[/quote]
,
be an acute triangle with 
and let 
and 
be its orthocenter and circumcenter, respectively. Let 
be the circle 
.
and the circle of radius 
cross 
and 
,
and circle 
are concurrent.
for which the following statement holds: among any five positive real numbers 
(not necessarily distinct), one can always choose distinct subscripts 
such that![\[ \left| \frac{a_i}{a_j} - \frac {a_k}{a_l} \right| \le C. \]](http://latex.artofproblemsolving.com/a/e/e/aeeab8e846634c7922e9312ef139739ad3fbe6eb.png)
,
,
.
at 
and 
,
be the midpoint of arc 
at 
.
intersects 
,
and 
meet on 
.
and 
respectively such that 
.
be the second intersection point of the circumcircle circumscribed to 
with 
and 
and 
with 
,
and 
be the intersection points of lines 
and 
with lines 
line passes through the midpoint of 
are real numbers, find the smallest possible value of the expression:
and 
be prime numbers. Prove that if 
is a perfect square, then 
is also a perfect square.
is a perfect square.
be a positive integer. Aslı and Zehra are playing a game on an 
chessboard. Initially, 
stones are placed on the squares of the board. In each move, Aslı chooses a row or a column; Zehra chooses a row or a column. The number of stones in each square of the chosen row or column must change such that the difference between the number of stones in a square with the most stones and a square with the fewest stones in that same row or column is at most 1. For which values of 
reals, and 
.
?
Y by cursed_tangent1434, NicoN9, EeEeRUT
I hope posting this in Site Support is fine? I'm not sure whether an HSO admin is doing this but-
The EGMO 2025 problem 1 and problem 2 were originally posted by me on the day of the contest and found deleted (not by me) yesterday. Someone else noticed this and posted the problems again, but these threads were deleted once more.
The EGMO 2025 problem 1 and problem 2 were originally posted by me on the day of the contest and found deleted (not by me) yesterday. Someone else noticed this and posted the problems again, but these threads were deleted once more.
