The signs "$+$" or "$-$" are placed in all cells of a $4 \times 4$ square table. It is allowed to change a sign of any cell altogether with signs of all its adjacent cells (i.e. cells having a common side with it). Find the number of different tables that could be obtained by iterating this procedure.
Problem
Source: Tournament of Towns Spring 2003 - Senior A-Level - Problem 6
Tags: combinatorics unsolved, combinatorics