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 Adventure10, Mango247
In a table 
we put 
blocks such that
i) Each block covers exactly 2 cells
ii) Each cell is covered by, at least, one block
iii) If we delete a block; there is, at least, one cell that is not covered.
Find the maximum value of.
Note: The blocks can overlap.
we put 
blocks such thati) Each block covers exactly 2 cells
ii) Each cell is covered by, at least, one block
iii) If we delete a block; there is, at least, one cell that is not covered.
Find the maximum value of
.Note: The blocks can overlap.
,![[asy]
for(int i = 0; i < 5; ++i) {
draw((0, i)--(4, i));
draw((i, 0)--(i, 4));
}
draw((0.5, 3.5)--(2.5,3.5));
draw((3.5, 3.5)--(3.5,1.5));
draw((3.5,0.5)--(1.5,0.5));
draw((0.5,0.5)--(0.5,2.5));
draw((1.5,3.5)--(1.5,2.5));
draw((2.5,2.5)--(3.5,2.5));
draw((2.5,1.5)--(2.5,0.5));
draw((0.5,1.5)--(1.5,1.5));
[/asy]](http://latex.artofproblemsolving.com/f/9/4/f94997125fd3487151040a3e5eecf5df94f3329d.png)
.
blocks that cover exactly one singly-covered cell, leading to having at least 
singly-covered cells outside of these blocks, and at most 
blocks in all. By averaging the estimates 
we get 
as desired.
