Question 28
Consider the grid consisting of all unit squares wholly contained in the disk $x^2+y^2\leq2014^2$ in an orthonormal coordinate plane $Oxy$. At each stage every square contains $1$ or $-1$. Initially every square contains $1$. A move selects a row, column or diagonal (a maximal set of squares whose centers lie on a line making an angle of $45$ degrees with a coordinate axis) and reverses all signs in it. Can one finish with exactly one square containing $-1$ and every other square containing $1$?