,
.
lies on 
such that 
.
passing trough 
at 
.
.
.
,
and 
such that 
.
and 
Prove that
Let 
Prove that
.
-
,
be the midpoint of side 
and 
be the midpoint of segment 
intersect at 
.
.
such that 
is a square perfect.
friends in this. However, if two people are not friends at least they have a friend in this party. What is the largest possible number of people in the party?
be real numbers such that 
Prove that
Let 
Prove that
Let 
Prove that
be the altitude and 
be the intersection point of the altitudes of triangle 
is symmetric to 
intersects 
.
.
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a polynomial whose roots 
are in geometric progression with ration 
.
.
satisfying:
satisfying 
Prove that 
Proposed by Phan Ngoc Chau
,
and let 
.
is:
,
,
and 
.
(in degrees) is:
Y by
The cheering team of Ubon Ratchathani University sits on the amphitheater that has 
seats arranged into a 
grid. Every seat is occupied by exactly one person, and each person has a blue sign and a yellow sign.
Count the number of ways for each person to raise one sign so that each row and column has an odd number of people raising a blue sign.
seats arranged into a 
grid. Every seat is occupied by exactly one person, and each person has a blue sign and a yellow sign.Count the number of ways for each person to raise one sign so that each row and column has an odd number of people raising a blue sign.
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The value 
and 
if the person in that seat raises blue and yellow sign respectively.
submetrices with black 
are labelled with 
,
ways to raise signs.
