be an acute triangle with incentre 
and 
.
and 
intersect the circumcircle of 
and 
,
and 
such that 
and 
are parallelograms (with 
,
)
be the point of intersection of lines 
and 
.
,
be the set of real numbers. Find all functions 
such that, for all real numbers 
and 
,
satisfying 
for all real numbers 
such that: 
for all 
.
Y by
points are marked on a circumference (
) so that the arcs formed have the same length. N tokens are placed on the marked points (one token for each point). Two players, Ricardo and Tomas, play by removing the placed chips, according to the following rules:
Game turns are staggered. Ricardo begins. If on a player's turn there are three checkers such that the corresponding marked points form a non-obtuse triangle, the player must remove one of those checkers. The player who cannot remove any tile on his turn loses.Does any player have a winning strategy? If so, what does such a strategy consist of?
This post has been edited 9 times. Last edited by parmenides51, May 13, 2024, 11:27 AM
