MathDB
Labeling 3x3 board with + or - (Serbia MO 2005 2nd Grade P2)

Source:

April 11, 2021
game

Problem Statement

Every square of a 3×33\times3 board is assigned a sign ++ or -. In every move, one square is selected and the signs are changed in the selected square and all the neighboring squares (two squares are neighboring if they have a common side). Is it true that, no matter how the signs were initially distributed, one can obtain a table in which all signs are - after finitely many moves?