G
Topic
First Poster
Last Poster
In a school of $800$ students, $224$ students play cricket, $240$ students play
Vulch 1
N
by RollingPanda4616
Hello everyone,
In a school of
students, 
students play cricket, 
students play hockey and 
students play basketball. 
students play both basketball and hockey, 
students play both cricket and basketball, 
students play both cricket and hockey, and 
students play all three: basketball, hockey, and cricket. Find the number of students who do not play any game.
Edit:
In the above problem,I just want to know that why the number of students who don't play any game shouldn't be 0, because,if we add 224,240 and 336 it comes out to be 800.I have solution,but I just want to know how to explain it without theoretically.Thank you!
In a school of
students, 
students play cricket, 
students play hockey and 
students play basketball. 
students play both basketball and hockey, 
students play both cricket and basketball, 
students play both cricket and hockey, and 
students play all three: basketball, hockey, and cricket. Find the number of students who do not play any game.Edit:
In the above problem,I just want to know that why the number of students who don't play any game shouldn't be 0, because,if we add 224,240 and 336 it comes out to be 800.I have solution,but I just want to know how to explain it without theoretically.Thank you!
1 reply
100th post
MathJedi108 1
N
by mdk2013
Well I guess this is my 100th post, it would be really funny if it isn't can yall share your favorite experience on AoPS here?
1 reply
Find all triples
pedronis 2
N
by Kempu33334
Find all triples of positive integers 
such that 
divides 
.
such that 
divides 
.
2 replies
Median geometry
Sedro 4
N
by Sedro
In triangle 
, points 
, 
, and 
are the midpoints of sides 
, 
, and 
, respectively. Prove that the area of the triangle with side lengths 
, 
, and 
has area ![$\tfrac{3}{4}[ABC]$](//latex.artofproblemsolving.com/9/8/a/98a118cb3595f9ea91f8b38b7293cc211f81295a.png)
.
, points 
, 
, and 
are the midpoints of sides 
, 
, and 
, respectively. Prove that the area of the triangle with side lengths 
, 
, and 
has area ![$\tfrac{3}{4}[ABC]$](http://latex.artofproblemsolving.com/9/8/a/98a118cb3595f9ea91f8b38b7293cc211f81295a.png)
.
4 replies
Combinatorial proof
MathBot101101 5
N
by Kempu33334
Is there a way to prove
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}
without induction and using only combinatorial arguments?
Induction proof wasn't quite as pleasing for me.
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}
without induction and using only combinatorial arguments?
Induction proof wasn't quite as pleasing for me.
5 replies
geometry
carvaan 1
N
by Lankou
The difference between two angles of a triangle is 24°. All angles are numerically double digits. Find the number of possible values of the third angle.
1 reply
weird permutation problem
Sedro 1
N
by Sedro
Let 
be a permutation of 
such that there are exactly 
ordered pairs of integers 
satisfying 
and 
. How many possible exist?
be a permutation of 
such that there are exactly 
ordered pairs of integers 
satisfying 
and 
. How many possible exist?
1 reply
Recursion
Sid-darth-vater 6
N
by vanstraelen
Help, I can't characterize ts and I dunno what to do
6 replies
geometry
carvaan 0
OABC is a trapezium with OC // AB and ∠AOB = 37°. Furthermore, A, B, C all lie on the circumference of a circle centred at O. The perpendicular bisector of OC meets AC at D. If ∠ABD = x°, find last 2 digit of 100x.
0 replies
Graph of polynomials
Ecrin_eren 1
N
by vanstraelen
The graph of the quadratic polynomial with real coefficients y = px^2 + qx + r, called G1, intersects the graph of the polynomial y = x^2, called G2, at points A and B. The lines tangent to G2 at points A and B intersect at point C. It is known that point C lies on G1. What is the value of p?
1 reply
