be the Fermat point of a 
.
,
,
are concurrent and the point of concurrence is 
,
(
well). i want to study so if you guys have some easy or normal problems please send me
?
chess board, except for the 
central square, there is a checker. In one move, a checker can jump over adjacent checker (diagonally), and this adjacent checker (that was jumped over) is removed. Is it possible to come up with a sequence of moves, so that only one checker is left on the board?
Y by
Ana and Carlos entertain themselves with the next game. At the beginning of game in each vertex of the square there is an empty box. In each step, the corresponding player has two possibilities: either he adds a stone to an arbitrary box, or move each box clockwise to the next vertex of the square. Carlos starts and they take 2012 steps in turn (each player 1006). So Carlos marks one of the vertices of the square and allows Ana to make a more play. Carlos wins if after this last step the number ofstones in some box is greater than the number of stones in the box which is at the vertex marked by Carlos; otherwise Ana wins. Which of the two players has a winning strategy?
