MathDB

S

is a board containing all unit squares in the

xy

plane whose vertices have integer coordinates and which lie entirely inside the circle

x^2 + y^2 = 1998^2

. In each square of

S

is written

+1

. An allowed move is to change the sign of every square in

S

in a given row, column or diagonal. Can we end up with exactly one

-1

and

+1

on the rest squares by a sequence of allowed moves?

Problem Statement