Question 186
A $2 \times n$ grid has a light bulb in each square. Each bulb has a switch that flips the state of its corresponding bulb as well as all (horizontally or vertically) adjacent bulbs. Determine whether it is always possible, regardless of the initial state of the bulbs, to turn all the bulbs off if
a) $n=2011$
b) $n=2012$.
a) $n=2011$
b) $n=2012$.