A Gale-Berlekamp permutation-switching problem in higher dimensions

Gustavo Araujo, Daniel Marinho Pellegrino

Let an $n\times n$ array $\left(a_{ij}\right)$ of lights be given, each either on (when $a_{ij}=1$) or off (when $a_{ij}=-1$). For each row and each column there is a switch so t…