RU-ALLRUSSIAN 1991 Problem 8

A minus sign is placed on one square of a $5 \mathrm{x} 5$ board and plus signs are placed on the remaining squares. A move is to select a $2 \mathrm{x} 2$ , $3 \mathrm{x} 3$ , $4 \mathrm{x} 4$ or $5 \mathrm{x} 5$ square and change all the signs in it. Which initial positions allow a series of moves to change all the signs to plus?

Answer only the central square