[/quote]
,
such that 
.
such that for all 
. 
. 
are colored blue. A set of six cells is called gremista when the cells are the intersection of three rows and two columns, or two rows and three columns, and are painted blue. Determine the greatest value of 
for which it is possible to color 
be non-negative real numbers such that 
Prove that
such that 
.
has no integer solution.
denotes a polynomial of degree 
such that 
for 
,
.
with 
,
to the sides 
are 
,
is the orthocenter. 
is the midpoint of segment 
.
and 
intersect at 
.
from 
and 
intersect at 
.
are colinear
and 
with real coefficients satisfying
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