The Lights Out game, originally an electronic game played on a
grid,
is a solitaire game that can be played on any simple graph. It has been generalized to
be played with multiple on-states, where each vertex state is represented by a label in
. We
define a new variant of the Lights Out game, where the vertex labels can come from any
group
.
This new game depends deeply on the group structure of
and gives us a significantly different game for cyclic groups. We
investigate problems related to counting winnable labelings in the case
.
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