Prove that
Is there an elegant way to prove this?
through 
.
.
,
,
with probability 
and to pad 
with probability 
.
,
,
be squares that have vertices at lattice points (i.e., points whose coordinates are both integers) in the coordinate plane, together with their interiors. The bottom edge of each square is on the x-axis. The left edge of 
-
as many lattice points as does 
,
of the lattice points contained in 
is 27 times the fraction of lattice points in 
.
Product of all even divisors of 
If 
dice are rolled, Then number of ways of getting sum at least 
is
,
,
,
such that ![\[\left(a_1+\frac1{a_1}\right)\left(a_2+\frac1{a_2}\right)\cdots\left(a_n+\frac1{a_n}\right)=2020.\]](http://latex.artofproblemsolving.com/3/6/2/362fccfa6353ffcbc4d29f24ccbfce73269080bf.png)
Compute 
.
be an isosceles triangle such that 
.
be a dot on the 
side.
at point 
at 
.
A
have angles 
and 
such that 
and 
. Moreover, suppose that the product of the side lengths of the triangle is equal to its area. Let 
denote the circumcircle of 
intersect 
at 
intersect 
at 
,
intersect 
at 
.
can be written as 
for relatively prime integers 
and 
and squarefree 
,
is 
)
divisors.
Y by aidan0626, kante314, Math4Life7, KevinYang2.71, SouradipClash_03, Danielzh
Hey everyone!
Thank you to all who participated in the third year of JMPSC. The solutions, statistics, and problems are linked to this post, and the top 20 of each division can be found here.
Enjoy the problems!
Thank you to all who participated in the third year of JMPSC. The solutions, statistics, and problems are linked to this post, and the top 20 of each division can be found here.
Enjoy the problems!
