  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 that if the switch is pulled ($x_{i}=-1$ for row
$i$ and $y_{j}=-1$ for column $j$) all of the lights in that line are switched:
on to off or off to on. The unbalancing lights problem (Gale-Berlekamp
switching game) consists in maximizing the difference between the lights on and
off. We obtain the exact parameters for a generalization of the unbalancing
lights problem in higher dimensions.
