Question 196
Suppose $2011$ light bulbs are arranged in a row. Each bulb has a button under it. Pressing the button will change the state of the bulb above it (on to off or vice versa) and will also change the two neighboring bulbs, or the single neighboring bulb in the case of one of the two end buttons. Is it always possible, regardless of the initial state of the bulbs, to turn them all off by pressing some buttons?