α+β.
Find K+N+K'....~Nithish
2 replies
find the value,please…
Cirno-fumofumo 1
N
by vanstraelen
cos(9π/13)*cos(3π/13)+cos(3π/13)*cos(π/13)+cos(9π/13)*cos(π/13)=?
1 reply
A problem of the number of paths in grid
Nikolai220 2
N
by Zhiyi
How many distinct paths are there from the bottom-left corner to the top-right corner of a 5×5 grid, where each edge can be traverled at most once?(not all edges must be travelled)
(further problem:how many paths are there if the grid is n*n?)
(further problem:how many paths are there if the grid is n*n?)
2 replies
Trig Identity
mithu542 6
N
by nithish_kumar138
Prove the following identity:
where 
is in radians.
where 
is in radians.
6 replies
Graph of 100 vertices. Each of degree 3. Is that possible?
Clueid 3
N
by KSH31415
Does there exist a graph with 100 vertices with each vertex having a degree of 3? If so, show that it exists. Otherwise, prove it's impossible to exist.
3 replies
